glm-ie_v1.4/0000755000175000017500000000000011755435662010612 5ustar hnhnglm-ie_v1.4/infEngine.m0000644000175000017500000001400311704107264012654 0ustar hnhn% [m,ga,b,z,zu,nlZ] = DLI(X,y,s2,B,pot,tau,opts,G) % % DLI - Double Loop Inference - Bayesian Inference using a Double Loop algorithm % The variational criterion whose stationary point is found has the form % phi(ga,b) = ln|A| + h(ga,b) + \min_u R(u,ga,b), where % A = X'*X/s2 + B'*diag(1./ga)*B, s=B*u, % h(ga,b) = \sum_{j=1}^q h_j(ga_j,b_j) % R(u,ga,b) = (1/s2) * ||X*u-y||^2 + s'*diag(1./ga)*s - 2*b'*s. % % The probabilistic model consists of % (i) Gaussian potentials y = X*u + e, e~N(0,s2*I) and % (ii) non-Gaussian potentials t_i(s_i), pot(s) = \prod_i t_i(tau_i*s_i) % leading to a posterior P(u) of the form % P(u) = (1/Z) N(u|Xu,s2*I) * pot(s) = N(u|m,V) where s = B*u and the % partition function is Z = \int N(u|Xu,s2*I) * pot(s) du. % Furthermore, m is the posterior mean and V = inv(A) is the posterior % covariance matrix with diagonal zu = diag(V). The normaliser is represented % in the log domain and hence nlZ = -log(Z). % % OUTER LOOP: z \approx diag(B'*inv(A)*B) = var(s) % % opts.innerType == 'VB' % INNER LOOP: min_u (1/s2)*||X*u-y||^2 + 2*pen(s) where r = sign(s)*sqrt(s^2+z) % pen(s) = tau*b*(r-s) - ln pot(tau*r), see pen/penVB.m. % Our variational inference relaxation uses Gaussian individual lower bounds % pot(s) \ge exp( b*s -s^2/ga +h(ga)/2 ) to obtain a joint a lower bound % Z \ge exp(h(ga)/2) * \int N(u|Xu,s2*I) * exp( b*s -s^2/ga ) du = Z_{VB} % having the form of a Gaussian integral that can be written as % Z_{VB} \ge C*exp( -phi(ga)/2 ), C = (2*pi)^(n/2) * (2*pi*s2)^(-m/2). % Here, the variational criterion phi(ga) is to be minimised w.r.t. the % variational parameters ga. For log-concave models, this constitutes a convex % variational optimisation problem (1). % Our approach to solve the problem uses Fenchel duality to decouple ln|A| by % upper bounding ln|A| \min_z z'*(1./ga) g*(z); a function that is just a sum % over individual components of ga. The algorithm consists of an outer loop % where the decoupling bound with coefficients z is refit and an inner loop % where the variational criterion is jointly minimised in both u and ga % (wich reduces to a PLS problem, pls/pls*.m). % % opts.innerType == 'EP' % INNER LOOP: % We interleave parallel EP updating steps and posterior mean recomputations % to find a stationary point of the inner loop criterion. % % For factorial meanfield inference, use opts.innerType = 'VB' along with % opts.outerMethod = 'factorial'. % % INPUT % ===== % X [mxn] measurement matrix or operator % y [mx1] measurement vector % s2 [1x1] measurement variance % B [qxn] matrix or operator % pot potential function handle or function name string from pot/pot*.m % tau [qx1] scale parameters of the potentials % opts. optimisation parameters % outerZinit initial value for upper bound [default 0.05] % outerGainit initial value for variational parameter [default 1] % outerNiter number of outer loop iterations [default 10] % outerMVM number of MVMs/Lanczos vectors/.. [default 50] % outerVarOpts extra params for z computation [default [] ] % outerMethod z computation algorithm [default 'lanczos'] % z = diag( B*inv(A)*B' ) with A = X'*R*X + B'*P*B % algorithm located in inf/diaginv_.m % 'full' exact dense matrix based computation % 'lanczos' Lanczos approximation based on MVMs % varOpts.MVM = 50 per default % 'sample' Monte Carlo estimate based on MVMs % varOpts.NSamples = 10 and % varOpts.Ncg = 20 per default % 'woodbury' exact dense matrix computation for B=I and P, R % cheaply invertable and X numeric % 'factorial' approximate computation for mean field % inference % outerOutput flag saying whether some output is shown [default false] % innerMVM number of inner loop MVMs or CG steps [default 50] % innerIt number of inner Newton steps for plsTN [default 15] % innerOutput flag saying whether some output is shown [default false] % innerType which inference method EP or VB [default 'VB'] % innerVBpls inner loop PLS solver [default 'plsLBFGS'] % => the opts struct is passed to the PLS solver which % allows to pass additional arguments to it % innerEPeta scalar parameter for fractional EP [default 1] % only possible for potGauss and potLaplace % G [qtxq] grouping matrix (for VB only) [default eye(q)] % this changes the inner loop penaliser to % pen(s) = -log( pot(tau*r) ) where r = sqrt( G*(s^2 + z) ). % % OUTPUT % ====== % m [nx1] posterior mean estimate m = mean(u) % ga [qx1] optimal value of the variational width parameters % b [qx1] optimal value of the variational position parameters % z [qx1] posterior marginal variance estimate z = var(s) = var(B*u) % zu [nx1] posterior marginal variance estimate zu = var(u) % nlZ [1x1] approxmation to the negative log marginal likelihood -log(Z) % Q [n,k] orthogonal (dense) matrix of Lanczos vectors, Q'*Q = I % T [k,k] diagonal (dense) matrix, T = Q'*A*Q % Note that Q and T are empty for outerMethod='woodbury' and n>m as well as for % outerMethod='sample'. 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CL9O._l~^-T?n/-3ϓJPԆ$LU,Fx6Q`E[.^ {ph`^׊Y+8'szJqW.](/L&rE D䊺8XAw}rUnNjC6u ^Z;AU1 v;+~'e.h-oa+F^|I:%A+Y[gx\V.J  "FL^J@J]4,:"?z8][>5 ;Zi0qևBZIΔxG2̼.PG8z^(@l/bPmVXn6qAHq\d / ]ɾp89`fkx'p~*\ir~E&0~?ЉUr)G:> $X'tR LLQiMmÉ@ X}̶>/S>LE8D$.W%7x螘Oty:aܱRYU WX6&MMo]HH=_oovKglm-ie_v1.4/doc/deblur_inference.m0000644000175000017500000000471411704102306015012 0ustar hnhn% Inference example doing sparse regression for image deblurring using glm-ie. % % We do nonblind deconvolution to recover the image u that has been blurred by % an optical device with known point spread function f. % The measurements are y = conv2(u,f) + e, e~N(0,s2). % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2012 January 13 clear all, close all load deblur ut = u; clear u, f = f(4:end,:); f = f/sum(f(:)); % image u and blur filter f su = size(ut); nu = prod(su); sf = size(f); % sizes % blur operator and noisy measurement X = matConv2(f, su, 'circ'); sy = su; s2 = 1e-5; % variance y = X*ut; y = y + sqrt(s2)*randn(size(y)); % observation % prior B = matFD2(su); % total variation = finite diff matrix tau = 15; % prior scale pot = @potLaplace; %% Inference outer loop variances can be computed using Lanczos or Monte Carlo % opts.outerMethod = 'lanczos'; % Lancos % opts.outerMethod = 'sample'; % Monte Carlo opts.outerMethod = 'factorial'; % factorial posterior approximation opts.innerOutput = 1; opts.outerOutput = 1; opts.outerNiter = 4; % Number of outer loop iterations opts.outerVarOpts = struct('MVM',170, ... % lanczos variances 'NSamples',20,'Ncg',20); % sample variances opts.innerMVM = 100; % Number of CG steps in inner loop opts.innerVBpls = 'plsLBFGS'; % PLS algorithm for inner loop [uinf,ga,b,z,zu,nlZ] = dli(X,y,s2,B,pot,tau,opts); uinf = reshape(uinf,su); sdinf = sqrt(reshape(zu,su)); %% Estimation opt.nMVM = 250; opt.output = 1; u0 = zeros(nu,1); uest = reshape( feval(opts.innerVBpls,u0,X,y,B,opt,s2,'penVB',pot,tau), su); % accuracy err_estimation = norm(uest(:)-ut(:)) err_inference = norm(uinf(:)-ut(:)) % di-f1.png and di-f2.png sz = [800,300]; figure('Position',[50,50,sz]) subplot('Position',[0/3,0,.32,.87]) imagesc(abs(uest-ut),[0,.2]), axis off, title('|true-mode|','FontSize',16) subplot('Position',[1/3,0,.32,.87]) imagesc(abs(uinf-ut),[0,.2]), axis off, title('|true-mean|','FontSize',16) subplot('Position',[2/3,0,.31,.87]) mn = min(sdinf(:)); mx = max(sdinf(:)); clim = [mn, mx/2]; if mn>mx/2, clim = [mn,mx]; end imagesc(sdinf,clim), axis off, title('standard dev.','FontSize',16), colorbar colormap(gray) glm-ie_v1.4/doc/mri_estimation.m0000644000175000017500000000602111646310767014554 0ustar hnhn% Estimation example doing MRI reconstruction using glm-ie. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 clear all, close all type_str = {'line', 'mask', 'spiral'}; type = 3; complex = [2,2]; if type==1 % line example load mri_line mfull = 1; X = matFFT2line(size(utrue),id,complex,mfull); nMVM = 75; elseif type==2 % mask example load mri_mask mfull = 1; X = matFFTNmask(mask,complex,mfull); nMVM = 100; else % spiral example load mri_spiral, type = 3; X = matFFT2nu(size(utrue),k,complex); nMVM = 100; end y = cx2re(y(:)); su = size(utrue); nu = numel(utrue); fprintf('MRI reconstruction from %s Fourier acquisition\n', type_str{type}) uls = reshape(re2cx(X'*y),su); % least squares reconstruction B = [matWav(su,[],[],complex); matFD2(su,'circ',complex)]; % wavelet + fin-diff. pen = @penAbs; % Laplace potential s2 = 4e-4; % noise variance opt.nMVM = nMVM; opt.output = 1; % optimisation parameters if type<3 % plsSB is only fast for matFFT2line and matFFTNmask pls1 = 'SB'; opt.SBouter = 75; opt.SBinner = 3; opt.SBga = 5; else pls1 = 'CGBT'; uls = uls*norm(utrue(:))/norm(uls(:)); % adjust scale end plsList = {pls1,'BB'}; % Estimation: apply two different PLS schemes for i=1:length(plsList) fprintf('PLS optimisation using %s.\n',plsList{i}) pls = ['pls',plsList{i}]; tic, [u{i},phi(i)] = feval(pls,cx2re(0*uls(:)),X,y,B,opt,s2,pen); t(i) = toc; u{i} = abs(re2cx(u{i})); d(i) = 100*norm(u{i}-utrue(:))/norm(utrue(:)); end fprintf('objective function values\n ') for i=1:length(plsList), fprintf('%s %1.4e, ',plsList{i},phi(i)), end fprintf('\b\b\n') fprintf('running times\n ') for i=1:length(plsList), fprintf('%s %1.2fs, ',plsList{i},t(i)), end fprintf('\b\b\n') fprintf('accuracies in %%\n ') for i=1:length(plsList), fprintf('%s %1.2f%%, ',plsList{i},d(i)), end fprintf('\b\b\n') % me-f1.png, me-f2.png, me-f3.png sz = [800,300]; figure('Position',[50,50,sz]) subplot('Position',[0/3,0,.32,.87]) imagesc(reshape(abs(uls),su)), axis off err = norm(abs(utrue(:))-abs(uls(:)))/norm(abs(utrue(:))); str = sprintf('u_{LS}, err=%1.3f',err); title(str,'FontSize',16) subplot('Position',[1/3,0,.32,.87]) if type==1 idx = zeros(su(1),1); idx(id) = 1; imagesc(idx) r = 100*sum(numel(id)*su(2))/nu; elseif type==2 imagesc(mask) r = 100*sum(mask(:))/nu; else plot(k,'.-') r = 100*numel(k)/nu; end axis off, title(sprintf('Pattern; %1.2f%% covered',r),'FontSize',16) subplot('Position',[2/3,0,.32,.87]) imagesc(reshape(u{end},su)), axis off err = norm(abs(utrue(:))-abs(u{end}(:)))/norm(abs(utrue(:))); 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While (MAP) estimation or equivalently penalised least squares estimation is a standard tool in statics, inference is less widely used and in general more tricky. The two approximate inference algorithms are described in the papers [1] Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models by Matthias Seeger and Hannes Nickisch SIAM Journal on Imaging Sciences, 2011 http://arxiv.org/abs/0810.0901 for a similar TR and [2] Efficient Bayesian multivariate fMRI analysis using a sparsifying spatio-temporal prior by Gerven, Cseske, Lange and Heskes Neuroimage 2010 http://homepages.inf.ed.ac.uk/bcseke/webpubs/gerven2010.pdf. The Monte Carlo marginal variance estimator is detailed in [3] Efficient Variational Inference in Large-Scale Bayesian Compressed Sensing by George Papandreou and Alan Yuille ICCV Workshop, 2011 http://www.stat.ucla.edu/~gpapan/pubs/confr/PapandreouYuille_VariationalBayesCompressedSensing_ieee-c-iccvw11.pdf There are 6 code subdirectories: doc, inf, mat, pen, pls and pot. doc/ contains an index.html file providing documentation. This information is also available from http://www.kyb.tue.mpg.de/bs/people/hn/glm-ie. Usage examples reaching from probabilistic classification, robust regression over nonblind deconvolution to MRI reconstruction can be found here. Further details are provided in the developer documentation manual.pdf. inf/ contains the double loop inference engine dli.m and code to compute Gaussian marginal variances i.e. the diagonal of a covariance matrix => see infEngine.m mat/ contains the lazy matrix class; mat/@mat is the base class all other classes are derived from and the two auxiliary functions cx2re.m and re2cx.m allow to convert between real and complex numbers pen/ contains the penalty functions pen*.m => see penFunctions.m pls/ contains the penalised least squares (pls) solvers pls*.m => see plsSolvers.m pot/ contains the potential functions pot*.m => see potFunctions.m Before running the demos or any other part of the code, you should execute startup.m to add all necessary directories to your path. In Octave, you can also use the .octaverc file. 2) ABOUT MEX FILES ================== Some of the programs make use of the MEX facility in matlab for more efficient implementation. Besides the L-BFGS minimiser, the wavelet transform mat/@matWav rely on C/C++ code. The wavelet code should compile right after the first call; if there are problems, see the help in mat/@matWav/private/fwtn.m. If you do not have a compiler installed on your system, you might want to consult [2]. In order to use the L-BFGS minimiser , you have to compile Peter Carbonetto's "Matlab interface for L-BFGS-B" [1]. The challenge here is the Fortran 77 code. We provide a Makefile suitable for Linux 32/64 bit and Mac whenever you have 1) g77 or 2) gfortran properly set up. Under Ubuntu, you can achieve this by installing the packages fort77 and gfortran, respectively. Compilation is done by editing util/lbfgsb/Makefile. In any case, you need to provide $MATLAB_HOME which can be found by the commands 'locate matlab' or 'find / -name "matlab"'. You can choose between two compilation modes: a) using the mex utility by Matlab [default] provide $MEX, then type 'make mex' b) without mex utility by Matlab provide $MEX_SUFFIX and $MATLAB_LIB, then type 'make nomex' In Ubuntu 10.04 LTS, the libg2c library needed for both 1)+a) and 1)+b) is not included per default. If 'ls /usr/lib/libg2c.*' does not list anything this is the case on your machine. You then whant to install the packages gcc-3.4-base and libg2c0 e.g. from http://packages.ubuntu.com/hardy/gcc-3.4-base and http://packages.ubuntu.com/hardy/libg2c0. After installation, you have to create a symbolic link by 'cd /usr/lib' and 'ln -s libg2c.so.0 libg2c.so'. Compilation under Windows is rather tricky but there is a way [3] of doing it as pointed out by Guillaume Jacquenot. Steps involved: * Install MinGW (including gfortran compiler) at C:\mingw * http://www.mingw.org/ * If the target was Matlab 64-bit, we would probably need MinGW-w64 instead? * Download http://gnumex.sourceforge.net/, unzip at C:\gnumex, and create Fortran/C mexopts.bat files for use with MinGW. * Add C:\mingw\bin and C:\gnumex in the PATH and reboot. * Create and run pls/make_lbfgsb_gnumex_windows.m script (replace the filenames for the mexopts.bat files accordingly). Other useful stuff: * MS Dependency walker (to debug missing DLL dependencies), links to download at http://www.dependencywalker.com [1] http://www.cs.ubc.ca/~pcarbo/lbfgsb-for-matlab.html [2] http://www.mathworks.com/support/compilers/R2010a [3] http://www.cs.ubc.ca/~pcarbo/Compile_LBFGSB_on_Windows.txt 3) CURRENT VERSION ================== The current version of the programs is 1.4. Previous versions of the code are available at http://hannes.nickisch.org/code/glm-ie/release/oldcode.html. 4) DIFFERENCES TO PREVIOUS VERSIONS =================================== NEW in version 1.4, 2011-10-20 ------------------------------ contributed by George Papandreou: - preconditioning support in the inf/linsolve_lcg.m CG routine. - @matConv2 and @matFD2 support different boundary conditions in deblurring - various mat/@*/diagFAtAFt.m support circulant preconditioning - bugfixes in nonnegativity option in pls/plsLBFGS.m and pen/penVBNorm.m when used together with EP - inf/diag_inv_sample.m, a Monte Carlo estimator gfortran support to pls/lbfgsb/Makefile (thanks to Ernst Kloppenburg) slight modification to mat/@matFFTN/mvm.m to make it more consistent simple gradient solver using Barzilai-Borwein step size pls/plsBB.m NEW in version 1.3, 2010-11-12 ------------------------------ extension of the matrix class; bugfixes plsSB - split Bregmin PLS solver new inference engine dli.m instead of vbidl.m - support of parallel EP in addition to VB - marginal likelihood computation extended documentation and demo programs NEW in version 1.2, 2010-08-25 ------------------------------ refactored the matrix classes added more penalty functions added non-linear potential support for group sparsity improved PLS solvers updated complex number treatment NEW in version 1.1, 2010-08-10 ------------------------------ added demo examples and documentation NEW in version 1.0, 2010-07-05 ------------------------------ initial version of the glm-ie toolbox glm-ie_v1.4/doc/me-f1.png0000644000175000017500000025024711467333127012775 0ustar hnhnPNG  IHDR ,O@m pHYs B(xtIME ("tEXtCreation Time12-Nov-2010 15:08:40м$tEXtSoftwareMATLAB, The Mathworks, Inc.R IDATx]$Yv#*'r*:s7w!5k(B%iْ`X&"@zA? 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C dszƒ%]^/ {jn|[koK5TL*{NNFulG Tt][(q-n,*DeI9ٔ l]^U::a@s?(Ȯ0`'jY>x2.GVK,~艬˚a lAe,ʿA[cJC:Q-K "^ռS/Uus]<&;5,|s+T5gXkn"4%^[o)ddح|UoJV.CT_ \9:>Xmj- i5v| ?|Rglm-ie_v1.4/doc/regress_inference.m0000644000175000017500000000452711650341054015216 0ustar hnhn% Inference example for sparse regression example using glm-ie. % Exercises opts.outerExact. % % We use the Nordborg Flowering Time dataset from http://walnut.usc.edu/. % X is a binary matrix of 166 individuals x 5k SNPs selected by prior % knowledge % y is a real vector with flowering times between 21 and 200 % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 21 clear all, close all load regress, y = (y-mean(y))/std(y); [m,n] = size(X); % get data s2 = 0.0078; % variance B = 1; tau = 125; % sparsity transform % Gaussian or non-Gaussian i.e. sparse weight prior % select by uncommenting the desired one % pot = @(s) potT(s,2); % Student's t % pot = @potLaplace; % Laplace pot = @(s) potExpPow(s,1.3); % Exponential Power family fprintf('Do sparse regression using a (sparse) '), str = func2str(pot); fprintf('%s weight prior.\n',str(8:end)) % split into training and test set itr = randperm(m); ite = itr(1:end/2); itr = itr(end/2+1:end); %% Inference opts.innerOutput = 1; opts.outerOutput = 1; opts.outerNiter = 3; % Number of outer loop iterations opts.outerMethod = 'lanczos'; % Lanczos marginal variance approximation % opts.outerMethod = 'sample'; % Monte Carlo marginal variance approximation % opts.outerMethod = 'full'; % Exact marginal variance computation (slow) % opts.outerMethod = 'woodbury'; % Exact marginal variance computation (fast) opts.innerMVM = 40; % number CG steps opts.innerVBpls = 'plsCG'; % PLS algorithm, also LBFGS if compiled [m,ga,b,z,zu,nlZ,Q,T] = dli(X(itr,:),y(itr),s2,B,pot,tau,opts); % posterior quantities: % m = E(u) posterior mean estimate % z = var(B*u) marginal variance estimate % nlZ sequence of negative log marginal likelihoods, nlZ(end) is the last one % zu = var(u) marginal variance estimate % Q,T yield cov(u) = V = inv(A) \approx Q'*inv(T)*Q the posterior covariance %% Estimation opt.nMVM = 50; opt.output = 1; opt.exactNewt = 1; uhat = feval(opts.innerVBpls,zeros(n,1),X(itr,:),y(itr),B,opt,s2,'penVB',pot,tau); fprintf('mean squared error (MSE)\n ') fprintf('inference %1.2f, ', sum((X(ite,:)*m-y(ite)).^2)/numel(ite) ) fprintf('estimation %1.2f, ', sum((X(ite,:)*uhat-y(ite)).^2)/numel(ite) ) fprintf('\b\b\n') glm-ie_v1.4/doc/di-f2.png0000644000175000017500000064512511704101530012755 0ustar hnhnPNG  IHDR ,O@m pHYs B(xtIME ,CC"tEXtCreation Time13-Jan-2012 20:17:449$tEXtSoftwareMATLAB, The Mathworks, Inc.R IDATxT\չ>3q@2 L$L42FEmx/z5klmM^R5Ҭ+5^ZjѢ%DPP0`F S89O&'H0jڞ0sw:}4ӠA 4hpA 4hMҠA 4h, 4hРA MҠA 4h, 4hРA MҠA 4h, 4hРA MҠA 4h, 4hРA MҠA 4h, 4hРA MҠA 4h, 4hРA 8k֬Yf[B Mxh>1ejU?5j0 M>5|i)X4hРA A 4hp!| "3|Y?WT, LOcp-Ԡι /9f^>;gOT>ISO35mY.  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Changes and small incremental bug fixes applied since last release. 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Documentation for the glm-ie Toolbox 1.4

0) What?

The glm-ie package (generalised linear models: inference and estimation) offers estimation procedures and approximate inference algorithms for Gaussian and non-Gaussian variable models that can be applied at large scales ($10^5$ and more variables).
Standard large-scale (sparse) regression and classification as well as $l_1$-regularised image reconstruction can be treated as an instance of penalised estimation. A strong emphasis of the code is scalability and numerical robustness. This is achieved by phrasing all operations as (fast) matrix vector multiplications (MVMs). A matrix class for lazy evaluation is a core ingredient to scalability.
After giving some theoretical background, we provide four exemplary aplications:

Estimation corresponds to finding the most likely model parameter and inference can be understood as finding a (Gaussian) approximation to the distribution over the model parameters. We offer no less than five solvers to compute the most likely model parameters; a penalised least squares (PLS) problem. Approximate inference can be done by two algorithms Variational Bounding (VB) and Expectation Propagation (EP).

The code is written by Hannes Nickisch; it runs on both Octave 3.3.x and Matlab® 7.x. Previous versions of the code are still available.

1) Download, Install and Documentation

All the code including demonstrations and html documentation can be downloaded in a tar or zip archive file.

Minor changes and incremental bugfixes are documented in the changelog.

Please read the copyright notice.

After unpacking the tar or zip file you will find 6 subdirectories: doc, inf, mat, pen, pls and pot. It is not necessary to install anything to get started, just run the startup.m script to set your path.

Details about the directory contents and on how to compile MEX files can be found in the README. The getting started guide is the remainder of the html file you are currently reading (also available at http://hannes.nickisch.org/code/glm-ie/doc). A Developer's Guide containing technical documentation is found in manual.pdf, but for the casual user, the guide is below.

2) Theory

Generalised linear models (GLMs) are used for a variety of different tasks such as classification to regression. Applications range from image processing over bioinformatics to ranking.

A generalised linear model over unknown parameters $\mathbf{u}\in\mathbb{R}^n$ is composed of Gaussian observations \[ \mathbf{y}=\mathbf{X}\mathbf{u} + \mathbf{\varepsilon}\in\mathbb{R}^m, \: \mathbf{\varepsilon} \sim \mathcal{N}(0,\sigma^2\mathbf{I}) \] and non-Gaussian potentials $\mathcal{T}_j(s_j)$ on linear projections thereof \[ \mathbf{s}=\mathbf{B}\mathbf{u}\in\mathbb{R}^q \] leading to a posterior of the form \[ \mathbb{P}(\mathbf{u}|\mathcal{D})\propto\mathcal{N}(\mathbf{y}|\mathbf{X}\mathbf{u},\sigma^2\mathbf{I})\prod_{j=1}^q\mathcal{T}_j(s_j). \]

The glm-ie toolbox allows to perform maximum a posterior (MAP) estimation i.e. finding the most probable configuration \[ \hat{\mathbf{u}}_{MAP} = \arg \max_{\mathbf{u}} \mathbb{P}(\mathbf{u}|\mathcal{D}) = \arg \min_{\mathbf{u}} -\ln\mathcal{N}(\mathbf{y}|\mathbf{X}\mathbf{u},\sigma^2\mathbf{I}) -\sum_{j=1}^q\ln\mathcal{T}_j(s_j) \] and inference i.e. approximate the Bayesian posterior by a tractable distribution (here a Gaussian with mean $\mathbf{m}$, and covariance $\mathbf{V}$) \[ \mathbb{P}(\mathbf{u}|\mathcal{D}) \approx \mathcal{N}(\mathbf{u}|\mathbf{m},\mathbf{V}) \]

2a) Estimation

MAP estimation involves solving a penalised least squares problem (PLS) \[ \hat{\mathbf{u}}_{MAP} = \arg\min_{\mathbf{u}} \frac{1}{\lambda} \left\Vert\mathbf{X}\mathbf{u}-\mathbf{y}\right\Vert_2^2 + 2 \cdot \rho(\mathbf{s}), \: \mathbf{s}=\mathbf{B}\mathbf{u}, \:\lambda\in\mathbb{R}_+ \] with penaliser $\rho(\mathbf{s})=-\sum_{j=1}^q\ln\mathcal{T}_j(s_j)$ and weight $\lambda=\sigma^2$.

2b) Inference by Variational Bounding (VB)

The general idea of the inference algorithm is to replace non-Gaussian potentials $\mathcal{T}_j(s_j)$ by Gaussians $\mathcal{N}(s_j|\mu_j,\gamma_j)$ with width $\gamma_j$ and to jointly adjust the vector of widths $\mathbf{\gamma}\in\mathbb{R}_+^q$ such that the Gaussian approximation $\mathcal{N}(\mathbf{u}|\hat{\mathbf{u}}_{VB},\mathbf{V})$ imitates the Bayesian posterior $\mathbb{P}(\mathbf{u}|\mathcal{D})$ as faithfully as possible.

2c) Inference by (factorial) Mean Field (MF)

This approach makes a factorial posterior approximation and turns out to admit an inference algorithm along the lines of variational bounding with modified outer loop computations. The outer loop computation is faster but only applicable to a restricted class of matrices, namely Fourier matrices, convolution matrices and finite difference matrices.

2d) Inference by Expectation Propagation (EP)

Again, non-Gaussian potentials $\mathcal{T}_j(s_j)$ are replace by Gaussians $\mathcal{N}(s_j|\mu_j,\gamma_j)$ such that the marginal distributions \[ \mathcal{N}(\mathbf{u}|\hat{\mathbf{u}}_{EP},\mathbf{V}) \text{ and } \mathcal{N}(\mathbf{u}|\hat{\mathbf{u}}_{EP},\mathbf{V}) \frac{\mathcal{T}_j(s_j)}{\mathcal{N}(s_j|\mu_j,\gamma_j)} \] have the same mean and variance for all $j=1,..,q$. This is achieved by iteratively adjusting the parameters $\mu_j$ and $\gamma_j$ such that the moments match.

Note that large-scale EP is far more difficult to run than VB because EP seems to not tolerate inaccurate marginal variance estimates. Marginal variances can be approximated using a Lanczos procedure or a Monte Carlo sampler.

2e) Code organisation

Before going straight to the examples, just a brief note about the organization of the package. There are four types of objects which you need to know about. Details can be found in the developer's manual :

mat: matrix operators
Matrices $\mathbf{B}$ and $\mathbf{X}$ are very large if the parameters $\mathbf{u}$ represent the pixels of and image. Most often, $\mathbf{B}$ and $\mathbf{X}$ do not need to be stored explicitly but only implicitly through their matrix vector multiplication (MVM). The glm-ie toolbox comprises a library of implicit matrices derived from the base matrix class mat. Matrices of type mat can be added, multiplied, concatenated, replicated and subindexed.
pen: penalty functions
A penalty function $\rho(\mathbf{s})$ defines a PLS problem. All penalty functions share a common interface. Penalty functions can be derived from potential functions by e.g. $\rho(\mathbf{s})=-\sum_{j=1}^q\ln\mathcal{T}_j(s_j)$. These mechanism is exploited in the inference engine where a sequence of PLS problems is solved.
pls: penalised least squares (PLS) solvers
PLS problems are not only specified but also solved. Our PLS solvers also obey a common interface. For LBFGSB to properly work, you have to compile some MEX functions as detailed in the README.
pot: potential functions
A potential function $\mathcal{T}_j(s_j)$ implementing the potential interface is needed to specify whether a probabilistic model performs ordinary regression (using the Gaussian distribution), sparse regression (based on the Laplace, Student's t, Exponential power family and Sech-squared distribution) or classification (aka Logistic regression).

3) Practice

3a) Sparse Regression

The unknown parameters $\mathbf{u}\in\mathbb{R}^n$ represent the weights of a linear predictor that -- given a data point $\mathbf{x}_i\in\mathbb{R}^n$ -- computes the label $y_i$ as $y_i = \mathbf{x}_i^{\top} \mathbf{u}$. We use a Laplace sparsity prior on the weights (i.e. $\mathbf{B}=\mathbf{I}$) such that $\mathcal{T}_i(u_i)=\exp(-\tau_i|u_i|)$ and a Gaussian noise model where $y_i=\mathbf{x}_i^{\top}\mathbf{u}+\varepsilon_i,\:\varepsilon_i\sim\mathcal{N}(0,\sigma^2)$, i.i.d. The posterior of the model can be written as \[ \mathbb{P}(\mathbf{u}|\mathcal{D})\propto\exp(-\frac{1}{2\sigma^2}\left\Vert\mathbf{X}\mathbf{u}-\mathbf{y}\right\Vert_2^2 - \tau\left\Vert\mathbf{u}\right\Vert_1). \]

In our example, we use the Nordborg Flowering Time dataset to estimate the flowering time $y_i$ from the genome represented as a binary vector $\mathbf{x}_i$. We have $m=166$ datapoints of dimension $n=5537$.

Estimation
We start by using PLS estimation regress_estimation.m to find $\hat{\mathbf{u}}_{MAP}$ using $\lambda=\sigma^2\tau$, where $\sigma^2=0.0078$ and $\tau=125$. The code compares four different solvers plsTN, plsCGBT, plsCG and plsBB in terms of the mean squared error $\frac{1}{N} \sum_i (\mathbf{x}_i^{\top}\hat{\mathbf{u}}_{MAP}-y_i)^2$, the computation time and the achieved objective $\phi(\hat{\mathbf{u}}_{MAP})$, where $\phi(\mathbf{u})=\frac{1}{\lambda}\left\Vert\mathbf{X}\mathbf{u}-\mathbf{y}\right\Vert_2^2 - 2\cdot\left\Vert\mathbf{u}\right\Vert_1$.

Inference
Next, we can approximate the posterior by a Gaussian using the scalable VB approach regress_inference.m. By uncommenting the appropriate of the following lines 

  pot = @(s) potT(s,2);            % Student's t
  pot = @potLaplace;               % Laplace
  pot = @(s) potExpPow(s,1.3);     % Exponential Power family
one can easily change the potentials from Laplace to others. Further, one can compare different marginal variance computation algorithms by choosing among 
  opts.outerMethod = 'lanczos';  % Lanczos marginal variance approximation
  opts.outerMethod = 'sample';   % Monte Carlo marginal variance approximation
  opts.outerMethod = 'full';     % Exact marginal variance computation (slow)
  opts.outerMethod = 'woodbury'; % Exact marginal variance computation (fast)
two exact algorithms and two approximate ones. In the code, we also demonstrate how to get a handle on the posterior approximation $\mathcal{N}(\mathbf{m},\mathbf{V})$ and the marginal likelihood estimate $Z$. 
  % m = E(u) posterior mean estimate
  % z = var(B*u) marginal variance estimate
  % nlZ sequence of negative log marginal likelihoods, nlZ(end) is the last one
  % zu = var(u) marginal variance estimate
  % Q,T yield cov(u) = V = inv(A) \approx Q'*inv(T)*Q the posterior covariance

3b) (Sparse) Pattern Classification or logistic regression

In classification, the unkown parameters $\mathbf{u}\in\mathbb{R}^n$ represent the weights of a linear classifier $c_i=\text{sign}(\mathbf{b}_i^{\top} \mathbf{u})\in\{\pm1\}$ computing the binary class label $c_i$ for a data point $\mathbf{b}_i\in\mathbb{R}^n$. We start with a Gaussian prior on the weights $\mathbb{P}(\mathbf{u})=\mathcal{N}(\mathbf{u}|\mathbf{0},\sigma^2\mathbf{I})$. Later, we can also use a sparsity prior on $\mathbf{u}$ so that the final model does not contain any Gaussian variables at all. The likelihood function is the logistic $\mathbb{P}(c_i|\mathbf{u},\mathbf{b}_i)=(1+\exp(-c_i\cdot\mathbf{b}_i^{\top}\mathbf{u}))^{-1}$.

In our example, we use the Adult dataset from the UCI machine learning repository. We have $q=32561$ datapoints of dimension $n=123$.

Estimation
Again, we can compare the performance of several PLS solvers by running classify_estimation.m. We can also choose to use a non-Gaussian prior by uncommenting the appropriate one of the following lines. 

  gauss = 1;                                   % Gaussian
  gauss = 0; potS = @(s) potT(s,2);            % Student's t
  gauss = 0; potS = @(s) potLaplace(s);        % Laplace
  gauss = 0; potS = @(s) potExpPower(s,0.7);   % Exponential Power family
The final potential is a concatenation of the prior and the logistic potential and the final matrix $\mathbf{B}$ is a concatenation of the former $\mathbf{X}=\mathbf{I}$ and the former $\mathbf{B}$ matrix. 
  B = [eye(n);B];
  pot = @(s,varargin) potCat(s, varargin{:}, {potS,@potLogistic}, {1:n,n+(1:q)} );

Inference
Along the same lines, we can perform inference as in classify_inference.m. The example illustrates how to toggle between EP and VB via the following two lines: 

  opts.innerType = 'VB';
  opts.innerType = 'EP'; opts.innerEPeta = 0.9;
Note that the concatenation of two potentials has to be done by 
  pot = @(s,varargin) potCat(s, varargin{:}, {potS,@potLogistic}, {1:n,n+(1:q)} );
in order to have EP working properly.

The following scatter plot illustrates the differences between the estimates $\hat{\mathbf{u}}_{MAP}$ and $\hat{\mathbf{u}}_{VB/EP}$ while offering similar predictive performance (16% error). It clearly shows that far more components of $\hat{\mathbf{u}}_{MAP}$ are zero. That means that the MAP estimator puts much more emphasis on driving entries to zero which effectively prunes out features from the model. A posterior mean estimate $\hat{\mathbf{u}}_{VB/EP}$ is far less rigorous. The rationale is that from finite data it is statistically hard to confidently rule out some parts of the model; here the posterior standard deviation (shown in cyan) provides a natural measure of uncertainty.

ci-f1.png

3c) (Nonblind) Image Deblurring

If a camera is moved while a picture is taken, the resulting image is blurry. If the motion is parallel to the image plane, the measured image $\mathbf{y}\in\mathbb{R}^n$ can be modeled as a noisy convolution of the sharp image $\mathbf{u}\in\mathbb{R}^n$ with a blurring filter/kernel $\mathbf{f}\in\mathbb{R}^f$ as expressed by \[ \mathbf{y}=\mathbf{f}\star\mathbf{u}+\mathbf{\varepsilon}=\mathbf{X}_{\mathbf{f}}\mathbf{u}+\mathbf{\varepsilon}, \] where $\star$ denotes the convolution operator which can equivalently be represented by a convolution matrix $\mathbf{X}_{\mathbf{f}}$. We assume Gaussian noise $\mathbf{\varepsilon}\sim\mathcal{N}(\mathbf{0},\sigma^2\mathbf{I})$, $\sigma^2=10^{-5}$.
The model is completed by prior knowledge on the distribution of filter responses of natural images. Multi-scale derivatives as computed by the (orthnormal) wavelet transform matrix $\mathbf{W}$ and the finite difference matrix $\mathbf{D}$ can be combined into a sparsity transform matrix $\mathbf{B}$ whose responses $\mathbf{s}=\mathbf{B}\mathbf{u}$ follow a sparse distribution that is peaked around zero and has heavy tails. The glm-ie toolbox allows the specification of such matrices by a single line of code 

  W = matWav(su); D = matFD2(su); B = [W; D];
where su denotes the size of the image. In the following, we use Laplace potentials $\mathcal{T}_j(s_j)=\exp(-\tau|s_j|)$ where we fix the scale to $\tau=15$.
The task in image deblurring consists of finding the sharp image $\mathbf{u}$ given the noisy and blurry measurement $\mathbf{y}$ and prior knowledge about the sparse distribution of multiscale derivatives $\mathbf{s}=\mathbf{B}\mathbf{u}$.

Estimation
We demonstrate estimation in deblur_estimation.m where we use the convolution matrix $\mathbf{X}_\mathbf{f}$ instantiated by 

  X = matConv2(f, su, 'circ');
We can use non-convex penalty functions like 
  dof = 2; pen = @(s) penLogSmooth(s,dof);
to enforce even more sparsity as the Laplace potential or equivalently the penAbs penalty. Note that, the penLogSmooth penalty $\rho(s_j)=\ln(s^2+\epsilon)$ corresponds to the negative log of the Student's t potential. The optimisation problem -- even though non-convex -- can efficiently be solved by LBFGSB or any other solver. For the special case of plsLBFGS, we can enforce nonnegativity $\mathbf{u}\ge\mathbf{0}$ be activating the following flag: 
  opt.LBFGSnonneg = 1;
The figure depicts the original image $\mathbf{u}$ from which the blurry image $\mathbf{y}$ was generated and the reconstructed sharp image $\hat{\mathbf{u}}_{MAP}$ as found be penalised least squares estimation.

de-f1.png

Inference
As in the other examples, we can go further and not only find the point of highest posterior density $\hat{\mathbf{u}}_{MAP}$ but to compute a Gaussian approximation to the posterior distribution that allows to quantify the uncertainty in our model. The script deblur_inference.m does exactly this.
Since the marginal variances $\mathbf{z}=\text{dg}(\mathbf{B}\mathbf{A}^{-1}\mathbf{B}^{\top})$ cannot be efficiently computed exactly (due to the $\mathcal{O}(n^3)$ matrix operation, where $n$ is the number of image pixels), we have to resort to an approximation. We use the Lanczos procedure to obtain an estimate $\mathbf{0}\le\hat{\mathbf{z}}_k\le\mathbf{z}$. For $k=n$, the estimate is exact but that is computationally prohibitive for images of realistic size. We can set $k=170$ by 

  opts.outerVarOpts.MVM = 170;
which is much smaller than $n=54910$ in our example.
As a result, we obtain in addition to the posterior mode estimate $\hat{\mathbf{u}}_{MAP}$ an estimate of the posterior mean $\hat{\mathbf{u}}_{VB}$ and an estimate of the marginal variances $\text{dg}(\mathbf{V})$ of the posterior. We visualise the respective differences of $\hat{\mathbf{u}}_{MAP}$ and $\hat{\mathbf{u}}_{VB}$ to the sharp underlying image as well as the marginal standard deviation. We see that mean and mode look very similar and the marginal variances are largest at corners and edges. Alternatively, we can compute the marginal variances by sampling. We just choose between the three lines: 
  opts.outerMethod = 'lanczos';       % Lancos
  opts.outerMethod = 'sample';        % Monte Carlo
  opts.outerMethod = 'factorial';     % factorial posterior approximation (MF)
In case, we choose sampling, we can set the number of preconditioned conjugate gradient steps and the number of samples by: 
  opts.outerVarOpts = struct('NSamples',20,'Ncg',20);
In estimation, we used a wavelet and a finite difference matrix for $\mathbf{B}$; for inference, we only use total variation since the factorial approximation cannot be computed efficiently for the wavelet matrix: 
  B = matFD2(su);
Note that the marginal standard deviations by Lanczos are one magnitude smaller (but also less noisy) than those obtained by sampling. Also the reconstruction error is better for the randomized approach. Note that MAP estimation yields an error of 7.34 in our example (an additional wavelet matrix improves the result, though).

Result obtained by Lanzos (error is 7.29):
di-f1.png

Result obtained by Monte Carlo (error is 6.49):
di-f2.png

Result obtained by factorial approximation (error is 6.52):
di-f3.png

3d) Undersampled Magnetic Resonance Imaging (MRI)

Along the lines of the deblurring example, we can also do sparse estimation from incomplete measurements using the same image prior based on $\mathbf{B}\in\mathbb{R}^{q\times n}$ as before. In magnetic resonance imaging (MRI), the measurements are Fourier coefficients along smooth curves. The number of acquired Fourier coefficients determines the scantime, hence one aims at reconstructing the underlying image $\mathbf{u}\in\mathbb{C}^n$ from incomplete measurements $\mathbf{y}\in\mathbb{C}^m$ where $m \le n$. The measurement matrix $\mathbb{X}$ is a Fourier-type matrix. Our example offers $3$ different measurement trajectories: lines, arbitrary positions on a grid (not sensible on a real scanner) and spirals as shown in the center of the illustrative figures. You can switch between the $3$ types by varying the type variable in the following code. 
  type_str = {'line', 'mask', 'spiral'};
  type = 2;
The measurement matrices themselves are generated by one of the following three lines of code. 
  X = matFFT2line(size(utrue),id,complex,mfull);
  X = matFFTNmask(mask,complex,mfull);
  X = matFFT2nu(size(utrue),k,complex);
Another subtlety comes from the fact that all PLS solvers of the glm-ie toolbox treat real variables only. For that reason, we embed the original complex variable $\mathbf{u}\in\mathbb{C}^n$ into $\mathbb{R}^{2n}$ and solve the corresponding real optimisation problem. The two auxiliary routines mat/re2cx.m and mat/cx2re.m can be used to switch between the two. Also the matrix class mat/@mat and all derived classes mat/@mat* have a mechanism to deal with real and complex vectors: the variable complex specifies whether the matrix $\mathbf{X}\in\mathbb{C}^{m \times n}$ acts as a linear operator $\mathbb{C}^n\rightarrow\mathbb{C}^m$, $\mathbb{R}^{2n}\rightarrow\mathbb{R}^{2m}$ or hybrids thereof.
Especially suited for complex valued PLS estimation problems where both matrices $\mathbf{X}$ and $\mathbf{B}$ correspond to simple pointwise operations in the Fourier domain i.e. $\mathbf{X}^{\top}\mathbf{X}$ and $\mathbf{B}^{\top}\mathbf{B}$ can be written as $\mathbf{F}^{H}\text{dg}(\mathbf{d})\mathbf{F}$ where $\mathbf{F}$ is the orthonormal $n\times n$ Fourier matrix is the solver plsSB solver implementing Bregman splitting.

Estimation
We compare two solvers on the task of undersampled reconstruction of a famous MR image from roughly $40$ percent of the measurements. We can see that simple least squares estimation produces much worse results than PLS estimation. mri_estimation.m

me-f1.png

me-f2.png

me-f3.png

4) Acknowledgements

Several colleagues have helped to improve this software. Some of these are: George Papandreou, Matthias Seeger, Alexander Loktyushin and Michael Hirsch.

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Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ jsMath.Script.Uncompress([ 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Use jsMath.Macro() to declare your own local macro definitions here, * and add "local/macros.js" to the loadFiles array in easy/load.js so * that they will be loaded automatically when jsMath is used. * * See http://www.math.union.edu/locate/jsMath/authors/macros.html * for details on defining macros for jsMath. */ // // Examples: // // jsMath.Macro('R','{\\bf R}'); // jsMath.Macro('red','\\color{red}{#1}',1); // glm-ie_v1.4/doc/jsMath/jsMath-fallback-mac-mozilla.js0000644000175000017500000001312011453154135020312 0ustar hnhn/* * jsMath-fallback-mac-mozilla.js * * Part of the jsMath package for mathematics on the web. * * This file makes changes needed by Mozilla-based browsers on the Mac * for when the TeX fonts are not available. * * --------------------------------------------------------------------- * * Copyright 2004-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /******************************************************************** * * Fix the default non-TeX-font characters to work with Mozilla * */ jsMath.Update.TeXfonts({ cmmi10: { // '41': // leftharpoondown // '43': // rightharpoondown '44': {c: '˓'}, '45': {c: '˒'}, '47': {c: '◁'}, // '92': // natural '126': {c: '→'} }, cmsy10: { '0': {c: '–', tclass: 'normal'}, '11': {c: '◯/', tclass: 'normal'}, '42': {c: '⥣'}, '43': {c: '⥥'}, '48': {c: '′', tclass: 'normal'}, '93': {c: '∪+'}, '104': {c: '〈'}, '105': {c: '〉'}, '109': {c: '⥣⥥'} //, '116': // sqcup // '117': // sqcap // '118': // sqsubseteq // '119': // sqsupseteq }, cmex10: { '10': {c: '〈'}, '11': {c: '〉'}, '14': {c: '/'}, '15': {c: '\\'}, '28': {c: '〈'}, '29': {c: '〉'}, '30': {c: '/'}, '31': {c: '\\'}, '42': {c: '〈'}, '43': {c: '〉'}, '44': {c: '/'}, '45': {c: '\\'}, '46': {c: '/'}, '47': {c: '\\'}, '68': {c: '〈'}, '69': {c: '〉'}, // '70': // sqcup // '71': // big sqcup '72': {ic: .194}, '73': {ic: .444}, '82': {tclass: 'bigop1cx', ic: .15}, '90': {tclass: 'bigop2cx', ic:.6}, '85': {c: '∪+'}, '93': {c: '∪+'} } }); jsMath.Setup.Styles({ '.typeset .symbol': "font-family: Osaka", '.typeset .arrow1': "font-family: Osaka; position: relative; top: .125em; margin: -1px", '.typeset .arrow2': "font-family: AppleGothic; font-size: 100%; position:relative; top: .11em; margin:-1px", '.typeset .bigop1': "font-family: AppleGothic; font-size: 110%; position:relative; top: .9em; margin:-.05em", '.typeset .bigop1b': "font-family: Osaka; font-size: 140%; position: relative; top: .8em; margin:-.1em", '.typeset .bigop1c': "font-family: AppleGothic; font-size: 125%; position:relative; top: .85em; margin:-.3em", '.typeset .bigop1cx': "font-family: 'Apple Chancery'; font-size: 125%; position:relative; top: .7em; margin:-.1em", '.typeset .bigop2': "font-family: AppleGothic; font-size: 175%; position:relative; top: .85em; margin:-.1em", '.typeset .bigop2b': "font-family: Osaka; font-size: 200%; position: relative; top: .75em; margin:-.15em", '.typeset .bigop2c': "font-family: AppleGothic; font-size: 300%; position:relative; top: .75em; margin:-.35em", '.typeset .bigop2cx': "font-family: 'Apple Chancery'; font-size: 250%; position:relative; top: .7em; margin-left:-.1em; margin-right:-.2em", '.typeset .delim1b': "font-family: Times; font-size: 150%; position:relative; top:.8em; margin:.01em", '.typeset .delim2b': "font-family: Times; font-size: 210%; position:relative; top:.8em; margin:.01em", '.typeset .delim3b': "font-family: Times; font-size: 300%; position:relative; top:.75em; margin:.01em", '.typeset .delim4b': "font-family: Times; font-size: 400%; position:relative; top:.725em; margin:.01em" }); /* * replace \not and \joinrel with better dimensions */ jsMath.Macro('not','\\mathrel{\\rlap{\\kern 3mu/}}'); jsMath.Macro('joinrel','\\mathrel{\\kern-3mu}'); glm-ie_v1.4/doc/jsMath/jsMath-fallback-mac-msie.js0000644000175000017500000002251111453154135017604 0ustar hnhn/* * jsMath-fallback-mac-msie.js * * Part of the jsMath package for mathematics on the web. * * This file makes changes needed by Internet Explorer on the Mac * for when the TeX fonts are not available. * * --------------------------------------------------------------------- * * Copyright 2004-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /******************************************************************** * * Fix the default non-TeX-font characters to work with MSIE * */ jsMath.Update.TeXfonts({ cmr10: { '0': {c: 'G', tclass: 'greek'}, '1': {c: 'D', tclass: 'greek'}, '2': {c: 'Q', tclass: 'greek'}, '3': {c: 'L', tclass: 'greek'}, '4': {c: 'X', tclass: 'greek'}, '5': {c: 'P', tclass: 'greek'}, '6': {c: 'S', tclass: 'greek'}, '7': {c: '¡', tclass: 'greek'}, '8': {c: 'F', tclass: 'greek'}, '9': {c: 'Y', tclass: 'greek'}, '10': {c: 'W', tclass: 'greek'}, '22': {c: '`', tclass: 'symbol3'} }, cmti10: { '0': {c: 'G', tclass: 'igreek'}, '1': {c: 'D', tclass: 'igreek'}, '2': {c: 'Q', tclass: 'igreek'}, '3': {c: 'L', tclass: 'igreek'}, '4': {c: 'X', tclass: 'igreek'}, '5': {c: 'P', tclass: 'igreek'}, '6': {c: 'S', tclass: 'igreek'}, '7': {c: '¡', tclass: 'igreek'}, '8': {c: 'F', tclass: 'igreek'}, '9': {c: 'Y', tclass: 'igreek'}, '10': {c: 'W', tclass: 'igreek'}, '22': {c: '`', tclass: 'symbol3'} }, cmbx10: { '0': {c: 'G', tclass: 'bgreek'}, '1': {c: 'D', tclass: 'bgreek'}, '2': {c: 'Q', tclass: 'bgreek'}, '3': {c: 'L', tclass: 'bgreek'}, '4': {c: 'X', tclass: 'bgreek'}, '5': {c: 'P', tclass: 'bgreek'}, '6': {c: 'S', tclass: 'bgreek'}, '7': {c: '¡', tclass: 'bgreek'}, '8': {c: 'F', tclass: 'bgreek'}, '9': {c: 'Y', tclass: 'bgreek'}, '10': {c: 'W', tclass: 'bgreek'}, '22': {c: '`', tclass: 'symbol3'} }, cmmi10: { '0': {c: 'G', tclass: 'igreek'}, '1': {c: 'D', tclass: 'igreek'}, '2': {c: 'Q', tclass: 'igreek'}, '3': {c: 'L', tclass: 'igreek'}, '4': {c: 'X', tclass: 'igreek'}, '5': {c: 'P', tclass: 'igreek'}, '6': {c: 'S', tclass: 'igreek'}, '7': {c: '¡', tclass: 'igreek'}, '8': {c: 'F', tclass: 'igreek'}, '9': {c: 'Y', tclass: 'igreek'}, '10': {c: 'W', tclass: 'igreek'}, '11': {c: 'a', tclass: 'greek'}, '12': {c: 'b', tclass: 'greek'}, '13': {c: 'g', tclass: 'greek'}, '14': {c: 'd', tclass: 'greek'}, '15': {c: 'e', tclass: 'greek'}, '16': {c: 'z', tclass: 'greek'}, '17': {c: 'h', tclass: 'greek'}, '18': {c: 'q', tclass: 'greek'}, '19': {c: 'i', tclass: 'greek'}, '20': {c: 'k', tclass: 'greek'}, '21': {c: 'l', tclass: 'greek'}, '22': {c: 'm', tclass: 'greek'}, '23': {c: 'n', tclass: 'greek'}, '24': {c: 'x', tclass: 'greek'}, '25': {c: 'p', tclass: 'greek'}, '26': {c: 'r', tclass: 'greek'}, '27': {c: 's', tclass: 'greek'}, '28': {c: 't', tclass: 'greek'}, '29': {c: 'u', tclass: 'greek'}, '30': {c: 'f', tclass: 'greek'}, '31': {c: 'c', tclass: 'greek'}, '32': {c: 'y', tclass: 'greek'}, '33': {c: 'w', tclass: 'greek'}, // '41': // leftharpoondown // '43': // rightharpoondown // '44': // hook left // '45': // hook right // '92': // natural '94': {c: '︶'}, '95': {c: '︵'} // '127': // half-circle down accent? }, cmsy10: { '0': {c: '–', tclass: 'normal'}, '11': {c: '◯/', tclass: 'normal'}, '16': {c: '︵︶', tclass: 'normal'}, '48': {c: '′'}, '93': {c: '∪+'}, '96': {c: '|–', tclass: 'normal'}, '104': {c: '〈'}, '105': {c: '〉'}, '109': {c: '⇑⇓'}, '110': {c: '\\', d:0, tclass: 'normal'} // '111': // wr //, '113': // amalg // '116': // sqcup // '117': // sqcap // '118': // sqsubseteq // '119': // sqsupseteq }, cmex10: { '10': {c: '〈'}, '11': {c: '〉'}, '14': {c: '/'}, '15': {c: '\\'}, '28': {c: '〈'}, '29': {c: '〉'}, '30': {c: '/'}, '31': {c: '\\'}, '42': {c: '〈'}, '43': {c: '〉'}, '44': {c: '/'}, '45': {c: '\\'}, '46': {c: '/'}, '47': {c: '\\'}, '68': {c: '〈'}, '69': {c: '〉'}, // '70': // sqcup // '71': // big sqcup '72': {ic: 0}, '73': {ic: 0}, '82': {tclass: 'bigop1cx', ic: .15}, '90': {tclass: 'bigop2cx', ic:.6}, '85': {c: '∪+'}, '93': {c: '∪+'}, // '96': // coprod // '97': // big coprod '98': {c: '︿', h: 0.722, w: .58, tclass: 'wide1'}, '99': {c: '︿', h: 0.722, w: .58, tclass: 'wide2'}, '100': {c: '︿', h: 0.722, w: .58, tclass: 'wide3'}, '101': {c: '~', h: 0.722, w: .42, tclass: 'wide1a'}, '102': {c: '~', h: 0.8, w: .73, tclass: 'wide2a'}, '103': {c: '~', h: 0.8, w: 1.1, tclass: 'wide3a'} } }); jsMath.Setup.Styles({ '.typeset .arrow1': "font-family: Osaka; position: relative; top: .125em; margin: -1px", '.typeset .arrow2': "font-family: Osaka; position: relative; top: .1em; margin:-1px", '.typeset .bigop1': "font-family: Symbol; font-size: 110%; position:relative; top: .8em; margin:-.05em", '.typeset .bigop1b': "font-family: Symbol; font-size: 140%; position: relative; top: .8em; margin:-.1em", '.typeset .bigop1c': "font-family: Osaka; font-size: 125%; position:relative; top: .85em; margin:-.3em", '.typeset .bigop1cx': "font-family: 'Apple Chancery'; font-size: 125%; position:relative; top: .7em; margin:-.1em", '.typeset .bigop2': "font-family: Symbol; font-size: 175%; position:relative; top: .8em; margin:-.07em", '.typeset .bigop2a': "font-family: Baskerville; font-size: 175%; position: relative; top: .65em", '.typeset .bigop2b': "font-family: Symbol; font-size: 175%; position: relative; top: .8em; margin:-.07em", '.typeset .bigop2c': "font-family: Osaka; font-size: 230%; position:relative; top: .85em; margin:-.35em", '.typeset .bigop2cx': "font-family: 'Apple Chancery'; font-size: 250%; position:relative; top: .6em; margin-left:-.1em; margin-right:-.2em", '.typeset .delim1b': "font-family: Times; font-size: 150%; position:relative; top:.8em", '.typeset .delim2b': "font-family: Times; font-size: 210%; position:relative; top:.75em;", '.typeset .delim3b': "font-family: Times; font-size: 300%; position:relative; top:.7em;", '.typeset .delim4b': "font-family: Times; font-size: 400%; position:relative; top:.65em;", '.typeset .symbol3': "font-family: Symbol", '.typeset .wide1': "font-size: 50%; position: relative; top:-1.1em", '.typeset .wide2': "font-size: 80%; position: relative; top:-.7em", '.typeset .wide3': "font-size: 125%; position: relative; top:-.5em", '.typeset .wide1a': "font-size: 75%; position: relative; top:-.5em", '.typeset .wide2a': "font-size: 133%; position: relative; top: -.15em", '.typeset .wide3a': "font-size: 200%; position: relative; top: -.05em", '.typeset .greek': "font-family: Symbol", '.typeset .igreek': "font-family: Symbol; font-style:italic", '.typeset .bgreek': "font-family: Symbol; font-weight:bold" }); glm-ie_v1.4/doc/jsMath/extensions/0000755000175000017500000000000011535375432014776 5ustar hnhnglm-ie_v1.4/doc/jsMath/extensions/leaders.js0000644000175000017500000001156511453154135016755 0ustar hnhn/* * extensions/leaders.js * * Part of the jsMath package for mathematics on the web. * * This file implements the \overbrace, \underbrace, \overrightarrow * and \overleftarrow macros. It will be loaded automatically when needed, * or can be loaded by * * jsMath.Extension.Require('leaders'); * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Add(jsMath.Box,{ /* * Create a horizontally stretchable "delimiter" (like over- and * underbraces). */ //### Add size? Leaders: function (W,leader) { var h; var d; var w; var html; var font; if (leader.lmid) {// braces font = jsMath.TeX.fam[leader.left[0]]; var left = this.GetCharCode(leader.left); var right = this.GetCharCode(leader.right); var lmid = this.GetCharCode(leader.lmid); var rmid = this.GetCharCode(leader.rmid); w = (W - left.w - right.w - lmid.w - rmid.w)/2 - .1; h = .4; d = .3; if (w < 0) {w = 0} html = this.AddClass(left.tclass,left.c,left.font) + jsMath.HTML.Rule(w,left.h) + this.AddClass(lmid.tclass,lmid.c+rmid.c,lmid.font) + jsMath.HTML.Rule(w,right.h) + this.AddClass(right.tclass,right.c,right.font); } else { //arrows font = jsMath.TeX.fam[leader.rep[0]]; var left = this.GetCharCode(leader.left? leader.left: leader.rep); var rep = this.GetCharCode(leader.rep); var right = this.GetCharCode(leader.right? leader.right: leader.rep); var n = Math.ceil((W - left.w - right.w + .4)/(rep.w - .3)); w = (W - left.w - right.w + .4 - n*(rep.w - .3)); if (leader.left) {h = left.h; d = left.d} else {h = right.h; d = right.d} if (d == null) {d = 0}; if (h == null) {h = 0} var html = this.AddClass(left.tclass,left.c,left.font); var m = Math.floor(n/2); var ext = jsMath.HTML.Place(rep.c,-.3,0); var ehtml = ''; for (var i = 0; i < m; i++) {ehtml += ext}; html += this.AddClass(rep.tclass,ehtml,rep.font) + jsMath.HTML.Spacer(w); ehtml = ''; for (var i = m; i < n; i++) {ehtml += ext}; html += this.AddClass(rep.tclass,ehtml,rep.font); if (jsMath.Browser.msieFontBug) {html += 'x'} html += jsMath.HTML.Place(this.AddClass(right.tclass,right.c,right.font),-.4,0); } w = jsMath.EmBoxFor(html).w; if (w != W) { w = jsMath.HTML.Spacer((W-w)/2); html = w + html + w; } var box = new jsMath.Box('html',html,W,h,d); box.bh = jsMath.TeX[font].h; box.bd = jsMath.TeX[font].d; return box; } }); jsMath.Package(jsMath.Parser,{ macros: { overbrace: ['HandleLeaders','downbrace',1], underbrace: ['HandleLeaders','upbrace',1,1,-.05], overrightarrow: ['HandleLeaders','rightarrow'], underrightarrow: ['HandleLeaders','rightarrow',null,1,-.2], overleftarrow: ['HandleLeaders','leftarrow'], underleftarrow: ['HandleLeaders','leftarrow',null,1,-.2], overleftrightarrow: ['HandleLeaders','leftrightarrow'], underleftrightarrow: ['HandleLeaders','leftrightarrow',null,1,-.2] }, /* * The horizontally stretchable delimiters */ leaders: { downbrace: {left: [3,0x7A], lmid: [3,0x7D], rmid: [3,0x7C], right: [3,0x7B]}, upbrace: {left: [3,0x7C], lmid: [3,0x7B], rmid: [3,0x7A], right: [3,0x7D]}, leftarrow: {left: [2,0x20], rep: [2,0x00]}, rightarrow: {rep: [2,0x00], right: [2,0x21]}, leftrightarrow: {left: [2,0x20], rep: [2, 0x00], right: [2,0x21]} }, /* * Implements \overbrace, \underbrace, etc. */ HandleLeaders: function (name,data) { var box = this.ProcessArg(this.cmd+name); if (this.error) return; box = jsMath.Box.Set(box,'D',this.mlist.data.size).Remeasured(); var leader = jsMath.Box.Leaders(box.w,this.leaders[data[0]]); if (data[2]) {leader.y = -leader.h-box.d+(data[3]||0)} else {leader.y = box.h + Math.max(0,leader.d)+(data[3]||0)} box.x = -(leader.w + box.w)/2; var space = jsMath.Box.Space((leader.w-box.w)/2); box = jsMath.mItem.Atom(data[1]? 'op': 'ord', jsMath.Box.SetList([leader,box,space],'T',this.mlist.data.size)); box.limits = (data[1]? 1: 0); this.mlist.Add(box); } }); glm-ie_v1.4/doc/jsMath/extensions/font.js0000644000175000017500000000225111453154135016274 0ustar hnhnjsMath.Package(jsMath.Parser,{ macros: {font: 'Font'}, fontCS: {}, /* * Get a CS name or give an error */ GetCSname: function (cmd) { var c = this.GetNext(); if (c != this.cmd) {this.Error(cmd+" must be followed by a control sequence"); return null} var cs = this.trimSpaces(this.GetArgument(cmd)); if (this.error) {return null}; return cs.substr(1); }, /* * Handle the \font command */ Font: function (name) { var cs = this.GetCSname(this.cmd+name); if (this.error) return; while (this.nextIsSpace()) {this.i++} if (this.string.charAt(this.i++) == '=') { while (this.nextIsSpace()) {this.i++} var font = this.string.slice(this.i).match(/^[a-z]+[0-9]+/i); if (font) { this.i += (new String(font)).length; if (jsMath.TeX.famName[font] != null) { this.macros[cs] = ['HandleFont',jsMath.TeX.famName[font]]; } else { this.macros[cs] = ['Extension',jsMath.Font.URL(font),"fontCS"]; this.fontCS[cs] = 1; // so Extension has something to delete } } else {this.Error("Missing font name")} } else {this.Error("Missing font definition")} } }); glm-ie_v1.4/doc/jsMath/extensions/boldsymbol.js0000644000175000017500000000411111453154135017471 0ustar hnhn/* * extensions/boldsymbol.js * * Part of the jsMath package for mathematics on the web. * * This file implements the \boldsymbol macro. You can activate it * by calling * * jsMath.Extension.Macro('boldsymbol'); * * which will cause the extension to be loaded only when it is * needed, or you can force it to be loaded via * * jsMath.Extension.Require('boldsymbol'); * * once jsMath.js has been loaded. * * Note that you will need to install the cmmib10 and cmbsy10 fonts * that are available from the jsMath extra font page at * * http://www.math.union.edu/locate/jsMath/download/extra-fonts/ * * to make this work in image mode. Note that there is no unicode * fallback for these fonts at the moment. * * --------------------------------------------------------------------- * * Copyright 2006-2007 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Package(jsMath.Parser,{ macros: {boldsymbol: 'BoldSymbol'}, /* * Implement \boldsymbol{...} */ BoldSymbol: function (name) { var fam = jsMath.TeX.fam; var restart = 0; var oldfam = [fam[0],fam[1],fam[2]]; fam[0] = "cmbx10"; fam[1] = "cmmib10"; fam[2] = "cmbsy10"; try{var box = this.ProcessArg(this.cmd+name)} catch (e) {restart = (e == "restart")} fam[0] = oldfam[0]; fam[1] = oldfam[1]; fam[2] = oldfam[2]; if (this.error) return; if (restart) {throw "restart"} this.mlist.Add(jsMath.mItem.Atom('ord',box)); } }); glm-ie_v1.4/doc/jsMath/extensions/underset-overset.js0000644000175000017500000000326411453154135020651 0ustar hnhn/* * extensions/underset-overset.js * * Part of the jsMath package for mathematics on the web. * * This file implements \underset and \overset macros. It will be loaded * automatically when needed, or can be loaded by * * jsMath.Extension.Require('underset-overset'); * * --------------------------------------------------------------------- * * Copyright 200-20065 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Package(jsMath.Parser,{ macros: { overset: 'Overset', underset: 'Underset' }, Overset: function (name) { var top = this.ProcessArg(this.cmd+name); if (this.error) return; var bot = this.ProcessArg(this.cmd+name); if (this.error) return; var op = jsMath.mItem.Atom('op',bot); op.limits = 1; op.sup = top; this.mlist.Add(op); }, Underset: function (name) { var bot = this.ProcessArg(this.cmd+name); if (this.error) return; var top = this.ProcessArg(this.cmd+name); if (this.error) return; var op = jsMath.mItem.Atom('op',top); op.limits = 1; op.sub = bot; this.mlist.Add(op); } }); glm-ie_v1.4/doc/jsMath/extensions/mathchoice.js0000644000175000017500000000440011453154135017430 0ustar hnhn/* * extensions/mathchoice.js * * Part of the jsMath package for mathematics on the web. * * This file implements the 4-way math choice. It will be loaded * automatically when needed, or can be loaded by * * jsMath.Extension.Require('mathchoice'); * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Add(jsMath.mList.prototype.Atomize,{ /* * Handle a 4-way choice atom. (Rule 4) */ choice: function (style,mitem,i,mlist) { if (style.charAt(style.length-1) == "'") {style = style.slice(0,style.length-1)} var nlist = []; var M = mitem[style]; if (!M) {M = {type: 'mlist', mlist: {mlist: []}}} if (M.type == 'mlist') { M = M.mlist.mlist; for (var k = 0; k < i; k++) {nlist[k] = mlist[k]} for (k = 0; k < M.length; k++) {nlist[i+k] = M[k]} for (k = i+1; k < mlist.length; k++) {nlist[nlist.length] = mlist[k]} return nlist; } else { mlist[i] = jsMath.mItem.Atom('ord',M); return mlist; } } }); jsMath.Package(jsMath.Parser,{ macros: {mathchoice: 'MathChoice'}, /* * Implements \mathchoice{}{}{}{} */ MathChoice: function (name) { var D = this.ProcessArg(this.cmd+name); if (this.error) return; var T = this.ProcessArg(this.cmd+name); if (this.error) return; var S = this.ProcessArg(this.cmd+name); if (this.error) return; var SS = this.ProcessArg(this.cmd+name); if (this.error) return; var box = new jsMath.mItem('choice',{D: D, T: T, S: S, SS: SS}); this.mlist.Add(new jsMath.mItem('choice',{D: D, T: T, S: S, SS: SS})); } }); glm-ie_v1.4/doc/jsMath/extensions/HTML.js0000644000175000017500000001001211453154135016064 0ustar hnhn/* * extensions/HTML.js * * Part of the jsMath package for mathematics on the web. * * This file implements a number of HTML-specific extensions to TeX, * including \color, \style, \class, \unicode, etc. It will be loaded * automatically when needed, or can be loaded by * * jsMath.Extension.Require('HTML'); * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Package(jsMath.Parser,{ macros: { color: 'Color', href: 'Href', 'class': 'Class', style: 'Style', cssId: 'CSSId', unicode: 'Unicode' }, /* * Show the argument in a particular color */ Color: function (name) { var color = this.GetArgument(this.cmd+name); if (this.error) return; this.CheckHTML(color,name); if (this.error) return; // check that it looks like a color? this.AddHTML(name,['','']); }, /* * Make the argument be a link */ Href: function (name) { var href = this.GetArgument(this.cmd+name); if (this.error) return; this.CheckHTML(href,name); if (this.error) return; this.AddHTML(name,['','']); }, /* * Apply a CSS class to the argument */ Class: function (name) { var clss = this.GetArgument(this.cmd+name); if (this.error) return; this.CheckHTML(clss,name); if (this.error) return; this.AddHTML(name,['','']); }, /* * Apply a CSS style to the argument */ Style: function (name) { var style = this.GetArgument(this.cmd+name); if (this.error) return; this.CheckHTML(style,name); if (this.error) return; this.AddHTML(name,['','']); }, /* * Add a CSS element ID to the argument */ CSSId: function (name) { var id = this.GetArgument(this.cmd+name); if (this.error) return; this.CheckHTML(id,name); if (this.error) return; this.AddHTML(name,['','']); }, /* * Insert some raw HTML around the argument (this will not affect * the spacing or other TeX features) */ AddHTML: function (name,params) { var data = this.mlist.data; var arg = this.GetArgument(this.cmd+name); if (this.error) return; arg = jsMath.Parse(arg,data.font,data.size,data.style); if (arg.error) {this.Error(arg); return} this.mlist.Add(jsMath.mItem.HTML(params[0])); for (var i = 0; i < arg.mlist.Length(); i++) {this.mlist.Add(arg.mlist.Get(i))} this.mlist.Add(jsMath.mItem.HTML(params[1])); }, CheckHTML: function (data,name) { if (data.match(/[<>&"]/)) {this.Error("Can't include raw HTML in first argument of "+this.cmd+name)} }, /* * Insert a unicode reference as an Ord atom. Its argument should * be the unicode code point, e.g. \unicode{8211}, or \unicode{x203F}. * You can also specify the height (offset from the x height) and depth * in ems, together with a CSS class for the character, e.g., * \unicode{8211,class,.2,-.3} */ Unicode: function (name) { var arg = this.GetArgument(this.cmd+name); if (this.error) return; this.CheckHTML(arg,name); if (this.error) return; arg = arg.split(','); arg[0] = '&#'+arg[0]+';'; if (!arg[1]) {arg[1] = 'normal'} this.mlist.Add(jsMath.mItem.TextAtom('ord',arg[0],arg[1],arg[2],arg[3])); } }); glm-ie_v1.4/doc/jsMath/extensions/autobold.js0000644000175000017500000000401011453154135017132 0ustar hnhn/* * extensions/autobold.js * * Part of the jsMath package for mathematics on the web. * * This file causes jsMath to use \boldsymbol{...} around mathematics * that appears within ... tags or has font-weight:bold applied * via CSS rule. You can activate it by calling * * jsMath.Extension.Require('autobold'); * * once jsMath.js has been loaded, or by adding "extensions/autobold.js" * to the loadFiles array in jsMath/easy/load.js. * * Note that you will need to install the cmmib10 and cmbsy10 fonts * that are available from the jsMath extra font page at * * http://www.math.union.edu/locate/jsMath/download/extra-fonts/ * * to make this work in image mode. Note that there is no unicode * fallback for these fonts at the moment. * * --------------------------------------------------------------------- * * Copyright 2008 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Extension.Require("boldsymbol"); jsMath.Translate.OldParse = jsMath.Translate.Parse; jsMath.Translate.Parse = function (style,text,noCache) { if (jsMath.BBoxFor('MMMMMMMMMM').w > jsMath.BBoxFor('MMMMMMMMMM').w) { text = '\\boldsymbol{' + text + '}'; } return jsMath.Translate.OldParse(style,text,noCache); } glm-ie_v1.4/doc/jsMath/extensions/fbox.js0000644000175000017500000000461711453154135016274 0ustar hnhn/* * extensions/fbox.js * * Part of the jsMath package for mathematics on the web. * * This file implements the \fbox macro. It will be loaded * automatically when needed, or can be loaded by * * jsMath.Extension.Require('fbox'); * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Add(jsMath.HTML,{ /* * Create a colored frame */ Frame: function (x,y,w,h,c,pos) { h -= 2/jsMath.em; // use 2 pixels to compensate for border size w -= 2/jsMath.em; y -= 1/jsMath.em; if (!c) {c = ''} else {c = ' '+c}; if (pos) {pos = 'absolute;'} else {pos = 'relative; margin-right: '+this.Em(-(w+2/jsMath.em))+'; '} return ''; } }); jsMath.Package(jsMath.Parser,{ macros: {fbox: 'FBox'}, /* * Implement \fbox{...} */ FBox: function (name) { var text = this.GetArgument(this.cmd+name); if (this.error) return; var arg = jsMath.Box.InternalMath(text,this.mlist.data.size); var f = 0.25 * jsMath.sizes[this.mlist.data.size]/100; var box = jsMath.Box.Set(arg,this.mlist.data.style,this.mlist.data.size,1).Remeasured(); var frame = jsMath.HTML.Frame(-f,-box.d-f,box.w+2*f,box.h+box.d+2*f); box.html = frame + box.html + jsMath.HTML.Spacer(f); box.h += f; box.d += f; box.w +=2*f; box.x += f; box.bh = Math.max(box.bh,box.h); box.bd = Math.max(box.bd,box.d); this.mlist.Add(jsMath.mItem.Atom('ord',box)); } }); glm-ie_v1.4/doc/jsMath/extensions/eqn-number.js0000644000175000017500000001634511453154135017410 0ustar hnhn/* * extensions/eqn-number.js * * Part of the jsMath package for mathematics on the web. * * This file causes jsMath to add equation numbers to displayed * equations. These are displayed at the right, but the styles can * be controlled through the jsMath.EqnNumber object. Equations * are numbered if they include a \label{xxx} call, and the macro * \ref{xxx} can be used to refer to the equation number elsewhere * in the document (it must appear by itself in a math formula, * e.g., $\ref{xxx}$). The "label-ref" CSS style can be used to * style the references. * * If jsMath.EqnNumber.autonumber is set to 1, then ALL displayed * equations will be numberd. Use the \nolabel macro to prevent * equation numbering on an equation. * * You can activate eqn-numbering by calling * * jsMath.Extension.Require('eqn-number'); * * once jsMath.js has been loaded, or by adding "extensions/eqn-number.js" * to the loadFiles array in jsMath/easy/load.js. * * --------------------------------------------------------------------- * * Copyright 2008 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ if (jsMath.EqnNumber) {jsMath.EqnNumber_old = jsMath.EqnNumber} jsMath.EqnNumber = { styles: { '.jsMath_displayBox, .tex2math_div': {position: 'relative'}, '.jsMath_number': { position: 'absolute', right: '2em', top: '50%', 'margin-top': '-.5em', height: 'auto', width: 'auto' }, '.jsMath_ref': {'text-decoration': 'none'} }, autonumber: 0, // set to 1 to have ALL equations numbered number: 0, format: function (n) {return n}, formatLabel: function (n) {return '('+n+')'}, formatRef: function (n) {return '('+n+')'}, _label: null, // flag set when \label{x} is used _labels: {}, // stores label-name => label-value pairs _refs: {}, // stores elements referring to undefined labels _nolabel: 0, // set by \nolabel nextNumber: function () { var ref = this.format(++this.number); if (this._label) { this._labels[this._label] = ref; if (this._refs[this._label]) this.fixRefs(this._label); } return this.formatLabel(ref); }, isRef: function (element) { var tex = element.innerHTML; var result = tex.match(/^\s*\\ref\s*\{([^\}]+)\}\s*$/); if (!result) {return 0} var ref = result[1]; if (this._labels[ref]) { this.setRef(element,ref); } else { if (!this._refs[ref]) {this._refs[ref] = []} this._refs[ref][this._refs[ref].length] = element; } return 1; }, setRef: function (element,ref) { element.innerHTML = this.formatRef(this._labels[ref]); element.className = "label-ref"; }, fixRefs: function (label) { for (var i = 0; i < this._refs[label].length; i++) {this.setRef(this._refs[label][i],label)} delete this._refs[label]; }, badRefs: function () { for (var label in this._refs) { for (var i = 0; i < this._refs[label].length; i++) { var element = this._refs[label][i]; element.className = "typeset"; element.innerHTML = "Reference '"+label+"' is undefined"; } } }, makeDIV: function (element) { var div = document.createElement('div'); div.className = 'jsMath_displayBox'; div.innerHTML = '
' + this.nextNumber() + '
'; element.parentNode.insertBefore(div,element); element.parentNode.removeChild(element); div.appendChild(element); }, makeSPAN: function (element) { var span = document.createElement('span'); span.className = 'jsMath_number'; span.style.display = 'inline-block'; span.innerHTML = jsMath.EqnNumber.nextNumber(); element.parentNode.insertBefore(span,element); }, ConvertMath: function (style,element,nocache) { var EqnNumber = jsMath.EqnNumber; if (EqnNumber.isRef(element)) return; EqnNumber._label = null; EqnNumber._nolabel = 0; this.ConvertMath_old(style,element,nocache); if (EqnNumber._label || (EqnNumber.autonumber && !EqnNumber._nolabel)) { if (element.tagName.toLowerCase() == 'div') { EqnNumber.makeDIV(element); } else if (element.parentNode.className == 'tex2math_div') { EqnNumber.makeSPAN(element); } } }, ProcessComplete: function () { jsMath.EqnNumber.badRefs(); this.ProcessComplete_old.apply(this,arguments); }, Init: function () { jsMath.Setup.Styles(this.styles); jsMath.Translate.ConvertMath_old = jsMath.Translate.ConvertMath; jsMath.Translate.ConvertMath = this.ConvertMath; jsMath.Translate.ProcessComplete_old = jsMath.Translate.ProcessComplete; jsMath.Translate.ProcessComplete = this.ProcessComplete; }, environments: { 'equation*': 'Star', 'eqnarray*': 'Star', 'align*': 'Star', 'multline*': 'Star', 'gather*': 'Star', align: ['StarExtension','AMSmath'], multline: ['StarExtension','AMSmath'], gather: ['StarExtension','AMSmath'] }, ResetStarEnvironments: function () { var Nenv = jsMath.EqnNumber.environments; var Penv = jsMath.Parser.prototype.environments; for (var name in Nenv) { if (name.match(/\*$/)) {Penv[name] = Nenv[name]} } } }; if (jsMath.EqnNumber_old) { jsMath.Insert(jsMath.EqnNumber,jsMath.EqnNumber_old); delete jsMath.EqnNumber_old; } jsMath.Package(jsMath.Parser,{ macros: { label: 'Label', nolabel: 'NoLabel', nonumber: 'NoLabel', ref: 'Ref' }, environments: jsMath.EqnNumber.environments, Label: function (name) { var label = this.GetArgument(this.cmd+name); if (this.error) return; var EqnNumber = jsMath.EqnNumber; if (!EqnNumber._label) { if (!EqnNumber._labels[label]) { EqnNumber._label = label; EqnNumber._nolabel = 0; } else { this.Error("Label '"+label+"' is already defined"); } } else { this.Error(this.cmd+name+' can only be used once in an equation'); } }, NoLabel: function (name) { var EqnNumber = jsMath.EqnNumber; EqnNumber._label = null; EqnNumber._nolabel = 1; }, Ref: function (name) { this.Error(this.cmd+name+' must be used by itself'); }, Star: function (name) { this.NoLabel(); var cmd = this.environments[name.substr(0,name.length-1)]; if (typeof(cmd) === 'string') {cmd = [cmd]} this[cmd[0]](name,cmd.slice(1)); }, StarExtension: function (name,data) { try {this.Extension(name,data)} catch (e) {} jsMath.Synchronize(jsMath.EqnNumber.ResetStarEnvironments); throw "restart"; } }); jsMath.EqnNumber.Init(); glm-ie_v1.4/doc/jsMath/extensions/double-click.js0000644000175000017500000002137311453154135017671 0ustar hnhn/* * extensions/double-click.js * * Part of the jsMath package for mathematics on the web. * * This file allows users to double click on typeset mathematics * to view the TeX source for the given expression. It will be loaded * automatically when needed, or can be loaded by * * jsMath.Extension.Require('double-click'); * * --------------------------------------------------------------------- * * Copyright 2005-2008 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ if (jsMath.Click && jsMath.Click.styles) {jsMath.Click.oldStyles = jsMath.Click.styles} jsMath.Add(jsMath.Click,{ dragging: 0, styles: { // Floating windows for displaying TeX source '#jsMath_float': { position: 'absolute', top: '0px', left: '0px', 'z-index': '101', 'max-width': '80%', width: 'auto', height: 'auto', padding: '0px', margin: '0px', 'font-size': '100%' }, '#jsMath_float .drag': { 'background-color': '#DDDDDD', border: 'outset 1px', padding: '0px', margin: '0px', width: 'auto', height: '12px', 'font-size': '1px' }, '#jsMath_float .close': { 'background-color': '#E6E6E6', border: 'inset 1px', margin: '1px 2px', padding: '0px', width: '8px', height: '8px' }, '#jsMath_float .source': { 'background-color': '#E2E2E2', border: 'outset 1px', margin: '0px', padding: '8px 15px', width: 'auto', height: 'auto', 'font-family': 'courier, fixed', 'font-size': '90%' } }, /* * Create the hidden DIV used for the tex source window */ Init: function () { if (this.oldStyles) {jsMath.Insert(this.styles,this.oldStyles)} jsMath.Setup.Styles(this.styles); this.source = jsMath.Setup.DIV("float",{display:'none'}); this.source.innerHTML = '
' + '
'; this.drag = this.source.firstChild; this.tex = this.drag.nextSibling.firstChild; this.drag.firstChild.onclick = jsMath.Click.CloseSource; this.drag.onmousedown = jsMath.Click.StartDragging; this.drag.ondragstart = jsMath.Click.False; this.drag.onselectstart = jsMath.Click.False; this.source.onclick = jsMath.Click.CheckClose; }, False: function () {return false}, /* * Handle a double-click on an equation */ DblClick: function (data) { var event = data[0]; var TeX = data[1]; var event = jsMath.Click.Event(event); var source = jsMath.Click.source var tex = jsMath.Click.tex; source.style.visibility = 'hidden'; source.style.display = ''; source.style.width = ''; source.style.left = ''; source.style.top = ''; tex.innerHTML = ''; TeX = TeX.replace(/^\s+|\s+$/g,''); TeX = TeX.replace(/&/g,'&'); TeX = TeX.replace(//g,'>'); TeX = TeX.replace(/\n/g,'
'); tex.innerHTML = TeX; var h = source.offsetHeight; var w; if (jsMath.Browser.msieDivWidthBug) { tex.className = 'source'; // Work around MSIE bug where w = tex.offsetWidth + 5; // DIV's don't collapse to tex.className = ''; // their natural widths } else { w = source.offsetWidth; } w = Math.max(50,Math.min(w,.8*event.W,event.W-40)); var x = Math.floor(event.x-w/2); var y = Math.floor(event.y-h/2); x = event.X + Math.max(Math.min(x,event.W-w-20),20); y = event.Y + Math.max(Math.min(y,event.H-h-5),5); source.style.left = x+'px'; source.style.top = y+'px'; source.style.width = w+'px'; source.style.visibility = ''; jsMath.Click.left = x + event.X; jsMath.Click.top = y + event.Y; jsMath.Click.w = w; jsMath.Click.h = source.offsetHeight; jsMath.Click.DeselectText(x,y); return false; }, /* * Get window width, height, and offsets plus * position of pointer relative to the window */ Event: function (event) { var W = jsMath.window.innerWidth || jsMath.document.body.clientWidth; var H = jsMath.window.innerHeight || jsMath.document.body.clientHeight; var X = jsMath.window.pageXOffset; var Y = jsMath.window.pageYOffset; if (X == null) { X = jsMath.document.body.clientLeft; Y = jsMath.document.body.clientTop; } var x = event.pageX; var y = event.pageY; if (x == null) { x = event.clientX; y = event.clientY; if (jsMath.browser == 'MSIE' && jsMath.document.compatMode == 'CSS1Compat') { X = jsMath.document.documentElement.scrollLeft; Y = jsMath.document.documentElement.scrollTop; W = jsMath.document.documentElement.clientWidth; H = jsMath.document.documentElement.clientHeight; } else { X = jsMath.document.body.scrollLeft; Y = jsMath.document.body.scrollTop; } } else {x -= X; y -= Y} return {x: x, y: y, W: W, H: H, X: X, Y: Y}; }, /* * Unselect whatever text is selected (since double-clicking * usually selects something) */ DeselectText: function (x,y) { if (jsMath.window.getSelection && jsMath.window.getSelection().removeAllRanges) {jsMath.window.getSelection().removeAllRanges()} else if (jsMath.document.getSelection && jsMath.document.getSelection().removeAllRanges) {jsMath.document.getSelection().removeAllRanges()} else if (jsMath.document.selection && jsMath.document.selection.empty) {jsMath.document.selection.empty()} else { /* Hack to deselect the text in Opera and Safari */ if (jsMath.browser == 'MSIE') return; // don't try it if MISE on Mac jsMath.hiddenTop.innerHTML = ''; jsMath.hiddenTop.firstChild.style.position = 'absolute'; jsMath.hiddenTop.firstChild.style.left = x+'px'; jsMath.hiddenTop.firstChild.style.top = y+'px'; setTimeout(jsMath.Click.SelectHidden,1); } }, SelectHidden: function () { jsMath.hiddenTop.firstChild.focus(); jsMath.hiddenTop.firstChild.select(); jsMath.hiddenTop.innerHTML = ''; }, /* * Close the TeX source window */ CloseSource: function () { jsMath.Click.tex.innerHTML = ''; jsMath.Click.source.style.display = 'none'; jsMath.Click.source.style.visibility = 'hidden'; jsMath.Click.StopDragging(); return false; }, CheckClose: function (event) { if (!event) {event = jsMath.window.event} if (event.altKey) {jsMath.Click.CloseSource(); return false} }, /* * Set up for dragging the source panel */ StartDragging: function (event) { if (!event) {event = jsMath.window.event} if (jsMath.Click.dragging) {jsMath.Click.StopDragging(event)} var event = jsMath.Click.Event(event); jsMath.Click.dragging = 1; jsMath.Click.x = event.x + 2*event.X - jsMath.Click.left; jsMath.Click.y = event.y + 2*event.Y - jsMath.Click.top; jsMath.Click.oldonmousemove = jsMath.document.onmousemove; jsMath.Click.oldonmouseup = jsMath.document.onmouseup; jsMath.document.onmousemove = jsMath.Click.DragSource; jsMath.document.onmouseup = jsMath.Click.StopDragging; return false; }, /* * Stop dragging the source window */ StopDragging: function (event) { if (jsMath.Click.dragging) { jsMath.document.onmousemove = jsMath.Click.oldonmousemove; jsMath.document.onmouseup = jsMath.Click.oldonmouseup; jsMath.Click.oldonmousemove = null; jsMath.Click.oldonmouseup = null; jsMath.Click.dragging = 0; } return false; }, /* * Move the source window (but stay within the browser window) */ DragSource: function (event) { if (!event) {event = jsMath.window.event} if (jsMath.Browser.buttonCheck && !event.button) {return jsMath.Click.StopDragging(event)} event = jsMath.Click.Event(event); var x = event.x + event.X - jsMath.Click.x; var y = event.y + event.Y - jsMath.Click.y; x = Math.max(event.X,Math.min(event.W+event.X-jsMath.Click.w,x)); y = Math.max(event.Y,Math.min(event.H+event.Y-jsMath.Click.h,y)); jsMath.Click.source.style.left = x + 'px'; jsMath.Click.source.style.top = y + 'px'; jsMath.Click.left = x + event.X; jsMath.Click.top = y + event.Y; return false; } }); jsMath.Click.Init(); glm-ie_v1.4/doc/jsMath/extensions/bbox.js0000644000175000017500000000777311453154135016276 0ustar hnhn/* * extensions/bbox.js * * Part of the jsMath package for mathematics on the web. * * This file implements the \bbox macro, which creates an HTML box that * can be styled (for background colors, and so on). You can include * an optional dimension that tells how much extra padding to include * around the bounding box for the mathematics. E.g., * * \bbox[2pt]{x+y} % an invisible box around x+y with 2pt of extra space * \bbox[green]{x+y} % a green box around x+y * \bbox[green,2pt]{x+y} % a green box with 2pt of extra space * \bbox[yellow,2pt,border:1px solid red]{x+y} * % a yellow box with a red border and 2pt space * * This extension is loaded automatically when needed, or you can call * it directly via * * jsMath.Extension.Require('bbox'); * * --------------------------------------------------------------------- * * Copyright 2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Add(jsMath.HTML,{ /* * Create a colored bbounding box */ BBox: function (w,h,d,c,s) { if (w <= 0) {return ''} if (d == null) {d = 0} var style = (jsMath.Browser.msieInlineBlockFix ? '' : 'overflow:visible;'); style += 'width:'+this.Em(w)+'; height:'+this.Em(h+d)+';'; if (jsMath.Browser.mozInlineBlockBug) {d = -h} if (jsMath.Browser.msieInlineBlockFix) {d -= jsMath.d} if (d) {style += ' vertical-align:'+this.Em(-d)+';'} if (c) {style += ' background-color:'+c+';'} var html = ''; return html; } }); jsMath.Add(jsMath.mList.prototype.Atomize,{ /* * Creates the box HTML */ bbox: function (style,size,mitem,prev,mlist) { var box; var w; var h; var d; var nuc = mitem.nuc = jsMath.Box.Set(mitem.nuc,style,size).Remeasured(); if (box == null) {w = nuc.w; h = nuc.h; d = nuc.d} // values before super/subs-cript var nuc = mitem.nuc; nuc.Styled(); var pad = mitem.pad; if (pad) {w += 2*pad; h += pad; d += pad; nuc.w += pad} if (jsMath.Browser.msieCenterBugFix) {nuc.html = ''+nuc.html+''} nuc.html = jsMath.HTML.BBox(w,h,d,mitem.color,mitem.style) + jsMath.HTML.Spacer(pad-w) + nuc.html; nuc.Remeasured(); if (pad && nuc.w < w) { nuc.html += jsMath.HTML.Spacer(w-nuc.w); nuc.w = w; } nuc.h = Math.max(nuc.h,h); nuc.d = Math.max(nuc.d,d); nuc.bh = Math.max(nuc.bh,nuc.h); nuc.bd = Math.max(nuc.bd,nuc.d); mitem.type = 'ord'; jsMath.mList.prototype.Atomize.SupSub(style,size,mitem); } }); jsMath.Package(jsMath.Parser,{ macros: {bbox: 'BBox'}, /* * Implement \bbox[...]{...} */ BBox: function (name) { var extra = this.GetBrackets(this.cmd+name); if (this.error) return; var arg = this.GetArgument(this.cmd+name); if (this.error) return; var nuc = this.Process(arg); if (this.error) return; var color; var pad = 0; var style = ''; if (extra != '') { var parts = extra.split(/,/); for (var i in parts) { if (parts[i].match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|px)\s*$/)) {pad = this.ParseDimen(parts[i],'',0,1)} else if (parts[i].match(/:/)) {style = parts[i]} else {color = parts[i]} } } var atom = {nuc: nuc, atom: 1, pad: pad, color: color, style: style}; this.mlist.Add(new jsMath.mItem('bbox',atom)); } }); glm-ie_v1.4/doc/jsMath/extensions/mimeTeX.js0000644000175000017500000000213211453154135016674 0ustar hnhn/* * extensions/mimeTeX.js * * Part of the jsMath package for mathematics on the web. * * This file loads the mimeTeX plugin, and can be called either * by * * jsMath.Extension.Require('mimeTeX'); * * or by using * * \require{mimeTeX} * * within a typeset equation. * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Setup.Script('plugins/mimeTeX.js'); glm-ie_v1.4/doc/jsMath/extensions/AMSsymbols.js0000644000175000017500000002133711453154135017365 0ustar hnhn/* * extensions/AMSsymbol.js * * Part of the jsMath package for mathematics on the web. * * This file defines the macros needed to access the AMS symbol fonts * available in msam10 and msbm10. You can activate it by calling * * jsMath.Extension.Require('AMSsymbols'); * * once jsMath.js has been loaded. * * Note that you will need to install the msam10 and msbm10 fonts * that are available from the jsMath extra font page at * * http://www.math.union.edu/locate/jsMath/download/extra-fonts/ * * in order to make this work in image mode. Note that there is no * unicode fallback mode for these fonts at this time. * * --------------------------------------------------------------------- * * Copyright 2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ delete jsMath.Parser.prototype.macros['hbar']; delete jsMath.Parser.prototype.macros['angle']; delete jsMath.Parser.prototype.macros['rightleftharpoons']; jsMath.Extension.MathChar("msam10",{ // Miscellaneous symbols vartriangle: [3,0x4D], triangledown: [0,0x4F], square: [0,0x03], lozenge: [0,0x06], circledS: [0,0x73], angle: [0,0x5C], measuredangle: [0,0x5D], backprime: [0,0x38], blacktriangle: [0,0x4E], blacktriangledown: [0,0x48], blacksquare: [0,0x04], blacklozenge: [0,0x07], bigstar: [0,0x46], sphericalangle: [0,0x5E], complement: [0,0x7B], // Binary operators dotplus: [2,0x75], Cap: [2,0x65], doublecap: [2,0x65], Cup: [2,0x64], doublecup: [2,0x64], barwedge: [2,0x5A], veebar: [2,0x59], doublebarwedge: [2,0x5B], boxminus: [2,0x0C], boxtimes: [2,0x02], boxdot: [2,0x00], boxplus: [2,0x01], leftthreetimes: [2,0x68], rightthreetimes: [2,0x69], curlywedge: [2,0x66], curlyvee: [2,0x67], circleddash: [2,0x7F], circledast: [2,0x7E], circledcirc: [2,0x7D], centerdot: [2,0x05], intercal: [2,0x7C], // Binary relations leqq: [3,0x35], leqslant: [3,0x36], eqslantless: [3,0x30], lesssim: [3,0x2E], lessapprox: [3,0x2F], lll: [3,0x6E], llless: [3,0x6E], lessgtr: [3,0x37], lesseqgtr: [3,0x51], lesseqqgtr: [3,0x53], doteqdot: [3,0x2B], Doteq: [3,0x2B], risingdotseq: [3,0x3A], fallingdotseq: [3,0x3B], backsim: [3,0x76], backsimeq: [3,0x77], subseteqq: [3,0x6A], Subset: [3,0x62], sqsubset: [3,0x40], preccurlyeq: [3,0x34], curlyeqprec: [3,0x32], precsim: [3,0x2D], vartriangleleft: [3,0x43], trianglelefteq: [3,0x45], vDash: [3,0x0F], Vvdash: [3,0x0E], smallsmile: [3,0x60], smallfrown: [3,0x61], bumpeq: [3,0x6C], Bumpeq: [3,0x6D], varpropto: [3,0x5F], blacktriangleleft: [3,0x4A], therefore: [3,0x29], geqq: [3,0x3D], geqslant: [3,0x3E], eqslantgtr: [3,0x31], gtrsim: [3,0x26], gtrapprox: [3,0x27], ggg: [3,0x6F], gggtr: [3,0x6F], gtrless: [3,0x3F], gtreqless: [3,0x52], gtreqqless: [3,0x54], eqcirc: [3,0x50], circeq: [3,0x24], triangleq: [3,0x2C], supseteqq: [3,0x6B], Supset: [3,0x63], sqsupset: [3,0x41], succcurlyeq: [3,0x3C], curlyeqsucc: [3,0x33], succsim: [3,0x25], vartriangleright: [3,0x42], trianglerighteq: [3,0x44], Vdash: [3,0x0D], between: [3,0x47], pitchfork: [3,0x74], blacktriangleright: [3,0x49], because: [3,0x2A], // Arrows leftleftarrows: [3,0x12], leftrightarrows: [3,0x1C], Lleftarrow: [3,0x57], twoheadleftarrow: [3,0x11], leftarrowtail: [3,0x1B], looparrowleft: [3,0x22], leftrightharpoons: [3,0x0B], circlearrowleft: [3,0x09], Lsh: [3,0x1E], upuparrows: [3,0x14], upharpoonleft: [3,0x18], downharpoonleft: [3,0x19], multimap: [3,0x28], leftrightsquigarrow:[3,0x21], rightrightarrows: [3,0x13], rightleftarrows: [3,0x1D], Rrightarrow: [3,0x56], twoheadrightarrow: [3,0x10], rightarrowtail: [3,0x1A], looparrowright: [3,0x23], rightleftharpoons: [3,0x0A], circlearrowright: [3,0x08], Rsh: [3,0x1F], downdownarrows: [3,0x15], upharpoonright: [3,0x16], downharpoonright: [3,0x17], rightsquigarrow: [3,0x20] }); jsMath.Extension.MathChar("msbm10",{ // Lowercase Greek letters digamma: [0,0x7A], varkappa: [0,0x7B], // Hebrew letters beth: [0,0x69], daleth: [0,0x6B], gimel: [0,0x6A], // Miscellaneous symbols hbar: [0,0x7E], hslash: [0,0x7D], nexists: [0,0x40], mho: [0,0x66], Finv: [0,0x60], Game: [0,0x61], Bbbk: [0,0x7C], varnothing: [0,0x3F], eth: [0,0x67], diagup: [0,0x1E], diagdown: [0,0x1F], // Binary operators smallsetminus: [2,0x72], divideontimes: [2,0x3E], ltimes: [2,0x6E], rtimes: [2,0x6F], // Binary relations approxeq: [3,0x75], lessdot: [3,0x6C], precapprox: [3,0x77], gtrdot: [3,0x6D], thicksim: [3,0x73], thickapprox: [3,0x74], succapprox: [3,0x76], shortmid: [3,0x70], shortparallel: [3,0x71], backepsilon: [3,0x7F], // Negated relations nless: [3,0x04], nleq: [3,0x02], nleqslant: [3,0x0A], nleqq: [3,0x14], lneq: [3,0x0C], lneqq: [3,0x08], lvertneqq: [3,0x00], lnsim: [3,0x12], lnapprox: [3,0x1A], nprec: [3,0x06], npreceq: [3,0x0E], precneqq: [3,0x16], precnsim: [3,0x10], precnapprox: [3,0x18], nsim: [3,0x1C], nshortmid: [3,0x2E], nmid: [3,0x2D], nvdash: [3,0x30], nVdash: [3,0x31], ntriangleleft: [3,0x36], ntrianglelefteq: [3,0x35], nsubseteq: [3,0x2A], nsubseteqq: [3,0x22], subsetneq: [3,0x28], varsubsetneq: [3,0x20], subsetneqq: [3,0x24], varsubsetneqq: [3,0x26], ngtr: [3,0x05], ngeq: [3,0x03], ngeqslant: [3,0x0B], ngeqq: [3,0x15], gneq: [3,0x0D], gneqq: [3,0x09], gvertneqq: [3,0x01], gnsim: [3,0x13], gnapprox: [3,0x1B], nsucc: [3,0x07], nsucceq: [3,0x0F], succneqq: [3,0x17], succnsim: [3,0x11], succnapprox: [3,0x19], ncong: [3,0x1D], nshortparallel: [3,0x2F], nparallel: [3,0x2C], nvDash: [3,0x32], nVDash: [3,0x33], ntriangleright: [3,0x37], ntrianglerighteq: [3,0x34], nsupseteq: [3,0x2B], nsupseteqq: [3,0x23], supsetneq: [3,0x29], varsupsetneq: [3,0x21], supsetneqq: [3,0x25], varsupsetneqq: [3,0x27], // Arrows curvearrowleft: [3,0x78], curvearrowright: [3,0x79], // Negated arrows nleftarrow: [3,0x38], nLeftarrow: [3,0x3A], nleftrightarrow: [3,0x3D], nrightarrow: [3,0x39], nRightarrow: [3,0x3B], nLeftrightarrow: [3,0x3C] }); jsMath.Macro('Bbb','{\\msbm #1}',1); jsMath.Macro('mathbb','{\\msbm #1}',1); jsMath.Extension.Font('msbm'); jsMath.Extension.Font('msam'); glm-ie_v1.4/doc/jsMath/extensions/verb.js0000644000175000017500000000412111453154135016262 0ustar hnhn/* * extensions/verb.js * * Part of the jsMath package for mathematics on the web. * * This file implements the \verb macro. You can activate it * by calling * * jsMath.Extension.Macro('verb'); * * which will cause the extension to be loaded only when it is * needed, or you can force it to be loaded via * * jsMath.Extension.Require('verb'); * * once jsMath.js has been loaded, or by adding "extensions/verb.js" * to the loadFiles array in the easy/load.js file. * * --------------------------------------------------------------------- * * Copyright 2008 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Package(jsMath.Parser,{ macros: {verb: 'Verb'}, /* * Implement \verb|...| */ Verb: function (name) { var c = this.GetNext(); var start = ++this.i; if (c == "" ) {this.Error(this.cmd+name+" requires an argument"); return} while (this.i < this.string.length && this.string.charAt(this.i) != c) {this.i++} if (this.i == this.string.length) {this.Error("Can't find closing delimiter for "+this.cmd+name); return} var text = this.string.slice(start,this.i); this.i++; text = text.replace(/&/g,'&').replace(//g,'>'); text = ''+text+''; var box = jsMath.Box.Text(text,'normal','T',this.mlist.data.size).Styled(); box.h = box.bh+box.bd -jsMath.d; box.d = jsMath.d; this.mlist.Add(jsMath.mItem.Typeset(box)); } }); glm-ie_v1.4/doc/jsMath/extensions/newcommand.js0000644000175000017500000001607611453154135017470 0ustar hnhn/* * extensions/newcommand.js * * Part of the jsMath package for mathematics on the web. * * This file implements the \newcommand and \def macros. It will be * loaded automatically when needed, or can be loaded by * * jsMath.Extension.Require('newcommand'); * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Package(jsMath.Parser,{ macros: { newcommand: 'NewCommand', newenvironment: 'NewEnvironment', def: 'MacroDef' }, /* * Implement \newcommand{\name}[n]{...} */ NewCommand: function (name) { var cs = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; var n = this.trimSpaces(this.GetBrackets(this.cmd+name)); if (this.error) return; var def = this.GetArgument(this.cmd+name); if (this.error) return; if (n == '') {n = null} if (cs.charAt(0) == this.cmd) {cs = cs.substr(1)} if (!cs.match(/^(.|[a-z]+)$/i)) {this.Error("Illegal control sequence name for "+this.cmd+name); return} if (n != null && !n.match(/^[0-9]+$/)) {this.Error("Illegal number of parameters specified in "+this.cmd+name); return} jsMath.Parser.prototype.macros[cs] = ['Macro',def,n]; }, /* * Implement \newenvironment{name}[n]{begincmd}{endcmd} */ NewEnvironment: function (name) { var env = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; var n = this.trimSpaces(this.GetBrackets(this.cmd+name)); if (this.error) return; var bdef = this.GetArgument(this.cmd+name); if (this.error) return; var edef = this.GetArgument(this.cmd+name); if (this.error) return; if (n == '') {n = null} if (n != null && !n.match(/^[0-9]+$/)) {this.Error("Illegal number of parameters specified in "+this.cmd+name); return} jsMath.Parser.prototype.environments[env] = ['Environment',bdef,edef,n]; }, /* * Implement \def command */ MacroDef: function (name) { var cs = this.GetCSname(this.cmd+name); if (this.error) return; var params = this.GetTemplate(this.cmd+name); if (this.error) return; var def = this.GetArgument(this.cmd+name); if (this.error) return; if (typeof(params) == 'number') { jsMath.Parser.prototype.macros[cs] = ['Macro',def,params]; } else { jsMath.Parser.prototype.macros[cs] = ['MacroWithTemplate',def,params[0],params[1]]; } }, /* * Get a CS name or give an error */ GetCSname: function (cmd) { var c = this.GetNext(); if (c != this.cmd) {this.Error(cmd+" must be followed by a control sequence"); return null} var cs = this.trimSpaces(this.GetArgument(cmd)); if (this.error) {return null}; return cs.substr(1); }, /* * Get a \def parameter template */ GetTemplate: function (cmd) { var c; var params = []; var n = 0; c = this.GetNext(); var i = this.i; while (this.i < this.string.length) { c = this.GetNext(); if (c == '#') { if (i != this.i) {params[n] = this.string.substr(i,this.i-i)} c = this.string.charAt(++this.i); if (!c.match(/[1-9]/)) {this.Error("Illegal use of # in "+cmd); return null} if (1*c != ++n) {this.Error("Parameters must be numbered sequentially"); return null} i = this.i+1; } else if (c == '{') { if (i != this.i) {params[n] = this.string.substr(i,this.i-i)} if (params.length > 0) {return [n,params]} else {return n} } this.i++; } this.Error("Missing replacement string for definition of "+cmd); return null; }, /* * Process a macro with a parameter template */ MacroWithTemplate: function (name,data) { var text = data[0]; var n = data[1]; var params = data[2]; if (n) { var args = []; var c = this.GetNext(); if (params[0] && !this.MatchParam(params[0])) {this.Error("Use of "+this.cmd+name+" doesn't match its definition"); return} for (var i = 0; i < n; i++) { args[args.length] = this.GetParameter(this.cmd+name,params[i+1]); if (this.error) return; } text = this.SubstituteArgs(args,text); } this.string = this.AddArgs(text,this.string.slice(this.i)); this.i = 0; }, /* * Process a user-defined environment */ Environment: function (name,data) { var bdef = data[0]; var edef = data[1]; var n = data[2]; if (n) { var args = []; for (var i = 0; i < n; i++) { args[args.length] = this.GetArgument(this.cmd+"begin{"+name+"}"); if (this.error) return; } bdef = this.SubstituteArgs(args,bdef); } var text = this.GetEnd(name); if (this.error) return; text = this.AddArgs(this.AddArgs(bdef,text),edef); this.string = this.AddArgs(text,this.string.slice(this.i)); this.i = 0; }, /* * Find a single parameter delimited by a trailing template */ GetParameter: function (name,param) { if (param == null) {return this.GetArgument(name)} var i = this.i; var j = 0; var hasBraces = 0; while (this.i < this.string.length) { if (this.string.charAt(this.i) == '{') { if (this.i == i) {hasBraces = 1} this.GetArgument(name); j = this.i - i; } else if (this.MatchParam(param)) { if (hasBraces) {i++; j -= 2} return this.string.substr(i,j); } else { this.i++; j++; hasBraces = 0; } } this.Error("Runaway argument for "+name+"?"); return null; }, /* * Check if a template is at the current location. * (The match must be exact, with no spacing differences. TeX is * a little more forgiving about spaces after macro names) */ MatchParam: function (param) { if (this.string.substr(this.i,param.length) != param) {return 0} this.i += param.length; return 1; } }); /* * Define a jsMath.Environment() command similar to the * jsMath.Macro() command. * * Usage: jsMath.Environment(name,begin,end[,n]) * * where "name" is the name of the environment, "begin" is the * text that replaces the \begin{name} and "end" is the text that * replaces the \end{name}. If "n" is provided, it is the number * of parameters that the \begin{name} accepts, and these are * used to replace #1, #2, etc within the "begin" text. */ jsMath.Add(jsMath,{ Environment: function (name) { var environments = jsMath.Parser.prototype.environments; environments[name] = ['Environment']; for (var i = 1; i < arguments.length; i++) {environments[name][environments[name].length] = arguments[i]} } }); glm-ie_v1.4/doc/jsMath/extensions/AMSmath.js0000644000175000017500000002500611453154135016623 0ustar hnhn/* * extensions/AMSmath.js * * Part of the jsMath package for mathematics on the web. * * This file defines most of the macros and environments from * the amsmath LaTeX package. You can activate it by calling * * jsMath.Extension.Require('AMSmath'); * * once jsMath.js has been loaded, or by adding "extensions/AMSmath.js" * to the loadFiles array in jsMath/easy/load.js. * * You may wish to load AMSsymbols.js as well, but note that it * requires the extra msam10 and msb10 fonts that you will have * to install on your server first. * * --------------------------------------------------------------------- * * Copyright 2007 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Extension.Require("moreArrows"); jsMath.Package(jsMath.Parser,{ macros: { intI: ['Macro','\\mathchoice{\\!}{}{}{}\\!\\!\\int'], iint: ['Macro','\\!\\!\\!\\mathop{\\,\\,\\,\\int\\intI}'], iiint: ['Macro','\\!\\!\\!\\mathop{\\,\\,\\,\\int\\intI\\intI}'], iiiint: ['Macro','\\!\\!\\!\\mathop{\\,\\,\\,\\int\\intI\\intI\\intI}'], idotsint: ['Macro','\\!\\!\\mathop{\\,\\,\\int\\cdots\\int}'], dddot: ['Macro','\\mathop{#1}\\limits^{\\textstyle ...}',1], ddddot: ['Macro','\\mathop{#1}\\limits^{\\textstyle ....}',1], sideset: ['Macro','\\mathop{\\rlap{\\phantom{#3}}}#1\\!{#3}#2',3], stackrel: ['Macro','\\mathrel{\\mathop{#2}\\limits^{#1}}',2], boxed: ['Macro','\\fbox{$\\displaystyle{#1}$}',1], tag: 'HandleTag', notag: ['Macro',''], substack: ['Macro','\\begin{subarray}{c}#1\\end{subarray}',1], varliminf: ['Macro','\\mathop{\\underline{\\raise1.5pt{\\rule{0pt}{.6em}{0pt}\\smash{\\lower1.5pt{\\rm lim}}}}}'], varlimsup: ['Macro','\\mathop{\\overline{\\rule{0pt}{.6em}{0pt}\\smash{\\rm lim}}}'], varinjlim: ['Macro','\\mathop{\\underrightarrow{\\rm lim}}'], varprojlim: ['Macro','\\mathop{\\underleftarrow{\\rm lim}}'], DeclareMathOperator: 'HandleDeclareOp', operatorname: 'HandleOperatorName', genfrac: 'Genfrac', frac: ['Genfrac',"","","",""], tfrac: ['Genfrac',"","","","1"], dfrac: ['Genfrac',"","","","0"], binom: ['Genfrac',"(",")","0pt",""], tbinom: ['Genfrac',"(",")","0pt","1"], dbinom: ['Genfrac',"(",")","0pt","0"], cfrac: 'CFrac', shoveleft: ['HandleShove','left'], shoveright: ['HandleShove','right'] }, environments: { align: ['Array',null,null,'rlrlrlrlrlrl',[5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18],1,'D'], 'align*': ['Array',null,null,'rlrlrlrlrlrl',[5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18],1,'D'], aligned: ['Array',null,null,'rlrlrlrlrlrl',[5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18],1,'D'], multline: 'Multline', 'multline*': 'Multline', split: ['Array',null,null,'rl',[5/18],1,'D'], gather: ['Array',null,null,'c',null,1,'D'], 'gather*': ['Array',null,null,'c',null,1,'D'], gathered: ['Array',null,null,'c',null,1,'D'], subarray: ['Array',null,null,null,[0,0,0,0],1,'S',0,.25], smallmatrix: ['Array',null,null,'cccccccccc',[1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3],1,'S',0] }, delimiter: { '\\lvert': [4,2,0x6A,3,0x0C], '\\rvert': [5,2,0x6A,3,0x0C], '\\lVert': [4,2,0x6B,3,0x0D], '\\rVert': [5,2,0x6B,3,0x0D] }, /* * Ignore the tag for now */ HandleTag: function (name) { var arg = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; if (arg == "*") this.GetArgument(this.cmd+name); }, /* * Handle \DeclareMathOperator */ HandleDeclareOp: function (name) { var limits = ""; var cs = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; if (cs == "*") { limits = "\\limits"; cs = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; } if (cs.charAt(0) == "\\") {cs = cs.substr(1)} var op = this.GetArgument(this.cmd+name); if (this.error) return; op = op.replace(/\*/g,'\\char{cmr10}{0x2A}').replace(/-/g,'\\char{cmr10}{0x2D}'); jsMath.Parser.prototype.macros[cs] = ['Macro','\\mathop{\\rm '+op+'}'+limits]; }, HandleOperatorName: function (name) { var limits = "\\nolimits"; var op = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; if (op == "*") { limits = "\\limits"; op = this.trimSpaces(this.GetArgument(this.cmd+name)); if (this.error) return; } op = op.replace(/\*/g,'\\char{cmr10}{0x2A}').replace(/-/g,'\\char{cmr10}{0x2D}'); this.string = '\\mathop{\\rm '+op+'}'+limits+this.string.slice(this.i); this.i = 0; }, /* * Record presence of \shoveleft and \shoveright */ HandleShove: function (name,data) { if (this.mlist.data.entry == null) {this.mlist.data.entry = {}} this.mlist.data.entry.shove = data[0]; }, /* * Handle \cfrac */ CFrac: function (name) { var lr = this.GetBrackets(this.cmd+name); if (this.error) return; var num = this.GetArgument(this.cmd+name); if (this.error) return; var den = this.GetArgument(this.cmd+name); if (this.error) return; num = this.Process('\\strut\\textstyle{'+num+'}'); if (this.error) return; den = this.Process('\\strut\\textstyle{'+den+'}'); if (this.error) return; var data = this.mlist.data; var TeX = jsMath.Typeset.TeX(data.style,data.size); if (lr != "") { if (lr != 'l' && lr != 'r') {this.Error("Illegal alignment specified in "+this.cmd+name); return} num = jsMath.Box.Set(num,data.style,data.size); den = jsMath.Box.Set(den,data.style,data.size); if (num.w > den.w) { if (lr == 'l') {den.html += jsMath.HTML.Spacer(num.w-den.w)} else {den.html = jsMath.HTML.Spacer(num.w-den.w) + den.html} den.w = num.w; } else if (num.w < den.w) { if (lr == 'l') {num.html += jsMath.HTML.Spacer(den.w-num.w)} else {num.html = jsMath.HTML.Spacer(den.w-num.w) + num.html} num.w = den.w; } } this.mlist.Add(jsMath.mItem.Fraction(name,num,den,TeX.default_rule_thickness)); }, /* * Implement AMS generalized fraction */ Genfrac: function (name,data) { var left = data[0]; var right = data[1]; var thickness = data[2]; var style = data[3]; if (left != null) {left = this.delimiter[left]} else {left = this.GetDelimiterArg(this.cmd+name); if (this.error) return} if (right != null) {right = this.delimiter[right]} else {right = this.GetDelimiterArg(this.cmd+name); if (this.error) return} if (thickness == null) {thickness = this.GetArgument(this.cmd+name); if (this.error) return} if (style == null) {style = this.GetArgument(this.cmd+name); if (this.error) return} var num = this.ProcessArg(this.cmd+name); if (this.error) return; var den = this.ProcessArg(this.cmd+name); if (this.error) return; if (left == "") {left = null}; if (right == "") {right = null} if (thickness == "") { var TeX =jsMath.Typeset.TeX(this.mlist.data.style,this.mlist.data.size); thickness = TeX.default_rule_thickness; } else { thickness = this.ParseDimen(thickness,this.cmd+name,0,0); } var frac = jsMath.mItem.Fraction(name,num,den,thickness,left,right); if (style != "") { style = (["D","T","S","SS"])[style]; if (style == null) {this.Error("Bad math style for "+this.cmd+name); return} var mlist = new jsMath.mList([new jsMath.mItem('style',{style:style}),frac]); this.mlist.Add(jsMath.mItem.Atom('inner',{type:'mlist',mlist: mlist})); } else { this.mlist.Add(frac); } }, /* * Implements the multline environment */ Multline: function (name,delim) { var data = this.mlist.data; var width = this.GetBrackets(this.cmd+'begin{'+name+'}'); if (this.error) return; var arg = this.GetEnd(name); if (this.error) return; var parse = new jsMath.Parser(arg+this.cmd+'\\',null,data.size,'D'); parse.matrix = name; parse.row = []; parse.table = []; parse.rspacing = []; parse.Parse(); if (parse.error) {this.Error(parse); return} parse.HandleRow(name,1); // be sure the last row is recorded // // check rows for extra columns and maximum width // var i; var row; var W = 0; for (i = 0; i < parse.table.length; i++) { row = parse.table[i]; if (row.length > 1) { this.Error("Rows can contain only one equation in '"+name+"' environment"); return; } if (row[0].w > W) {W = row[0].w} } // // Determine width of display // if (width == "") {width = W+2} else { width = this.ParseDimen(width,name,0,0); if (width < W) {width = W} } // // Shove the top and bottom lines // if (parse.table.length > 1) { parse.table[0][0].entry.shove = 'left'; row = parse.table[parse.table.length-1]; if (!row[0].entry.shove) {row[0].entry.shove = 'right'} } // // Adjust widths of shoved lines // for (i = 0; i < parse.table.length; i++) { row = parse.table[i][0]; if (row.entry.shove && row.w < width) { switch (row.entry.shove) { case 'left': row.html += jsMath.HTML.Spacer(width-row.w); break; case 'right': row.html = jsMath.HTML.Spacer(width-row.w)+row.html; break; } row.w = width; } } // // Do the layout // var box = jsMath.Box.Layout(data.size,parse.table); this.mlist.Add(jsMath.mItem.Atom('ord',box)); }, /* * Get a delimiter or empty argument */ GetDelimiterArg: function (name) { var c = this.trimSpaces(this.GetArgument(name)); if (this.error) return null; if (c == "") return null; if (this.delimiter[c]) return this.delimiter[c]; this.Error("Missing or unrecognized delimiter for "+name); return null; } });glm-ie_v1.4/doc/jsMath/extensions/moreArrows.js0000644000175000017500000000462711453154135017477 0ustar hnhn/* * extensions/moreArrows.js * * Part of the jsMath package for mathematics on the web. * * This file implements additional arrow macros with under- and * overset labels. It can be loaded by * * jsMath.Extension.Require('moreArrows'); * * or using \require{moreArrows} within a math formula. * * --------------------------------------------------------------------- * * Copyright 2005-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /********************************************************************/ jsMath.Extension.Require('leaders'); jsMath.Package(jsMath.Parser,{ macros: { xrightarrow: ['HandleArrows','rightarrow'], xleftarrow: ['HandleArrows','leftarrow'], xuprightharpoon: ['HandleArrows','uprightharpoon'], xupleftharpoon: ['HandleArrows','upleftharpoon'], xdownrightharpoon: ['HandleArrows','downrightharpoon'], xdownleftharpoon: ['HandleArrows','downleftharpoon'] }, leaders: { upleftharpoon: {left: [1,0x28], rep: [2,0x00]}, uprightharpoon: {rep: [2,0x00], right: [1,0x2A]}, downleftharpoon: {left: [1,0x29], rep: [2,0x00]}, downrightharpoon: {rep: [2,0x00], right: [1,0x2B]} }, HandleArrows: function (name,data) { var bot = this.GetBrackets(this.cmd+name); if (this.error) return; var top = this.ProcessArg(this.cmd+name); if (this.error) return; var box = jsMath.Box.Set(top,'S',this.mlist.data.size).Remeasured(); var w = box.w; if (bot) { bot = this.Process(bot); if (this.error) return; var box = jsMath.Box.Set(bot,'S',this.mlist.data.size).Remeasured(); w = Math.max(w,box.w); } var leader = jsMath.Box.Leaders(w+.75,this.leaders[data[0]]); box = jsMath.mItem.Atom('op',jsMath.Box.SetList([leader],'T',this.mlist.data.size)); box.limits = 1; box.sup = top; box.sub = bot; this.mlist.Add(box); } }); glm-ie_v1.4/doc/jsMath/jsMath-loader-omniweb4.js0000644000175000017500000000240611453154135017345 0ustar hnhn/* * jsMath-loader-omniweb4.js * * Part of the jsMath package for mathematics on the web. * * This file synchronizes the jsMath-loader.html file with * the actual loading of the source javascript file. * OmniWeb 4 has a serious bug where the loader file is run * several times (and out of sequence), which plays havoc * with the Start() and End() calls. * * --------------------------------------------------------------------- * * Copyright 2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ if (window.jsMath.Autoload) { jsMath.Autoload.Script.endLoad(); } else { if (!window.phase2) { jsMath.Script.Start(); window.phase2 = 1; } else { jsMath.Script.End(); jsMath.Script.endLoad(); } }glm-ie_v1.4/doc/jsMath/easy/0000755000175000017500000000000011755435657013552 5ustar hnhnglm-ie_v1.4/doc/jsMath/easy/load.js0000644000175000017500000001400011453154135015002 0ustar hnhn/********************************************************************** * * Customize the values given below to suit your needs. * You can make additional copies of this file with * different customizated settings if you need to load * jsMath with different parameters. * * Load this page via: * * * * (If you are including this file into your page via Server-Side * Includes, you should remove line above.) * * You can make copies of this file with different settings * if you need to have several different configurations. * **********************************************************************/ if (!window.jsMath) {window.jsMath = {}} jsMath.noImgFonts = 1; if (!jsMath.Font) {jsMath.Font = {}} if (!jsMath.Font.message) { jsMath.Font.message = 'No jsMath TeX fonts found -- using unicode fonts instead.
\n' + 'This may be slow and might not print well.
\n' + 'Use the jsMath control panel to get additional information.'; } if (!jsMath.Font.extra_message) { jsMath.Font.extra_message = 'Extra TeX fonts not found:
' + 'Using unicode fonts instead. This may be slow and might not print well.
\n' + 'Use the jsMath control panel to get additional information.'; } jsMath.Easy = { // The URL of the root jsMath directory on your server // (it must be in the same domain as the HTML page). // It should include "http://yoursite.com/", or should // be relative to the root of your server. It is possible // to be a relative URL, but it will be relative to the // HTML page loading this file. // // If you leave this blank, jsMath will try to look it up from // the URL where it loaded this file, but that may not work. root: "", // The default scaling factor for mathematics compared to the // surrounding text. scale: 100, // 1 means use the autoload plug-in to decide if jsMath should be loaded // 0 means always load jsMath autoload: 1, // Setting any of these will cause the tex2math plugin to be used // to add the
and tags that jsMath needs. See the // documentation for the tex2math plugin for more information. processSlashParens: 1, // process \(...\) in text? processSlashBrackets: 1, // process \[...\] in text? processDoubleDollars: 1, // process $$...$$ in text? processSingleDollars: 1, // process $...$ in text? processLaTeXenvironments: 0, // process \begin{xxx}...\end{xxx} outside math mode? fixEscapedDollars: 0, // convert \$ to $ outside of math mode? doubleDollarsAreInLine: 1, // make $$...$$ be in-line math? allowDisableTag: 1, // allow ID="tex2math_off" to disable tex2math? // If you want to use your own custom delimiters for math instead // of the usual ones, then uncomment the following four lines and // insert your own delimiters within the quotes. You may want to // turn off processing of the dollars and other delimiters above // as well, though you can use them in combination with the // custom delimiters if you wish. See the tex2math documentation // for more details. // //customDelimiters: [ // '[math]','[/math]', // to begin and end in-line math // '[display]','[/display]' // to begin and end display math //], // Disallow the use of the @(...) mechanism for including raw HTML // in the contents of \hbox{}? (If used in a content-management system // where users are allowed to enter mathematics, setting this to 0 // would allow them to enter arbitrary HTML code within their // math formulas, and that poses a security risk.) safeHBoxes: 1, // Show TeX source when mathematics is double-clicked? allowDoubleClicks: 1, // Show jsMath font warning messages? (Disabling this prevents yours // users from finding out that they can have a better experience on your // site by installing some fonts, so don't disable this). showFontWarnings: 0, // Use "Process" or "ProcessBeforeShowing". See the jsMath // author's documentation for the difference between these // two routines. method: "Process", // List of plug-ins and extensions that you want to be // loaded automatically. E.g. // ["extensions/font.js","plugins/mimeTeX.js","extensions/AMSsymbols.js"] loadFiles: [], // List of fonts to load automatically. E.g. // ["msbm10"] loadFonts: [], // List of macros to define. These are of the form // name: value // where 'value' is the replacement text for the macro \name. // The 'value' can also be [value,n] where 'value' is the replacement // text and 'n' is the number of parameters for the macro. // Note that backslashes must be doubled in the replacement string. // E.g., // { // RR: '{\\bf R}', // bold: ['{\\bf #1}', 1] // } macros: {}, // Allow jsMath to enter global mode? // (Uses frames, so may not always work with complex web sites) allowGlobal: 1, // Disable image fonts? (In case you don't load them on your server.) noImageFonts: 0 }; /****************************************************************/ /****************************************************************/ // // DO NOT MAKE CHANGES BELOW THIS // /****************************************************************/ /****************************************************************/ if (jsMath.Easy.root == "") { jsMath.Easy.root = document.getElementsByTagName("script"); jsMath.Easy.root = jsMath.Easy.root[jsMath.Easy.root.length-1].src if (jsMath.Easy.root.match(/\/easy\/[^\/]*$/)) { jsMath.Easy.root = jsMath.Easy.root.replace(/\/easy\/[^\/]*$/,""); } else { jsMath.Easy.root = jsMath.Easy.root.replace(/\/(jsMath\/(easy\/)?)?[^\/]*$/,"/jsMath"); } } jsMath.Easy.root = jsMath.Easy.root.replace(/\/$/,""); // trim trailing "/" if any document.write(' * * (If you are including this file into your page via Server-Side * Includes, you should remove line above.) * * You can make copies of this file with different settings * if you need to have several different configurations. * **********************************************************************/ if (!window.jsMath) {window.jsMath = {}} jsMath.Easy = { // The URL of the root jsMath directory on your server // (it must be in the same domain as the HTML page). // It should include "http://yoursite.com/", or should // be relative to the root of your server. It is possible // to be a relative URL, but it will be relative to the // HTML page loading this file. // // If you leave this blank, jsMath will try to look it up from // the URL where it loaded this file, but that may not work. root: "", // The default scaling factor for mathematics compared to the // surrounding text. scale: 100, // 1 means use the autoload plug-in to decide if jsMath should be loaded // 0 means always load jsMath autoload: 1, // Setting any of these will cause the tex2math plugin to be used // to add the
and tags that jsMath needs. See the // documentation for the tex2math plugin for more information. processSlashParens: 1, // process \(...\) in text? processSlashBrackets: 1, // process \[...\] in text? processDoubleDollars: 1, // process $$...$$ in text? processSingleDollars: 1, // process $...$ in text? processLaTeXenvironments: 0, // process \begin{xxx}...\end{xxx} outside math mode? fixEscapedDollars: 0, // convert \$ to $ outside of math mode? doubleDollarsAreInLine: 1, // make $$...$$ be in-line math? allowDisableTag: 1, // allow ID="tex2math_off" to disable tex2math? // If you want to use your own custom delimiters for math instead // of the usual ones, then uncomment the following four lines and // insert your own delimiters within the quotes. You may want to // turn off processing of the dollars and other delimiters above // as well, though you can use them in combination with the // custom delimiters if you wish. See the tex2math documentation // for more details. // //customDelimiters: [ // '[math]','[/math]', // to begin and end in-line math // '[display]','[/display]' // to begin and end display math //], // Disallow the use of the @(...) mechanism for including raw HTML // in the contents of \hbox{}? (If used in a content-management system // where users are allowed to enter mathematics, setting this to 0 // would allow them to enter arbitrary HTML code within their // math formulas, and that poses a security risk.) safeHBoxes: 1, // Show TeX source when mathematics is double-clicked? allowDoubleClicks: 1, // Show jsMath font warning messages? (Disabling this prevents yours // users from finding out that they can have a better experience on your // site by installing some fonts, so don't disable this). showFontWarnings: 0, // Use "Process" or "ProcessBeforeShowing". See the jsMath // author's documentation for the difference between these // two routines. method: "Process", // List of plug-ins and extensions that you want to be // loaded automatically. E.g. // ["extensions/font.js","plugins/mimeTeX.js","extensions/AMSsymbols.js"] loadFiles: [], // List of fonts to load automatically. E.g. // ["msbm10"] loadFonts: ["msbm10"], // List of macros to define. These are of the form // name: value // where 'value' is the replacement text for the macro \name. // The 'value' can also be [value,n] where 'value' is the replacement // text and 'n' is the number of parameters for the macro. // Note that backslashes must be doubled in the replacement string. // E.g., // { // RR: '{\\bf R}', // bold: ['{\\bf #1}', 1] // } macros: {}, // Allow jsMath to enter global mode? // (Uses frames, so may not always work with complex web sites) allowGlobal: 1, // Disable image fonts? (In case you don't load them on your server.) noImageFonts: 0 }; /****************************************************************/ /****************************************************************/ // // DO NOT MAKE CHANGES BELOW THIS // /****************************************************************/ /****************************************************************/ if (jsMath.Easy.root == "") { jsMath.Easy.root = document.getElementsByTagName("script"); jsMath.Easy.root = jsMath.Easy.root[jsMath.Easy.root.length-1].src if (jsMath.Easy.root.match(/\/easy\/[^\/]*$/)) { jsMath.Easy.root = jsMath.Easy.root.replace(/\/easy\/[^\/]*$/,""); } else { jsMath.Easy.root = jsMath.Easy.root.replace(/\/(jsMath\/(easy\/)?)?[^\/]*$/,"/jsMath"); } } jsMath.Easy.root = jsMath.Easy.root.replace(/\/$/,""); // trim trailing "/" if any document.write('
glm-ie_v1.4/doc/jsMath/jsMath-autoload.html0000644000175000017500000000331511453154135016515 0ustar hnhn glm-ie_v1.4/doc/jsMath/jsMath-fallback-pc.js0000644000175000017500000007302111453154135016515 0ustar hnhn/* * jsMath-fallback-pc.js * * Part of the jsMath package for mathematics on the web. * * This file makes changes needed for when the TeX fonts are not available * with a browser on the PC. * * --------------------------------------------------------------------- * * Copyright 2004-2010 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ jsMath.Script.Uncompress([ 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jsMath.Easy.tex2math = (jsMath.Easy.processSingleDollars || jsMath.Easy.processDoubleDollars || jsMath.Easy.processSlashParens || jsMath.Easy.processSlashBrackets || jsMath.Easy.processLaTeXenvironments || jsMath.Easy.fixEscapedDollars || jsMath.Easy.customDelimiters); if (!jsMath.Setup) {jsMath.Setup = {}} if (!jsMath.Setup.UserEvent) {jsMath.Setup.UserEvent = {}} jsMath.Setup.UserEvent.onload = function () { var easy = jsMath.Easy; if (easy.tex2math) jsMath.Setup.Script("plugins/tex2math.js"); var i; if (easy.loadFiles) { for (i = 0; i < easy.loadFiles.length; i++) jsMath.Setup.Script(easy.loadFiles[i]); } if (easy.loadFonts) { for (i = 0; i < easy.loadFonts.length; i++) jsMath.Font.Load(easy.loadFonts[i]); } if (easy.macros) { for (i in easy.macros) { if (typeof(easy.macros[i]) == 'string') { jsMath.Macro(i,easy.macros[i]); } else { jsMath.Macro(i,easy.macros[i][0],easy.macros[i][1]); } } } } document.write(''+"\n"); } jsMath.Easy.onload = function () { if (jsMath.Easy.loaded) {return} else {jsMath.Easy.loaded = 1} if (jsMath.Easy.autoloadCheck) jsMath.Autoload.Check(); if (jsMath.Easy.tex2math) { jsMath.Synchronize(function () { if (jsMath.Easy.findCustomSettings) jsMath.tex2math.Convert(document,jsMath.Easy.findCustomSettings); if (jsMath.Easy.customDelimiters) { var s = jsMath.Easy.customDelimiters; jsMath.tex2math.CustomSearch(s[0],s[1],s[2],s[3]); jsMath.tex2math.ConvertCustom(); } }); } (jsMath[jsMath.Easy.method])(); } if (window.addEventListener) {window.addEventListener("load",jsMath.Easy.onload,false)} else if (window.attachEvent) {window.attachEvent("onload",jsMath.Easy.onload)} else {window.onload = jsMath.Easy.onload} glm-ie_v1.4/doc/jsMath/COPYING.txt0000644000175000017500000002613611453154135014452 0ustar hnhn Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. 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We also recommend that a file or class name and description of purpose be included on the same "printed page" as the copyright notice for easier identification within third-party archives. Copyright [yyyy] [name of copyright owner] Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. glm-ie_v1.4/doc/jsMath/jsMath-loader.html0000644000175000017500000000550211453154135016153 0ustar hnhn glm-ie_v1.4/doc/jsMath/jsMath-msie-mac.js0000644000175000017500000000325211453154135016050 0ustar hnhn/* * jsMath-msie-mac.js * * Part of the jsMath package for mathematics on the web. * * This file makes changes needed for use with MSIE on the Mac. * * --------------------------------------------------------------------- * * Copyright 2004-2006 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /* * MSIE crashes if it changes the page too quickly, so we add a * delay between processing math entries. 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Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ if (!window.jsMath) {window.jsMath = {}} if (!jsMath.Controls) {jsMath.Controls = {}} if (!jsMath.Controls.cookie) {jsMath.Controls.cookie = {}} jsMath.noGoGlobal = 1; jsMath.noChangeGlobal = 1; jsMath.noShowGlobal = 1; jsMath.Controls.cookie.global = 'never'; glm-ie_v1.4/doc/jsMath/plugins/CHMmode.js0000644000175000017500000000624011453154124016064 0ustar hnhn/* * CHMmode.js * * Part of the jsMath package for mathematics on the web. * * This file makes jsMath work with MicroSoft's HTML Help system * from within .chm files (compiled help archives). * * This file should be loaded BEFORE jsMath.js. * * --------------------------------------------------------------------- * * Copyright 2006-2007 by Davide P. 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See * * http://www.math.union.edu/locate/jsMath * * for the latest version, and for documentation on how to use jsMath. * * Copyright 2004-2010 by Davide P. 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hnhnGIF89a1!,D;glm-ie_v1.4/doc/jsMath/jsMath-BaKoMa-fonts.js0000644000175000017500000004013611453154135016600 0ustar hnhn/* * jsMath-BaKoMa-fonts.js * * Part of the jsMath package for mathematics on the web. * * This file makes changes needed to use the BaKoMa fonts and * their encoding. * * --------------------------------------------------------------------- * * Copyright 2004-2007 by Davide P. Cervone * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /******************************************************************** * * The BaKoMa fonts have a different encoding, so change the characters * to correspond to the their encoding. */ if (jsMath.browser == "Mozilla" && jsMath.platform != "mac") { /* * Mozilla/PC */ jsMath.Update.TeXfontCodes({ cmr10: [ 'Γ', 'Δ', 'Θ', 'Λ', 'Ξ', 'Π', 'Σ', 'Υ', 'Φ', 'Ψ', 'Ω', 'ff', 'fi', 'fl', 'ffi', 'ffl', 'ı', '', '̀', '́', '̌', '̆', '̅', '̊', '̧', 'ß', 'æ', 'œ', 'ø', 'Æ', 'Œ', 'Ø', '̷', '!', '”', '#', '$', '%', '&', ''', '(', ')', '*', '+', ',', '-', '.', '/', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', ':', ';', '¡', '=', '¿', '?', '@', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '[', '“', ']', '̂', '̇', '‘', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', '–', '—', '̋', '̃', '̈' ], cmmi10: [ 'Γ', 'Δ', 'Θ', 'Λ', 'Ξ', 'Π', 'Σ', 'Υ', 'Φ', 'Ψ', 'Ω', 'α', 'β', 'γ', 'δ', 'ε', 'ζ', 'η', 'θ', 'ι', 'κ', 'λ', 'μ', 'ν', 'ξ', 'π', 'ρ', 'σ', 'τ', 'υ', 'φ', 'χ', 'ψ', 'ω', 'ɛ', 'ϑ', 'ϖ', 'ϱ', 'ς', 'ϕ', '↼', '↽', '⇀', '⇁', '', '', '▹', '◃', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '.', ',', '<', '/', '>', '⋆', '∂', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '♭', '♮', '♯', '⌣', '⌢', 'ℓ', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'ı', '', '℘', '⃗', '̑' ], cmsy10: [ '−', '·', '×', '⋆', '÷', '⋄', '±', '∓', '⊕', '⊖', '⊗', '⊘', '⊙', '○', '∘', '∙', '≃', '≍', '⊆', '⊇', '≤', '≥', '≼', '≽', '∼', '≅', '⊂', '⊃', '≪', '≫', '≺', '≻', '←', '→', '↑', '↓', '↔', '↗', '↘', '≂', '⇐', '⇒', '⇑', '⇓', '⇔', '↖', '↙', '∝', '′', '∞', '∈', '∋', '△', '▽', '̸', '', '∀', '∃', '¬', '∅', 'ℜ', 'ℑ', '⊤', '⊥', 'ℵ', '', 'ℬ', '', '', 'ℰ', 'ℱ', '', 'ℋ', 'ℐ', '', '', 'ℒ', 'ℳ', '', '', '', '', 'ℛ', '', '', '', '', '', '', '', '', '∪', '∩', '⊎', '∧', '∨', '⊢', '⊣', '⌊', '⌋', '⌈', '⌉', '{', '}', '〈', '〉', '∣', '∥', '↕', '⇕', '∖', '≀', '√', '∐', '∇', '∫', '⊔', '⊓', '⊑', '⊒', '§', '†', '‡', '¶', '♣', '♢', '♡', '♠' ], cmex10: [ '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '' ] }); /* * Adjust a few other characters as well */ jsMath.Update.TeXfonts({ cmr10: {'20': {c: 'ˇ', tclass: 'normal', w: .3}}, cmmi10: { '20': {c: '&kappa', tclass: 'normal'}, '58': {c: '.', tclass: 'normal'}, '59': {c: ',', tclass: 'normal'}, '61': {c: '/', tclass: 'cmr10'} }, cmsy10: { '3': {c: '*', tclass: 'normal'}, '16': {c: '≍'}, '17': {c: '≡', tclass: 'normal'}, '25': {c: '≈', tclass: 'normal'}, '39': {c: '≃'}, '20': {c: '≤', tclass: 'normal'} }, cmex10: {'20': {c: ''}}, cmti10: {'10': {c: 'Ω', tclass: 'normal'}}, cmbx10: {'10': {c: 'Ω', tclass: 'normal'}} }); } else { jsMath.Font.BaKoMa = [ '¡', '¢', '£', '¤', '¥', '¦', '§', '¨', '©', 'ª', '­', '®', '¯', '°', '±', '²', '³', '´', 'µ', '¶', '∙', '¸', '¹', 'º', '»', '¼', '½', '¾', '¿', 'À', 'Á', 'Â', 'Ã', '!', '"', '#', '$', '%', '&', '\'', '(', ')', '*', '+', ',', '-', '.', '/', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', ':', ';', '<', '=', '>', '?', '@', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '[', '\\', ']', '^', '_', '`', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', '{', '|', '}', '~', 'Ä' ]; jsMath.Update.TeXfontCodes({ cmr10: jsMath.Font.BaKoMa, cmmi10: jsMath.Font.BaKoMa, cmsy10: jsMath.Font.BaKoMa, cmex10: jsMath.Font.BaKoMa, cmti10: jsMath.Font.BaKoMa, cmbx10: jsMath.Font.BaKoMa }); /* * MSIE corrections */ switch (jsMath.browser) { case "MSIE": if (jsMath.platform == "pc") { /* * MSIE/PC */ jsMath.Browser.msieFontBug = 1; jsMath.Update.TeXfonts({ cmr10: {'10': {c: 'Ω', tclass: 'normal'}}, cmmi10: { '10': {c: 'Ω', tclass: 'normal'}, '126': {c: '~'} }, cmsy10: { '10': {c: '⊗', tclass: 'arial'}, '55': {c: '7'} }, cmex10: {'10': {c: 'D'}}, cmti10: {'10': {c: 'Ω', tclass: 'normal'}}, cmbx10: {'10': {c: 'Ω', tclass: 'normal'}} }); } else { /* * MSIE/Mac */ jsMath.Update.TeXfonts({ cmr10: { '3': {c: 'L', tclass: 'normal'}, '5': {c: 'P', tclass: 'normal'}, '10': {c: 'W', tclass: 'normal'}, '15': {c: 'ffl', tclass: 'normal'}, '16': {c: 'ı', tclass: 'normal'}, '20': {c: 'ˇ', tclass: 'normal'}, '22': {c: '¯', tclass: 'normal', w: .3}, '25': {c: 'ß', tclass: 'normal'}, '26': {c: 'æ', tclass: 'normal'}, '27': {c: 'œ', tclass: 'normal'} }, cmmi10: { '3': {c: 'L', tclass: 'italic'}, '5': {c: 'P', tclass: 'italic'}, '10': {c: 'W', tclass: 'italic'}, '15': {c: 'e', tclass: 'italic'}, '16': {c: 'z', tclass: 'italic'}, '20': {c: 'k', tclass: 'italic'}, '22': {c: 'm', tclass: 'italic'}, '25': {c: 'p', tclass: 'italic'}, '26': {c: 'r', tclass: 'italic'}, '27': {c: 's', tclass: 'italic'} }, cmsy10: { '3': {c: '*', tclass: 'normal'}, '5': {c: 'Ή', tclass: 'normal'}, '10': {c: '⊗', tclass: 'normal'}, '15': {c: '•', tclass: 'normal'}, '16': {c: '≍', tclass: 'normal'}, '20': {c: '≤', tclass: 'normal'}, '22': {c: '≤', tclass: 'normal'}, '25': {c: '≈', tclass: 'normal'}, '26': {c: 'Ì', tclass: 'normal'}, '27': {c: 'É', tclass: 'normal'} }, cmex10: { '3': {c: 'i'}, '5': {c: 'k'}, '10': {c: 'D'}, '15': {c: 'Â'}, '16': {c: 'µ'}, '20': {c: '"'}, '22': {c: '$'}, '25': {c: '\''}, '26': {c: '('}, '27': {c: ')'} }, cmti10: { '3': {c: 'L', tclass: 'italic'}, '5': {c: 'P', tclass: 'italic'}, '10': {c: 'W', tclass: 'italic'}, '16': {c: 'ı', tclass: 'italic'}, '20': {c: '­', tclass: 'italic'}, '22': {c: '¯', tclass: 'italic', w: .3}, '25': {c: 'ß', tclass: 'italic'}, '26': {c: 'æ', tclass: 'italic'}, '27': {c: 'œ', tclass: 'italic'} }, cmbx10: { '3': {c: 'L', tclass: 'bold'}, '5': {c: 'P', tclass: 'bold'}, '10': {c: 'W', tclass: 'bold'}, '16': {c: 'ı', tclass: 'bold'}, '20': {c: '­', tclass: 'bold'}, '22': {c: '¯', tclass: 'bold', w: .3}, '25': {c: 'ß', tclass: 'bold'}, '26': {c: 'æ', tclass: 'bold'}, '27': {c: 'œ', tclass: 'bold'} } }); } break; case "Mozilla": if (jsMath.platform == "mac") { /* * Mozilla/Mac */ jsMath.Update.TeXfonts({ cmr10: {'10': {c: 'Ω', tclass: 'normal'}}, cmmi10: {'10': {c: 'Ω', tclass: 'normal'}}, cmsy10: {'10': {c: '⊗', tclass: 'normal'}}, cmex10: {'10': {c: 'D'}}, cmti10: {'10': {c: 'Ω', tclass: 'normal'}}, cmbx10: {'10': {c: 'Ω', tclass: 'normal'}} }); } break; case "Opera": jsMath.Update.TeXfonts({ cmr10: { '10': {c: 'Ω', tclass: 'normal'}, '20': {c: 'ˇ', tclass: 'normal'} }, cmmi10: { '10': {c: 'Ω', tclass: 'normal'}, '20': {c: 'κ', tclass: 'normal'} }, cmsy10: { '10': {c: '⊗', tclass: 'normal'}, '20': {c: '≤', tclass: 'normal'} }, cmex10: { '10': {c: 'D'}, '20': {c: '"'} }, cmti10: { '10': {c: 'Ω', tclass: 'normal'}, '20': {c: 'ˇ', tclass: 'normal'} }, cmbx10: { '10': {c: 'Ω', tclass: 'normal'}, '20': {c: 'ˇ', tclass: 'normal'} } }); break; case "Konqueror": jsMath.Update.TeXfonts({ cmr10: {'20': {c: 'ˇ', tclass: 'normal'}}, cmmi10: {'20': {c: 'κ', tclass: 'normal'}}, cmsy10: {'20': {c: '≤', tclass: 'normal'}}, cmex10: {'20': {c: '"'}}, cmti10: {'20': {c: 'ˇ', tclass: 'normal'}}, cmbx10: {'20': {c: 'ˇ', tclass: 'normal'}} }); break; } } jsMath.Setup.Styles({ '.typeset .cmr10': 'font-family: CMR10, serif', '.typeset .cmbx10': 'font-family: CMBX10, CMR10', '.typeset .cmti10': 'font-family: CMTI10, CMR10', '.typeset .cmmi10': 'font-family: CMMI10', '.typeset .cmsy10': 'font-family: CMSY10', '.typeset .cmex10': 'font-family: CMEX10', '.typeset .arial': "font-family: 'Arial unicode MS'" }); glm-ie_v1.4/doc/classify_inference.m0000644000175000017500000000473211650334232015357 0ustar hnhn% Inference example for logistic regression using glm-ie demonstrating the % sparsity occuring in estimation but similar classification performance in % inference where probabilities can readily be evaluated. % % We use the well known a9a dataset from the UCI machine learning repository % with 32561 instances of dimension 123. % B data matrix % c binary labels % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 21 clear all, close all potS = @potLaplace; % Laplace weight prior % load and split into train and test set load classify % load a part of the UCI a9a dataset nte = 30000; 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7n~|BuOUOG3cO3>ߟ٦37 es#]oK>Z0C37ƵK,~ּj̟_o- U%GI|ڨ cUN25ꗲYx:X00Hy.lJgUqEuH+)vXTQS9Zᛮ:Jg5R]y;{i+\~A@Y kkL =<&ݜeOv̆m֚ pOuceH'WuQV3pg[w{psf2\dyPw- %m;wwq},IUN6o'ǖFw:M}RmV-GB=q#mgr}͹&;Eb;,!z,j~zFY-z֔s~rxE5j&pcrzwxf{ߵgU(?gn0 C^`z\hǖ)d==Ϲ~`;w>uFi~V]u5K1;N/ Wt#NZzgLgF5mP_Ev63VfQ]ñj~N,J8tH*,sӻܩvO;<|ݲXs MTz|$gg'qorZSArt| x59<69yyG]n#Yu0;t:e|Y?Zwr {^'*6Gc}[:眦ӓǣ=o51dGH:We;b_:g6ܓ/DcgΞut̷OК+Rvf Ifc߹׎;\!GS$eRLۆq3<"?y$Sz^J9ĆXϭ{1H]W-]sǻzfI*u|ݞCU5eskWwSк˿8$ >kCa;^z$k숪xê0avr9>;=WȽ*(4{%R;wWscCw-cEf6{+_) X|nꈯyOEHJԳjf+k9fs}\);}c̵UT*9wo|2J} R܉=lv#~(Os=AgKڍglm-ie_v1.4/README0000644000175000017500000001604111755435657011500 0ustar hnhn GENERALISED LINEAR MODELS: INFERENCE AND ESTIMATION Toolbox version 1.4 for GNU Octave 3.3.x and Matlab 7.x Copyright (c) by Hannes Nickisch, 2011-10-20. 0) HOW TO READ ============== If you want to get started without further delay, then read section 1) below and jump right to the examples in doc/index.html. 1) ABOUT THESE PROGRAMS ======================= This collection of matlab programs implements and demonstrates estimation and inference algorithms for generalised linear models. While (MAP) estimation or equivalently penalised least squares estimation is a standard tool in statics, inference is less widely used and in general more tricky. The two approximate inference algorithms are described in the papers [1] Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models by Matthias Seeger and Hannes Nickisch SIAM Journal on Imaging Sciences, 2011 http://arxiv.org/abs/0810.0901 for a similar TR and [2] Efficient Bayesian multivariate fMRI analysis using a sparsifying spatio-temporal prior by Gerven, Cseske, Lange and Heskes Neuroimage 2010 http://homepages.inf.ed.ac.uk/bcseke/webpubs/gerven2010.pdf. The Monte Carlo marginal variance estimator is detailed in [3] Efficient Variational Inference in Large-Scale Bayesian Compressed Sensing by George Papandreou and Alan Yuille ICCV Workshop, 2011 http://www.stat.ucla.edu/~gpapan/pubs/confr/PapandreouYuille_VariationalBayesCompressedSensing_ieee-c-iccvw11.pdf There are 6 code subdirectories: doc, inf, mat, pen, pls and pot. doc/ contains an index.html file providing documentation. This information is also available from http://www.kyb.tue.mpg.de/bs/people/hn/glm-ie. Usage examples reaching from probabilistic classification, robust regression over nonblind deconvolution to MRI reconstruction can be found here. Further details are provided in the developer documentation manual.pdf. inf/ contains the double loop inference engine dli.m and code to compute Gaussian marginal variances i.e. the diagonal of a covariance matrix => see infEngine.m mat/ contains the lazy matrix class; mat/@mat is the base class all other classes are derived from and the two auxiliary functions cx2re.m and re2cx.m allow to convert between real and complex numbers pen/ contains the penalty functions pen*.m => see penFunctions.m pls/ contains the penalised least squares (pls) solvers pls*.m => see plsSolvers.m pot/ contains the potential functions pot*.m => see potFunctions.m Before running the demos or any other part of the code, you should execute startup.m to add all necessary directories to your path. In Octave, you can also use the .octaverc file. 2) ABOUT MEX FILES ================== Some of the programs make use of the MEX facility in matlab for more efficient implementation. Besides the L-BFGS minimiser, the wavelet transform mat/@matWav rely on C/C++ code. The wavelet code should compile right after the first call; if there are problems, see the help in mat/@matWav/private/fwtn.m. If you do not have a compiler installed on your system, you might want to consult [2]. In order to use the L-BFGS minimiser , you have to compile Peter Carbonetto's "Matlab interface for L-BFGS-B" [1]. The challenge here is the Fortran 77 code. We provide a Makefile suitable for Linux 32/64 bit and Mac whenever you have 1) g77 or 2) gfortran properly set up. Under Ubuntu, you can achieve this by installing the packages fort77 and gfortran, respectively. Compilation is done by editing util/lbfgsb/Makefile. In any case, you need to provide $MATLAB_HOME which can be found by the commands 'locate matlab' or 'find / -name "matlab"'. You can choose between two compilation modes: a) using the mex utility by Matlab [default] provide $MEX, then type 'make mex' b) without mex utility by Matlab provide $MEX_SUFFIX and $MATLAB_LIB, then type 'make nomex' In Ubuntu 10.04 LTS, the libg2c library needed for both 1)+a) and 1)+b) is not included per default. If 'ls /usr/lib/libg2c.*' does not list anything this is the case on your machine. You then whant to install the packages gcc-3.4-base and libg2c0 e.g. from http://packages.ubuntu.com/hardy/gcc-3.4-base and http://packages.ubuntu.com/hardy/libg2c0. After installation, you have to create a symbolic link by 'cd /usr/lib' and 'ln -s libg2c.so.0 libg2c.so'. Compilation under Windows is rather tricky but there is a way [3] of doing it as pointed out by Guillaume Jacquenot. Steps involved: * Install MinGW (including gfortran compiler) at C:\mingw * http://www.mingw.org/ * If the target was Matlab 64-bit, we would probably need MinGW-w64 instead? * Download http://gnumex.sourceforge.net/, unzip at C:\gnumex, and create Fortran/C mexopts.bat files for use with MinGW. * Add C:\mingw\bin and C:\gnumex in the PATH and reboot. * Create and run pls/make_lbfgsb_gnumex_windows.m script (replace the filenames for the mexopts.bat files accordingly). Other useful stuff: * MS Dependency walker (to debug missing DLL dependencies), links to download at http://www.dependencywalker.com [1] http://www.cs.ubc.ca/~pcarbo/lbfgsb-for-matlab.html [2] http://www.mathworks.com/support/compilers/R2010a [3] http://www.cs.ubc.ca/~pcarbo/Compile_LBFGSB_on_Windows.txt 3) CURRENT VERSION ================== The current version of the programs is 1.4. Previous versions of the code are available at http://hannes.nickisch.org/code/glm-ie/release/oldcode.html. 4) DIFFERENCES TO PREVIOUS VERSIONS =================================== NEW in version 1.4, 2011-10-20 ------------------------------ contributed by George Papandreou: - preconditioning support in the inf/linsolve_lcg.m CG routine. - @matConv2 and @matFD2 support different boundary conditions in deblurring - various mat/@*/diagFAtAFt.m support circulant preconditioning - bugfixes in nonnegativity option in pls/plsLBFGS.m and pen/penVBNorm.m when used together with EP - inf/diag_inv_sample.m, a Monte Carlo estimator gfortran support to pls/lbfgsb/Makefile (thanks to Ernst Kloppenburg) slight modification to mat/@matFFTN/mvm.m to make it more consistent simple gradient solver using Barzilai-Borwein step size pls/plsBB.m NEW in version 1.3, 2010-11-12 ------------------------------ extension of the matrix class; bugfixes plsSB - split Bregmin PLS solver new inference engine dli.m instead of vbidl.m - support of parallel EP in addition to VB - marginal likelihood computation extended documentation and demo programs NEW in version 1.2, 2010-08-25 ------------------------------ refactored the matrix classes added more penalty functions added non-linear potential support for group sparsity improved PLS solvers updated complex number treatment NEW in version 1.1, 2010-08-10 ------------------------------ added demo examples and documentation NEW in version 1.0, 2010-07-05 ------------------------------ initial version of the glm-ie toolbox glm-ie_v1.4/pen/0000755000175000017500000000000011755435662011374 5ustar hnhnglm-ie_v1.4/pen/penVB.m0000644000175000017500000000340011650073614012546 0ustar hnhn% [p,dp,d2p] = penVB(s,pot,tau,z,theta) - Potential derived penalty % % pen(s) = tau*b*(r-s) - log( pot(tau*r) ) where r = sign(s)*sqrt(s^2 + z). % % Here, theta are additional parameters for the potential function pot % which is invoked by the call feval(pot, tau.*r, theta{:}). % % For z->0, we have r->s and hence pen(s)->-log( pot(tau*s) ) => MAP estimation. % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 21 function [p,dp,d2p,b,pi] = penVB(s,pot,tau,z,varargin) if nargin<4, z = 1e-6; end % default value for smoothing parameter z sign_s = 2*(s>=0)-1; % strict sign mapping 0 to 1 r = sign_s.*sqrt(s.*s + z); % signed z-smoothed variable [lp,dlp,d2lp,b] = colsplit( feval(pot,tau.*r,varargin{:}) ); % eval. potentials dlp = tau.*dlp; d2lp = tau.*tau.*d2lp; b = tau.*b; % correct for the scale p = b.*(r-s) - lp; % penalty s_r = (abs(s)+eps)./(abs(r)+eps); % stabilised s./r to cover z=0 and s=0 dp = (b-dlp).*s_r - b; % first derivative r_e = r + sign_s*eps; z_r3 = z./(r_e.*r_e.*r_e); % stabilised z./r.^3 to cover z=0 and s=0 d2p = (b-dlp).*z_r3 - d2lp.*s_r.*s_r; % second derivative id = z==0 | abs(s./sqrt(z+eps))>1e10; % correct asymptotics of s -> +/-Inf p(id) = -lp(id); dp(id) = -dlp(id); d2p(id) = -d2lp(id); if nargout>4, pi = abs( (b-dlp)./(r+sign_s/1.5e8) ); end % return optimal pi function varargout = colsplit(A) % split a matrix into its columns ncol = size(A,2); varargout = cell(1,nargout); for n=1:nargout, if n>ncol, varargout{n}=[]; else varargout{n}=A(:,n); end, endglm-ie_v1.4/pen/penNegQuad.m0000644000175000017500000000106011453154115013560 0ustar hnhn% [p,dp,d2p] = penNegQuad(s) - Quadratic penalty on negative part % % pen(s) = min(s,0)^2/2 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 27 function [p,dp,d2p] = penNegQuad(s) sn = min(s,0); % negative part p = sn'*sn/2; % penalty dp = sn; % first derivative d2p = double(sn<0); % second derivativeglm-ie_v1.4/pen/penQuad.m0000644000175000017500000000070011454010427013124 0ustar hnhn% [p,dp,d2p] = penQuad(s) - Quadratic penalty % % pen(s) = s^2/2 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 13 function [p,dp,d2p] = penQuad(s) p = s.*s/2; % penalty dp = s; % first derivative d2p = ones(size(s)); % second derivativeglm-ie_v1.4/pen/penNegLin.m0000644000175000017500000000074211453154115013416 0ustar hnhn% [p,dp,d2p] = penNegLin(s) - Linear penalty on negative part % % pen(s) = max(-s,0) = -min(s,0) % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 27 function [p,dp,d2p] = penNegLin(s) p = max(-s,0); % penalty dp = -(p>0); % first derivative d2p = zeros(size(s)); % second derivativeglm-ie_v1.4/pen/penAbs.m0000644000175000017500000000070111453154115012742 0ustar hnhn% [p,dp,d2p] = penAbs(s) - Absolute value penalty % % pen(s) = |s| % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 20 function [p,dp,d2p] = penAbs(s) p = abs(s); % penalty dp = sign(s); % first derivative d2p = 0*s; % second derivativeglm-ie_v1.4/pen/penVBNorm.m0000644000175000017500000000337011646243363013415 0ustar hnhn% [p,dp,d2p] = penVBNorm(s,pot,tau,z,G,theta) - Penalty derived from a % norm/group potential % % pen(s) = -log( pot(tau*r) ) where r = sqrt( G*(s^2 + z) ). % % Here, theta are additional parameters for the potential function pot % which is invoked by the call feval(pot, tau.*r, theta{:}). % % Note that d2p is as large as G'*G and has the same sparsity structure. % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function [p,dp,d2p,b,pi] = penVBNorm(s,pot,tau,z,G,varargin) if nargin<4, z = 1e-6; end % default value for smoothing parameter z r = sqrt( G*(s.*s + z) + eps ); % stabilised z-smoothed variable if max(imag(r))>0, error('G and z need to be nonnegative.'), end q = numel(s); qt = numel(r); % dimensions [lp,dlp,d2lp,b] = colsplit( feval(pot,tau.*r,varargin{:}) ); % eval. potentials dlp = tau.*dlp; d2lp = tau.*tau.*d2lp; % correct for the scale if any(b)~=0, error('Only symmetric potentials (b=0) are allowed.'), end p = -lp; % penalty if nargout>1 v = G'*(dlp./r); dp = -s.*v; % first derivative if nargout>2 w = dlp./(r.*r.*r) - d2lp./(r.*r); GS = G*sparse(1:q,1:q,s,q,q); d2p = GS'*sparse(1:qt,1:qt,w,qt,qt)*GS - sparse(1:q,1:q,v,q,q); % 2nd deriv end end if nargout>4, pi = G'*abs(-dlp./r); end % return optimal pi function varargout = colsplit(A) % split a matrix into its columns ncol = size(A,2); varargout = cell(1,nargout); for n=1:nargout, if n>ncol, varargout{n}=[]; else varargout{n}=A(:,n); end, end glm-ie_v1.4/pen/penAbsSmooth.m0000644000175000017500000000110111453154115014127 0ustar hnhn% [p,dp,d2p] = penAbsSmooth(s,ep) - Absolute value penalty % % pen(s) = sqrt(s^2+ep), ep>0, default 1e-6 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 20 function [p,dp,d2p] = penAbsSmooth(s,ep) if nargin<2, ep = 1e-6; end % default p = sqrt(s.*s+ep); % penalty dp = s./p; % first derivative d2p = ep./(p.*p.*p); % second derivativeglm-ie_v1.4/pen/penLogSmooth.m0000644000175000017500000000111111453154115014144 0ustar hnhn% [p,dp,d2p] = penLogSmooth(s,ep) - Smoothed logarithmic penalty % % pen(s) = log(s^2+ep), ep>0, default ep=1e-6 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 20 function [p,dp,d2p] = penLogSmooth(s,ep) if nargin<2, ep = 1e-6; end % default a = s.*s+ep; p = log(a); % penalty dp = 2*s./a; % first derivative d2p = 2*(2*ep./a - 1)./a; % second derivativeglm-ie_v1.4/pen/penZero.m0000644000175000017500000000042511454010427013155 0ustar hnhn% [p,dp,d2p] = penZero(s) - Zero penalty % % pen(s) = 0 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 13 function [p,dp,d2p] = penZero(s) p = zeros(size(s)); dp = p; d2p = p; % penalty and first two derivativesglm-ie_v1.4/pen/penPow.m0000644000175000017500000000104711453154115013006 0ustar hnhn% [p,dp,d2p] = penPow(s,al) - Power penalty % % pen(s) = |s|^al, al>0, default al=1 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 20 function [p,dp,d2p] = penPow(s,al) if nargin<2, al = 1; end % default value p = abs(s).^al; % penalty dp = al*sign(s).*abs(s).^(al-1); % first derivative d2p = (al^2-al)*abs(s).^(al-2); % second derivative glm-ie_v1.4/pen/penPowSmooth.m0000644000175000017500000000131311453154115014174 0ustar hnhn% [p,dp,d2p] = penPowSmooth(s,al,ep) - Smoothed power penalty % % pen(s) = sqrt(s^2+ep)^al, al>0, default al=1, ep>0, default ep=1e-6 % % See also PENFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 September 20 function [p,dp,d2p] = penPowSmooth(s,al,ep) if nargin<2, al = 1; end % default value if nargin<3, ep = 1e-6; end % default value r = sqrt(s.*s+ep); p = r.^al; % penalty dp = al*s.*r.^(al-2); % first derivative d2p = al*r.^(al-4).*( ep + (al-1)*s.*s); % second derivative glm-ie_v1.4/pot/0000755000175000017500000000000011755435662011414 5ustar hnhnglm-ie_v1.4/pot/potSech2.m0000644000175000017500000000775111466250654013266 0ustar hnhn% P = potSech2(s) - Sech-squared potential (Logistic distribution) % % pot(s) = 1 / cosh(s)^2 % % See also POTFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 September 29 function P = potSech2(s,type,z) if nargin==1 q = numel(s); P = zeros(q,4); % allocate memory, b=0 a = exp(-2*abs(s(:))); % always between 0 and 1 and therefore safe to evaluate P(:,1) = -2*(abs(s(:)) + log(1+a) - log(2));% log potential, -2*log( cosh(s) ) b = 2*a./(1+a); P(:,2) = -2*sign(s(:)).*(1-b); % 1st derivative of log potential P(:,3) = -4*b./(1+a); % 2nd derivative of log potential else if strcmp(type,'VB') P = potSech2(s); elseif strcmp(type,'EP') q = numel(s); P = zeros(q,3); % allocate memory, b=0, d2lp=0 fac = 1e1; % factor between the widths of the two distributions ... % ... from when one considered a delta peak, we use 3 orders of magnitude idpot = fac0 % % See also POTFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 September 26 function P = potExpPow(s,al,type,z) if nargin<=2 if nargin<2, error('Parameter al is unspecified.'), end q = numel(s); P = zeros(q,4); % allocate memory, b=0 P(:,1) = -abs(s(:)).^ al; % log potential P(:,2) = -al*sign(s(:)) .*abs(s(:)).^(al-1); % 1st derivative of log potential P(:,3) = -al*(al-1)*abs(s(:)).^(al-2); % 2nd derivative of log potential else if strcmp(type,'VB') P = potExpPow(s,al); elseif strcmp(type,'EP') error('EP is not supported.') else error('Unknown type') end endglm-ie_v1.4/pot/potLogistic.m0000644000175000017500000001231611453154122014055 0ustar hnhn% P = potLogistic(s) - Logistic potential for classification % % pot(s) = 1/(1+exp(-s)) % % See also POTFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 September 26 function P = potLogistic(s,type,z) if nargin==1 q = numel(s); P = zeros(q,4); % allocate memory P(:,1) = min(0,s(:)) - log(1+exp(-abs(s(:)))); % safe since abs(s)>=0 p = exp(P(:,1)); P(:,2) = 1-p; % 1st derivative of log potential, exp(-s)/(1+exp(-s)) P(:,3) = p.*(p-1); % 2nd derivative of log potential, -exp(-s)/(1+exp(-s))^2 P(:,4) = ones(size(s))/2; else if strcmp(type,'VB') P = potLogistic(s); elseif strcmp(type,'EP') q = numel(s); P = zeros(q,3); % allocate memory % likLogistic(t) \approx 1/2 + \sum_{i=1}^5 (c_i/2) erf(lam_i/sqrt(2)t) lam = sqrt(2)*[0.44 0.41 0.40 0.39 0.36]; % approx coeffs lam_i and c_i c = [1.146480988574439e+02; -1.508871030070582e+03; 2.676085036831241e+03; -1.356294962039222e+03; 7.543285642111850e+01 ]; [lZc,dlZc,d2lZc] = intErf(s*lam, z*(lam.^2)); P(:,1) = log_expA_x(lZc,c); % A=lZc, B=dlZc, d=c.*lam', lZ=log(exp(A)*c) P(:,2) = expABz_expAx(lZc, c, dlZc, c.*lam'); % ((exp(A).*B)*d)./(exp(A)*c) % d2lZ = ((exp(A).*Z)*e)./(exp(A)*c) - dlZ.^2 where e = c.*(lam.^2)' P(:,3) = expABz_expAx(lZc, c, dlZc.^2+d2lZc, c.*(lam.^2)') - P(:,2).^2; % The scale mixture approximation does not capture the correct asymptotic % behavior; we have linear decay instead of quadratic decay as suggested % by the scale mixture approximation. By observing that for large values % of -s ln(pot(s)) of potLogistic is linear in s with slope 1, we are % able to analytically integrate the tail region; there is no contribution % to the second derivative val = abs(s)-196/200*z-4; % empirically determined bound at val==0 lam = 1./(1+exp(-10*val)); % interpolation weights lZtail = min(z/2-abs(s),-.1); % apply the same to pot(s) = 1 - pot(-s) dlZtail = -sign(s); id = s>0; lZtail(id) = log(1-exp(lZtail(id))); % label and mean agree dlZtail(id) = 0; P(:,1) = (1-lam).*P(:,1) + lam.* lZtail; % interpolate between scale mixture P(:,2) = (1-lam).*P(:,2) + lam.*dlZtail; % .. and tail approximation else error('Unknown type') end end % Gaussian integral wrt. error function function [lZ,dlZ,d2lZ] = intErf(mu,s2) z = mu./sqrt(1+s2); lZ = logphi(z); % log part function if nargout>1 n_p = gauOverCumGauss(z,exp(lZ)); dlZ = n_p./sqrt(1+s2); % 1st derivative wrt mean if nargout>2 d2lZ = -n_p.*(z+n_p)./(1+s2); % 2nd derivative wrt mean end end % safe implementation of the log of phi(x) = \int_{-\infty}^x N(f|0,1) df % logphi(z) = log(normcdf(z)) function lp = logphi(z) p = (1+erf(z/sqrt(2)))/2; lp = zeros(size(z)); % allocate memory zmin = -6.2; zmax = -5.5; ok = z>zmax; % safe evaluation for large values bd = z-5; % naive evaluation for large values of f n_p(ok) = (exp(-f(ok).^2/2)/sqrt(2*pi)) ./ p(ok); bd = f<-6; % tight upper bound evaluation n_p(bd) = sqrt(f(bd).^2/4+1)-f(bd)/2; interp = ~ok & ~bd; % linearly interpolate between both of them tmp = f(interp); lam = -5-f(interp); n_p(interp) = (1-lam).*(exp(-tmp.^2/2)/sqrt(2*pi))./p(interp) + ... lam .*(sqrt(tmp.^2/4+1)-tmp/2); % computes y = log( exp(A)*x ) in a numerically safe way by subtracting the % maximal value in each row to avoid cancelation after taking the exp function y = log_expA_x(A,x) N = size(A,2); maxA = max(A,[],2); % number of columns, max over columns y = log(exp(A-maxA*ones(1,N))*x) + maxA; % exp(A) = exp(A-max(A))*exp(max(A)) % computes y = ( (exp(A).*B)*z ) ./ ( exp(A)*x ) in a numerically safe way % The function is not general in the sense that it yields correct values for % all types of inputs. We assume that the values are close together. function y = expABz_expAx(A,x,B,z) N = size(A,2); maxA = max(A,[],2); % number of columns, max over columns A = A-maxA*ones(1,N); % subtract maximum value y = ( (exp(A).*B)*z ) ./ ( exp(A)*x );glm-ie_v1.4/pot/potLaplace.m0000644000175000017500000001001511464465444013651 0ustar hnhn% P = potLaplace(s) - Laplace (double exponential) potential % % pot(s) = exp(-|s|) % % See also POTFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 03 function P = potLaplace(s,type,z) if nargin==1 q = numel(s); P = zeros(q,4); % allocate memory, b=0, d2lp=0 P(:,1) = -abs(s(:)); % log potential P(:,2) = 1-2*(s(:)>0); % 1st derivative of log potential else if strcmp(type,'VB') P = potLaplace(s); elseif strcmp(type,'EP') q = numel(s); P = zeros(q,3); % allocate memory, b=0, d2lp=0 fac = 1e3; % factor between the widths of the two distributions ... % ... from when one considered a delta peak, we use 3 orders of magnitude idpot = faczmax; % safe evaluation for large values bd = z0 degrees of freedom % % See also POTFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function P = potT(s,nu,type,z) if nargin<=2 if nargin<2, error('Parameter nu is unspecified.'), end q = numel(s); P = zeros(q,4); % allocate memory, b=0 ss = s(:).*s(:); P(:,1) = -(nu+1)*log( 1+ss./nu )/2; % log potential a = s(:) + nu./s(:); P(:,2) = -(nu+1)./a; % 1st derivative of log potential P(:,3) = (nu+1)*(1-nu./(1e-10+ss))./(a.*a); % 2nd derivative of log potential else if strcmp(type,'VB') P = potT(s,nu); elseif strcmp(type,'EP') error('EP is not supported.') else error('Unknown type') end endglm-ie_v1.4/pot/potGauss.m0000644000175000017500000000173011453154122013360 0ustar hnhn% P = potGauss(s) - Gaussian potential % % pot(s) = exp(-s^2/2) % % See also POTFUNCTIONS.M. % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 September 26 function P = potGauss(s,type,z) if nargin==1 q = numel(s); P = zeros(q,4); % allocate memory, b=0 P(:,1) = -s(:).*s(:)/2; % log potential P(:,2) = -s(:); % 1st derivative of log potential P(:,3) = -1; % 2nd derivative of log potential else if strcmp(type,'VB') P = potGauss(s); elseif strcmp(type,'EP') q = numel(s); P = zeros(q,3); % allocate memory P(:,1) = -s(:).*s(:)./(1+z(:))/2 - log(1+z(:))/2; % log part function P(:,2) = -s(:)./(1+z(:)); % 1st derivative w.r.t. mean P(:,3) = -1./(1+z(:)); % 2nd derivative w.r.t. mean else error('Unknown type') end endglm-ie_v1.4/.octaverc0000644000175000017500000000001011453154140012370 0ustar hnhnstartup glm-ie_v1.4/potFunctions.m0000644000175000017500000000665411466567326013500 0ustar hnhn% A potential pot(s) is a scalar positive function IR -> IR_+. % Applied to a vector valued input s, a potential function is understood as % pointwise evaluation of every component s(i). % % We currently support two classes of inference algorithms beyond Laplace's % approximation aka MAP estimation: Variational bounding and expectation % propagation. They are specified by the type parameter in the general call % P = pot(s,theta,type,z) % where theta contains additional (hyper)parameter(s). The input s is only % used as s(:), that is, matrix structure is ignored. % % 1) Variational bounding (VB) [for ExpPow, Gauss, Laplace, Logistic, Sech2, T] % P = pot(s,theta) = pot(s,theta,'VB') % - pot(s) Needs to be strongly super-Gaussian. % - pot(s) Has to be symmetric or symmetrisable i.e. there is a constant b % such that f(s) = pot(s)*exp(-b*s) is even or symmetric f(s)=f(-s). % The return argument is a matrix P of size [qx4] whose columns % [lp,dlp,d2lp,b] are as long as there are elements in the input s. % lp(s) = log( pot(s) ), [simple log evaluation] % dlp(s) = d lp(s) / ds, [first derivative of the log] % d2lp(s) = d^2 lp(s) / ds^2, and [second derivative of the log] % b s.t. f(s)=f(-s), f(s) = pot(s)*exp(-b*s). [linear symmetry parameter] % % 2) Expectation propagation (EP) [for Gauss, Laplace, Logistic, Sech2] % P = pot(s,theta,'EP',z) % - pot(s) Does not need to be strongly super-Gaussian or symmetric; we need % Gaussian expectations w.r.t. pot(s) in order to run EP. % The return argument is a matrix P of size [qx3] whose columns % [lZ,dlZ,d2lZ] are as long as there are elements in the input s. % lZ(s,z) = log( \int N(t|s,z) pot(t) dt ), [log partition function] % dlZ(s,z) = d lZ(s,z) / ds, and [first derivative of the log] % d2lZ(s,z) = d^2 lZ(s,z) / ds^2. [second derivative of the log] % % We use a single matrix-valued output argument to allow very compact % specifications of mixed potentials, see the last line of the examples below. % This ease of specification, however, comes at the expense of some computional % overhead since we always evaluate the full matrix P even if only the first % column is needed. % % Currently, the following potentials are implemented in pot/pot.m: % Analytic Expression Param Description % ---------------------------------------------------------------------------- % ExpPow(s,al) = exp(-|s|^al) al>0 Exponential power distribution % Gauss(s) = exp(-s^2/2) Gaussian distribution % Laplace(s) = exp(-abs(s)) Laplace distribution % Logistic(s) = 1/(1+exp(-s)) Logistic function % Sech2(s) = 1 / cosh(s)^2 Sech-squared distribution % T(s,nu) = (1+s^2/nu)^(-nu/2-1/2) nu>0 Student's t distribution % % Examples: % >> s=0.3; pot = @(s) potLogistic(s,'EP'); % >> s=2.7; nu=3; pot = @(s) potT(s,'VB',nu); % >> s=[1;2]; al=4; pot = @(s) [potGauss(s(1),'VB'); potExpPow(s(2),'VB',al)]; % % Another way of concatenating potentials is provided by pot/potCat.m, which % allows concatenation by: % >> pot = @(s,varargin) potCat(s,varargin{:},{@potT,@potGauss},{1:5,6:9}); % % See also PENFUNCTIONS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 10glm-ie_v1.4/mat/0000755000175000017500000000000011755435662011373 5ustar hnhnglm-ie_v1.4/mat/@matFFTN/0000755000175000017500000000000011755435662012732 5ustar hnhnglm-ie_v1.4/mat/@matFFTN/matFFTN.m0000644000175000017500000000216211512275067014340 0ustar hnhn% n-dimensional FFT matrix: constructor % % A = matFFTN(sz,dims,complex) % % The transform is centered. % % sz [1,D]: size the data to process % dims [1,d]: dimensions along which the FFT is computed default 1:D % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 21 function A = matFFTN(sz,dims,complex) if numel(sz)<2, sz = [sz(:); 1]; end, A.imsz = fix(sz(:)'); % image size sz = prod(sz)*[1,1]; % matrix size if nargin<2, dims = 1:numel(A.imsz); end A.dims = unique(fix(dims(:)))'; if nargin<3, complex = [1,1]; end % set default A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matFFTN/diagFAtAFt.m0000644000175000017500000000030611646242776015002 0ustar hnhn% n-dimensional FFT matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function d = diagFAtAFt(A,opt) d = ones(A.imsz); glm-ie_v1.4/mat/@matFFTN/mvmAA.m0000644000175000017500000000042611701406160014071 0ustar hnhn% base matrix: matrix vector multiplication with A.*conj(A) % Note that (A.*conj(A))*x = diag(A'*diag(x)*A). % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2012 January 05 function y = mvmAA(A,x,ctransp) N = prod(A.imsz(A.dims)); y = ones(A.imsz)*sum(x(:))/N;glm-ie_v1.4/mat/@matFFTN/mvm.m0000644000175000017500000000062111521732633013673 0ustar hnhn% n-dimensional FFT matrix: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 January 31 function y = mvm(A,x,ctransp) y = reshape(x,A.imsz); N = prod(A.imsz(A.dims)); if ctransp for d=A.dims, y=fftshift(ifft(ifftshift(y,d),[],d),d); end, y = y*sqrt(N); else for d=A.dims, y=fftshift( fft(ifftshift(y,d),[],d),d); end, y = y/sqrt(N); endglm-ie_v1.4/mat/@matFFTnu/0000755000175000017500000000000011755435662013157 5ustar hnhnglm-ie_v1.4/mat/@matFFTnu/matFFTnu.m0000644000175000017500000001223211533771557015021 0ustar hnhn% Non-uniformly spaced 2d/3d FFT matrix: constructor % % A = matFFTnu(sz,k,type) % % sz: size of the array; either 2d or 3d % k: normalized k-space coordinates i.e. in [-1,1]/2 % In case of 2d input, either a [m,1] array where real and complex part % contain first and second cooordinate or an [m,2] array containing the % locations in k-space. For 3 input, simply an [m,3] array. % % type: string indicating the nufft interpolation type, % we support 'dense/full', 'nearest', 'linear', 'cubic', % 'fessler' and 'ferrara' default 'linear' % 'dense' or 'full' % We return the exact dense matrix. This requires quite some memory, hence it % is only possible for small sz. % 'nearest', 'linear', 'cubic' % We use nearest neighbor, linear or cubic interpolation after oversampling. % 'fessler' % Code inspired by Jeff Fessler's nufft library [2], implementing [1]. % The package is very general, we use Kaiser-Bessel windows of size 3. % The matrix is approximated by P*F*diag(d) where d is a (real) scaling % vector, P is a highly sparse (complex) matrix containting interpolation % weights and F is the Fourier transform matrix twice as large as the % original image due to overgridding. % 'ferrara' % Code inspired by Matthew Ferrara's nufft package [4], implementing [3]. % The code uses Gaussian windows which speeds up computations and makes sure % that the nufft and fftn coincide if the points are placed on a grid. % We use overgridding with a factor of 2. % % [1] Jeff Fessler and Brad P. Sutton, Nonuniform fast Fourier transforms using % min-max interpolation, IEEE-SP, 2003, Vol. 51, pp. 560-574. % [2] http://www.eecs.umich.edu/~fessler/irt/irt/nufft/ % [3] Leslie Greengard and June-Yub Lee, Accelerating the nonuniform fast % Fourier transform, SIAM Review, Vol. 46, pp. 443-454. % [4] http://www.mathworks.com/matlabcentral/fileexchange/25135-nufft-nfft-usfft % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 March 03 function A = matFFTnu(sz,k,type,complex) if numel(sz)==3 && sz(3)==1, sz = sz(1:2); k = k(:,1:2); end % pseudo 3d image A.imsz = sz; A.ndims = numel(sz); % Are we doing 2d or 3d stuff? if A.ndims<2 || A.ndims>3, error('We support only 2d and 3d nufft.'), end sz = [size(k,1),prod(A.imsz)]; if nargin<2, error('We need at least two input arguments.'), end if nargin<3, A.type = 'ferrara'; else A.type = type; end % set default if any(strfind(A.type,'full')) || any(strfind(A.type,'dense')) % full matrix c = ceil((A.imsz-1)/2)+1; % center gvec = cell(A.ndims,1); for i=1:A.ndims, gvec{i} = (1:A.imsz(i))-c(i); end [gvec{:}] = ndgrid(gvec{:}); g = reshape(cat(A.ndims+1,gvec{:}),[],A.ndims); A = exp(-2i*pi*conj(k)*g')/sqrt(sz(2)); return % g is integer Cartesian grid end A.ogf = 2; % overgridding factor A.kbwsz=[]; A.fftsz=[]; A.accuracy=[]; A.k=[]; A.w=[]; A.f=[]; A.P=[]; A.id=[]; A.in=[]; A.dP=cell(A.ndims,1); A.di=0; A.F=[]; % init if any(strfind(A.type,'fessler')) % Fessler's nufft kbwsz = 3; A.k = k; % Kaiser-Bessel window size A.kbwsz = kbwsz*ones(1, A.ndims); A.fftsz = fix(A.ogf*A.imsz); [A.f, A.P] = nufft_init(A.k, A.imsz, A.fftsz, A.kbwsz, 0); % precompute elseif any(strfind(A.type,'ferrara')) % Ferrara's nufft A.accuracy = 2; % 1..6, high = slow & precise if ~all(mod(A.imsz,2)), error('Method ferrara requires odd sizes.'), end % remember outside grid points kk = bsxfun(@times,k,A.imsz); kk = bsxfun(@plus,kk,ceil((A.imsz-1)/2)+1); A.in = 02, A.in = A.in & 0dimax, error('i is too large.'), end if i<0, error('i is too small.'), end if strcmp(A.type,'fessler') if numel(A.dP{i})==0 % precompute [junk, A.dP{i}] = nufft_init(A.k, A.imsz, A.fftsz, A.kbwsz, i); end elseif strcmp(A.type,'ferrara') error('Derivative for ferrara not implemented.') end end A.di = i; % which derivative, 0 means no derivative dAi = A; % assign outputglm-ie_v1.4/mat/@matFFTnu/mvm.m0000644000175000017500000002210511533225620014115 0ustar hnhn% Non-uniformly spaced 2d/3d FFT matrix: matrix vector multiplication % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 March 01 function y = mvm(A,x,ctransp) N = prod(A.imsz); if any(strfind(A.type,'fessler')) % Fessler's nufft if ctransp if A.di==0 Ptx = A.P'*x(:); % sparse interpolation matrix P else Ptx = A.dP{A.di}'*x(:); % derivative of sparse interpolation matrix P end Ptx = reshape(full(Ptx), A.fftsz); y = prod(A.fftsz)/sqrt(N) * ifftn(Ptx); % apply oversampled fft if A.ndims==2 % 2 dimensions y = y(1:A.imsz(1),1:A.imsz(2),:); % eliminate zero padding else y = y(1:A.imsz(1),1:A.imsz(2),1:A.imsz(3),:); end y = conj(A.f) .* y; % apply diagonal filter matrix else Sx = A.f .* reshape(x,A.imsz); % apply diagonal filter matrix FSx = fftn(Sx,A.fftsz)/sqrt(N); % apply oversampled fft if A.di==0 y = A.P*FSx(:); % apply sparse interpolation matrix P else y = A.dP{A.di}*FSx(:); % apply derivative of interpolation matrix P end end elseif any(strfind(A.type,'ferrara')) % Ferrara's nufft R=2; % M_sp is the length of the convolution kernel M_sp=A.accuracy; % This gives roughly 6 digits of accuracy % The variance, tau, of the Gaussian filter may be different in each dimension tau = (pi*M_sp./(A.imsz.*A.imsz*R*(R-.5))); % Suggested value Greengard [1] %The length of the oversampled grid M_r = R*A.imsz; % Type-II NUFFT: % Precompute E_3, the constant component of the (truncated) Gaussian: E_3x(1,1:M_sp) = exp(-((pi*(1:M_sp)/M_r(1)).^2)/tau(1)); % don't waste (slow) exponential calculations E_3x=[fliplr(E_3x(1:(M_sp-1))),1,E_3x]; E_3y(1,1:M_sp) = exp(-((pi*(1:M_sp)/M_r(2)).^2)/tau(2)); % don't waste (slow) exponential calculations E_3y=[fliplr(E_3y(1:(M_sp-1))),1,E_3y]; % Precompute E_4 (for devonvolution after the FFT) kx_vec = (-floor(A.imsz(1)/2)):(ceil(A.imsz(1)/2)-1); % The Hadamard Inverse of the Fourier Transform of the truncated Gaussian E_4x(1:A.imsz(1),1)=sqrt(pi/tau(1))*exp(tau(1)*(kx_vec.^2)); ky_vec = (-floor(A.imsz(2)/2)):(ceil(A.imsz(2)/2)-1); % The Hadamard Inverse of the Fourier Transform of the truncated Gaussian E_4y(1,1:A.imsz(2))=sqrt(pi/tau(2))*exp(tau(2)*(ky_vec.^2));% k = A.k; %Ensure that the knots fit in a 2*pi interval M=size(k,1); kmin=min(k); kmax=max(k); bw=kmax-kmin; scale=(A.imsz-1)./bw; shift=-floor(A.imsz/2)-kmin.*scale; knots=repmat(scale,[M,1]).*k + repmat(shift,[M,1]); knots=mod(2*pi*knots./repmat(A.imsz,[M,1]),2*pi); %shift to [0,2*pi) if A.ndims==2 % 2 dimensions if ctransp % Type I transform x = x(:); x = x(A.in); x = x(A.id); [f_taur,f_taui] = FGG_Convolution2D(real(x(:)),imag(x(:)),... knots(:),E_3x,E_3y,[M_sp, tau(1), tau(2), M_r(1), M_r(2)]); f_tau = reshape(f_taur+sqrt(-1)*f_taui,[M_r(1), M_r(2)]); % Perform FFT and deconvolve the result F_tau=fftshift(fftn(fftshift(f_tau)))/sqrt(numel(f_tau)); %Chop off excess pixels(the fine spacing in the frequency domain expanded %the image in the transform domain) F_tau(1:round(.5*(R-1)*A.imsz(1)),:)=[]; F_tau(A.imsz(1)+1:end,:)=[]; F_tau(:,1:round(.5*(R-1)*A.imsz(2)))=[]; F_tau(:,A.imsz(2)+1:end)=[]; %Deconvolve the FFT % AL: 27.01 Corrects for scaling %changed from: %y=F_tau.*(E_4x*E_4y)/(M*R*R); % to: y=F_tau.*(E_4x*E_4y)/(prod(A.imsz)*R*R); %Note that the scaling factor is 1/M, which is %apparently not 1/M_r as shown in eqn (9) in [1]. This makes sense because %the scaling factor for the DFT we are attempting to approximate (in eqn %(1) of [1]) is 1/M. % Rescale by factor of 2 y = y(:)*2; else % Type II transform % Zero pad for convolution on finer mesh in frequency domain F = reshape(x, A.imsz(1), A.imsz(2)); % AL: 27.01 Corrects for scaling %changed from: %F = F.*(E_4x*E_4y)/M; % to: F = F.*(E_4x*E_4y)/(prod(A.imsz)); % AL: 04.04 padding for odd-sized images F = padarray(F,floor(A.imsz/2)); F = padarray(F,[1 1],'pre'); f_tau = fftshift(ifftn(ifftshift(F)))*sqrt(numel(F)); % XX.A: sqrt(numel(F)) for orthonormality [f_r,f_i] = FGG_Convolution2D_type2(real(f_tau(:)),imag(f_tau(:)),... knots,E_3x,E_3y,[M_sp, tau(1), tau(2), M_r(1), M_r(2)]); f = (f_r + 1i*f_i)/2; % adjust the scaling yy = zeros(sum(A.in),1); yy(A.id) = f(:); y = zeros(numel(A.in),1); y(A.in) = yy; end else % 3 dimensions E_3z(1,1:M_sp) = exp(-((pi*(1:M_sp)/M_r(3)).^2)/tau(3)); %don't waste (slow) exponential calculations E_3z=[fliplr(E_3z(1:(M_sp-1))),1,E_3z]; kz_vec = (-floor(A.imsz(3)/2)):(ceil(A.imsz(3)/2)-1); %The Hadamard Inverse of the Fourier Transform of the truncated Gaussian E_4z(1:A.imsz(3),1)=sqrt(pi/tau(3))*exp(tau(3)*(kz_vec.^2));% if ctransp % Type I transform x = x(:); x = x(A.in); x = x(A.id); %Perform convolution onto finely-spaced grid [f_taur,f_taui]=... FGG_Convolution3D(double(real(x(:))),double(imag(x(:))),... double(knots(:)),double(E_3x), double(E_3y), double(E_3z), ... [double(M_sp), double(tau(1)), double(tau(2)), double(tau(3)),... double(M_r(1)), double(M_r(2)), double(M_r(3))]); f_tau = reshape(f_taur+sqrt(-1)*f_taui,[M_r(1), M_r(2), M_r(3)]); %Perform FFT F_tau=fftshift(fftn(ifftshift(f_tau)))/sqrt(numel(f_tau)); % AL: Correct the scaling with sqrt(numel(f_tau)); %Chop off excess pixels(the fine spacing in the frequency domain expanded %the image in the transform domain) F_tau(1:round(.5*(R-1)*A.imsz(1)),:,:)=[]; F_tau(A.imsz(1)+1:end,:,:)=[]; F_tau(:,1:round(.5*(R-1)*A.imsz(2)),:)=[]; F_tau(:,A.imsz(2)+1:end,:)=[]; F_tau(:,:,1:round(.5*(R-1)*A.imsz(3)))=[]; F_tau(:,:,A.imsz(3)+1:end)=[]; %Deconvolve the FFT by Hadamard multiplication with the Gaussian S=kron(E_4z,E_4x*E_4y);%Scalars for 3D kronecker product (matrix must be %reshaped) D=permute(reshape(S,[A.imsz(1),A.imsz(3),A.imsz(2)]),[1,3,2]); % AL: 27.01.11 Changed from %y=F_tau.*D/(M*R*R*R); % to: y=F_tau.*D/(prod(A.imsz)*R*R*R); %Note that the scaling factor is 1/M, which is %apparently not 1/M_r as shown in eqn (9) in [1]. This makes sense because %the scaling factor for the DFT we are attempting to approximate (in eqn %(1) of [1]) is 1/M. % AL: Scaling adjusted y = abs(y)*3; y = y/1.06; y = y(:); else % Type II transform %Deconvolve S=kron(E_4z,E_4x*E_4y); %Scalars for 3D kronecker product (matrix must be reshaped) D=permute(reshape(S,[A.imsz(1),A.imsz(3),A.imsz(2)]),[1,3,2]); % AL: 27.01.11 Changed from %F=reshape(x, A.imsz).*D/M; % to: F=reshape(x, A.imsz).*D/(prod(A.imsz)); % AL: 04.04 padding for odd-sized images padF = padarray(F,floor(A.imsz/2)); padF = padarray(padF,[1 1 1],'pre'); f_tau = fftshift(ifftn(ifftshift(padF)))*sqrt(numel(padF)); % XX.A: sqrt(numel(F)) for orthonormality [f_r,f_i]=... FGG_Convolution3D_type2(double(real(f_tau(:))),double(imag(f_tau(:))),... double(knots),E_3x,E_3y,E_3z,[M_sp, tau(1), tau(2), tau(3), M_r(1), M_r(2), M_r(3)]); f = (f_r + 1i*f_i)/3; % scaling adjusted f = f * 1.06; yy = zeros(sum(A.in),1); yy(A.id) = f(:); y = zeros(numel(A.in),1); y(A.in) = yy; end end else % nufft using matResample x = A.f*x; % rescaling needed due to zero padding if A.di==0 if ctransp, y = A.F'*( A.P' *x); else y = A.P *(A.F *x); end else if ctransp, y = A.F'*(d(A.P,A.di)'*x); else y = d(A.P,A.di) *(A.F *x); end y = 2*y*A.imsz(A.di); % account for pretransformation of A.k end endglm-ie_v1.4/mat/@matFastFFTmotion/0000755000175000017500000000000011755435662014660 5ustar hnhnglm-ie_v1.4/mat/@matFastFFTmotion/mvmAtA.m0000644000175000017500000000114211702646436016214 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion: % matrix vector multiplication with A'*A which is symmetric block Toeplitz % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 March 03 function y = mvmAtA(A,x) if any([strfind(lower(A.type),'near'), strfind(lower(A.type),'lin'), ... strfind(lower(A.type),'cub')]) y = mvmAtA(A.RF,x); else y = []; error('Only implemented for types nearest, linear and cubic.'); endglm-ie_v1.4/mat/@matFastFFTmotion/matFastFFTmotion.m0000644000175000017500000001720411703613616020215 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion % % A = matFastFFTmotion(sz,trans,rot,complex,type) % % sz: size of the array; either 2d or 3d % % 2d i.e. numel(sz)=2 % trans: [2,1] or [2,sz(2)], the translation in pixels, default [0;0] % rot: [1,1] or [1,sz(2)], the rotation angle in radian, default 0 % % 3d i.e. numel(sz)=3 % trans: [3,1] or [3,sz(2),sz(3)], the translation in pixels, default [0;0;0] % rot: [3,1] or [3,sz(2),sz(3)], the rotation axis, whose norm equals the % rotation angle in radian, default [0;0;0] % Note that by convention, translation is done after rotation. % Note further that the matrix relies on the fact that the pixels/voxels are % cubes i.e. we have the same resolution along every dimension. % % complex: [1,2] complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % % We use cubic interpolation after oversampling. One can set type{mex,gpu} % to indicate whether CPU or GPU implementation of resampling is used. % % (c) Alexander Loktyushin, MPI for Biological Cybernetics, 2011 function A = matFastFFTmotion(sz, trans, rot, complex, type, pre_op) %% general info A.ndims = numel(sz); % Are we doing 2d or 3d stuff? if A.ndims<2 || A.ndims>3, error('We support only 2d and 3d.'), end A.imsz = sz; sz = prod(A.imsz)*[1,1]; if nargin<4, complex = 1; end, if numel(complex)==0, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end center = ceil((A.imsz-1)/2)+1; A.center = center; % center in k-space if nargin<5, type = 'linear'; end, A.type = type; % set (default) nufft type if nargin<6, pre_op = []; end; %% derivatives A.dkind = 'none'; % kind of derivative, either rot or trans A.di = 0; % which derivative, 0 means all of the respective kind %% rotation % The outcome of the computations below is % 1) a matrix A.RF implementing the Fourier transform followed by a rotation, % which is done by means of a non-uniform Fourier transform with griding % interpolation and oversampling to reduce artefacts; % 2) a bunch of vectors A.k indicating the rotated k-space points, some of % which can be placed outside the image rectangle; % 3) a set of bunches of vectors A.dk containing the perturbed versions of % A.k needed to compute the rotational derivatives; % 4) an array of booleans indicating whether the vectors in A.k are placed % inside the image rectangle. nrot = A.ndims*(A.ndims-1)/2; % number of rotational parameters if nargin<3, rot = zeros(nrot,1); end if numel(rot)nrot % bring into proper shape A.rot = reshape(A.rot,[nrot,prod(A.imsz(2:end))]); end sc = A.imsz/A.imsz(1); % correction for A.imsz(1) ~= A.imsz(2:end) k = zeros(A.ndims,prod(A.imsz)); % allocate memory A.dk = repmat(k,[1,1,nrot]); % init with no rotation at all T = size(A.rot,2); % number of different rotations dR = cell(1,nrot); % derivatives of the rotation matrices if A.ndims==2 % construct target grid [i2,i1]=meshgrid(1:A.imsz(2),1:A.imsz(1)); ii=[i1(:)';i2(:)']; clear i1 i2 else [i2,i1,i3] = meshgrid(1:A.imsz(2),1:A.imsz(1),1:A.imsz(3)); ii = [i1(:)'; i2(:)'; i3(:)']; clear i1 i2 i3 end %{ for t = 1:T % loop over scanlines if T==1 i = 1:prod(A.imsz); % all indices at once else i = (t-1)*A.imsz(1) + (1:A.imsz(1)); % indices of individual scanline end [R,dR{:}] = rotmatsc(A.rot(:,t),sc); % rotation matrix and its derivatives k(:,i) = bsxfun(@minus,ii(:,i),center(:)); % centered grid for j=1:nrot, A.dk(:,i,j) = dR{j}'*k(:,i); end % dk/dx grid derivative k(:,i) = R'*k(:,i); % non-integer src grid end %} setenv('OMP_NUM_THREADS', num2str(feature('numCores'))); dkR = cell(1,nrot); % derivatives of the rotation matrices [k, dkR{:}] = grid_create(ii, A.rot, T, A.imsz, center, sc, nrot); for i = 1:nrot A.dk(:,:,i) = dkR{i}; end; A.k = bsxfun(@times,k,1./A.imsz(:)); A.dk = bsxfun(@times,A.dk,1./A.imsz(:)); % matFFTnu supplement k = A.k'; nusz = A.imsz; if numel(nusz)==3 && nusz(3)==1, nusz = nusz(1:2); k = k(:,1:2); end % pseudo 3d image A.nuimsz = nusz; A.nundims = numel(nusz); % Are we doing 2d or 3d stuff? A.ogf = 2; % overgridding factor A.kbwsz=[]; A.fftsz=[]; A.accuracy=[]; A.k=[]; A.w=[]; A.f=[]; A.P=[]; A.id=[]; A.in=[]; A.dP=cell(A.nundims,1); A.di=0; A.F=[]; % init A.k = 2*bsxfun(@times, k', A.nuimsz(:) ); % get back scale, padding 2 psz = fix(A.nuimsz/2); % padding size A.k = bsxfun(@plus, A.k, A.nuimsz(:)+1 ); % add back center A.F = matFFTN(2*A.nuimsz)*matZpad(A.nuimsz,psz,A.nuimsz-psz); % padded Fourier A.f = 2; % scaling factor due to padding if any(strfind(lower(A.type),'mex')) mode = 'mex'; elseif any(strfind(lower(A.type),'gpu')) mode = 'mex'; % !! disable GPU capability for this class for now, otherwise set mode = 'gpu'; else mode = 'mat'; end A.mode = mode; %% translation % The outcome of the computations below is % 1) a vector A.t implementing the translation; % 2) a set of vectors A.dt needed for the translation derivatives; % 3) a vector A.tc needed to correct for the rotation that is not exactly % done around the center. if nargin<2, trans = zeros(A.ndims,1); end if numel(trans)A.ndims % bring into proper shape A.trans = reshape(A.trans,[A.ndims,A.imsz(2:end)]); end [A.t,A.dt] = trans_diag(A.imsz,A.trans); % diag translation matrix and derivs % compute translational correction for not rotating around the origin A.tc = 1; A.dtc = zeros(1,nrot); %% construct matrix class, inherit from mat A = class(A,mfilename,mat(sz,complex)); % Compute diagonal translation equivalent in Fourier space function [t,dt] = trans_diag(sz,tr) ndims = numel(sz); N = prod(sz); % number of dimensions, number of pixels deriv = nargout>1; % flag saying, whether we compute derivatives t = ones(sz); if deriv, dt = ones(N,ndims); end % allocate memory for d=1:ndims rp = ((1:sz(d))-fix(1+sz(d)/2))/sz(d); % ramp in direction of dimension d rp = -2i*pi*reshape(rp,[ones(1,d-1),sz(d),ones(1,ndims-d)]); erp = exp(bsxfun(@times,rp,tr(d,:,:))); % tr is singleton in dim 1 t = bsxfun(@times, t, erp); if deriv for dd=1:ndims dtdd = bsxfun(@times, reshape(dt(:,dd),sz), erp); if dd==d dtdd = bsxfun(@times, dtdd, rp); end dt(:,dd) = reshape(dtdd,N,1); end end end glm-ie_v1.4/mat/@matFastFFTmotion/d.m0000644000175000017500000000210211702646436015247 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion: % derivative % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 February 02 function dAi = d(A,kind,i) if nargin<2, kind = 'none'; end % default kind of derivative if nargin<3 % default derivative index i = 0; else dimax = A.ndims; % maximal derivative index if A.ndims==2 && strcmp(A.dkind,'rot'), dimax = 1; end i = fix(i); if i>dimax, error('i is too large.'), end if i<1, error('i is too small.'), end end if strcmp(kind,'rot') || strcmp(kind,'trans') || strcmp(kind,'all') % kind of derivative A.dkind = kind; else error('Select either rot or trans.') end A.di = i; % which derivative, 0 means all of the respective kind dAi = A; % assign output glm-ie_v1.4/mat/@matFastFFTmotion/get_k.m0000644000175000017500000000004211702646436016116 0ustar hnhnfunction k = get_k(X) k = X.k; glm-ie_v1.4/mat/@matFastFFTmotion/mvm.m0000644000175000017500000001305011703613616015622 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion: % matrix vector multiplication % % (c) by Alexander Loktyushin, MPI for Biological Cybernetics, 2011 February 19 function y = mvm(A,x,ctransp) t = A.t(:).*A.tc(:); % translation if strcmp(A.dkind,'none') if ctransp % translation after after rotation y = A.f*(conj(t).*x(:)); y = resample_mex(A.k(:),y(:),2*A.nuimsz,ctransp,0,2); y = A.F'*y; else y = A.F*(A.f*x(:)); if strcmp(A.mode,'mex') y = resample_mex(A.k(:),y(:),2*A.nuimsz,ctransp,0,2); else y = resample_gpu(A.k(:),y(:),2*A.nuimsz,ctransp,0,2); end; y = t.*y; % Fourier transform followed by rotation & translation end elseif strcmp(A.dkind,'all') % NO TRANSPOSE if A.ndims == 3 y = zeros(prod(A.imsz),size(A.dk,7)); dy = zeros(prod(A.imsz),A.ndims); if strcmp(A.mode,'mex') [y(:,1) dy(:,1) dy(:,2) dy(:,3)] = resample_mex(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[0 1 2 3],2); else [y(:,1) dy(:,1) dy(:,2) dy(:,3)] = resample_gpu(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[0 1 2 3],2); end; for i=1:A.ndims dy(:,i) = 2*A.nuimsz(i)*dy(:,i); end for dd=1:size(A.dk,3) y(:,dd+1) = t.*reshape(sum(dy.'.*A.dk(:,:,dd),1),[],1); % Rotation end y(:,5:7) = A.dt.*repmat(A.tc(:).*y(:,1),1,size(A.dt,2)); % Translation y(:,1) = t.*y(:,1); % No derivative else y = zeros(prod(A.imsz),size(A.dk,4)); dy = zeros(prod(A.imsz),A.ndims); if strcmp(A.mode,'mex') [y(:,1) dy(:,1) dy(:,2)] = resample_mex(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[0 1 2],2); else [y(:,1) dy(:,1) dy(:,2)] = resample_gpu(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[0 1 2],2); end; for i=1:A.ndims dy(:,i) = 2*A.nuimsz(i)*dy(:,i); end for dd=1:size(A.dk,3) y(:,dd+1) = t.*reshape(sum(dy.'.*A.dk(:,:,dd),1),[],1); % Rotation end y(:,3:4) = A.dt.*repmat(A.tc(:).*y(:,1),1,size(A.dt,2)); % Translation y(:,1) = t.*y(:,1); % No derivative end; else if strcmp(A.dkind,'rot') % rotational derivative if ctransp, error('Transpose of rot derivative is not implemented.'), end dy = zeros(prod(A.imsz),A.ndims); % dy / dk if any(strfind(A.type,'lin')) || any(strfind(A.type,'cub')) ... || any(strfind(A.type,'fessler')) if ctransp y = zeros(prod(A.imsz),1); warning('No transpose of rotational derivatives implemented.') else if A.ndims == 3 if strcmp(A.mode,'mex') [dy(:,1) dy(:,2) dy(:,3)] = resample_mex(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[1 2 3],2); else [dy(:,1) dy(:,2) dy(:,3)] = resample_gpu(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[1 2 3],2); end; else if strcmp(A.mode,'mex') [dy(:,1) dy(:,2)] = resample_mex(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[1 2],2); else [dy(:,1) dy(:,2)] = resample_gpu(A.k(:),A.F*(A.f*x),2*A.nuimsz,ctransp,[1 2],2); end; end; for i=1:A.ndims dy(:,i) = 2*A.nuimsz(i)*dy(:,i); end %for i=1:A.ndims, dy(:,i) = d(A.RF,i)*x(:); end if A.di==0 % all derivatives y = zeros(prod(A.imsz),size(A.dk,3)); for dd=1:size(A.dk,3) y(:,dd) = t.*reshape(sum(dy.'.*A.dk(:,:,dd),1),[],1); % trans end else % a single derivative y = t.*sum(dy.'.*A.dk(:,:,A.di),1).'; % translation end end else y = zeros(prod(A.imsz),1); warning('Only linear/cubic/fessler rotational derivs implemented.') end else % translational derivative if ctransp y = conj(A.tc(:)) .* x(:); if A.di==0 % all derivatives y = conj(A.dt) .* (y*ones(1,A.ndims)); for dd=1:A.ndims y(:,dd) = A.f*(y(:,dd)); y(:,dd) = resample_mex(A.k(:),y(:,dd),2*A.nuimsz,ctransp,0,2); y(:,dd) = A.F'*y(:,dd); end else y = A.f*( conj(A.dt(:,A.di)).*x(:)); y = resample_mex(A.k(:),y(:),2*A.nuimsz,ctransp,0,2); y = A.F'*y; end else y = A.F*(A.f*x(:)); % proceed as usual since rotation is not affected if strcmp(A.mode,'mex') y = resample_mex(A.k(:),y(:),2*A.nuimsz,ctransp,0,2); else y = resample_gpu(A.k(:),y(:),2*A.nuimsz,ctransp,0,2); end; if A.di==0 % all derivatives y = A.dt.*repmat(A.tc(:).*y,1,size(A.dt,2)); % center correction else % a particular derivative y = A.dt(:,A.di).*A.tc(:).*y; % center correction end end end endglm-ie_v1.4/mat/@matFD2/0000755000175000017500000000000011755435662012550 5ustar hnhnglm-ie_v1.4/mat/@matFD2/matFD2.m0000644000175000017500000000310211646243303013763 0ustar hnhn% 2d finite difference matrix: constructor % % A = matFD2(sz,shape,complex) % % sz [1,2]: size of the image to transform % shape one of 'zero', 'circ', 'same' or 'valid' default 'circ' % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function A = matFD2(sz, shape, complex) if any(sz<2), error('[%s.m] size missmatch', mfilename), end imsz = sz(:)'; A.imsz = imsz; % image size if numel(A.imsz)==1, A.imsz = [A.imsz,1]; end if nargin<2, shape = 'circ'; end, A.shape = shape; switch shape case 'zero' sz = prod(imsz)*[2,1]; case 'circ' sz = prod(imsz)*[2,1]; case 'valid' sz = [prod(imsz-[1,0])+prod(imsz-[0,1]), prod(imsz)]; case 'same' sz = prod(imsz)*[2,1]; otherwise error('[matFD2.m] Unknown shape. Choose between ''circ'', ''same'' and ''valid'''); end % A.d is used in diagFAtAFt f1 = fftn([1;-1],imsz); f2 = fftn([1,-1],imsz); A.d = real(fftshift(f1.*conj(f1) + f2.*conj(f2))); if nargin<3, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end A = class(A,mfilename,mat(sz,complex)); glm-ie_v1.4/mat/@matFD2/diagFAtAFt.m0000644000175000017500000000055311646243260014611 0ustar hnhn% 2d finite difference matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function d = diagFAtAFt(A,opt) sz = A.imsz; if strcmp(A.shape,'circ') || (nargin>1 && strcmp(opt,'cheap')) d = A.d; else F = matFFTNmask(ones(sz)); d = real(reshape(diag(F*A'*A*F'),sz)); end glm-ie_v1.4/mat/@matFD2/mvmAA.m0000644000175000017500000000344711701403262013715 0ustar hnhn% base matrix: matrix vector multiplication with A.*conj(A) % Note that (A.*conj(A))*x = diag(A'*diag(x)*A). % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2012 January 05 function y = mvmAA(A,x,ctransp) if nargin<3, ctransp = false; end if ctransp switch A.shape case 'zero' n = prod(A.imsz); x1 = reshape(x(1:n),A.imsz); x2 = reshape(x(n+1:end),A.imsz); y = vertcat(zeros(1,size(x1,2)),x1(1:end-1,:))+x1 ... + horzcat(zeros(size(x1,1),1),x2(:,1:end-1))+x2; case 'circ' n = prod(A.imsz); x1 = reshape(x(1:n),A.imsz); x2 = reshape(x(n+1:end),A.imsz); y = x1([end,1:end-1],:)+x1 ... + x2(:,[end,1:end-1])+x2; case 'valid' sz1 = A.imsz-[1,0]; n1 = prod(sz1); x1 = reshape(x(1:n1),sz1); x2 = reshape(x(n1+1:end),A.imsz-[0,1]); y = [x1(1,:); x1(1:end-1,:)+x1(2:end,:); x1(end,:)] ... + [x2(:,1), x2(:,1:end-1)+x2(:,2:end), x2(:,end)]; case 'same' n = prod(A.imsz); x1 = reshape(x(1:n),A.imsz); x2 = reshape(x(n+1:end),A.imsz); y = [x1(1,:); x1(1:end-1,:)+x1(2:end,:)] ... + [x2(:,1), x2(:,1:end-1)+x2(:,2:end)]; end else x = reshape(x,A.imsz); switch A.shape case 'zero' y = [ vec( vertcat(x(2:end,:),zeros(1,size(x,2)))+x ); vec( horzcat(x(:,2:end),zeros(size(x,1),1))+x ) ]; case 'circ' y = [ vec( x([2:end,1],:)+x ); vec( x(:,[2:end,1])+x ) ]; case 'valid' y = [ vec( x(2:end,:)+x(1:end-1,:) ); vec( x(:,2:end)+x(:,1:end-1) ) ]; case 'same' y = [ vec( [x(2:end,:)+x(1:end-1,:); x(end,:)] ); vec( [x(:,2:end)+x(:,1:end-1), x(:,end)] ) ]; end end function y = vec(x) y = x(:);glm-ie_v1.4/mat/@matFD2/mvm.m0000644000175000017500000000332711701407454013517 0ustar hnhn% 2d finite difference matrix: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function y = mvm(A,x,ctransp) if ctransp switch A.shape case 'zero' n = prod(A.imsz); x1 = reshape(x(1:n),A.imsz); x2 = reshape(x(n+1:end),A.imsz); y = vertcat(zeros(1,size(x1,2)),x1(1:end-1,:))-x1 ... + horzcat(zeros(size(x1,2),1),x2(:,1:end-1))-x2; case 'circ' n = prod(A.imsz); x1 = reshape(x(1:n),A.imsz); x2 = reshape(x(n+1:end),A.imsz); y = x1([end,1:end-1],:)-x1 ... + x2(:,[end,1:end-1])-x2; case 'valid' sz1 = A.imsz-[1,0]; n1 = prod(sz1); x1 = reshape(x(1:n1),sz1); x2 = reshape(x(n1+1:end),A.imsz-[0,1]); y = [-x1(1,:); x1(1:end-1,:)-x1(2:end,:); x1(end,:)] ... + [-x2(:,1), x2(:,1:end-1)-x2(:,2:end), x2(:,end)]; case 'same' n = prod(A.imsz); x1 = reshape(x(1:n),A.imsz); x2 = reshape(x(n+1:end),A.imsz); y = [-x1(1,:); x1(1:end-1,:)-x1(2:end,:)] ... + [-x2(:,1), x2(:,1:end-1)-x2(:,2:end)]; end else x = reshape(x,A.imsz); switch A.shape case 'zero' y = [ vec( vertcat(x(2:end,:),zeros(1,size(x,2)))-x ); vec( horzcat(x(:,2:end),zeros(size(x,1),1))-x ) ]; case 'circ' y = [ vec( x([2:end,1],:)-x ); vec( x(:,[2:end,1])-x ) ]; case 'valid' y = [ vec( x(2:end,:)-x(1:end-1,:) ); vec( x(:,2:end)-x(:,1:end-1) ) ]; case 'same' y = [ vec( [x(2:end,:)-x(1:end-1,:); -x(end,:)] ); vec( [x(:,2:end)-x(:,1:end-1), -x(:,end)] ) ]; end end function y = vec(x) y = x(:);glm-ie_v1.4/mat/cx2re.m0000644000175000017500000000067011512275071012562 0ustar hnhn% transform a complex array into a real array; real and imaginary part are % stored in an interleaved way along the first dimension % % INPUT % a complex array of size [ m,n,..] % % OUTPUT % a real array of size [2*m,n,..] % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function ab = cx2re(z) sz = size(z); sz(1) = 2*sz(1); ab = reshape([real(z(:))'; imag(z(:))'], sz); % two rowsglm-ie_v1.4/mat/@matDiag/0000755000175000017500000000000011755435662013041 5ustar hnhnglm-ie_v1.4/mat/@matDiag/matDiag.m0000644000175000017500000000052311512275070014547 0ustar hnhn% diagonal matrix (analogue to Matlab's diag) % % A = matDiag(a) % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 23 function A = matDiag(a, complex) sz = numel(a)*[1,1]; A.a = a(:); if nargin<2, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end A = class(A,mfilename,mat(sz,complex)); glm-ie_v1.4/mat/@matDiag/diag.m0000644000175000017500000000023211512275070014102 0ustar hnhn% diagonal matrix, return vector of diagonal % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 23 function a = diag(A) a = A.a; glm-ie_v1.4/mat/@matDiag/mvm.m0000644000175000017500000000036111512275070014000 0ustar hnhn% diagonal matrix: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 20 function y = mvm(A,x,ctransp) if ctransp y = conj(A.a(:)) .* x(:); else y = A.a(:) .* x(:); endglm-ie_v1.4/mat/@matFFTmotion/0000755000175000017500000000000011755435662014042 5ustar hnhnglm-ie_v1.4/mat/@matFFTmotion/mvmAtA.m0000644000175000017500000000114211533771557015403 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion: % matrix vector multiplication with A'*A which is symmetric block Toeplitz % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 March 03 function y = mvmAtA(A,x) if any([strfind(lower(A.type),'near'), strfind(lower(A.type),'lin'), ... strfind(lower(A.type),'cub')]) y = mvmAtA(A.RF,x); else y = []; error('Only implemented for types nearest, linear and cubic.'); endglm-ie_v1.4/mat/@matFFTmotion/matFFTmotion.m0000644000175000017500000002234711533470034016561 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion % % A = matFFTmotion(sz,trans,rot,complex,type) % % sz: size of the array; either 2d or 3d % % 2d i.e. numel(sz)=2 % trans: [2,1] or [2,sz(2)], the translation in pixels, default [0;0] % rot: [1,1] or [1,sz(2)], the rotation angle in radian, default 0 % % 3d i.e. numel(sz)=3 % trans: [3,1] or [3,sz(2),sz(3)], the translation in pixels, default [0;0;0] % rot: [3,1] or [3,sz(2),sz(3)], the rotation axis, whose norm equals the % rotation angle in radian, default [0;0;0] % Note that by convention, translation is done after rotation. % Note further that the matrix relies on the fact that the pixels/voxels are % cubes i.e. we have the same resolution along every dimension. % % complex: [1,2] complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % % type: string indicating the nufft interpolation type, % we support 'nearest', 'linear', 'cubic', % 'fessler' and 'ferrara' default 'linear' % 'nearest', 'linear', 'cubic' % We use nearest neighbor, linear or cubic interpolation after oversampling. % One can use type{mex,mat} to indicate whether the mex or the mat option is % chosen in the matResample class. E.g 'cubicmex' is possible. % 'fessler' % Code inspired by Jeff Fessler's nufft library [2], implementing [1]. % The package is very general, we use Kaiser-Bessel windows of size 3. % The matrix is approximated by P*F*diag(d) where d is a (real) scaling % vector, P is a highly sparse (complex) matrix containting interpolation % weights and F is the Fourier transform matrix twice as large as the % original image due to overgridding. % 'ferrara' % Code inspired by Matthew Ferrara's nufft package [4], implementing [3]. % The code uses Gaussian windows which speeds up computations and makes sure % that the nufft and fftn coincide if the points are placed on a grid. % We use overgridding with a factor of 2. % % [1] Jeff Fessler and Brad P. Sutton, Nonuniform fast Fourier transforms using % min-max interpolation, IEEE-SP, 2003, Vol. 51, pp. 560-574. % [2] http://www.eecs.umich.edu/~fessler/irt/irt/nufft/ % [3] Leslie Greengard and June-Yub Lee, Accelerating the nonuniform fast % Fourier transform, SIAM Review, Vol. 46, pp. 443-454. % [4] http://www.mathworks.com/matlabcentral/fileexchange/25135-nufft-nfft-usfft % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 March 02 function A = matFFTmotion(sz, trans, rot, complex, type) %% general info A.ndims = numel(sz); % Are we doing 2d or 3d stuff? if A.ndims<2 || A.ndims>3, error('We support only 2d and 3d.'), end A.imsz = sz; sz = prod(A.imsz)*[1,1]; if nargin<4, complex = 1; end, if numel(complex)==0, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end center = ceil((A.imsz-1)/2)+1; A.center = center; % center in k-space if nargin<5, type = 'linear'; end, A.type = type; % set (default) nufft type %% derivatives A.dkind = 'none'; % kind of derivative, either rot or trans A.di = 0; % which derivative, 0 means all of the respective kind %% rotation % The outcome of the computations below is % 1) a matrix A.RF implementing the Fourier transform followed by a rotation, % which is done by means of a non-uniform Fourier transform with griding % interpolation and oversampling to reduce artefacts; % 2) a bunch of vectors A.k indicating the rotated k-space points, some of % which can be placed outside the image rectangle; % 3) a set of bunches of vectors A.dk containing the perturbed versions of % A.k needed to compute the rotational derivatives; % 4) an array of booleans indicating whether the vectors in A.k are placed % inside the image rectangle. nrot = A.ndims*(A.ndims-1)/2; % number of rotational parameters if nargin<3, rot = zeros(nrot,1); end if numel(rot)nrot % bring into proper shape A.rot = reshape(A.rot,[nrot,prod(A.imsz(2:end))]); end if any(strfind(lower(A.type),'fessler')) ctrans = zeros(A.ndims,size(A.rot,2)); % center translation due to rotation dctrans = zeros(A.ndims,size(A.rot,2),nrot); end sc = A.imsz/A.imsz(1); % correction for A.imsz(1) ~= A.imsz(2:end) k = zeros(A.ndims,prod(A.imsz)); % allocate memory A.dk = repmat(k,[1,1,nrot]); % init with no rotation at all T = size(A.rot,2); % number of different rotations dR = cell(1,nrot); % derivatives of the rotation matrices if A.ndims==2 % construct target grid [i2,i1]=meshgrid(1:A.imsz(2),1:A.imsz(1)); ii=[i1(:)';i2(:)']; clear i1 i2 else [i2,i1,i3] = meshgrid(1:A.imsz(2),1:A.imsz(1),1:A.imsz(3)); ii = [i1(:)'; i2(:)'; i3(:)']; clear i1 i2 i3 end for t = 1:T % loop over scanlines if T==1 i = 1:prod(A.imsz); % all indices at once else i = (t-1)*A.imsz(1) + (1:A.imsz(1)); % indices of individual scanline end [R,dR{:}] = rotmatsc(A.rot(:,t),sc); % rotation matrix and its derivatives k(:,i) = bsxfun(@minus,ii(:,i),center(:)); % centered grid for j=1:nrot, A.dk(:,i,j) = dR{j}'*k(:,i); end % dk/dx grid derivative k(:,i) = R'*k(:,i); % non-integer src grid if any(strfind(lower(A.type),'fessler')) % correction ctrans(:,t) = -diag(sc)*R*diag(1./sc)*A.imsz(:)/2; % off-center-rotation for j=1:nrot dctrans(:,t,j) = -diag(sc)*dR{j}*diag(1./sc)*A.imsz(:)/2; end end end A.k = bsxfun(@times,k,1./A.imsz(:)); A.dk = bsxfun(@times,A.dk,1./A.imsz(:)); A.RF = matFFTnu(A.imsz,A.k',A.type); % Fourier followed by rot, using gridding %% translation % The outcome of the computations below is % 1) a vector A.t implementing the translation; % 2) a set of vectors A.dt needed for the translation derivatives; % 3) a vector A.tc needed to correct for the rotation that is not exactly % done around the center. if nargin<2, trans = zeros(A.ndims,1); end if numel(trans)A.ndims % bring into proper shape A.trans = reshape(A.trans,[A.ndims,A.imsz(2:end)]); end [A.t,A.dt] = trans_diag(A.imsz,A.trans); % diag translation matrix and derivs % compute translational correction for not rotating around the origin if any(strfind(lower(A.type),'fessler')) if numel(ctrans)>A.ndims % bring into proper shape ctrans = reshape(ctrans,[A.ndims,A.imsz(2:end)]); end [A.tc,dtc] = trans_diag(A.imsz,ctrans); % diagonal trans matrix, derivs A.dtc = zeros(numel(A.tc),nrot); dtc = reshape(dtc,[A.imsz,A.ndims]); for j=1:nrot dctrans_j = dctrans(:,:,j).'; if numel(dctrans_j)>A.ndims dctrans_j = reshape(dctrans_j,[1,A.imsz(2:end),A.ndims]); else dctrans_j = reshape(dctrans_j,[ones(1,A.ndims),A.ndims]); end A.dtc(:,j) = reshape(sum(bsxfun(@times,dtc,dctrans_j),A.ndims+1),[],1); end else A.tc = 1; A.dtc = zeros(1,nrot); end %% construct matrix class, inherit from mat A = class(A,mfilename,mat(sz,complex)); % Compute diagonal translation equivalent in Fourier space function [t,dt] = trans_diag(sz,tr) ndims = numel(sz); N = prod(sz); % number of dimensions, number of pixels deriv = nargout>1; % flag saying, whether we compute derivatives t = ones(sz); if deriv, dt = ones(N,ndims); end % allocate memory for d=1:ndims rp = ((1:sz(d))-fix(1+sz(d)/2))/sz(d); % ramp in direction of dimension d rp = -2i*pi*reshape(rp,[ones(1,d-1),sz(d),ones(1,ndims-d)]); erp = exp(bsxfun(@times,rp,tr(d,:,:))); % tr is singleton in dim 1 t = bsxfun(@times, t, erp); if deriv for dd=1:ndims dtdd = bsxfun(@times, reshape(dt(:,dd),sz), erp); if dd==d dtdd = bsxfun(@times, dtdd, rp); end dt(:,dd) = reshape(dtdd,N,1); end end end % Compute scaled rotation matrices and their derivatives function [R,varargout] = rotmatsc(rot,sc) R = diag(1./sc)*rotmat(rot)*diag(sc); % scaled rotation matrix if nargout>1 varargout = cell(nargout-1, 1); % allocate right number of output arguments [varargout{:}] = drotmat(rot); for i=1:nargout-1 varargout{i} = diag(1./sc)*varargout{i}*diag(sc); % scaled derivative end end glm-ie_v1.4/mat/@matFFTmotion/d.m0000644000175000017500000000205311527231266014432 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion: % derivative % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 February 02 function dAi = d(A,kind,i) if nargin<2, kind = 'none'; end % default kind of derivative if nargin<3 % default derivative index i = 0; else dimax = A.ndims; % maximal derivative index if A.ndims==2 && strcmp(A.dkind,'rot'), dimax = 1; end i = fix(i); if i>dimax, error('i is too large.'), end if i<1, error('i is too small.'), end end if strcmp(kind,'rot') || strcmp(kind,'trans') % kind of derivative A.dkind = kind; else error('Select either rot or trans.') end A.di = i; % which derivative, 0 means all of the respective kind dAi = A; % assign outputglm-ie_v1.4/mat/@matFFTmotion/get_k.m0000644000175000017500000000004211674575144015305 0ustar hnhnfunction k = get_k(X) k = X.k; glm-ie_v1.4/mat/@matFFTmotion/mvm.m0000644000175000017500000000542011527714541015011 0ustar hnhn% Two and threedimensional (centered) Fourier transformation % where the input can be subject to rigid body motion: % matrix vector multiplication % % (c) by Hannes Nickisch & Alexander Loktyushin, % MPI for Biological Cybernetics, 2011 February 19 function y = mvm(A,x,ctransp) t = A.t(:).*A.tc(:); % translation if strcmp(A.dkind,'none') if ctransp % translation after after rotation y = A.RF'*( conj(t).*x(:) ); else y = t.*(A.RF*x(:)); % Fourier transform followed by rotation & translation end else if strcmp(A.dkind,'rot') % rotational derivative dy = zeros(prod(A.imsz),A.ndims); % dy / dk if any(strfind(A.type,'lin')) || any(strfind(A.type,'cub')) ... || any(strfind(A.type,'fessler')) if ctransp y = zeros(prod(A.imsz),1); warning('No transpose of rotational derivatives implemented.') else for i=1:A.ndims, dy(:,i) = d(A.RF,i)*x(:); end if A.di==0 % all derivatives y = zeros(prod(A.imsz),size(A.dk,3)); for dd=1:size(A.dk,3) y(:,dd) = t.*reshape(sum(dy.'.*A.dk(:,:,dd),1),[],1); % trans if any(strfind(A.type,'fessler')) y(:,dd) = y(:,dd) + A.dtc(:,dd).*A.t(:).*(A.RF*x(:)); end end else % a single derivative y = t.*sum(dy.'.*A.dk(:,:,A.di),1).'; % translation if any(strfind(A.type,'fessler')) y = y + A.dtc(:,A.di).*A.t(:).*(A.RF*x(:)); end end end else y = zeros(prod(A.imsz),1); warning('Only linear/cubic/fessler rotational derivs implemented.') end else % translational derivative if ctransp y = conj(A.tc(:)) .* x(:); if A.di==0 % all derivatives y = conj(A.dt) .* (y*ones(1,A.ndims)); for dd=1:A.ndims, y(:,dd) = A.RF'*y(:,dd); end else y = A.RF'*( conj(A.dt(:,A.di)).*x(:) ); end else y = A.RF*x(:); % proceed as usual since rotation is not affected if A.di==0 % all derivatives y = A.dt.*repmat(A.tc(:).*y,1,size(A.dt,2)); % center correction else % a particular derivative y = A.dt(:,A.di).*A.tc(:).*y; % center correction end end end endglm-ie_v1.4/mat/@matFFT2line/0000755000175000017500000000000011755435662013546 5ustar hnhnglm-ie_v1.4/mat/@matFFT2line/matFFT2line.m0000644000175000017500000000307611646243203015770 0ustar hnhn% 2d partial FFT matrix (orthonormal) selecting rows: constructor % % A = matFFT2line(imsz,id,complex) % % sz [1,2]: size of the image to transform % id [1,p]: row indices to keep, default id=1:sz(1); the transform is % centered i.e. floor(sz(1)/2+1) is the center line % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % full [1,1]: flag saying whether A*x contains removed indices as zeros or % only the non-removed parts, default false % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function A = matFFT2line(imsz,id,complex,full) A.imsz = imsz; if numel(A.imsz) == 1, A.imsz = A.imsz*[1,1]; end % image size if nargin>1 id(id<1) = 1; id(id>A.imsz(1)) = A.imsz(1); % put into interval A.id = unique(fix(id(:))); % subset of 1..imsz(1), double is ok else A.id = 1:A.imsz(1); end sz = [numel(A.id)*A.imsz(2),prod(A.imsz)]; % matrix size if nargin<3, complex = [1,1]; end % set default if nargin>3, A.full = full; else A.full = false; end if A.full, sz(1) = sz(2); end A = class(A,mfilename,mat(sz,complex)); glm-ie_v1.4/mat/@matFFT2line/diagFAtAFt.m0000644000175000017500000000033011620304263015571 0ustar hnhn% 2d partial FFT matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function d = diagFAtAFt(A,opt) d = false(A.imsz); d(A.id,:) = true; glm-ie_v1.4/mat/@matFFT2line/mvm.m0000644000175000017500000000116711512275071014513 0ustar hnhn% 2d partial FFT matrix selecting rows: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function y = mvm(A,x,ctransp) N = prod(A.imsz); if ctransp if A.full y = reshape(x,A.imsz); else y = zeros(A.imsz); % allocate memory for output y(A.id,:) = reshape(x,[numel(A.id),A.imsz(2)]); end y = ifft2(ifftshift(y))*sqrt(N); else y = fftshift( fft2( reshape(x,A.imsz) )/sqrt(N) ); if A.full zid = true(A.imsz(1),1); zid(A.id) = 0; y(zid,:) = 0; else y = y(A.id,:); end endglm-ie_v1.4/mat/@matWav/0000755000175000017500000000000011755435662012732 5ustar hnhnglm-ie_v1.4/mat/@matWav/matWav.m0000644000175000017500000000321511512275067014340 0ustar hnhn% wavelet transform matrix: constructor % % A = matWav(sz,qmf,nl,complex) % % sz [1,2]: size of the tensor to transform % qmf [1,p]: quadrature mirror filter, default is Haar qmf = [1,1]/sqrt(2) % nl [1,1]: number of layers, default is full nl % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 26 function A = matWav(sz,qmf,nl,complex) imsz = sz(:)'; A.imsz = imsz; % image size if numel(A.imsz)==1, A.imsz = [A.imsz,1]; end sz = prod(imsz)*[1,1]; % matrix size if nargin<4, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end % quadrature mirror filter A.qmf = [1,1]/sqrt(2); % default is Haar if nargin>1, if numel(qmf)>0, A.qmf = qmf; end, end imsz = imsz/2; % compute maximum number of layers for nlmax = 1:max(min(fix(log2(imsz))),1) if any(imsz ~= fix(imsz)), nlmax = nlmax-1; break, end imsz = imsz/2; end A.nl = nlmax; % default is maximum possible if nargin>2, if numel(nl)>0, A.nl = min(fix(nl),nlmax); end, end A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matWav/private/0000755000175000017500000000000011755435662014404 5ustar hnhnglm-ie_v1.4/mat/@matWav/private/fwtn.c0000644000175000017500000000643311512275067015524 0ustar hnhn/* FWTN.C - Periodized Wavelet Transform and its Inverse Transform The wavelet transform is an orthonormal transform i.e. norm(x(:))==norm(y(:)) with linear computational complexity O(numel(x)). The calling syntax is: y = FWTN(x,l,f{,transp}); x data whose size is l times divisable by 2 i.e. size(x) = sz*2^l l number of levels in the pyramid, 0 means FWTN reduces to y=x; f 1d quadrature mirror filter coefficients transp 0 for Fast Wavelet Transform and 1 for Inverse Fast Wavelet Transform, default is 0 y output data of same size (and norm) as input data x Examples for f corresponding to well-known kinds of wavelets [-0.075765714789341, -0.029635527645954, (Symmlet,4) 0.497618667632458, 0.803738751805216, 0.297857795605542, -0.099219543576935, -0.012603967262261, 0.032223100604071] [ 1+sqrt(3), 3+sqrt(3), 3-sqrt(3), 1-sqrt(3) ]/sqrt(32) (Daubechies, 4) [ 1, 1 ]/sqrt(2) (Haar) Written by Hannes Nickisch, 17 Jan 2008 */ #include "wavelet.h" #include "mex.h" #include #include /* Input Arguments */ #define SIG_IN prhs[0] /* X */ #define LEV_IN prhs[1] #define FIL_IN prhs[2] #define TRP_IN prhs[3] /* Output Arguments */ #define SIG_OUT plhs[0] /* Y */ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { double *in, *out, *f, *tmp, *dnl; int i, j, k, nf, d, *n, nl, max; mxArray *temp; int transpose=0; /* Check for proper number of arguments */ if (nrhs < 3) { mexErrMsgTxt("FWTN requires at least 3 input arguments."); } else if (nlhs != 1) { mexErrMsgTxt("FWTN requires one output argument."); } if (nrhs > 3) if(mxGetM(TRP_IN)>0) transpose = (int)mxGetPr(TRP_IN)[0]; /* Analyze input */ d = mxGetNumberOfDimensions(SIG_IN); n = mxMalloc(d*sizeof(int)); memcpy(n, mxGetDimensions(SIG_IN), d*sizeof(int)); if (mxGetM(LEV_IN)*mxGetN(LEV_IN)!=1) mexErrMsgTxt("FWTN requires a suitable numbers of layers"); nl = floor((mxGetPr(LEV_IN))[0]+.5); if(nl<0) mexErrMsgTxt("FWTN requires a suitable numbers of layers"); for(i=0; i #include /* 1d downsampling using high-pass filter * IN: x - vector of (even) length nx * f - high-pass filter of length nf * OUT: y - vector of length nx/2 */ void downhi( double *x, int nx, double *f, int nf, double *y ) { int nx2, nf2, h, i, j; double s; nx2 = nx/2; nf2 = nf/2-1; if(2*nf2+1-(nf-1) < 0) nf2++; for(i=nf2; i nx2) nf2 = nx2; for(i=0; i= nx) --dn2; if(dn2 < 0) dn2 = -1; for(i=0; i<=dn2; i++){ /* Calculate y[0] till y[nx2-nf2-1] */ s = 0.0; for(h=0; h= nx) j -= nx; s += f[h]*x[j]; j++; } y[i] = s; } } /* 1d upsampling using high-pass filter * IN: x - vector of length nx * f - high-pass filter of length nf * OUT: y - vector of length 2*nx */ void uphi(double *x, int nx, double *f, int nf, double *y) { int even, odd, min, h, i, j; double s; even = (nf+1)/2; odd = nf/2; min = nx-even; if(min < 0) min = 0; for(i=0; i+even= nx) j -= nx; s += f[2*h]*x[j]; j++; } y[2*i+1] = s; s = 0.0; j = i; for(h=0; h= nx) j -= nx; s += f[2*h+1]*x[j]; j++; } y[2*i] = s; } } /* 1d upsampling using low-pass filter * IN: x - vector of length nx * f - low-pass filter of length nf * OUT: y - vector of length 2*nx */ void uplo(double *x, int nx, double *f, int nf, double *y) { int even, odd, max, h, i, j; double s; even = (nf+1)/2; odd = nf/2; max = even; if(max > nx) max = nx; for(i=even; i=Nl[dd] && dd=0; l--) { /* Iterate over levels l */ for(d=D-1; d>=0; d--) { /* Iterate over dimensions d */ length = Nl[d]/2; Nl[d] = 1; /* Length of the 1d slice */ tmplo = &tmp[2*length]; tmphi = &tmp[3*length]; tmptop = &tmp[4*length]; /* Temp pointers */ offset=0; for(dd=0; dd=Nl[dd] && dd> cd ~/glm-ie/mat/@matWav/private\n'); fprintf('>> mkoctfile --mex fwtn.c wavelet.c\n'); fprintf('>> delete fwtn.o\n'); fprintf('>> delete wavelet.o\n'); fprintf('>> cd ../../..\n'); fprintf('\n\n END GLM-IE MESSAGE\n\n') fprintf('##############################################################\n'); error end me = mfilename; % what is my filename mydir = which(me); mydir = mydir(1:end-2-numel(me)); % where am I located mycd = pwd; eval(['cd ',mydir]) mex -O fwtn.c wavelet.c clear functions y = fwtn(x,l,f,0); eval(['cd ',mycd]) endglm-ie_v1.4/mat/@matWav/diagFAtAFt.m0000644000175000017500000000031111646243027014764 0ustar hnhn% 2d wavelet transform matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function d = diagFAtAFt(A,opt) d = ones(A.imsz); glm-ie_v1.4/mat/@matWav/mvm.m0000644000175000017500000000075211512275067013703 0ustar hnhn% 2d wavelet transform matrix: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 19 function y = mvm(A,x,ctransp) x = reshape(x,A.imsz); if ctransp if isreal(x) y = fwtn(x,A.nl,A.qmf,1); else y = fwtn(real(x),A.nl,A.qmf,1) + 1i*fwtn(imag(x),A.nl,A.qmf,1); end else if isreal(x) y = fwtn(x, A.nl, A.qmf); else y = fwtn(real(x), A.nl, A.qmf) + 1i*fwtn(imag(x), A.nl, A.qmf); end endglm-ie_v1.4/mat/@matConv2/0000755000175000017500000000000011755435662013164 5ustar hnhnglm-ie_v1.4/mat/@matConv2/diagFAtAFt.m0000644000175000017500000000060211646243146015223 0ustar hnhn% 2d convolution matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function d = diagFAtAFt(A,opt) if strcmp(A.shape,'circ') || (nargin>1 && strcmp(opt,'cheap')) d = abs(A.F); d = fftshift(d.*d); else sz = size(A.F); F = matFFTNmask(ones(sz)); d = real(reshape(diag(F*A'*A*F'),sz)); end glm-ie_v1.4/mat/@matConv2/mvmAA.m0000644000175000017500000000075111701654753014341 0ustar hnhn% base matrix: matrix vector multiplication with A.*conj(A) % Note that (A.*conj(A))*x = diag(A'*diag(x)*A). % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2012 January 06 function y = mvmAA(A,x,ctransp) if strcmp(A.type,'conv') AA = matConv2(A.f.*conj(A.f), A.sx, A.shape, A.type, A.complex); if nargin<3, ctransp = false; end if ctransp y = AA'*x; else y = AA*x; end else error('[%s.m] works for ''conv'' only.', mfilename) endglm-ie_v1.4/mat/@matConv2/matConv2.m0000644000175000017500000000412611701654274015027 0ustar hnhn% matrix object for 2d convolutions in the frequency domain. % % Inputs: % f the left-hand-side of the convolution % sx the size of the right-hand-side of the convolution % shape one of 'circ', 'same' or 'valid' [default 'circ'] % type one of 'conv' or 'corr' [default 'conv'] % % Example of usage: % F = matConv2(f, sx, 'same'); % y = F*x; % same as y = imfilter(x, f, 'same', 'conv'); % % Michael Hirsch * 20/07/2010 % wrapped by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function A = matConv2(f, sx, shape, type, complex) sf = size(f); % size of the psf, not of the matrix if any(sf < sx) && any(sf > sx) error('[%s.m] size missmatch', mfilename) end sF = max(sx, sf); % the bigger one sw = min(sx, sf); % the smaller one if nargin<3, shape = 'circ'; end switch shape case 'circ' sy = sF; case 'valid' sy = sF - sw + 1; case 'same' sy = sF; sF = sx + sf - 1; otherwise error('[matConv2.m] Unknown shape. Choose between ''circ'', ''same'' and ''valid'''); end if nargin<4, type = 'conv'; end switch type case 'conv' case 'corr' f = rot90(f,2); otherwise error('[matConv2.m] Unknown type. Choose between ''conv'' and ''corr'''); end F = fftn(f, sF); % precompute fft of filter sz = [prod(sy), prod(sx)]; % calculate its size % store all stuff in the structure A.shape = shape; % shape of the convolution A.type = type; % conv or corr A.f = f; % PSF A.F = F; % precomputed FFT A.sx = sx; % input dimension A.sy = sy; % output dimension A.sf = sf; % size of the PSF A.sF = sF; % size of the FFT A.sw = sw; % size of the PSF if nargin<5, complex = 1; end A.complex = complex; % just memorise the complex type for later use if numel(complex)==1, complex = complex*[1,1]; end A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matConv2/mvm.m0000644000175000017500000000227711512275067014141 0ustar hnhn% 2d convolution matrix: matrix vector multiplication % % Michael Hirsch * 20/07/2010 % wrapped by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 19 function y = mvm(A,x,ctransp) sx = A.sx; sy = A.sy; sF = A.sF; sw = A.sw; % sizes if ctransp % transposed x = reshape(x,sy); switch A.shape case 'circ' x = circshift(x, floor(sw/2)); case 'same' sw2 = floor(sw/2); xx = zeros(sF); xx(sw2(1)+(1:sy(1)), sw2(2)+(1:sy(2))) = x; x = xx; case 'valid' x = [zeros(sw-1), zeros(sw(1)-1, sy(2)); zeros(sy(1), sw(2)-1), x]; % zero padding end y = ifftn(fftn(x) .* conj(A.F)); y = y(1:sx(1), 1:sx(2)); else % not transposed y = ifftn(fftn(reshape(x,sx),sF) .* A.F); switch A.shape case 'circ' y = circshift(y, -floor(sw/2)); case 'same' sw2 = floor(sw/2); y = y((sw2(1)+1):end, (sw2(2)+1):end); y = y(1:sy(1), 1:sy(2)); case 'valid' y = y(sw(1):end, sw(2):end); end endglm-ie_v1.4/mat/@matFFTNmask/0000755000175000017500000000000011755435662013606 5ustar hnhnglm-ie_v1.4/mat/@matFFTNmask/diagFAtAFt.m0000644000175000017500000000031011646243226015640 0ustar hnhn% n-dimensional partial FFT matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function d = diagFAtAFt(A,opt) d = A.mask; glm-ie_v1.4/mat/@matFFTNmask/matFFTNmask.m0000644000175000017500000000233211512275071016062 0ustar hnhn% n-dimensional partial FFT matrix: constructor % % A = matFFTNmask(mask,complex,full) % % The transform is centered. % % mask [m,n,..]: indices to keep % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % full [1,1]: flag saying whether A*x contains removed indices as zeros or % only the non-removed parts, default false % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 23 function A = matFFTNmask(mask,complex,full) A.mask = logical(mask); A.imsz = size(A.mask); % image size sz = [sum(A.mask(:)),prod(A.imsz)]; % matrix size if nargin<2, complex = [1,1]; end % set default if nargin>2, A.full = full; else A.full = false; end if A.full, sz(1) = sz(2); end A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matFFTNmask/mvm.m0000644000175000017500000000133211512275071014545 0ustar hnhn% n-dimensional partial FFT matrix: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 20 function y = mvm(A,x,ctransp) N = prod(A.imsz); if ctransp if A.full y = reshape(x,A.imsz); else y = zeros(A.imsz); % allocate memory for output y(A.mask) = x; end if numel(A.imsz)<3 y = ifft2(ifftshift(y))*sqrt(N); else y = ifftn(ifftshift(y))*sqrt(N); end else if numel(A.imsz)<3 y = fftshift( fft2( reshape(x,A.imsz) )/sqrt(N) ); else y = fftshift( fftn( reshape(x,A.imsz) )/sqrt(N) ); end if A.full y(~A.mask) = 0; else y = y(A.mask); end endglm-ie_v1.4/mat/@mat/0000755000175000017500000000000011755435662012254 5ustar hnhnglm-ie_v1.4/mat/@mat/disp.m0000644000175000017500000000041211512275067013356 0ustar hnhn% base matrix: display something, relies on size % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 22 function disp(A) str = class(A); if strcmp(str,'mat'), str = [str,'_',A.type]; end fprintf('<%dx%d %s>\n', size(A,1), size(A,2), str);glm-ie_v1.4/mat/@mat/ctranspose.m0000644000175000017500000000026111512275067014602 0ustar hnhn% base matrix: complex conjugate transpose % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function A = ctranspose(A) A.ctransp = xor(A.ctransp,1);glm-ie_v1.4/mat/@mat/imagesc.m0000644000175000017500000000036411512275067014035 0ustar hnhn% base matrix: show as an image, relies on full % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function imagesc(A) Af = full(A); if ~isreal(Af), Af = [real(Af), -imag(Af); imag(Af), real(Af)]; end imagesc(Af)glm-ie_v1.4/mat/@mat/mat.m0000644000175000017500000000260311516606726013210 0ustar hnhn% base matrix: constructor % % sz [1,2]: size of the matrix, sz = [m,n] default [1,1] % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % A1 [m,n]: matrix of size sz, default zeros(m,n) % type string: {'','hcat','prod','scale','sub','sum','vcat'}, default '' % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 04 function A = mat(sz,complex,varargin) if nargin<3 type = 'zero'; args = []; if nargin==0, sz = [1,1]; else if numel(sz)==0, sz = [1,1]; end, end elseif nargin==3 type = 'full'; args = varargin{1}; sz = size(args); else type = varargin{end}; args = varargin(1:end-1); end if nargin<2, complex = 1; else if numel(complex)==0, complex = 1; end, end if numel(complex)==1, complex = complex*[1,1]; end if complex(1)==2, sz(1) = 2*sz(1); end if complex(2)==2, sz(2) = 2*sz(2); end A.args = args; A.type = type; A.sz = sz; A.complex = complex; A.ctransp = 0; A = class(A,'mat');glm-ie_v1.4/mat/@mat/horzcat.m0000644000175000017500000000115511512275067014076 0ustar hnhn% base matrix: horizontal concatenation % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 04 function C = horzcat(varargin) if nargin<2, error('We need at least 2 inputs'), end szs = zeros(nargin,2); for i=1:nargin if ~isa(varargin{i},'mat') && ... ~isnumeric(varargin{i}), error('Wrong type'), end szs(i,:) = size(varargin{i}); varargin{i} = [varargin{i}']; % transposition of arguments end if any(diff(szs(:,1))~=0), error('Matrices need same number of rows'), end C = mat([sum(szs(:,2)),szs(1,1)],1,varargin{:},'hcat')'; % transpositionglm-ie_v1.4/mat/@mat/real.m0000644000175000017500000000023711512275067013347 0ustar hnhn% base matrix: real part of full matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function B = real(A) B = real(full(A));glm-ie_v1.4/mat/@mat/subsref.m0000644000175000017500000000245511516607142014076 0ustar hnhn% base matrix: access elements: relies on size and mtimes % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 23 function Aid = subsref(A,id) if ~strcmp(id.type,'()') error('Cell contents reference from a non-cell array object.') end if all(numel(id.subs)~=[1,2]) error('The object is a 2d matrix.') end if numel(id.subs)==1 % only a single index => returns a full matrix if id.subs{1} == ':' Aid = reshape(full(A),[],1); else m = size(A,1); jj = fix(1+(id.subs{1}-1)/m); % determine the columns ... ii = mod(id.subs{1}-1,m)+1; % ... and the corresponding rows [jju,mm,nn] = unique(jj); % those columns will be computed Ajju=zeros(size(A,1),numel(jju)); ei=zeros(size(A,2),1); for i=1:numel(jju), ei(jju(i))=1; Ajju(:,i)=A*ei; ei(jju(i))=0; end Aid = zeros(size(jj)); % allocate memory for return argument for i=1:numel(jj), Aid(i) = Ajju(ii(i),nn(i)); end end else % two indices => returns a matrix object ii = 1:size(A,1); if ~all(id.subs{1}==':'), ii = ii(id.subs{1}); end jj = 1:size(A,2); if ~all(id.subs{2}==':'), jj = jj(id.subs{2}); end Aid = mat([numel(ii),numel(jj)],1,A,ii,jj,'sub'); endglm-ie_v1.4/mat/@mat/vec.m0000644000175000017500000000026611512275067013203 0ustar hnhn% base matrix: vectorisation % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 29 function v = vec(A) id.type = '()'; id.subs{1} = ':'; v = subsref(A,id);glm-ie_v1.4/mat/@mat/norm.m0000644000175000017500000000023511512275067013375 0ustar hnhn% base matrix: norm of the full matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 15 function y = norm(A) y = norm(full(A));glm-ie_v1.4/mat/@mat/numel.m0000644000175000017500000000034411512275067013543 0ustar hnhn% base matrix: number of elements in matrix: relies on size % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function N = numel(A,varargin) if nargin>1, N=1; return, end [m,n] = size(A); N = n*m;glm-ie_v1.4/mat/@mat/end.m0000644000175000017500000000031011512275067013162 0ustar hnhn% base matrix: return max element, relies on A.sz % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function e = end(A,id,dummy) if id>2 e = 1; else e = size(A,id); endglm-ie_v1.4/mat/@mat/mtimes.m0000644000175000017500000001331511512275067013723 0ustar hnhn% base matrix: mtimes, relies on mvm, A.ctransp and A.complex % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 23 function C = mtimes(A,B) if isa(A,'mat') if isnumeric(B) if numel(B)==1 && size(A,2)>1 % scaled matrix: MATRIX*scalar C = mat(size(A),1,B,A,'scale'); else % MVM: MATRIX*vector % here, we specify, how MVMs are evaluated; in general, our computation % tree has nodes {hcat,prod,scale,sub,sum,vcat} and leaves {full,zero} x = B(:); switch A.type case {'hcat','vcat'} % node: concatenation (horzcat.m, vertcat.m) if A.ctransp y = 0; j = 0; for i=1:length(A.args) si1 = size(A.args{i},1); id = j + (1:si1); y = y + [A.args{i}']*x(id); j = j + si1; end else y = []; for i=1:length(A.args), y = [y; A.args{i}*x]; end end case 'kron' % node: Kronecker product (kron.m) if A.ctransp B = A.args{1}; C = A.args{2}; % kron(B,C)'*vec(x) = C'*x*B sb = size(B); sc = size(C); x = reshape(x,sc(1),sb(1)); Ctxt = zeros(sc(2),sb(1)); for i=1:sb(1), Ctxt(:,i) = [C']*x(:,i); end, Ctxt = Ctxt'; y = zeros(sb(2),sc(2)); for i=1:sc(2), y(:,i) = [B']*Ctxt(:,i); end, y = y'; else B = A.args{1}; C = A.args{2}; % kron(B,C)*vec(x) = C*x*B' sb = size(B); sc = size(C); x = reshape(x,sc(2),sb(2)); Cxt = zeros(sc(1),sb(2)); for i=1:sb(2), Cxt(:,i) = C*x(:,i); end, Cxt = Cxt'; y = zeros(sb(1),sc(1)); for i=1:sc(1), y(:,i) = B*Cxt(:,i); end, y = y'; end case 'prod' % node: product (mtimes.m) if A.ctransp y = [A.args{2}']*([A.args{1}']*x); else y = A.args{1}*(A.args{2}*x); end case 'rep' % node: replication (repmat.m) if A.ctransp C = A.args{1}; sb = A.args{2}; sc = size(C); % kron(ones(r),C)' x = reshape(x,sc(1),sb(1)); Ctx = zeros(sc(2),sb(1)); for i=1:sb(1), Ctx(:,i) = [C']*x(:,i); end y = sum(Ctx,2)*ones(1,sb(2)); else C = A.args{1}; sc = size(C); sb = A.args{2}; % kron(ones(r),C) x = reshape(x,sc(2),sb(2)); Cx = zeros(sc(1),sb(2)); for i=1:sb(2), Cx(:,i) = C*x(:,i); end y = sum(Cx,2)*ones(1,sb(1)); end case 'scale' % node: scalar multiplication (mtimes.m, uminus.m) al = A.args{1}; Amat = A.args{2}; if A.ctransp, y = al*([Amat']*x); else y = al*(Amat*x); end case 'sub' % node: indexing (subsref.m) Amat = A.args{1}; ii = A.args{2}; jj = A.args{3}; if A.ctransp xf = zeros(size(Amat,1),1); xf(ii) = x; yf = [Amat']*xf; y = yf(jj); else xf = zeros(size(Amat,2),1); xf(jj) = x; yf = Amat*xf; y = yf(ii); end case 'sum' % node: sum (minus.m, plus.m) if A.ctransp y = [A.args{1}']*x + [A.args{2}']*x; else y = A.args{1} *x + A.args{2} *x; end case 'full' % leaf: dense matrix if A.ctransp, y = [A.args']*x; else y = A.args*x; end case 'zero' % leaf: matrix-vector-multiplication (mvm.m) if strcmp(class(A),'mat') y = zeros(size(A,1),1); else if numel(x)~=size(A,2), error('Wrong size'), end if A.ctransp, in = 1; out = 2; else in = 2; out = 1; end if A.complex(in)==3 % input is real only x = real(x); elseif A.complex(in)==2 % input represented by IR^2 x = re2cx(x); else % input is complex IC if A.complex(in)~=1, error('Unknown option for complex'), end end y = mvm(A,x,A.ctransp); if A.complex(out)==3 % input is real only y = real(y); elseif A.complex(out)==2 % output represented by IR^2 y = cx2re(y); else % input is complex IC if A.complex(out)~=1, error('Unknown option for complex'), end end end otherwise error('Unknown type.') end C = y(:); end elseif isa(B,'mat') sa = size(A); sb = size(B); sz = [size(A,1),size(B,2)]; if sa(2)~=sb(1), error('Wrong matrix sizes'), end C = mat(sz,1,A,B,'prod'); else error('Wrong argument type.') end elseif isnumeric(A) % B is of type mat if numel(A)==1 && size(B,1)>1 % scaled matrix: scalar*MATRIX C = mat(size(B),1,A,B,'scale'); else % MVM: vector*MATRIX C = [mtimes([B'],A')']; end else error('Wrong argument type.') endglm-ie_v1.4/mat/@mat/diag.m0000644000175000017500000000023611512275067013327 0ustar hnhn% base matrix: diagonal of full matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function B = diag(A) B = diag(full(A));glm-ie_v1.4/mat/@mat/minus.m0000644000175000017500000000034411512275067013556 0ustar hnhn% base matrix: minus % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 23 function C = minus(A,B) sa = size(A); sb = size(B); if any(sa~=sb), error('Wrong matrix sizes'), end C = mat(sa,1,A,-B,'sum');glm-ie_v1.4/mat/@mat/type.m0000644000175000017500000000036411512275067013406 0ustar hnhn% base matrix: type of the matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function str = type(A) str = A.type; if strcmp(str,'zero') str = class(A); if strcmp(str,'mat'), str = 'zero'; end endglm-ie_v1.4/mat/@mat/diagFAtAFt.m0000644000175000017500000000102611646243055014313 0ustar hnhn% base matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 function d = diagFAtAFt(A,opt) if nargin<2, opt=[]; end d = []; if strcmp(type(A),'vcat') d = 0; arg = args(A); for i=1:numel(arg) di = diagFAtAFt(arg{i},opt); if numel(di)>0 d = d + di; else d = []; return end end elseif strcmp(type(A),'scale') arg = args(A); d = arg{1}*arg{1}*diagFAtAFt(arg{2},opt); else d = []; end glm-ie_v1.4/mat/@mat/mvmAA.m0000644000175000017500000000161211701411672013415 0ustar hnhn% base matrix: matrix vector multiplication with A.*conj(A) % Note that (A.*conj(A))*x = diag(A'*diag(x)*A). % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2012 January 05 function y = mvmAA(A,x,ctransp) if nargin<3, ctransp = false; end if ctransp if strcmp(type(A),'vcat') y = zeros(size(A,2),1); arg = args(A); ii = 0; for i=1:numel(arg) j = size(arg{i},1); y = y + vec(mvmAA(arg{i},x(ii+(1:j)),ctransp)); ii = ii+j; end else fA = full(A)'; y = (fA.*conj(fA))*x; end else if strcmp(type(A),'vcat') y = zeros(size(A,1),1); arg = args(A); ii = 0; for i=1:numel(arg) j = size(arg{i},1); y(ii+(1:j)) = mvmAA(arg{i},x,ctransp); ii = ii+j; end else fA = full(A); y = (fA.*conj(fA))*x; end end function y = vec(x) y = x(:);glm-ie_v1.4/mat/@mat/imag.m0000644000175000017500000000024411512275067013337 0ustar hnhn% base matrix: imaginary part of full matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function B = imag(A) B = imag(full(A));glm-ie_v1.4/mat/@mat/isempty.m0000644000175000017500000000027711512275067014122 0ustar hnhn% base matrix: say whether matrix is empty, relies on size % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function y = isempty(A) [m,n] = size(A); y = m*n==0;glm-ie_v1.4/mat/@mat/plus.m0000644000175000017500000000034111512275067013403 0ustar hnhn% base matrix: plus % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 23 function C = plus(A,B) sa = size(A); sb = size(B); if any(sa~=sb), error('Wrong matrix sizes'), end C = mat(sa,1,A,B,'sum');glm-ie_v1.4/mat/@mat/angle.m0000644000175000017500000000023511512275067013510 0ustar hnhn% base matrix: angle of full matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function B = angle(A) B = angle(full(A));glm-ie_v1.4/mat/@mat/kron.m0000644000175000017500000000025611512275067013376 0ustar hnhn% base matrix: Kronecker product % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 29 function C = kron(A,B) C = mat(size(A).*size(B),1,A,B,'kron');glm-ie_v1.4/mat/@mat/repmat.m0000644000175000017500000000036611512275067013717 0ustar hnhn% base matrix: replication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 29 function C = repmat(A,r) r = [1,1].*r(:)'; % make sure, r has two components C = mat(r.*size(A),1,A,r,'rep');glm-ie_v1.4/mat/@mat/args.m0000644000175000017500000000024711512275067013361 0ustar hnhn% base matrix: argument list for composed matrices % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function arg = args(A) arg = A.args;glm-ie_v1.4/mat/@mat/uminus.m0000644000175000017500000000025711512275067013746 0ustar hnhn% base matrix: uminus % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 04 function C = uminus(A) if size(A,1)==1, C = A*(-1); else C = (-1)*A; endglm-ie_v1.4/mat/@mat/vertcat.m0000644000175000017500000000100711512275067014070 0ustar hnhn% base matrix: vertical concatenation % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 04 function C = vertcat(varargin) if nargin<2, error('We need at least 2 inputs'), end szs = zeros(nargin,2); for i=1:nargin if ~isa(varargin{i},'mat') && ... ~isnumeric(varargin{i}), error('Wrong type'), end szs(i,:) = size(varargin{i}); end if any(diff(szs(:,2))~=0), error('Matrices need same number of columns'), end C = mat([sum(szs(:,1)),szs(1,2)],1,varargin{:},'vcat');glm-ie_v1.4/mat/@mat/abs.m0000644000175000017500000000024211512275067013165 0ustar hnhn% base matrix: absolute value of full matrix % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function B = abs(A) B = abs(full(A));glm-ie_v1.4/mat/@mat/get.m0000644000175000017500000000044011526270544013177 0ustar hnhn% base matrix: generic getter % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 February 14 function field = get(A,fieldname) A = struct(A); field = []; if isfield(A,fieldname) eval(['field=A.',fieldname,';']); else error('Field does not exist.') end glm-ie_v1.4/mat/@mat/size.m0000644000175000017500000000077411512275067013404 0ustar hnhn% base matrix: return size, relies on A.sz % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function [sz1,sz2] = size(A,id) sz = A.sz; if A.ctransp, sz = fliplr(sz); end if nargin==1 if nargout==2 sz1 = sz(1); sz2 = sz(2); else sz1 = sz; end elseif nargin==2 if nargout>1, error('too many output arguments'), end if id(1)>numel(sz) sz1 = 1; else sz1 = sz(id); end else error('wrong number of input arguments') endglm-ie_v1.4/mat/@mat/full.m0000644000175000017500000000041511512275067013364 0ustar hnhn% base matrix: convert to full matrix, relies on size and mtimes % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 18 function B = full(A) [m,n] = size(A); B = zeros(m,n); ei = zeros(n,1); for i=1:n, ei(i) = 1; B(:,i) = A*ei; ei(i) = 0; endglm-ie_v1.4/mat/@matFConv2/0000755000175000017500000000000011755435662013272 5ustar hnhnglm-ie_v1.4/mat/@matFConv2/diagFAtAFt.m0000644000175000017500000000053011703615501015321 0ustar hnhn% 2d convolution matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function d = diagFAtAFt(A) if strcmp(A.shape,'circ') d = abs(A.F); d = fftshift(d.*d); else sz = size(A.F); F = matFFTNmask(ones(sz)); d = real(reshape(diag(F*A'*A*F'),sz)); endglm-ie_v1.4/mat/@matFConv2/matFConv2.m0000644000175000017500000000242711703615501015235 0ustar hnhn% FFT-free 2D Convolution % % Inputs: % f the left-hand-side of the convolution % sx the size of the right-hand-side of the convolution % shape one of 'circ', 'same' or 'valid' [default 'circ'] % % Example of usage: % F = matFConv2(f, sx, 'same'); % y = F*x; % same as y = imfilter(x, f, 'same'); % function A = matFConv2(f, sx, shape, complex) sf = size(f); % size of the psf, not of the matrix if any(sf < sx) && any(sf > sx) error('[%s.m] size missmatch', mfilename); end sF = max(sx, sf); % the bigger one sw = min(sx, sf); % the smaller one sy = sF; sF = sx; F = fftshift(fftn(f, sF)); % precompute fft of filter sz = [prod(sy), prod(sx)]; % calculate its size % store all stuff in the structure A.shape = shape; % shape of the convolution A.f = f; % PSF A.F = F; % precomputed FFT A.sx = sx; % input dimension A.sy = sy; % output dimension A.sf = sf; % size of the PSF A.sF = sF; % size of the FFT A.sw = sw; % size of the PSF if nargin<4, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matFConv2/mvm.m0000644000175000017500000000102211703615501014223 0ustar hnhn% 2d convolution matrix: matrix vector multiplication % % Michael Hirsch * 20/07/2010 % wrapped by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 19 function y = mvm(A,x,ctransp) %keyboard; sx = A.sx; sy = A.sy; sF = A.sF; sw = A.sw; % sizes if ctransp % transposed x = reshape(x,sy); y = x .* conj(A.F); else % not transposed y = reshape(x,sx) .* A.F; endglm-ie_v1.4/mat/@matFFT2nu/0000755000175000017500000000000011755435662013241 5ustar hnhnglm-ie_v1.4/mat/@matFFT2nu/matFFT2nu.m0000644000175000017500000001440211512275070015150 0ustar hnhn% Non-uniformly spaced 2d FFT matrix: constructor % % We approximate the matrix A by P*F*diag(d) where d is a (real) scaling vector, % P is a highly sparse (complex) matrix containting interpolation weights and % F is the Fourier transform matrix twice as large as the original image due % to overgridding. % % The implementation is based on Jeffrey Fessler's code: % http://www.eecs.umich.edu/~fessler/irt/irt/nufft/ % % A = matFFT2nu(imsz,k,complex,kbwsz,ogf) % % imsz [1,2]: size of the image to transform % k [m,1]: normalized k-space coordinates i.e. real&imag from[-1,1]/2 % complex [1,2]: complex number treatment A:IN^n->OUT^m, default [1,1] % first number specifies output field OUT^m and the second the % input field IN^m of the matrix A % 1 - real(z) + 1i*imag(z) IC: native complex numbers % 2 - [real(z); imag(z)] IR^2: stacked real numbers % 3 real(z) IR: real part only % kbwsz [1,2]: Kaiser-Bessel interpolation window size, default [3,3] % ogf [1,1]: overgridding factor [default 2] % % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 December 9 function A = matFFT2nu(imsz,k,complex,kbwsz,ogf) if numel(imsz)==1, imsz = imsz*[1,1]; end, A.imsz = imsz; % image size sz = [numel(k),prod(imsz)]; % matrix size if nargin<3, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end if nargin>3, A.kbwsz = max(fix(kbwsz(:)'),3); else A.kbwsz = [3,3]; end if nargin<5, ogf = 2; end % default overgridding factor of 2 A.fftsz = fix(ogf*imsz); [A.d, A.P] = nufft_init(k, A.imsz, A.fftsz, A.kbwsz); % nufft precomputation A = class(A,mfilename,mat(sz,complex)); % Initialize structure for NUFFT using KB interpolator, % particularly the interpolation matrix in sparse format. % caution: this routine can require a lot of memory! % INPUT % k k-space coordinates % imsz image size % OUTPUT % P [M, fftsz] sparse interpolation matrix % d [(imsz)] scaling factors % % Like fft(), the NUFFT expects the signals to be x(0,0), ... % % (c) by Jeff Fessler, The University of Michigan function [d,P] = nufft_init(k, imsz, fftsz, kbwsz) %% 1) (real) scaling factors d: outer product of vectors [d1, alpha{1}] = nufft_scale(imsz(1), kbwsz(1), fftsz(1)); [d2, alpha{2}] = nufft_scale(imsz(2), kbwsz(2), fftsz(2)); d = d1*d2'; %% 2) interpolation coefficient matrix P: huge sparse matrix om = [-imag(k(:)), real(k(:))]; % separate real and imaginary part for id=1:2 N = imsz(id); J = kbwsz(id); K = fftsz(id); al = alpha{id}; % compute matrix T = [C' S S' C]\inv used in NUFFT, independent of frequency L = length(al) - 1; cssc = zeros(J,J); [j1 j2] = ndgrid(1:J, 1:J); for l1 = -L:L for l2 = -L:L alf1 = al(abs(l1)+1); if l1 < 0, alf1 = conj(alf1); end alf2 = al(abs(l2)+1); if l2 < 0, alf2 = conj(alf2); end tmp = j2 - j1 + l1 - l2; tmp = nufft_sinc(tmp/(K/N)); cssc = cssc + alf1 * conj(alf2) * tmp; end end T = inv(cssc); % compute NUFFT r vector M = length(om(:,id)); % offset for NUFFT if mod(J,2) % odd J koff = round(K*om(:,id)) - (J+1)/2; else % even J koff = floor(K*om(:,id)) - J/2; end dk = K*om(:,id) - koff; arg = outer_sum(-(1:J)', dk'); r = zeros(J,M); for l1 = -L:L alf = al(abs(l1)+1); if l1<0, alf = conj(alf); end r1 = nufft_sinc( (arg+l1)/(K/N) ); r = r + alf * r1; end ud{id} = exp(2i*pi*(N-1)/(2*K) * arg) .* (T*r); % linear phase % indices into oversampled FFT components kd{id} = mod(outer_sum((1:J)', koff'), K) + 1; if id > 1 % trick: pre-convert these indices into offsets! kd{id} = (kd{id}-1) * prod(fftsz(1:(id-1))); end end % build sparse matrix with entries per frequency point kk = kd{1}; uu = ud{1}; kk = block_outer_sum(kk, kd{2}); % outer sum of indices kk = reshape(kk, prod(kbwsz), M); uu = block_outer_prod(uu, ud{2}); % outer product of coefficients uu = reshape(uu, prod(kbwsz), M); mm = (1:M); mm = mm(ones(prod(kbwsz),1),:); % pre-do transpose P = sparse(mm(:), kk(:), conj(uu(:)), M, prod(fftsz)); % sparse matrix % scaling factors for 1D NUFFT (from Fourier series coefficients) function [d,al] = nufft_scale(N, J, K) % real out % Compute scaling factors using the "do no harm" strategy. ssn = 1 ./ kaiser_bessel_ft( J, (1/2-N/2:N/2-1/2)'/K ); % use regression to match NUFFT with best Kaiser scalings nn = -(N-1)/2:(N-1)/2; L = min(ceil(N/3),13); X = cos(2*pi*nn'*(0:L)/K); al = (X \ ssn)'; al(2:end) = al(2:end)/2; % LS regress L = length(al)-1; d = exp( 1i*2*pi/K * nn'*(-L:L) ) * [fliplr(al(2:end)),al]'; d = real(d); % generalized Kaiser-Bessel function for x in support [-J/2,J/2] function [alpha,kb] = kaiser_bessel(J,x) % real in real out o2 = [1 1]; % hardwired, because it was nearly the best zn = [2.5 2.27 2.31 2.34 2.32*o2 2.35 2.34*o2 2.35 2.34 2.35*[1 1 1] 2.33]'; alpha = J*zn(J==(2:16)'); if nargout>1 && nargin>1 ii = abs(x) < J/2; f = sqrt(1 - (x(ii)/(J/2)).^2); kb = zeros(size(x)); kb(ii) = real( besseli(0, alpha*f) / besseli(0,alpha) ); end % Fourier transform of generalized Kaiser-Bessel function function y = kaiser_bessel_ft(J, x) % real in real out alpha = kaiser_bessel(J); z = sqrt( (2*pi*(J/2)*x).^2 - alpha^2 ); y = real( sqrt(2*pi)*J/2 * besselj(1/2,z) ./ besseli(0,alpha) ./ sqrt(z) ); % sinc function y = nufft_sinc(x) iz = find(x == 0); x(iz) = 1; y = sin(pi*x) ./ (pi*x); y(iz) = 1; function y = block_outer_sum(x1, x2) x1 = reshape(x1, size(x1,1), 1, []); x2 = reshape(x2, 1, size(x2,1), []); y = x1(:,ones(size(x2,2),1),:) + x2(ones(size(x1,1),1),:,:); function y = block_outer_prod(x1, x2) x1 = reshape(x1, size(x1,1), 1, []); x2 = reshape(x2, 1, size(x2,1), []); y = x1(:,ones(size(x2,2),1),:) .* x2(ones(size(x1,1),1),:,:); function s = outer_sum(x,y) x = x(:); y = y(:)'; s = x(:, ones(numel(y),1)) + y(ones(numel(x),1),:);glm-ie_v1.4/mat/@matFFT2nu/mvm.m0000644000175000017500000000142411521037315014177 0ustar hnhn% Non-uniformly spaced 2d FFT matrix: matrix vector multiplication % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 17 function y = mvm(A,x,ctransp) N = prod(A.imsz); if ctransp Ptx = reshape(full(A.P'*x), A.fftsz); % apply sparse interpolation matrix P y = prod(A.fftsz)/sqrt(N) * ifft2(Ptx); % apply oversampled fft y = y(1:A.imsz(1),1:A.imsz(2),:); % eliminate zero padding y = conj(A.d) .* y; % apply diagonal scaling matrix D else Sx = A.d .* reshape(x,A.imsz); % apply diagonal scaling matrix D FSx = fft2(Sx,A.fftsz(1),A.fftsz(2))/sqrt(N); % apply oversampled fft y = A.P*FSx(:); % apply sparse interpolation matrix P endglm-ie_v1.4/mat/@matEye/0000755000175000017500000000000011755435662012717 5ustar hnhnglm-ie_v1.4/mat/@matEye/matEye.m0000644000175000017500000000054111754255277014322 0ustar hnhn% Identity matrix example function A = matEye(n,m, par, complex) sz = [n,m]; % size of the matrix if nargin<3, A.par = ''; else A.par = par; end % additional parameters if nargin<4, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matEye/mvm.m0000644000175000017500000000102111754255271013661 0ustar hnhn% Identity matrix example function y = mvm(A,x,ctransp) sz = size(A); % size p = A.par; % additional parameter if ctransp % transposed fprintf('We did an MVM with eye(%d,%d)'' par=%s.\n',sz,p) y = x; else % not transposed fprintf('We did an MVM with eye(%d,%d) par=%s.\n',sz,p) y = x; endglm-ie_v1.4/mat/re2cx.m0000644000175000017500000000064711512275071012566 0ustar hnhn% transform a real array into a complex array; real and imaginary part are % assumed to be stored in an interleaved way along the first dimension % % INPUT % a real array of size [2*m,n,..] % % OUTPUT % a complex array of size [ m,n,..] % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 10 function z = re2cx(ab) sz = size(ab); sz(1) = sz(1)/2; z = reshape(ab(1:2:end) + 1i*ab(2:2:end), sz); glm-ie_v1.4/mat/matResample.m0000644000175000017500000000671011674575145014030 0ustar hnhn% Resampling matrix % % Signal resampling in 2d and 3d. % % A = matResample(sz,x,g,method,deriv) % sz size of the image % x new coordinates % method is the interpolation method nearest, linear, cubic [default nearest] % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 February 08 function W = matResample(sz,x,method,deriv) ndims = numel(sz); if ndims==2 [i2,i1]=meshgrid(1:sz(2),1:sz(1)); i1=i1(:)'; i2=i2(:)'; % target grid else [i2,i1,i3] = meshgrid(1:sz(2),1:sz(1),1:sz(3)); i1=i1(:)'; i2=i2(:)'; i3=i3(:)'; end if nargin<3, method = 'nearest'; end % set default values if nargin<4, deriv = 0; end if strfind(lower(method),'lin') % set window functions nn = 0:1; k = @(x) klin(x); dk = @(x) dklin(x); elseif strfind(lower(method),'cub') nn = -1:2; k = @(x) kcub(x); dk = @(x) dkcub(x); else nn = 0:1; k = @(x) knea(x); dk = @(x) dknea(x); end N = prod(sz); M = size(x,2); W = sparse(M,N); % interpolation weight matrix for n1 = nn, j1 = floor(x(1,:))+n1; % linear interpolation from source for n2 = nn, j2 = floor(x(2,:))+n2; % .. neighbours; iterate over those if ndims==2 ok = 02) = 0; function y = klin(x) y = max(1-abs(x),0); function y = dklin(x) y = -sign(x); y(abs(x)>1) = 0; function y = knea(x) y = zeros(size(x)); y(abs(x)<=1/2) = 1; function y = dknea(x) y = zeros(size(x));glm-ie_v1.4/mat/make.m0000644000175000017500000000222311527231266012454 0ustar hnhn% compilation script of the glm-ie package % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 February 17 function make(str) me = mfilename; % what is my filename mydir = which(me); mydir = mydir(1:end-2-numel(me)); % where am I located cd(mydir) % go to correct location if nargin==0 % compile cd @matNoise2/private mex -O realnoiselet.c cd(mydir) cd @matResample/private mex -O resample_mex.c CFLAGS="\$CFLAGS -fopenmp" LDFLAGS="\$LDFLAGS -fopenmp" cd(mydir) cd @matFFTnu/private mex -O FGG_Convolution2D.c mex -O FGG_Convolution3D.c mex -O FGG_Convolution2D_type2.c mex -O FGG_Convolution3D_type2.c cd(mydir) cd @matWav/private mex -O fwtn.c wavelet.c cd(mydir) else % remove ALL mex files if strcmp('clean',str) !rm -f @matNoise2/private/realnoiselet.mex* !rm -f @matResample/private/resample_mex.mex* !rm -f @matFFTnu/private/FGG_Convolution*D*.mex* !rm -f @matWav/private/fwtn.mex* end endglm-ie_v1.4/mat/@matFConv3/0000755000175000017500000000000011755435662013273 5ustar hnhnglm-ie_v1.4/mat/@matFConv3/matFConv3.m0000644000175000017500000000242711703615501015237 0ustar hnhn% FFT-free 3D Convolution % % Inputs: % f the left-hand-side of the convolution % sx the size of the right-hand-side of the convolution % shape one of 'circ', 'same' or 'valid' [default 'circ'] % % Example of usage: % F = matFConv3(f, sx, 'same'); % y = F*x; % same as y = imfilter(x, f, 'same'); % function A = matFConv3(f, sx, shape, complex) sf = size(f); % size of the psf, not of the matrix if any(sf < sx) && any(sf > sx) error('[%s.m] size missmatch', mfilename); end sF = max(sx, sf); % the bigger one sw = min(sx, sf); % the smaller one sy = sF; sF = sx; F = fftshift(fftn(f, sF)); % precompute fft of filter sz = [prod(sy), prod(sx)]; % calculate its size % store all stuff in the structure A.shape = shape; % shape of the convolution A.f = f; % PSF A.F = F; % precomputed FFT A.sx = sx; % input dimension A.sy = sy; % output dimension A.sf = sf; % size of the PSF A.sF = sF; % size of the FFT A.sw = sw; % size of the PSF if nargin<4, complex = 1; end if numel(complex)==1, complex = complex*[1,1]; end A = class(A,mfilename,mat(sz,complex));glm-ie_v1.4/mat/@matFConv3/diagFAtAFt.m0000644000175000017500000000053011703615501015322 0ustar hnhn% 2d convolution matrix: (real) diagonal in Fourier space of A'*A % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 12 function d = diagFAtAFt(A) if strcmp(A.shape,'circ') d = abs(A.F); d = fftshift(d.*d); else sz = size(A.F); F = matFFTNmask(ones(sz)); d = real(reshape(diag(F*A'*A*F'),sz)); endglm-ie_v1.4/mat/@matFConv3/mvm.m0000644000175000017500000000101111703615501014222 0ustar hnhn% 2d convolution matrix: matrix vector multiplication % % Michael Hirsch * 20/07/2010 % wrapped by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 19 function y = mvm(A,x,ctransp) sx = A.sx; sy = A.sy; sF = A.sF; sw = A.sw; % sizes if ctransp % transposed x = reshape(x,sy); y = x .* conj(A.F); else % not transposed y = reshape(x,sx) .* A.F; endglm-ie_v1.4/pls/0000755000175000017500000000000011755435662011410 5ustar hnhnglm-ie_v1.4/pls/plsTN.m0000644000175000017500000000607511466026135012624 0ustar hnhn% Penalised least squares solved by TRUNCATED NEWTON % i.e. Newton steps approximated by conjugate gradients % % [u,phi] = plsTN(u,X,y,B,opt,lam,pen,varargin) % % Additional options: % opt. % nit: maximum number of Newton steps [default 15] % we have nMVM/nit MVMs to approximate the Newton dir. by CG % nline: max. bisection steps in Brent's line search [default 10] % exactNewt: flag indicating whether we want to compute the Newton % direction exactly instead of CG [default false] % this works only if B=1 and X is numeric % % See also PLSSOLVERS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 07 function [u,phi] = plsTN(u,X,y,B,opt,lam,pen,varargin) % optimisation parameters if isfield(opt,'nMVM') % maximum number of MVMs with A nMVM = opt.nMVM; else nMVM = 100; end if isfield(opt,'nit') % maximum number of Newton steps nit = opt.nit; else nit = 15; end ncg = max(fix(nMVM/nit),1); % maximum number of CG steps for Newton direction if isfield(opt,'nline') % max. bisection steps in Brent's line search nline = opt.nline; else nline = 10; end if isfield(opt,'exactNewt') % Do we want to compute the Newton dir. exactly? exactNewt = opt.exactNewt; else exactNewt = false; end % information parameters if isfield(opt,'output') % flag saying whether some output is shown output = opt.output; else output = false; end n = numel(u); if output, if exist('fflush','builtin'), fflush(stdout); end, end for i=1:nit s = B*u; r = X*u-y; % sparse coeffs, residuals [h,dh,d2h] = feval(pen,s,varargin{:}); g = [X']*r/lam+[B']*dh; if exactNewt woodbury = isnumeric(B) && numel(B)==1 && isnumeric(X); if woodbury, woodbury = woodbury && B==1; end % Is Woodbury possible? if woodbury % compute Newton direction by exploiting the Woodbury formula d = -H\g; d = linsolve_woodbury( X, 1/lam, d2h, -g ); else % compute Newton direction by full matrices d = linsolve_full( X, 1/lam, B, d2h, -g); end else % compute Newton direction by LCG: d = -H\g; % gradient g = X'*(X*u-y)/lam + B'*dh; % Hessian H = X'*X/lam + B'*diag(d2h)*B; % A = X'*R*X + B'*diag(pi)*B, R = eye(m)/lam, P = diag(d2h) d = linsolve_lcg( X, 1/lam, B, d2h, -g,min(ncg,n+1)); end % line search along Newton direction d, stepsize t Phi = @(t,r,X_d,s,B_d,lam,varargin) ... norm(r+t*X_d)^2/lam + 2*sum(feval(pen,s+t*B_d,varargin{:})); [t,phi] = brentmin(0,2,nline,1e-8,Phi,r,X*d,s,B*d,lam,varargin{:}); % t=[0,2] % update estimate u = u+t*d; du = t*norm(d)/max(norm(u),1e-9); if output fprintf('%5i, phi=%4.4e; du=%1.3e\r', i, phi, du ) if exist('fflush','builtin'), fflush(stdout); end end if du1e-10 [y,G] = feval(f,rewrap(strctX,X),varargin{3:end}); else y = minimize_lbfgs_objective(minimize_lbfgs_iteration_number); G = minimize_lbfgs_gradient; end % memorise gradient and position minimize_lbfgs_gradient = G; minimize_lbfgs_X = X; G = unwrap(G); % Extract the numerical values from "s" into the column vector "v". The % variable "s" can be of any type, including struct and cell array. % Non-numerical elements are ignored. See also the reverse rewrap.m. function v = unwrap(s) v = []; if isnumeric(s) v = s(:); % numeric values are recast to column vector elseif isstruct(s) v = unwrap(struct2cell(orderfields(s)));% alphabetize, conv to cell, recurse elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially v = [v; unwrap(s{i})]; end end % other types are ignored % Map the numerical elements in the vector "v" onto the variables "s" which can % be of any type. The number of numerical elements must match; on exit "v" % should be empty. Non-numerical entries are just copied. See also unwrap.m. function [s v] = rewrap(s, v) if isnumeric(s) if numel(v) < numel(s) error('The vector for conversion contains too few elements') end s = reshape(v(1:numel(s)), size(s)); % numeric values are reshaped v = v(numel(s)+1:end); % remaining arguments passed on elseif isstruct(s) [s p] = orderfields(s); p(p) = 1:numel(p); % alphabetize, store ordering [t v] = rewrap(struct2cell(s), v); % convert to cell, recurse s = orderfields(cell2struct(t,fieldnames(s),1),p); % conv to struct, reorder elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially [s{i} v] = rewrap(s{i}, v); end end % other types are not processed glm-ie_v1.4/pls/plsBB.m0000644000175000017500000000523511646247775012602 0ustar hnhn% Penalised least squares by Barzilai/Borwein stepsize gradient descent [1] % % [u,phi] = plsBB(u,X,y,B,opt,lam,pen,varargin) % % See also PLSSOLVERS.M. % % opt. optimisation parameters % eps_grad gradient norm convergence threshold [default 1e-10] % plsBBstepsizetype flag saying which stepsize rule to use [default 1] % 1: a = (du'*dg)/(dg'*dg) => eq. (5) in [1] % else: a = (du'*du)/(du'*dg) => eq. (6) in [1] % % The optimiser is purely gradient based; it does not use the objective % function values for line searches etc. % Further, the solver is not guaranteed to decrease the objective in every % step. The solver has very good empirical behavior for high-dimensional % optimisation problems such as l1-regularised least squares. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 % % [1] Jonathan Barzilai and Jonathan M. Borwein, Two-Point Step Size Gradient % Methods, IMA Journal of Numerical Analysis (1988) 8, 141-148 function [u,phi] = plsBB(u,X,y,B,opt,lam,pen,varargin) % optimisation parameters if isfield(opt,'eps_grad') % gradient norm convergence threshold eps_grad = opt.eps_grad; else eps_grad = 1e-10; end if isfield(opt,'nMVM') % maximal number of steps nMVM = opt.nMVM; else nMVM = 100; end if isfield(opt,'plsBBstepsizetype') % type of step size plsBBstepsizetype = opt.plsBBstepsizetype; else plsBBstepsizetype = 1; end % information parameters if isfield(opt,'output') % flag saying whether some output is shown output = opt.output; else output = false; end if output, if exist('fflush','builtin'), fflush(stdout); end, end for n=1:nMVM [f,g] = feval('phi',u,X,y,B,lam,pen,varargin{:}); if n==1 uold = randn(size(u))/1e2; % draw a virtual initial location [fold,gold] = feval('phi',uold,X,y,B,lam,pen,varargin{:}); if fold2, cmax = cmax*be; end, if nl<1, cmax = cmax/be; end if nl==nline, warning(1,'Max line search; operator bug?'); return, end u = u + c*du; % update [g1,Xu,Bu] = gradPhi(u,X,y,B,varargin{:}); % Fletcher-Reeves CG update bk = g1(:)'*g1(:)/( g0(:)'*g0(:)+eps ); g0 = g1; du = bk*du-g1; if output fprintf('%5i, phi=%4.4e; du=%1.3e\r', n, f1, c*norm(du)/max(norm(u),1e-9) ) if exist('fflush','builtin'), fflush(stdout); end end if norm(du(:)) < eps_grad, break, end % stopping criterion end phi = f1; if output, fprintf('\n'); if exist('fflush','builtin'), fflush(stdout); end, end function phi = Phi(Xu,Xdu,y,Bu,Bdu,c,lam,pen,varargin) % objective Phi(u+c*du) s = Bu+c*Bdu; r = Xu+c*Xdu - y; h = feval(pen,s,varargin{:}); phi = (r'*r)/lam + 2*sum(h); function [g,Xu,Bu] = gradPhi(u,X,y,B,lam,pen,varargin) % gradient of objective Bu = B*u; Xu = X*u; r = Xu-y; [h,dh] = feval(pen,Bu,varargin{:}); g = 2*([X']*r + lam*([B']*dh));glm-ie_v1.4/pls/prox.m0000644000175000017500000000653011472522302012542 0ustar hnhn% [s,f] = PROX(r,lam,pen,varargin) % % PROX - Proximity operator minimising the decoupling criterion f(s) using a % Newton algorithm % % f(s) = (s-r).^2/2 + lam*pen(s) % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 22 function [s,f] = prox(r,lam,pen,varargin) if ischar(pen) penstr = pen; else penstr = func2str(pen); if numel(strfind(penstr,'@'))>0 penstr = penstr(1+min(strfind(penstr,')')):max(strfind(penstr,'('))-1); end end if numel(varargin)>0 && strcmp('newton',varargin{end}) penstr = ''; varargin = varargin(1:end-1); end if strcmp(penstr,'penAbs') % analytical solution whenever possible s = max(abs(r)-lam,0).*sign(r); if nargout>1, f = (s-r).^2/2 + lam*abs(s); end elseif strcmp(penstr,'penQuad') s = r/(1+lam); if nargout>1, f = (s-r).^2/2 + (lam/2)*(s.*s); end elseif strcmp(penstr,'penZero') s = r; if nargout>1, f = (s-r).^2/2; end elseif strcmp(penstr,'penVB') && numel(varargin)==3 ... && strcmp(varargin{1},'potLaplace') tau = lam.*varargin{2}; z = varargin{3}; % solve the quartic: x.^4 + a.*x.^3 + b.*x.^2 + c.*x + d = 0 a = 2*tau; b = tau.*tau - z - r.*r; c = -2*tau.*z; d = -z.*tau.*tau; X = solve_quartic(a,b,c,d); % x = sqrt(s*s+z) needs to be real and larger than sqrt(z) x = X( abs(imag(X))<1e-10 & real(X) > sqrt(z)); s = sign(r).*sqrt(x.*x-z); if nargout>1, f = (s-r).^2/2 + tau*sqrt(s.*s + z); end else args = {lam,pen,varargin{:}}; % arguments to fun nit = 15; nline = 15; % #Newton loops, #line searches s = newton(r/2,r,nit,nline,@fun,args{:}); if nargout>1, f = fun(s,r,args{:}); end end function varargout = fun(s,r,lam,pen,varargin) % f(s) = (s-r)^2/2 + lam*pen(s) varargout = cell(nargout, 1); % allocate the right number of output arguments [varargout{:}] = feval(pen,s,varargin{:}); varargout{1} = lam*varargout{1} + (s-r).*(s-r)/2; if nargout>1 varargout{2} = lam*varargout{2} + (s-r); if nargout>2 varargout{3} = lam*varargout{3} + 1; end end function s = newton(s,r,nit,nline,fun,varargin) q = numel(s); ncv = true(q,1); % not converged flag i = 0; % init loop th = (r.*r)/1e8; % convergence threshold while if0; % indices for which the objective did increase oiq = false(q,1); oiq(ncv) = oi; % oi expanded to length q j = 0; al = ones(q,1); % stepsizes while jf0; oiq = false(q,1); oiq(ncv) = oi; j = j+1; end s(ncv) = s(ncv) + al(ncv).*d; % final Newton step for not converged f = fun(s(ncv),r(ncv),varargin{:}); cv = f0-f0, S='Linesearch'; else S=''; end i = 0; % zero the run length counter ls_failed = 0; % no previous line search has failed [f0 df0] = feval(f, X, varargin{:}); % get function value and gradient Z = X; X = unwrap(X); df0 = unwrap(df0); if exist('fflush','builtin'), fflush(stdout); end fX = f0; i = i + (length<0); % count epochs?! s = -df0; d0 = -s'*s; % initial search direction (steepest) and slope x3 = red/(1-d0); % initial step is red/(|s|+1) while i < abs(length) % while not finished i = i + (length>0); % count iterations?! X0 = X; F0 = f0; dF0 = df0; % make a copy of current values if length>0, M = MAX; else M = min(MAX, -length-i); end while 1 % keep extrapolating as long as necessary x2 = 0; f2 = f0; d2 = d0; f3 = f0; df3 = df0; success = 0; while ~success && M > 0 try M = M - 1; i = i + (length<0); % count epochs?! [f3 df3] = feval(f, rewrap(Z,X+x3*s), varargin{:}); df3 = unwrap(df3); if isnan(f3) || isinf(f3) || any(isnan(df3)+isinf(df3)), error(''), end success = 1; catch % catch any error which occured in f x3 = (x2+x3)/2; % bisect and try again end end if f3 < F0, X0 = X+x3*s; F0 = f3; dF0 = df3; end % keep best values d3 = df3'*s; % new slope if d3 > SIG*d0 || f3 > f0+x3*RHO*d0 || M == 0 % are we done extrapolating? break end x1 = x2; f1 = f2; d1 = d2; % move point 2 to point 1 x2 = x3; f2 = f3; d2 = d3; % move point 3 to point 2 A = 6*(f1-f2)+3*(d2+d1)*(x2-x1); % make cubic extrapolation B = 3*(f2-f1)-(2*d1+d2)*(x2-x1); x3 = x1-d1*(x2-x1)^2/(B+sqrt(B*B-A*d1*(x2-x1))); % num. error possible, ok! if ~isreal(x3) || isnan(x3) || isinf(x3) || x3 < 0 % num prob | wrong sign? x3 = x2*EXT; % extrapolate maximum amount elseif x3 > x2*EXT % new point beyond extrapolation limit? x3 = x2*EXT; % extrapolate maximum amount elseif x3 < x2+INT*(x2-x1) % new point too close to previous point? x3 = x2+INT*(x2-x1); end end % end extrapolation while (abs(d3) > -SIG*d0 || f3 > f0+x3*RHO*d0) && M > 0 % keep interpolating if d3 > 0 || f3 > f0+x3*RHO*d0 % choose subinterval x4 = x3; f4 = f3; d4 = d3; % move point 3 to point 4 else x2 = x3; f2 = f3; d2 = d3; % move point 3 to point 2 end if f4 > f0 x3 = x2-(0.5*d2*(x4-x2)^2)/(f4-f2-d2*(x4-x2)); % quadratic interpolation else A = 6*(f2-f4)/(x4-x2)+3*(d4+d2); % cubic interpolation B = 3*(f4-f2)-(2*d2+d4)*(x4-x2); x3 = x2+(sqrt(B*B-A*d2*(x4-x2)^2)-B)/A; % num. error possible, ok! end if isnan(x3) || isinf(x3) x3 = (x2+x4)/2; % if we had a numerical problem then bisect end x3 = max(min(x3, x4-INT*(x4-x2)),x2+INT*(x4-x2)); % don't accept too close [f3 df3] = feval(f, rewrap(Z,X+x3*s), varargin{:}); df3 = unwrap(df3); if f3 < F0, X0 = X+x3*s; F0 = f3; dF0 = df3; end % keep best values M = M - 1; i = i + (length<0); % count epochs?! d3 = df3'*s; % new slope end % end interpolation if abs(d3) < -SIG*d0 && f3 < f0+x3*RHO*d0 % if line search succeeded X = X+x3*s; f0 = f3; fX = [fX' f0]'; % update variables fprintf('%s%5i, phi=%4.4e; du=%1.3e\r', S, i, f0, ... norm(x3*s)/max(norm(X),1e-9)); if exist('fflush','builtin'), fflush(stdout); end s = (df3'*df3-df0'*df3)/(df0'*df0)*s - df3; % Polack-Ribiere CG direction df0 = df3; % swap derivatives d3 = d0; d0 = df0'*s; if d0 > 0 % new slope must be negative s = -df0; d0 = -s'*s; % otherwise use steepest direction end x3 = x3 * min(RATIO, d3/(d0-realmin)); % slope ratio but max RATIO ls_failed = 0; % this line search did not fail else X = X0; f0 = F0; df0 = dF0; % restore best point so far if ls_failed || i > abs(length) % line search failed twice in a row break; % or we ran out of time, so we give up end s = -df0; d0 = -s'*s; % try steepest x3 = 1/(1-d0); ls_failed = 1; % this line search failed end end X = rewrap(Z,X); fprintf('\n'); if exist('fflush','builtin') fflush(stdout); end % Extract the numerical values from "s" into the column vector "v". The % variable "s" can be of any type, including struct and cell array. % Non-numerical elements are ignored. See also the reverse rewrap.m. function v = unwrap(s) v = []; if isnumeric(s) v = s(:); % numeric values are recast to column vector elseif isstruct(s) v = unwrap(struct2cell(orderfields(s))); % alphabetize, conv to cell, recurse elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially v = [v; unwrap(s{i})]; end end % other types are ignored % Map the numerical elements in the vector "v" onto the variables "s" which can % be of any type. The number of numerical elements must match; on exit "v" % should be empty. Non-numerical entries are just copied. See also unwrap.m. function [s v] = rewrap(s, v) if isnumeric(s) if numel(v) < numel(s) error('The vector for conversion contains too few elements') end s = reshape(v(1:numel(s)), size(s)); % numeric values are reshaped v = v(numel(s)+1:end); % remaining arguments passed on elseif isstruct(s) [s p] = orderfields(s); p(p) = 1:numel(p); % alphabetize, store ordering [t v] = rewrap(struct2cell(s), v); % convert to cell, recurse s = orderfields(cell2struct(t,fieldnames(s),1),p); % conv to struct, reorder elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially [s{i} v] = rewrap(s{i}, v); end end % other types are not processed glm-ie_v1.4/pls/plsLBFGS.m0000644000175000017500000000345011646243640013134 0ustar hnhn% Penalised least squares solved by the LIMITED memory % BROYDEN-FLETCHER-GOLDFARB-SHANNO (L-BFGS) algorithm which is a quasi Newton or % variable metric method. % We use Peter Carbonetto's "Matlab interface for L-BFGS-B" [1]. % % [u,phi] = plsTN(u,X,y,B,opt,lam,pen,varargin) % % Additional options: % opt. % nonneg: enforce positive u [default false] % % See also PLSSOLVERS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 % % [1] http://www.cs.ubc.ca/~pcarbo/lbfgsb-for-matlab.html function [u,phi] = plsLBFGS(u,X,y,B,opt,lam,pen,varargin) % optimisation parameters if isfield(opt,'nMVM') % maximal number of steps nMVM = opt.nMVM; else nMVM = 100; end if isfield(opt,'LBFGSnonneg') % nonnegativity desired? nonneg = opt.LBFGSnonneg; else nonneg = false; end % information parameters if isfield(opt,'output') % flag saying whether some output is shown output = opt.output; else output = false; end OCT = exist('OCTAVE_VERSION') ~= 0; % check if we run Matlab or Octave if output || OCT % evalc is not implemented for Octave if output, if exist('fflush','builtin'), fflush(stdout); end, end if nonneg if output, fprintf(' => non-negativity enforced\n'), end [u,phi] = minimize_lbfgs(u,'phi', abs(nMVM),X,y,B,lam,pen,varargin{:}); else [u,phi] = minimize_lbfgs(u,'phi',-abs(nMVM),X,y,B,lam,pen,varargin{:}); end if output, fprintf('\n'); if exist('fflush','builtin') fflush(stdout); end, end else if nonneg [t,u,phi] = evalc('minimize_lbfgs(u,''phi'',nMVM,X,y,B,lam,pen,varargin{:})'); else [t,u,phi] = evalc('minimize_lbfgs(u,''phi'',-nMVM,X,y,B,lam,pen,varargin{:})'); end end phi = phi(end); glm-ie_v1.4/pls/minimize_lbfgs_objfun.m0000644000175000017500000000546211466026135016124 0ustar hnhnfunction y = minimize_lbfgs_objfun(X,varargin) % extract input arguments varargin = varargin{1}; strctX = varargin{2}; f = varargin{1}; % global variables serve as communication interface between calls global minimize_lbfgs_iteration_number global minimize_lbfgs_objective global minimize_lbfgs_gradient global minimize_lbfgs_X recompute = 0; if minimize_lbfgs_iteration_number==0 recompute = 1; else if norm(unwrap(X)-unwrap(minimize_lbfgs_X))>1e-10 recompute = 1; end end if recompute [y,G] = feval(f,rewrap(strctX,X),varargin{3:end}); else y = minimize_lbfgs_objective(minimize_lbfgs_iteration_number); G = minimize_lbfgs_gradient; end % increase global counter, memorise objective function, gradient and position minimize_lbfgs_iteration_number = minimize_lbfgs_iteration_number+1; minimize_lbfgs_objective(minimize_lbfgs_iteration_number,1) = y; minimize_lbfgs_gradient = G; dX = norm(X - minimize_lbfgs_X)/max(norm(X),1e-9); minimize_lbfgs_X = X; fprintf('%5i, phi=%4.4e; du=%1.3e\r', minimize_lbfgs_iteration_number, y, dX ) if exist('fflush','builtin'), fflush(stdout); end % Extract the numerical values from "s" into the column vector "v". The % variable "s" can be of any type, including struct and cell array. % Non-numerical elements are ignored. See also the reverse rewrap.m. function v = unwrap(s) v = []; if isnumeric(s) v = s(:); % numeric values are recast to column vector elseif isstruct(s) v = unwrap(struct2cell(orderfields(s)));% alphabetize, conv to cell, recurse elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially v = [v; unwrap(s{i})]; end end % other types are ignored % Map the numerical elements in the vector "v" onto the variables "s" which can % be of any type. The number of numerical elements must match; on exit "v" % should be empty. Non-numerical entries are just copied. See also unwrap.m. function [s v] = rewrap(s, v) if isnumeric(s) if numel(v) < numel(s) error('The vector for conversion contains too few elements') end s = reshape(v(1:numel(s)), size(s)); % numeric values are reshaped v = v(numel(s)+1:end); % remaining arguments passed on elseif isstruct(s) [s p] = orderfields(s); p(p) = 1:numel(p); % alphabetize, store ordering [t v] = rewrap(struct2cell(s), v); % convert to cell, recurse s = orderfields(cell2struct(t,fieldnames(s),1),p); % conv to struct, reorder elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially [s{i} v] = rewrap(s{i}, v); end end % other types are not processed glm-ie_v1.4/pls/plsSB.m0000755000175000017500000001257711467333126012620 0ustar hnhn% Penalised least squares solved by Bregman Splitting. % The algorithm is inspired by the code mrics.m from Tom Goldstein % http://www.math.ucla.edu/~tagoldst/public_codes/mrics.zip. % % [u,phi] = plsSB(u,X,y,B,opt,lam,pen,varargin) % % The method will be fast if two conditions are satisfied % (i) The matrices X'*X and B'*B are diagonal in Fourier space i.e. % the matrix F*A'*A*F' is diagonal for A = {X,B}. This is the % case for X, B being equal to matWav, matFFT2line, matFFTNmask, matConv2, % matFFTN, matFD2 or scaled vertical concatentations thereof. % The function diagFAtAFt.m provides the diagonal matrix. % (ii) The proximity operator pls/prox.m can be evaluated analytically. This is % possible for penAbs, penQuad, penZero and penFromPot/potLaplace. % % Additional options: % opt. % SBeta : coefficient for the constraint term [default 1] % => Data is rescaled such that 1 should work. % SBga : regularization parameter [default 0.01/lam] % SBinner : number of (inner) loops for the constraint [default 30] % => Sometimes 5-10 iterations are OK. % SBncg : number of (inner) conjugate gradient steps [default 30] % => CG has to be used if the inner update % in u cannot be done analytically % SBouter : number of (outer) Bregman iterations [default 15] % % See also PLSSOLVERS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 12 function [u,phi] = plsSB(u,X,y,B,opt,lam,pen,varargin) % optimisation parameters if isfield(opt,'SBeta') % coefficient of the constraint term eta = opt.SBeta; else eta = 1; end if isfield(opt,'SBga') % regularization parameter ga = opt.SBga; else ga = 1/(lam*100); end if isfield(opt,'SBinner') % number of (inner) loops for the constraint nInner = opt.SBinner; else nInner = 30; end if isfield(opt,'SBncg') % number of CG steps to solve step a) nCG = opt.SBncg; else nCG = 50; end if isfield(opt,'SBouter') % number of (outer) Bregman iterations nOuter = opt.SBouter; else nOuter = 15; end % information parameters if isfield(opt,'output') % flag saying whether some output is shown output = opt.output; else output = false; end [q,n] = size(B); if output, if exist('fflush','builtin'), fflush(stdout); end, end fac = lam*sqrt(n)/norm(y); y = fac*y; % normalize the data y0 = y; s = zeros(q,1); b = zeros(q,1); % allocate memory % Given that the matrices X and B can be diagonalised in Fourier space i.e. both % F*X'*X'*F and F*B'*B*F' are diagonal if F is the Fourier matrix, the % least-squares problem can be solved by only two ffts and some pointwise % operations. Otherwise, we have to run conjugate gradients which is much more % expensive. fftdiag = ~isnumeric(X) && ~isnumeric(B); if fftdiag dX = diagFAtAFt(X); dB = diagFAtAFt(B); fftdiag = numel(dX)>0 && numel(dB)>0; if fftdiag d = dX + eta*dB + ga; F = matFFTNmask(true(size(d))); d = d(:); % orthonormal Fourier transform end else if isnumeric(X) && isnumeric(B) A = X'*X + eta*B'*B; end end for o = 1:nOuter Xty = X'*y; uold = u; for i = 1:nInner % max_b min_u,s phi(b,u,s) where % phi(b,u,s) = ||X*u-y||_2^2 + 2*lam*sum( pen(s) ) % + 2*eta*b'*(B*u-s) + eta*||B*u-s||_2^2 + ga*||u-v||_2^2 % u: optimisation variable % s: constraint variable % b: Bregman parameters % v: proximity regulariser, here v is the last estimate for u % a) update u for b and s fixed % u = argmin 1/2*||X*u-y||_2^2 + eta/2*||B*u-s+b||_2^2 + ga/2*||u-v||_2^2 % = A\g, g = X'*y + eta*B'*(s-b) + ga*v, A = X'*X + eta*B'*B + ga*I g = Xty + eta*B'*(s-b); if fftdiag if numel(u)>numel(d) u = cx2re(F'*((F*re2cx(g+ga*u))./d)); % make complex else u = F'*((F*(g+ga*u))./d); end else if isnumeric(X) && isnumeric(B) u = A\g; else u = linsolve_lcg(X,1,B,eta,g,nCG); % A = X'*X + eta*B'*B end end % b) update s for u and b fixed % s_j <-argmin lam/eta*pen(s_j) + (r_j-s_j)^2/2, r = B*u Bu = B*u; r = Bu + b; if any(imag(r)>0) % apply proximity operator s = prox(real(r),lam/eta,pen,varargin{:}) ... % treat real and imag + 1i*prox(imag(r),lam/eta,pen,varargin{:}); % separately else s = prox(r,lam/eta,pen,varargin{:}); end % c) update b for u and s fixed % b <- b + B*u -s bold = b; b = r - s; db = norm(bold-b); if db<1e-10, break, end % converged end y = y + y0 - X*u; du = norm(uold-u)/max(norm(uold),1e-9); if output phi = feval('phi',u/fac,X,y0/fac,B,lam,pen,varargin{:}); fprintf('%5i, phi=%4.4e; du=%1.3e\r', o, phi, du ) if exist('fflush','builtin'), fflush(stdout); end end if du1, phi = feval('phi',u,X,y0/fac,B,lam,pen,varargin{:}); end if output, fprintf('\n'); if exist('fflush','builtin'), fflush(stdout); end, endglm-ie_v1.4/pls/plsCG.m0000644000175000017500000000201111472734734012566 0ustar hnhn% Penalised least squares solved by CONJUGATE GRADIENTS using the function % minimize.m [1] by Carl E. Rasmussen. % % [u,phi] = plsCG(u,X,y,B,opt,lam,pen,varargin) % % See also PLSSOLVERS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 23 % % [1] http://www.kyb.tuebingen.mpg.de/bs/people/carl/code/minimize/ function [u,phi] = plsCG(u,X,y,B,opt,lam,pen,varargin) % optimisation parameters if isfield(opt,'nMVM') % maximal number of steps nMVM = opt.nMVM; else nMVM = 100; end % information parameters if isfield(opt,'output') % flag saying whether some output is shown output = opt.output; else output = false; end OCT = exist('OCTAVE_VERSION') ~= 0; % check if we run Matlab or Octave if output || OCT % evalc is not implemented for Octave [u,phi] = minimize(u,'phi',-nMVM,X,y,B,lam,pen,varargin{:}); else [t,u,phi] = evalc('minimize(u,''phi'',-nMVM,X,y,B,lam,pen,varargin{:})'); end phi = phi(end);glm-ie_v1.4/pls/minimize_lbfgs.m0000644000175000017500000001032611455163066014557 0ustar hnhnfunction [X, fX, i] = minimize_lbfgs(X, f, length, varargin) % Minimize a differentiable multivariate function using quasi Newton. % % Usage: [X, fX, i] = minimize_lbfgs(X, f, length, P1, P2, P3, ... ) % % X initial guess; may be of any type, including struct and cell array % f the name or pointer to the function to be minimized. The function % f must return two arguments, the value of the function, and it's % partial derivatives wrt the elements of X. The partial derivative % must have the same type as X. % length absolute value is the number of function evaluations allowed % if it is positive, only positive X are allowed i.e. X>=0 is enforced % P1, P2 ... parameters are passed to the function f. % % X the returned solution % fX vector of function values indicating progress made % i number of iterations (line searches or function evaluations, % depending on the sign of "length") used at termination. % % The function returns when either its length is up, or if no further progress % can be made (ie, we are at a (local) minimum, or so close that due to % numerical problems, we cannot get any closer). NOTE: If the function % terminates within a few iterations, it could be an indication that the % function values and derivatives are not consistent (ie, there may be a bug in % the implementation of your "f" function). % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 27 % global variables serve as communication interface between calls global minimize_lbfgs_iteration_number global minimize_lbfgs_objective global minimize_lbfgs_gradient global minimize_lbfgs_X % init global variables minimize_lbfgs_iteration_number = 0; minimize_lbfgs_objective = Inf; minimize_lbfgs_gradient = 0*unwrap(X); minimize_lbfgs_X = X; X0 = X; if length>0 lb = zeros(size(unwrap(X0))); else lb = -Inf*ones(size(unwrap(X0))); end ub = Inf*ones(size(unwrap(X0))); maxiter = abs(length); % max number of iterations % no callback routine used so far % m is the number of saved vectors used to estimate the Hessian % factr is the precision 1e-12 X = lbfgsb( unwrap(X0), lb, ub, 'minimize_lbfgs_objfun', ... 'minimize_lbfgs_gradfun', ... {f,X0,varargin{:}}, [], ... 'maxiter',maxiter, 'm',4, 'factr',1e-12, 'pgtol',1e-5); i = minimize_lbfgs_iteration_number; fX = minimize_lbfgs_objective; X = rewrap(X0,X); % clear global variables clear minimize_lbfgs_iteration_number clear minimize_lbfgs_objective clear minimize_lbfgs_gradient clear minimize_lbfgs_X % Extract the numerical values from "s" into the column vector "v". The % variable "s" can be of any type, including struct and cell array. % Non-numerical elements are ignored. See also the reverse rewrap.m. function v = unwrap(s) v = []; if isnumeric(s) v = s(:); % numeric values are recast to column vector elseif isstruct(s) v = unwrap(struct2cell(orderfields(s)));% alphabetize, conv to cell, recurse elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially v = [v; unwrap(s{i})]; end end % other types are ignored % Map the numerical elements in the vector "v" onto the variables "s" which can % be of any type. The number of numerical elements must match; on exit "v" % should be empty. Non-numerical entries are just copied. See also unwrap.m. function [s v] = rewrap(s, v) if isnumeric(s) if numel(v) < numel(s) error('The vector for conversion contains too few elements') end s = reshape(v(1:numel(s)), size(s)); % numeric values are reshaped v = v(numel(s)+1:end); % remaining arguments passed on elseif isstruct(s) [s p] = orderfields(s); p(p) = 1:numel(p); % alphabetize, store ordering [t v] = rewrap(struct2cell(s), v); % convert to cell, recurse s = orderfields(cell2struct(t,fieldnames(s),1),p); % conv to struct, reorder elseif iscell(s) for i = 1:numel(s) % cell array elements are handled sequentially [s{i} v] = rewrap(s{i}, v); end end % other types are not processed glm-ie_v1.4/pls/lbfgsb/0000755000175000017500000000000011755435662012647 5ustar hnhnglm-ie_v1.4/pls/lbfgsb/matlabmatrix.cpp0000644000175000017500000000315611455163061016031 0ustar hnhn#include "matlabmatrix.h" #include "matlabexception.h" // Function definitions. // ----------------------------------------------------------------- double* getMatlabMatrixDouble (const mxArray* ptr) { if (mxGetNumberOfDimensions(ptr) != 2) throw MatlabException("Matlab array must be a matrix"); if (!mxIsDouble(ptr)) throw MatlabException("Matlab array must be of type double"); return mxGetPr(ptr); } double* createMatlabMatrixDouble (mxArray*& ptr, int height, int width) { ptr = mxCreateDoubleMatrix(height,width,mxREAL); return mxGetPr(ptr); } // Function definitions for class Matrix. // ----------------------------------------------------------------- Matrix::Matrix (int height, int width) : Array(height*width) { h = height; w = width; } Matrix::Matrix (double* data, int height, int width) : Array(data,height*width) { h = height; w = width; } Matrix::Matrix (const mxArray* ptr) : Array(getMatlabMatrixDouble(ptr),mxGetNumberOfElements(ptr)) { h = mxGetM(ptr); w = mxGetN(ptr); } Matrix::Matrix (mxArray*& ptr, int height, int width) : Array(createMatlabMatrixDouble(ptr,height,width), height*width) { h = height; w = width; } Matrix::Matrix (const Matrix& source) : Array(source) { h = source.h; w = source.w; } Matrix& Matrix::operator= (const Matrix& source) { inject(source); return *this; } bool Matrix::operator== (const Matrix& X) const { return (h == X.h) && (w == X.w); } double& Matrix::entry (int r, int c) { return elems[h*c + r]; } double Matrix::entry (int r, int c) const { return elems[h*c + r]; } glm-ie_v1.4/pls/lbfgsb/program.h0000644000175000017500000001164711455163061014464 0ustar hnhn#ifndef INCLUDE_PROGRAM #define INCLUDE_PROGRAM // Type definitions. // ----------------------------------------------------------------- // This defines the possible results of running the L-BFGS-B solver. enum SolverExitStatus { success, // The algorithm has converged to a stationary // point or has reached the maximum number of // iterations. abnormalTermination, // The algorithm has terminated abnormally and // was unable to satisfy the convergence // criteria. errorOnInput // The routine has detected an error in the // input parameters. }; // Constants. // ----------------------------------------------------------------- const int defaultm = 5; const int defaultmaxiter = 100; const double defaultfactr = 1e7; const double defaultpgtol = 1e-5; const int defaultprintlevel = -1; // Function declarations. // ----------------------------------------------------------------- // This is the L-BFGS-B routine implemented in Fortran 77. extern "C" void setulb_ (int* n, int* m, double x[], double l[], double u[], int nbd[], double* f, double g[], double* factr, double* pgtol, double wa[], int iwa[], char task[], int* iprint, char csave[], bool lsave[], int isave[], double dsave[]); // Class Program. // ----------------------------------------------------------------- // This class encapsulates execution of the L-BFGS-B routine for // solving a nonlinear optimization problem with bound constraints // using limited-memory approximations to the Hessian. // // This is an abstract class since some of the class methods have not // been implemented (they are "pure virtual" functions). In order to // use this class, one needs to define a child class and provide // definitions for the pure virtual methods. class Program { public: // The first input argument "n" is the number of variables, and "x" // must be set to the suggested starting point for the optimization // algorithm. See the L-BFGS-B documentation for more information on // the inputs to the constructor. Program (int n, double* x, double* lb, double* ub, int* btype, int m = defaultm, int maxiter = defaultmaxiter, double factr = defaultfactr, double pgtol = defaultpgtol); // This is the same constructor as above, except that the // appropriate amount of memory is dynamically allocated for the // variables, the bounds, and the bound types. The destructor also // makes sure that the memory is properly deallocated, but not so // for the other constructor. Program (int n, int m = defaultm, int maxiter = defaultmaxiter, double factr = defaultfactr, double pgtol = defaultpgtol); // The destructor. virtual ~Program(); // An implementation of this method should return the value of the // objective at the current value of the variables "x", where "n" is // the number of variables. virtual double computeObjective (int n, double* x) = 0; // An implementation of this method should fill in the values of the // gradient "g" and the current point "x". virtual void computeGradient (int n, double* x, double* g) = 0; // The child class may optionally override this method which is // called once per iteration of the L-BFGS-B routine. The input // arguments are the current iteration "t", the current value of the // variables "x" and the current value of the objective "f". virtual void iterCallback (int t, double* x, double f) { }; // Run the solver. Upon completion, the solution is stored in "x". SolverExitStatus runSolver(); protected: // The copy constructor and copy assignment operator are kept // private so that they are not used. Program (const Program& source) { }; Program& operator= (const Program& source) { return *this; }; int n; // The number of variables. double* x; // The current point. double* lb; // The lower bounds. double* ub; // The upper bounds. int* btype; // The bound types. private: // Execute a single step the L-BFGS-B solver routine. void callLBFGS (const char* cmd = 0); // Initialize some of the structures used by the L-BFGS-B routine. void initStructures(); bool owner; // If true, then the blocks of memory pointed to by // x, lb, ub and btype must be deallocated in the // destructor. double f; // The value of the objective. double* g; // The value of the gradient. int iprint; // The print level. int maxiter; // The maximum number of iterations. double pgtol; // Convergence parameter passed to L-BFGS-B. double factr; // Convergence parameter passed to L-BFGS-B. int m; // The number of variable corrections to the // limited-memory approximation to the Hessian. // These are structures used by the L-BFGS-B routine. double* wa; int* iwa; char task[60]; char csave[60]; bool lsave[4]; int isave[44]; double dsave[29]; }; #endif glm-ie_v1.4/pls/lbfgsb/matlabstring.cpp0000644000175000017500000000200711455163061016025 0ustar hnhn#include "matlabstring.h" #include "matlabexception.h" // Function definitions. // ----------------------------------------------------------------- char* copystring (const char* source) { int n = strlen(source); // The length of the string. char* dest = new char[n+1]; // The return value. strcpy(dest,source); return dest; } // Function definitions for class MatlabString. // ----------------------------------------------------------------- MatlabString::MatlabString (const mxArray* ptr) { s = 0; // Check to make sure the Matlab array is a string. if (!mxIsChar(ptr)) throw MatlabException("Matlab array must be a string (of type CHAR)"); // Get the string passed as a Matlab array. s = mxArrayToString(ptr); if (s == 0) throw MatlabException("Unable to obtain string from Matlab array"); } MatlabString::MatlabString (const MatlabString& source) { s = 0; // Copy the source string. s = copystring(source.s); } MatlabString::~MatlabString() { if (s) mxFree(s); } glm-ie_v1.4/pls/lbfgsb/lbfgsb.cpp0000644000175000017500000000773411455163061014611 0ustar hnhn#include "mex.h" #include "matrix.h" #include "matlabexception.h" #include "matlabscalar.h" #include "matlabstring.h" #include "matlabmatrix.h" #include "arrayofmatrices.h" #include "program.h" #include "matlabprogram.h" #include #include extern void _main(); // Constants. // ----------------------------------------------------------------- const int minNumInputArgs = 5; // Function definitions. // ----------------------------------------------------------------- void mexFunction (int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) try { // Check to see if we have the correct number of input and output // arguments. if (nrhs < minNumInputArgs) throw MatlabException("Incorrect number of input arguments"); // Get the starting point for the variables. This is specified in // the first input argument. The variables must be either a single // matrix or a cell array of matrices. int k = 0; // The index of the current input argument. ArrayOfMatrices x0(prhs[k++]); // Create the output, which stores the solution obtained from // running IPOPT. There should be as many output arguments as cell // entries in X. if (nlhs != x0.length()) throw MatlabException("Incorrect number of output arguments"); ArrayOfMatrices x(plhs,x0); // Load the lower and upper bounds on the variables as // ArrayOfMatrices objects. They should have the same structure as // the ArrayOfMatrices object "x". ArrayOfMatrices lb(prhs[k++]); ArrayOfMatrices ub(prhs[k++]); // Check to make sure the bounds make sense. if (lb != x || ub != x) throw MatlabException("Input arguments LB and UB must have the same \ structure as X"); // Get the Matlab callback functions. MatlabString objFunc(prhs[k++]); MatlabString gradFunc(prhs[k++]); // Get the auxiliary data. const mxArray* auxData; const mxArray* ptr = prhs[k++]; if (nrhs > 5) { if (mxIsEmpty(ptr)) auxData = 0; else auxData = ptr; } else auxData = 0; // Get the intermediate callback function. MatlabString* iterFunc; ptr = prhs[k++]; if (nrhs > 6) { if (mxIsEmpty(ptr)) iterFunc = 0; else iterFunc = new MatlabString(ptr); } else iterFunc = 0; // Set the options for the L-BFGS algorithm to their defaults. int maxiter = defaultmaxiter; int m = defaultm; double factr = defaultfactr; double pgtol = defaultpgtol; // Process the remaining input arguments, which set options for // the IPOPT algorithm. while (k < nrhs) { // Get the option label from the Matlab input argument. MatlabString optionLabel(prhs[k++]); if (k < nrhs) { // Get the option value from the Matlab input argument. MatlabScalar optionValue(prhs[k++]); double value = optionValue; if (!strcmp(optionLabel,"maxiter")) maxiter = (int) value; else if (!strcmp(optionLabel,"m")) m = (int) value; else if (!strcmp(optionLabel,"factr")) factr = value / mxGetEps(); else if (!strcmp(optionLabel,"pgtol")) pgtol = value; else { if (iterFunc) delete iterFunc; throw MatlabException("Nonexistent option"); } } } // Create a new instance of the optimization problem. x = x0; MatlabProgram program(x,lb,ub,&objFunc,&gradFunc,iterFunc, (mxArray*) auxData,m,maxiter,factr,pgtol); // Run the L-BFGS-B solver. SolverExitStatus exitStatus = program.runSolver(); if (exitStatus == abnormalTermination) { if (iterFunc) delete iterFunc; throw MatlabException("Solver unable to satisfy convergence \ criteria due to abnormal termination"); } else if (exitStatus == errorOnInput) { if (iterFunc) delete iterFunc; throw MatlabException("Invalid inputs to L-BFGS routine"); } // Free the dynamically allocated memory. if (iterFunc) delete iterFunc; } catch (std::exception& error) { mexErrMsgTxt(error.what()); } glm-ie_v1.4/pls/lbfgsb/matlabprogram.cpp0000644000175000017500000001645211455163061016177 0ustar hnhn#include "matlabprogram.h" #include "array.h" // Function definitions. // ----------------------------------------------------------------- // Copy the matrix elements to the destination array. It is assumed // that sufficient memory has been allocated for the destination // array. The copying preserves the column-major ordering of the // matrix elements. void copyElemsFromMatrix (const Matrix& source, double* dest) { Matrix destmatrix(dest,source.height(),source.width()); destmatrix = source; } // Copy the elements from the source array into the matrix. void copyElemsToMatrix (const double* source, Matrix& dest) { dest.inject(source); } // Copy the elements contained in all the matrices to the destination // array. It is assumed that sufficient memory has been allocated for // the destination array. The copying preserves the column-major // ordering of the matrix elements. void copyElemsFromArrayOfMatrices (const ArrayOfMatrices& source, double* dest) { // Repeat for each matrix. for (int i = 0; i < source.length(); i++) { copyElemsFromMatrix(*source[i],dest); dest += source[i]->length(); } } // Copy the elements from the source array into the array of matrices. void copyElemsToArrayOfMatrices (const double* source, ArrayOfMatrices& dest) { // Repeat for each matrix. for (int i = 0; i < dest.length(); i++) { copyElemsToMatrix(source,*dest[i]); source += dest[i]->length(); } } int getBoundType (double& lb, double& ub) { bool haslb = !mxIsInf(lb); bool hasub = !mxIsInf(ub); int btype = haslb + 3*hasub - 2*(haslb && hasub); lb = haslb ? lb : 0; ub = hasub ? ub : 0; return btype; } // Function definitions for class MatlabProgram. // ----------------------------------------------------------------- MatlabProgram::MatlabProgram (ArrayOfMatrices& variables, const ArrayOfMatrices& lowerbounds, const ArrayOfMatrices& upperbounds, const MatlabString* objFunc, const MatlabString* gradFunc, const MatlabString* iterFunc, mxArray* auxData, int m, int maxiter, double factr, double pgtol) : Program(variables.numelems(),0,0,0,0,m,maxiter,factr,pgtol), variables(variables) { x = new double[n]; lb = new double[n]; ub = new double[n]; btype = new int[n]; this->objFunc = objFunc; this->gradFunc = gradFunc; this->iterFunc = iterFunc; // Copy some pieces of information from the input arguments to the // respective program structures. copyElemsFromArrayOfMatrices(variables,x); copyElemsFromArrayOfMatrices(lowerbounds,lb); copyElemsFromArrayOfMatrices(upperbounds,ub); // Set the bound types. for (int i = 0; i < n; i++) btype[i] = getBoundType(lb[i],ub[i]); // Create a Matlab array for the variables. int nv = variables.length(); varInputs = new mxArray*[nv]; varMatlab = new ArrayOfMatrices(varInputs,variables); // Set up the inputs to the objective callback function. numInputsObjFunc = nv + (bool) auxData; inputsObjFunc = new mxArray*[numInputsObjFunc]; copymemory(varInputs,inputsObjFunc,nv); if (auxData) inputsObjFunc[nv] = auxData; // Set up the inputs to the gradient callback function. numInputsGradFunc = numInputsObjFunc; inputsGradFunc = inputsObjFunc; // If necessary, set up the inputs to the iterative callback // function. The first two inputs are the iteration and the function // objective. The next of inputs are the values of the variables // then, optionally, the auxiliary data. if (iterFunc) { numInputsIterFunc = 2 + nv + (bool) auxData; inputsIterFunc = new mxArray*[numInputsIterFunc]; mxArray** ptr = inputsIterFunc; tMatlab = new MatlabScalar(*ptr++,0); fMatlab = new MatlabScalar(*ptr++,0); copymemory(varInputs,ptr,nv); ptr += nv; if (auxData) *ptr = auxData; } } MatlabProgram::~MatlabProgram() { delete[] x; delete[] lb; delete[] ub; delete[] btype; // Deallocate the Matlab arrays. int nv = variables.length(); for (int i = 0; i < nv; i++) mxDestroyArray(varInputs[i]); delete varMatlab; delete[] varInputs; // If necessary, deallocate the additional Matlab arrays that act as // inputs to the iterative callback function. if (iterFunc) { delete fMatlab; delete tMatlab; // delete[] inputsIterFunc; } } double MatlabProgram::computeObjective (int n, double* x) { int nlhs = 1; // The number of outputs from Matlab. mxArray* plhs[nlhs]; // The outputs from the Matlab routine. // Copy the current value of the optimization variables. copyElemsToArrayOfMatrices(x,*varMatlab); // Call the designated Matlab routine for evaluating the objective // function. It takes as input the values of the variables, and // returns a single output, the value of the objective function. if (mexCallMATLAB(nlhs,plhs,numInputsObjFunc,inputsObjFunc,*objFunc)) throw MatlabException("Evaluation of objective function failed in \ call to MATLAB routine"); // Get the result passed back from the Matlab routine. MatlabScalar matlabOutput(plhs[0]); double objective = matlabOutput; // Free the dynamically allocated memory. mxDestroyArray(plhs[0]); return objective; } void MatlabProgram::computeGradient (int n, double* x, double* g) { int nlhs = variables.length(); // The number of outputs from Matlab. mxArray* plhs[nlhs]; // The outputs from the Matlab routine. // Copy the current value of the optimization variables. copyElemsToArrayOfMatrices(x,*varMatlab); // Call the designated Matlab routine for computing the gradient // of the objective function. It takes as input the values of the // variables, and returns as many outputs corresponding to the // partial derivatives of the objective function with respect to // the variables at their curent values. if (mexCallMATLAB(nlhs,plhs,numInputsGradFunc,inputsGradFunc,*gradFunc)) throw MatlabException("Evaluation of objective gradient failed in \ call to MATLAB routine"); // Get the result passed back from the Matlab routine. ArrayOfMatrices matlabOutput((const mxArray**) plhs,nlhs); for (int i = 0; i < variables.length(); i++) if (matlabOutput[i]->length() != variables[i]->length()) throw MatlabException("Invalid gradient passed back from MATLAB \ routine"); copyElemsFromArrayOfMatrices(matlabOutput,g); // Free the dynamically allocated Matlab outputs. for (int i = 0; i < variables.length(); i++) mxDestroyArray(plhs[i]); } void MatlabProgram::iterCallback (int t, double* x, double f) { if (iterFunc) { // Copy the current iteration, the current value of the objective // function, and the current value of the optimization variables. *tMatlab = t; *fMatlab = f; copyElemsToArrayOfMatrices(x,*varMatlab); // Call the Matlab iterative callback routine. Since there are no // outputs, there is no memory to deallocate. if (mexCallMATLAB(0,0,numInputsIterFunc,inputsIterFunc,*iterFunc)) throw MatlabException("Call to MATLAB iterative callback function \ failed"); } } SolverExitStatus MatlabProgram::runSolver() { SolverExitStatus status; // The return value. status = Program::runSolver(); // Copy the solution to the class member "variables". copyElemsToArrayOfMatrices(x,variables); return status; } glm-ie_v1.4/pls/lbfgsb/Makefile0000644000175000017500000000426511526675015014310 0ustar hnhn# path to your Matlab installation # you can find it by the commands 'locate matlab' or 'find / -name "matlab"' #MATLAB_HOME=/agbs/share/sw/matlab MATLAB_HOME=/usr/local/share/matlabR2008b # for 'make mex' you need to provide the variable MEX and have mex set up # for 'make nomex' you need to provide the variables MEX_SUFFIX and MATLAB_LIB # Choose Operating System ###################################################### # For 32 bit Linux, uncomment the following three lines.------------------------ MEX = $(MATLAB_HOME)/bin/mex MEX_SUFFIX = mexglx MATLAB_LIB = -L$(MATLAB_HOME)/bin/glnx86 -lmex # For 64 bit Linux, uncomment the following three lines.------------------------ #MEX = $(MATLAB_HOME)/bin/mex #MEX_SUFFIX = mexa64 #MATLAB_LIB = -L$(MATLAB_HOME)/bin/glnxa64 -lmex # For Mac OS X, uncomment the following three lines.---------------------------- #MEX = /Applications/MATLAB7/bin/mex #MEX_SUFFIX = mexmac #MATLAB_LIB = -L$(MATLAB_HOME)/bin/maci -lmex # Choose FORTRAN compiler ###################################################### # To work with f77, uncomment the following two lines.-------------------------- F77 = f77 FORTRAN_LIB = g2c # To use gfortran, uncomment the following two lines.--------------------------- #F77 = gfortran #FORTRAN_LIB = gfortran # Do not edit below ############################################################ CXX = g++ CFLAGS = -O3 -ffast-math -fomit-frame-pointer -fPIC -Werror -pthread -Wall -ansi FFLAGS = -O3 -fPIC -fexceptions MATLAB_INCLUDE=-I$(MATLAB_HOME)/extern/include TARGET = lbfgsb OBJS = solver.o matlabexception.o matlabscalar.o matlabstring.o \ matlabmatrix.o arrayofmatrices.o program.o matlabprogram.o \ lbfgsb.o %.o: %.cpp $(CXX) $(CFLAGS) $(MATLAB_INCLUDE) -o $@ -c $^ %.o: %.f $(F77) $(FFLAGS) -o $@ -c $^ mex: $(TARGET) clean nomex: $(TARGET)_nomex clean $(TARGET): $(OBJS) $(MEX) -cxx CXX=$(CXX) CC=$(CXX) FC=$(FCC) LD=$(CXX) -l$(FORTRAN_LIB) -lm \ -O -output $@ $^ $(TARGET)_nomex: $(OBJS) $(CXX) $^ -shared -o $(TARGET).$(MEX_SUFFIX) $(MATLAB_LIB) -l$(FORTRAN_LIB) -lm clean: rm -f *.o cp $(TARGET).$(MEX_SUFFIX) ../$(TARGET).mex mv $(TARGET).$(MEX_SUFFIX) .. glm-ie_v1.4/pls/lbfgsb/matlabmatrix.h0000644000175000017500000000456211455163061015500 0ustar hnhn#ifndef INCLUDE_MATLABMATRIX #define INCLUDE_MATLABMATRIX #include "array.h" #include "mex.h" // Class Matrix // --------------------------------------------------------------- // A matrix object stores its elements in column-major format, as in // Fortran and Matlab. This means that columns are stored one after // another. For example, the matrix // // 1 2 3 // 4 5 6 // // is stored in memory as // // 1 4 2 5 3 6 // // Like Array objects, Matrix objects are not necessarily // encapsulated, and they exhibit analogous behaviour. class Matrix : public Array { public: // This constructor allocates memory for matrix of the specified // heigth and width. Matrix (int height, int width); // This constructor basically follows the lead of the analagous // constructor for the Array class. Matrix (double* data, int height, int width); // This constructor retrieves a matrix from a Matlab array. This // particular constructor is only defined for Matrix. // Since Matlab handles storage, the object created by this // constructor is not encapsulated. explicit Matrix (const mxArray* ptr); // This constructor creates a new Matlab array as a side effect. // Since Matlab handles storage, the object created by this // constructor is not encapsulated. Matrix (mxArray*& ptr, int height, int width); // The copy constructor makes a shallow copy of the data. Matrix (const Matrix& source); // The destructor. ~Matrix() { }; // Copy assignment operator that observes the same behaviour as // the Array copy assignment operator. Matrix& operator= (const Matrix& source); // Get the height and width of the matrix. int height() const { return h; }; int width () const { return w; }; // Returns true if the two matrices have the same dimensions // (i.e. the same height and width). bool operator== (const Matrix& X) const; bool operator!= (const Matrix& X) const { return !(*this == X); }; // If X is an object of type Matrix, X.entry(r,c) accesses the // entry of the rth row and cth column. double entry (int r, int c) const; double& entry (int r, int c); double operator() (int r, int c) const { return entry(r,c); }; double& operator() (int r, int c) { return entry(r,c); }; protected: int h; // The height of the matrix. int w; // The width of the matrix. }; #endif glm-ie_v1.4/pls/lbfgsb/matlabscalar.h0000644000175000017500000000226411455163061015436 0ustar hnhn#ifndef INCLUDE_MATLABSCALAR #define INCLUDE_MATLABSCALAR #include "mex.h" // Class MatlabScalar // ----------------------------------------------------------------- // The main appeal of this class is that one can create a scalar // object that accesses a MATLAB array. // // Note that the copy assignment operator is not valid for this class // because we cannot reassign a reference. class MatlabScalar { public: // This constructor accepts as input a pointer to a Matlab array // which must be a scalar in double precision. explicit MatlabScalar (const mxArray* ptr); // This constructor creates a new Matlab array which is a scalar // in double precision. MatlabScalar (mxArray*& ptr, double value); // The copy constructor. MatlabScalar (MatlabScalar& source); // The destructor. ~MatlabScalar() { }; // Access the value of the scalar. operator const double () const { return x; }; // Assign the value of the scalar. MatlabScalar& operator= (double value); protected: double& x; // The copy assignment operator is kept protected because it is // invalid. MatlabScalar& operator= (const MatlabScalar& source) { return *this; }; }; #endif glm-ie_v1.4/pls/lbfgsb/array.h0000644000175000017500000001071411455163061014125 0ustar hnhn#ifndef INCLUDE_ARRAY #define INCLUDE_ARRAY #include "matlabexception.h" #include // Function definitions. // ----------------------------------------------------------------- template void copymemory (const Type* source, Type* dest, int length) { memcpy(dest,source,sizeof(Type)*length); } // Class Array // ----------------------------------------------------------------- // An Array object stores a collection of ordered elements. The key // aspect of Array objects is that they do not necessarily achieve // encapsulation; they do not necessarily retain independent // ownership of their data. That is, the data could be modified // externally by another agent. This behaviour is determined by the // data member "owner". If "owner" is false, the array does not take // care of allocation and deallocation of the data in memory. // // Copy assignment behaves different than usual---it copies the // data, but requires that the destination already have the proper // resources allocated in memory. // // The copy constructor performs a shallow copy. template class Array { public: // This constructor allocates memory for an array of elements of // the specificed length. explicit Array (int length); // This constructor is set to point to an already existing // array. As such, it does not gain ownership of the elements. Array (Type* data, int length); // The copy constructor performs a shallow copy, so that both // arrays share the same copy of the data. Array (const Array& source); // The destructor. ~Array(); // Set all the elements of the array to the specified value. void setvalue (const Type& value); // Copy the elements to from the source array. Both the source and // destination array must have the same length. void inject (const Type* source); void inject (const Array& source); Array& operator= (const Type* source); Array& operator= (const Array& source); // Get the number of elements in the array. int length() const { return n; }; // Elements of an array A can be accessed the subscript operator; // e.g. A[i]. For the sake of efficiency, no checks are made to // ensure that the subscripting is legal. It is up to the user to // ensure that i is non-negative and less than A.length(). Note // that subscripts, as per C++ convention, start at 0. Type& operator[] (int i); const Type& operator[] (int i) const; // Returns true if the two arrays have the same dimensions // (i.e. the same lengths). bool operator== (const Array& a) const { return n == a.n; }; bool operator!= (const Array& a) const { return !(*this == a); }; protected: Type* elems; int n; // The number of elements in the array. bool owner; // Whether the object has ownership of the data. }; // Function definitions for class Array. // ----------------------------------------------------------------- template Array::Array (int length) { n = length; owner = true; elems = 0; elems = new Type[length]; } template Array::Array (Type* data, int length) { n = length; owner = false; elems = data; } template Array::Array (const Array& source) { n = source.n; owner = false; elems = source.elems; } template Array::~Array () { if (owner && elems) delete[] elems; } template void Array::setvalue (const Type& value) { for (int i = 0; i < n; i++) elems[i] = value; } template void Array::inject (const Type* source) { // Check for self-assignment. If there is self-assignment, there // is no need to copy because the objects share the same data! if (elems != source) copymemory(source,elems,n); } template void Array::inject (const Array& source) { if (n != source.n) throw MatlabException("Unable to perform copy; arrays have \ different lengths"); inject(source.elems); } template Array& Array::operator= (const Type* source) { inject(source); return *this; } template Array& Array::operator= (const Array& source) { inject(source); return *this; } template Type& Array::operator[] (int i) { return elems[i]; } template const Type& Array::operator[] (int i) const { return elems[i]; } #endif glm-ie_v1.4/pls/lbfgsb/arrayofmatrices.cpp0000644000175000017500000000465511455163061016544 0ustar hnhn#include "arrayofmatrices.h" #include "matrix.h" // Function definitions for class ArrayOfMatrices. // ----------------------------------------------------------------- ArrayOfMatrices::ArrayOfMatrices (const mxArray* ptr) : Array(getnummatlabmatrices(ptr)) { setvalue(0); if (mxIsCell(ptr)) // Fill in the entries of the array with the entries of the Matlab // cell array. for (int i = 0; i < n; i++) elems[i] = new Matrix(mxGetCell(ptr,i)); else // Fill in the single entry of the array with the Matlab matrix. elems[0] = new Matrix(ptr); } ArrayOfMatrices::ArrayOfMatrices (const mxArray* ptrs[], int numptrs) : Array(numptrs) { setvalue(0); for (int i = 0; i < numptrs; i++) elems[i] = new Matrix(ptrs[i]); } ArrayOfMatrices::ArrayOfMatrices (mxArray* ptrs[], const ArrayOfMatrices& source) : Array(source.length()) { setvalue(0); // Create the new Matlab matrices and copy the data from the // source. for (int i = 0; i < n; i++) { int h = source[i]->height(); int w = source[i]->width(); elems[i] = new Matrix(ptrs[i],h,w); *elems[i] = *source[i]; } } ArrayOfMatrices::ArrayOfMatrices (const ArrayOfMatrices& source) : Array(source) { } ArrayOfMatrices::ArrayOfMatrices (double* data, const ArrayOfMatrices& model) : Array(model.length()) { setvalue(0); // Repeat for each matrix. for (int i = 0; i < n; i++) { const Matrix* A = model[i]; elems[i] = new Matrix(data,A->height(),A->width()); data += A->length(); } } ArrayOfMatrices::~ArrayOfMatrices() { for (int i = 0; i < n; i++) if (elems[i]) delete elems[i]; } int ArrayOfMatrices::numelems() const { int m = 0; // The return value. // Repeat for each matrix. for (int i = 0; i < n; i++) m += elems[i]->length(); return m; } ArrayOfMatrices& ArrayOfMatrices::operator= (const ArrayOfMatrices& source) { // Copy each matrix. for (int i = 0; i < n; i++) *elems[i] = *source.elems[i]; return *this; } int ArrayOfMatrices::getnummatlabmatrices (const mxArray* ptr) { int n; // The return value. if (mxIsCell(ptr)) n = mxGetNumberOfElements(ptr); else if (mxGetNumberOfDimensions(ptr) == 2 && mxIsDouble(ptr)) n = 1; else throw MatlabException("The Matlab array must either be a cell \ array or a double precision matrix"); return n; } glm-ie_v1.4/pls/lbfgsb/arrayofmatrices.h0000644000175000017500000000414411455163061016202 0ustar hnhn#ifndef INCLUDE_ARRAYOFMATRICES #define INCLUDE_ARRAYOFMATRICES #include "array.h" #include "matlabmatrix.h" #include "mex.h" // Class ArrayOfMatrices. // ----------------------------------------------------------------- class ArrayOfMatrices : public Array { public: // This version of the constructor behaves just like its parent. explicit ArrayOfMatrices (int length) : Array(length) { }; // This constructor creates an array of matrices from a Matlab // array. It accepts either a matrix in double precision, or a cell // array with entries that are matrices. explicit ArrayOfMatrices (const mxArray* ptr); // This constructor creates an array of matrices from a collection // of Matlab arrays. The Matlab arrays must be matrices. ArrayOfMatrices (const mxArray* ptrs[], int numptrs); // This constructor creates an array of matrices and the // associated Matlab structures. The Matlab structures are // matrices. The second input argument acts as a template for the // creation of the matrices, but the data from "model" is not // actually copied into the new ArrayOfMatrices object. It is up // to the user to make sure that the array of mxArray pointers has // enough room for the pointers to the Matlab arrays. ArrayOfMatrices (mxArray* ptrs[], const ArrayOfMatrices& model); // This constructor creates an array of matrices using the second // input argument as a model. The input argument "data" contains // the element data. Note that the information is NOT copied from // the model! ArrayOfMatrices (double* data, const ArrayOfMatrices& model); // The copy constructor makes a shallow copy of the source object. ArrayOfMatrices (const ArrayOfMatrices& source); // The destructor. ~ArrayOfMatrices(); // Copy assignment operator that observes the same behaviour as // the Array copy assignment operator. ArrayOfMatrices& operator= (const ArrayOfMatrices& source); // Return the total number of elements in all the matrices. int numelems() const; protected: static int getnummatlabmatrices (const mxArray* ptr); }; #endif glm-ie_v1.4/pls/lbfgsb/README.html0000644000175000017500000004352111455163061014463 0ustar hnhn MATLAB interface for L-BFGS-B


A MATLAB interface for L-BFGS-B

by Peter Carbonetto
Dept. of Computer Science
University of British Columbia

L-BFGS-B is a collection of Fortran 77 routines for solving large-scale nonlinear optimization problems with bound constraints on the variables. One of the key features of the nonlinear solver is that knowledge of the Hessian is not required; the solver computes search directions by keeping track of a quadratic model of the objective function with a limited-memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) approximation to the Hessian.1 The algorithm was developed by Ciyou Zhu, Richard Byrd and Jorge Nocedal. For more information, go to the original distribution site for the L-BFGS-B software package.

I've designed an interface to the L-BFGS-B solver so that it can be called like any other function in MATLAB.2 See the text below for more information on installing and calling it in MATLAB. Along the way, I've also developed a C++ class that encapsulates all the "messy" details in executing the L-BFGS-B code. See below for instructions on how to use this class for your own C++ code.

If you have any questions, praise, or comments, or would like to report a bug, do not hesitate to contact the author. I've tested this software in MATLAB version 7.2 on both the Mac OS X and Linux operating systems.

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Canada License. Please cite the source as Peter Carbonetto, Department of Computer Science, University of British Columbia.

Installation

These installation instructions assume you have a UNIX-based operating system, such as Mac OS X or Linux. It is surely possible to install this software on Windows, I'm just not sure how. These instructions also assume you have GNU make installed.

Download the source. First, download and unpack the tar archive. It contains some MATLAB files (ending in .m), some C++ source and header files (ending in .h and .cpp), a single Fortran 77 source file solver.f containing the L-BFGS-B routines, and a Makefile. I've included a version of the Fortran routines that is more recent than what is available for download at the distribution site at Northwestern University.

What we will do is create a MEX file, which is basically a file that contains a routine that can be called from MATLAB as if it were a built-it function. To learn about MEX files, I refer you to this document at the MathWorks website.

Install the C++ and Fortran 77 compilers. In order to build the MEX file, you will need both a C++ compiler and a Fortran 77 compiler. Unfortunately, you can't just use any compiler. You have to use the precise one supported by MATLAB. For instance, if you are running Mac OS X 7.2 on a Linux operating system, you will need to install the GNU compiler collection (GCC) version 3.4.4. Even if you already have a compiler installed on Linux, it may be the wrong version, and if you use the wrong version things could go horribly wrong! It is important that you use the correct version of the compiler, otherwise you will encounter linking errors. Refer to this document to find out which compiler is supported by your version of MATLAB.

Configure MATLAB. Next, you need to set up and configure MATLAB to build MEX Files. This is explained quite nicely in this MathWorks support document.

Modify the Makefile. You are almost ready to build the MEX file. But before you do so, you need to edit the Makefile to coincide with your system setup. At the top of the file are several variables you may need to modify. The variable MEX is the executable called to build the MEX file. The variables CXX and F77 must be the names of your C++ and Fortran 77 compilers. MEXSUFFIX is the MEX file extension specific to your platform. (For instance, the extension for Linux is mexglx.) The variable MATLAB_HOME must be the base directory of your MATLAB installation. Finally, CFLAGS and FFLAGS are options passed to the C++ and Fortran compilers, respectively. Often these flags coincide with your MEX options file (see here for more information on the options file). But often the settings in the MEX option file are incorrect, and so the options must be set manually. MATLAB requires some special compilation flags for various reasons, one being that it requires position-independent code. These instructions are vague (I apologize), and this step may require a bit of trial and error until before you get it right.

On my laptop running Mac OS X 10.3.9 with MATLAB 7.2, my settings for the Makefile are

  MEX         = mex
  MEXSUFFIX   = mexmac
  MATLAB_HOME = /Applications/MATLAB72
  CXX         = g++
  F77         = g77 
  CFLAGS      = -O3 -fPIC -fno-common -fexceptions \
                -no-cpp-precomp 
  FFLAGS      = -O3 -x f77-cpp-input -fPIC -fno-common

On my Linux machine, I set the variables in the Makefile like so:

  MEX         = mex
  MEXSUFFIX   = mexglx
  MATLAB_HOME = /cs/local/generic/lib/pkg/matlab-7.2
  CXX         = g++-3.4.5
  F77         = g77-3.4.5
  CFLAGS      = -O3 -fPIC -pthread 
  FFLAGS      = -O3 -fPIC -fexceptions

It may be helpful to look at the GCC documentation in order to understand what these various compiler flags mean.

Build the MEX file. If you are in the directory containing all the source files, typing make in the command prompt will first compile the Fortran and C++ source files into object code (.o files). After that, the make program calls the MEX script, which in turn links all the object files together into a single MEX file. If you didn't get any errors, then you are ready to try out the bound-constrained solver in MATLAB. Note that even if you didn't get any errors, there's still a possibility that you didn't link the MEX file properly, in which case executing the MEX file will cause MATLAB to crash. But there's only one way to find out: the hard way.

A brief tutorial

I've written a short script examplehs038.m which demonstrates how to call lbfgsb for solving a small optimization problem, the Hock & Schittkowski test problem no. 38.3 The optimization problem has four variables. They are bounded from below by -10 and bounded from above by +10. We've set the starting point to (-3, -1, -3, -1). We've written two MATLAB functions for computing the objective function and the gradient of the objective function at a given point. These functions can be found in the files computeObjectiveHS038.m and computeGradientHS038.m. If you run the script, the solver should very quickly progress toward the point (1, 1, 1, 1). The objective is 0 at this point.

The basic MATLAB function call is

  lbfgsb(x0,lb,ub,objfunc,gradfunc)

The first input argument x0 declares the starting point for the solver. The second and third input arguments define the lower and upper bounds on the variables, respectively. If an entry of lb is set to -Inf, then this is equivalent to no lower bound for that entry (the same applies to upper bounds, except that it must be +Inf instead). The next two input arguments must be the names of MATLAB routines (M-files). The first routine must calculate the objective function at the current point. The output must be a scalar representing the objective evaluated at the current point. The second function must compute the gradient of the objective at the current point. The input is the same as objfunc, but it must return as many outputs as there are inputs. For a complete guide on using the MATLAB interface, type help lbfgsb in the MATLAB prompt.

The script exampleldaimages.m is a more complicated example. It uses the L-BFGS-B solver to compute some statistics of a posterior distribution for a text analysis model called latent Dirichlet allication (LDA). The model is used to estimate the topics for a collection of documents. The optimization problem is to compute an approximation to the posterior, since it is not possible to compute the posterior exactly. In this case, the optimization problem corresponds to minimizing the distance between the true posterior distribution and an approximate distribution. For more information, see the paper of Blei, Ng and Jordan (2003).4 In order to run this example, you will need to install the lightspeed toolbox for MATLAB developed by Tom Minka at Microsoft Research.

The script starts by generating a bunch of canonical images that represent topics; if a pixel is white then a word at that position is more likely to appear in that topic. Note that the order of the pixels in the image is unimportant, since LDA is a "bag of words" model. In another figure we show a small sample of the data generated from the topics. Each image represents a document, and the pixels in the image depict the word proportions in that document.5

Next, the script runs the L-BFGS-B solver to find a local minimum to the variational objective. Buried in the M-file mflda.m is the call to the solver: 

  [xi gamma Phi] = lbfgsb({xi gamma Phi},...
      {repmat(lb,W,K)  repmat(lb,K,D)  repmat(lb,K,M)},...
      {repmat(inf,W,K) repmat(inf,K,D) repmat(inf,K,M)},...
      'computeObjectiveMFLDA','computeGradientMFLDA',...
      {nu eta L w lnZconst},'callbackMFLDA',...
      'm',m_lbfgs,'factr',1e-12,'pgtol',...
      tolerance,'maxiter',maxiter);

This example will give us the opportunity to demonstrate some of the more complicated aspects of the our MATLAB interface. The first input to lbfgsb sets the initial iterate of the optimization algorithm. Notice that we've passed a cell array with entries that are matrices. Indeed, it is possible to pass either a matrix or a cell array. Whatever structure is passed, the other input arguments (and outputs) must also abide by this structure. The lower and upper bounds on variables are also cell arrays. All the upper bounds are set to infinity, which means that the variables are only bounded from below.

It is instructive to examine the callback routines. They look like: 

  f = computeObjectiveMFLDA(xi,gamma,Phi,auxdata)

  [dxi, dgamma, dPhi] = ...
      computeGradientMFLDA(xi,gamma,Phi,auxdata)

Notice that each entry to the cell array is its own input argument to the callback routines. The same applies for the output arguments of the gradient callback function.

The sixth input argument is a cell array that contains auxiliary data. This data will be passed to the MATLAB functions that evaluate the objective and gradient. The seventh input argument specifies a callback routine that is called exactly once for every iteration. This callback routine is most useful for examining the progress of the solver. The remaining input arguments are label/value pairs that override some of the default settings of L-BFGS-B.

After converging to a solution, we display topic samples drawn from the variational approximation. A good solution should come close to recovering the true topics from which the data was generated (although they might not be in the same order).

Don't be surprised if it takes many iterations before the optimization algorithm converges on a local minimum. (In repeated trials, I found it as many as two thousand iterations to converge to a stationary point of the objective.) This particular problem demonstrates the limitations of limited-memory quasi-Newton approximations to the Hessian; the low storage requirements can come at the cost of slow convergence to the solution.

The C++ interface

One of the nice byproducts of writing a MATLAB interface for L-BFGS-B is that I've ended up with a neat little C++ class that encapsulates the nuts and bolts of executing the solver. A brief description of the Program class can be found in the header file program.h.

Program is an abstract class, which means that its impossible to instantiate a Program object. This is because the class has member functions that aren't yet implemented. These are called pure virtual functions. In order to use the Program class, one needs to define another class that inherits the Program class and that implements the pure virtual functions. In fact, the class MatlabProgram (in matlabprogram.h) is an example of such a class.

The new child class must declare and implement these two functions:

  virtual double computeObjective (int n, double* x);
  virtual void computeGradient (int n, double* x, double* g);

See the header file for a detailed description of these functions. The only remaining detail is calling the Program constructor. After that, it is just a matter of declaring a new object of type MyProgram then calling the function runSolver.

Contents of the tar archive

solver.f
Fortran 77 source for the L-BFGS-B solver routines.

program.h
program.cpp
Header and source file for the C++ interface.

array.h
arrayofmatrices.h
matlabexception.h
matlabmatrix.h
matlabprogram.h
matlabscalar.h
matlabstring.h
arrayofmatrices.cpp
matlabexception.cpp
matlabmatrix.cpp
matlabprogram.cpp
matlabscalar.cpp
matlabstring.cpp
lbfgsb.cpp
Header and source files for the MATLAB interface.

lbfgsb.m
Usage instructions for the MEX file.

examplehs038.m
MATLAB script for solving the H&S test example no. 38.

computeObjectiveHS038.m
computeGradientHS038.m
genericcallback.m
MATLAB functions used by the script examplehs038.m.

exampleldaimages.m
MATLAB script that generates synthetic documents and topics, then computes a mean field variational approximation to the posterior distribution of the latent Dirichlet allocation model, then displays the result.

mflda.m
This function computes a mean field variational approximation to the posterior distribution of the latent Dirichlet allocation model by minimizing the distance between the variational distribution and the true distribution. It uses the L-BFGS-B to minimize the objective function subject to the bound constraints. The objective function also acts as a lower bound on the logarithm of the denominator that appears from the application of Bayes' rule.4

callbackMFLDA.m
computeObjectiveMFLDA.m
computeGradientMFLDA.m
computelnZ.m
computelnZconst.m
computem.m
dirichletrnd.m
gammarnd.m
createsyntheticdata.m
mfldainit.m
Some functions used by exampleldaimages.m and mflda.m.

Footnotes

1 Ciyou Zhu, Richard H. Byrd, Peihuang Lu and Jorge Nocedal (1997). Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Transactions on Mathematical Software, Vol. 23, No. 4., pp. 550-560.

1 Another MATLAB interface for the L-BFGS-B routines has been developed by Liam Stewart at the University of Toronto.

3 Willi Hock and Klaus Schittkowski (1981). Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer-Verlag.

4 David M. Blei, Andrew Y. Ng, Michael I. Jordan (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, Vol. 3, pp. 993-1022.

5 Tom L. Griffiths and Mark Steyvers (2004). Finding scientific topics. Proceedings of the National Academy of Sciences, Vol. 101, pp. 5228-5235.


March 3, 2007
glm-ie_v1.4/pls/lbfgsb/matlabexception.cpp0000644000175000017500000000100011455163061016505 0ustar hnhn#include "matlabexception.h" // Function definitions for class MatlabException. // ----------------------------------------------------------------- MatlabException::MatlabException (const char* message) throw() : exception() { this->message = message; } MatlabException::MatlabException (const MatlabException& source) throw() : exception() { message = source.message; } MatlabException& MatlabException::operator= (const MatlabException& source) { message = source.message; return *this; } glm-ie_v1.4/pls/lbfgsb/program.cpp0000644000175000017500000000767511455163061015025 0ustar hnhn#include "program.h" #include // Function definitions. // ----------------------------------------------------------------- // Copy a C-style string (a null-terminated character array) to a // non-C-style string (a simple character array). The length of the // destination character array is given by "ndest". If the source is // shorter than the destination, the destination is padded with blank // characters. void copyCStrToCharArray (const char* source, char* dest, int ndest) { // Get the length of the source C string. int nsource = strlen(source); // Only perform the copy if the source can fit into the destination. if (nsource < ndest) { // Copy the string. strcpy(dest,source); // Fill in the rest of the string with blanks. for (int i = nsource; i < ndest; i++) dest[i] = ' '; } } // Return true if the two strings are the same. The second input // argument must be a C-style string (a null-terminated character // array), but the first input argument need not be one. We only // compare the two strings up to the length of "cstr". bool strIsEqualToCStr (const char* str, const char* cstr) { // Get the length of the C string. int n = strlen(cstr); return !strncmp(str,cstr,n); } // Function definitions for class Program. // ----------------------------------------------------------------- Program::Program (int n, double* x, double* lb, double* ub, int* btype, int m, int maxiter, double factr, double pgtol) { this->n = n; this->x = x; this->lb = lb; this->ub = ub; this->btype = btype; this->m = m; this->maxiter = maxiter; this->factr = factr; this->pgtol = pgtol; this->iprint = defaultprintlevel; this->owner = false; initStructures(); } Program::Program (int n, int m, int maxiter, double factr, double pgtol) { this->n = n; this->x = new double[n]; this->lb = new double[n]; this->ub = new double[n]; this->btype = new int[n]; this->m = m; this->maxiter = maxiter; this->factr = factr; this->pgtol = pgtol; this->iprint = defaultprintlevel; this->owner = true; initStructures(); } Program::~Program() { if (owner) { delete[] x; delete[] lb; delete[] ub; delete[] btype; } delete[] g; delete[] wa; delete[] iwa; } SolverExitStatus Program::runSolver() { SolverExitStatus status = success; // The return value. // Initialize the objective function and gradient to zero. f = 0; for (int i = 0; i < n; i++) g[i] = 0; // This initial call sets up the structures for L-BFGS. callLBFGS("START"); // Repeat until we've reached the maximum number of iterations. int t = 0; while (true) { // Do something according to the "task" from the previous call to // L-BFGS. if (strIsEqualToCStr(task,"FG")) { // Evaluate the objective function and the gradient of the // objective at the current point. f = computeObjective(n,x); computeGradient(n,x,g); } else if (strIsEqualToCStr(task,"NEW_X")) { // Go to the next iteration and call the iterative callback // routine. t++; iterCallback(t,x,f); // If we've reached the maximum number of iterations, terminate // the optimization. if (t == maxiter) { callLBFGS("STOP"); break; } } else if (strIsEqualToCStr(task,"CONV")) break; else if (strIsEqualToCStr(task,"ABNO")) { status = abnormalTermination; break; } else if (strIsEqualToCStr(task,"ERROR")) { status = errorOnInput; break; } // Call L-BFGS again. callLBFGS(); } return status; } void Program::callLBFGS (const char* cmd) { if (cmd) copyCStrToCharArray(cmd,task,60); setulb_(&n,&m,x,lb,ub,btype,&f,g,&factr,&pgtol,wa,iwa,task,&iprint, csave,lsave,isave,dsave); } void Program::initStructures() { f = 0; g = new double[n]; wa = new double[(2*m + 4)*n + 12*m*(m + 1)]; iwa = new int[3*n]; } glm-ie_v1.4/pls/lbfgsb/matlabstring.h0000644000175000017500000000220211455163061015467 0ustar hnhn#ifndef INCLUDE_MATLABSTRING #define INCLUDE_MATLABSTRING #include "mex.h" #include // Function declarations. // ----------------------------------------------------------------- // Copy a C-style string (i.e. a null-terminated character array). char* copystring (const char* source); // Class MatlabString. // ----------------------------------------------------------------- // This class encapsulates read-only access to a MATLAB character // array. class MatlabString { public: // The constructor accepts as input a pointer to a Matlab array, // which must be a valid string (array of type CHAR). explicit MatlabString (const mxArray* ptr); // The copy constructor makes a full copy of the source string. MatlabString (const MatlabString& source); // The destructor. ~MatlabString(); // Conversion operator for null-terminated string. operator const char* () const { return s; }; protected: char* s; // The null-terminated string. // The copy assignment operator is not proper, thus remains // protected. MatlabString& operator= (const MatlabString& source) { return *this; }; }; #endif glm-ie_v1.4/pls/lbfgsb/matlabprogram.h0000644000175000017500000000550111455163061015635 0ustar hnhn#ifndef INCLUDE_MATLABPROGRAM #define INCLUDE_MATLABPROGRAM #include "mex.h" #include "program.h" #include "matlabscalar.h" #include "matlabstring.h" #include "arrayofmatrices.h" // Class MatlabProgram. // ----------------------------------------------------------------- // This is an implementation of the abstract class Program. class MatlabProgram: public Program { public: // On input, "variables" should contain the initial point for the // optimization routine. If no iterative callback function is // specified, "iterFunc" may be set to 0. Also, if no auxiliary data // is needed, it may also be set to 0. MatlabProgram (ArrayOfMatrices& variables, const ArrayOfMatrices& lowerbounds, const ArrayOfMatrices& upperbounds, const MatlabString* objFunc, const MatlabString* gradFunc, const MatlabString* iterFunc, mxArray* auxData, int m = defaultm, int maxiter = defaultmaxiter, double factr = defaultfactr, double pgtol = defaultpgtol); // The destructor. virtual ~MatlabProgram(); // These provide definitions for the pure virtual functions of the // abstract parent class. virtual double computeObjective (int n, double* x); virtual void computeGradient (int n, double* x, double* g); virtual void iterCallback (int t, double* x, double f); // Run the solver. Upon completion, the solution is stored in // "variables". SolverExitStatus runSolver(); protected: ArrayOfMatrices& variables; // Storage for the initial value and // solution. const MatlabString* objFunc; // The objective callback function. const MatlabString* gradFunc; // The gradient callback function. const MatlabString* iterFunc; // The iterative callback function. ArrayOfMatrices* varMatlab; // Inputs to the Matlab callback mxArray** varInputs; // functions representing the // current values of the variables. MatlabScalar* fMatlab; // Input to the Matlab callback // functions representing the // current value of the objective. MatlabScalar* tMatlab; // Input to the Matlab callback // functions representing the // current iteration. int numInputsObjFunc; // The number of inputs passed to the // objective callback function. int numInputsGradFunc; // The number of inputs passed to the // gradient callback function. int numInputsIterFunc; // The number of inputs passed to the // iterative callback function. mxArray** inputsObjFunc; // The inputs passed to the objective // callback function. mxArray** inputsGradFunc; // The inputs passed to the gradient // callback function. mxArray** inputsIterFunc; // The inputs passed to the iterative // callback function. }; #endif glm-ie_v1.4/pls/lbfgsb/matlabscalar.cpp0000644000175000017500000000173011455163061015766 0ustar hnhn#include "matlabscalar.h" #include "matlabexception.h" // Function definitions. // ----------------------------------------------------------------- double& getMatlabScalar (const mxArray* ptr) { if (!mxIsDouble(ptr)) throw MatlabException("Matlab array must be of type double"); if (mxGetNumberOfElements(ptr) != 1) throw MatlabException("The Matlab array must be a scalar"); return *mxGetPr(ptr); } double& createMatlabScalar (mxArray*& ptr) { ptr = mxCreateDoubleScalar(0); return *mxGetPr(ptr); } // Function definitions for class MatlabScalar. // --------------------------------------------------------------- MatlabScalar::MatlabScalar (const mxArray* ptr) : x(getMatlabScalar(ptr)) { } MatlabScalar::MatlabScalar (mxArray*& ptr, double value) : x(createMatlabScalar(ptr)) { x = value; } MatlabScalar::MatlabScalar (MatlabScalar& source) : x(source.x) { } MatlabScalar& MatlabScalar::operator= (double value) { x = value; return *this; } glm-ie_v1.4/pls/lbfgsb/solver.f0000644000175000017500000042341011455163061014320 0ustar hnhnc================ L-BFGS-B (version 2.4) ========================== subroutine setulb(n, m, x, l, u, nbd, f, g, factr, pgtol, wa, iwa, + task, iprint, csave, lsave, isave, dsave) character*60 task, csave logical lsave(4) integer n, m, iprint, + nbd(n), iwa(3*n), isave(44) double precision f, factr, pgtol, x(n), l(n), u(n), g(n), + wa(2*m*n+4*n+11*m*m+8*m), dsave(29) c ************ c c Subroutine setulb c c This subroutine partitions the working arrays wa and iwa, and c then uses the limited memory BFGS method to solve the bound c constrained optimization problem by calling mainlb. c (The direct method will be used in the subspace minimization.) c c n is an integer variable. c On entry n is the dimension of the problem. c On exit n is unchanged. c c m is an integer variable. c On entry m is the maximum number of variable metric corrections c used to define the limited memory matrix. c On exit m is unchanged. c c x is a double precision array of dimension n. c On entry x is an approximation to the solution. c On exit x is the current approximation. c c l is a double precision array of dimension n. c On entry l is the lower bound on x. c On exit l is unchanged. c c u is a double precision array of dimension n. c On entry u is the upper bound on x. c On exit u is unchanged. c c nbd is an integer array of dimension n. c On entry nbd represents the type of bounds imposed on the c variables, and must be specified as follows: c nbd(i)=0 if x(i) is unbounded, c 1 if x(i) has only a lower bound, c 2 if x(i) has both lower and upper bounds, and c 3 if x(i) has only an upper bound. c On exit nbd is unchanged. c c f is a double precision variable. c On first entry f is unspecified. c On final exit f is the value of the function at x. c c g is a double precision array of dimension n. c On first entry g is unspecified. c On final exit g is the value of the gradient at x. c c factr is a double precision variable. c On entry factr >= 0 is specified by the user. The iteration c will stop when c c (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch c c where epsmch is the machine precision, which is automatically c generated by the code. Typical values for factr: 1.d+12 for c low accuracy; 1.d+7 for moderate accuracy; 1.d+1 for extremely c high accuracy. c On exit factr is unchanged. c c pgtol is a double precision variable. c On entry pgtol >= 0 is specified by the user. The iteration c will stop when c c max{|proj g_i | i = 1, ..., n} <= pgtol c c where pg_i is the ith component of the projected gradient. c On exit pgtol is unchanged. c c wa is a double precision working array of length c (2mmax + 4)nmax + 11mmax^2 + 8mmax. c c iwa is an integer working array of length 3nmax. c c task is a working string of characters of length 60 indicating c the current job when entering and quitting this subroutine. c c iprint is an integer variable that must be set by the user. c It controls the frequency and type of output generated: c iprint<0 no output is generated; c iprint=0 print only one line at the last iteration; c 0100 print details of every iteration including x and g; c When iprint > 0, the file iterate.dat will be created to c summarize the iteration. c c csave is a working string of characters of length 60. c c lsave is a logical working array of dimension 4. c On exit with 'task' = NEW_X, the following information is c available: c If lsave(1) = .true. then the initial X has been replaced by c its projection in the feasible set; c If lsave(2) = .true. then the problem is constrained; c If lsave(3) = .true. then each variable has upper and lower c bounds; c c isave is an integer working array of dimension 44. c On exit with 'task' = NEW_X, the following information is c available: c isave(22) = the total number of intervals explored in the c search of Cauchy points; c isave(26) = the total number of skipped BFGS updates before c the current iteration; c isave(30) = the number of current iteration; c isave(31) = the total number of BFGS updates prior the current c iteration; c isave(33) = the number of intervals explored in the search of c Cauchy point in the current iteration; c isave(34) = the total number of function and gradient c evaluations; c isave(36) = the number of function value or gradient c evaluations in the current iteration; c if isave(37) = 0 then the subspace argmin is within the box; c if isave(37) = 1 then the subspace argmin is beyond the box; c isave(38) = the number of free variables in the current c iteration; c isave(39) = the number of active constraints in the current c iteration; c n + 1 - isave(40) = the number of variables leaving the set of c active constraints in the current iteration; c isave(41) = the number of variables entering the set of active c constraints in the current iteration. c c dsave is a double precision working array of dimension 29. c On exit with 'task' = NEW_X, the following information is c available: c dsave(1) = current 'theta' in the BFGS matrix; c dsave(2) = f(x) in the previous iteration; c dsave(3) = factr*epsmch; c dsave(4) = 2-norm of the line search direction vector; c dsave(5) = the machine precision epsmch generated by the code; c dsave(7) = the accumulated time spent on searching for c Cauchy points; c dsave(8) = the accumulated time spent on c subspace minimization; c dsave(9) = the accumulated time spent on line search; c dsave(11) = the slope of the line search function at c the current point of line search; c dsave(12) = the maximum relative step length imposed in c line search; c dsave(13) = the infinity norm of the projected gradient; c dsave(14) = the relative step length in the line search; c dsave(15) = the slope of the line search function at c the starting point of the line search; c dsave(16) = the square of the 2-norm of the line search c direction vector. c c Subprograms called: c c L-BFGS-B Library ... mainlb. c c c References: c c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited c memory algorithm for bound constrained optimization'', c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. c c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: a c limited memory FORTRAN code for solving bound constrained c optimization problems'', Tech. Report, NAM-11, EECS Department, c Northwestern University, 1994. c c (Postscript files of these papers are available via anonymous c ftp to ece.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer l1,l2,l3,lws,lr,lz,lt,ld,lwa,lwy,lsy,lss,lwt,lwn,lsnd if (task .eq. 'START') then isave(1) = m*n isave(2) = m**2 isave(3) = 4*m**2 isave(4) = 1 isave(5) = isave(4) + isave(1) isave(6) = isave(5) + isave(1) isave(7) = isave(6) + isave(2) isave(8) = isave(7) + isave(2) isave(9) = isave(8) isave(10) = isave(9) + isave(2) isave(11) = isave(10) + isave(3) isave(12) = isave(11) + isave(3) isave(13) = isave(12) + n isave(14) = isave(13) + n isave(15) = isave(14) + n isave(16) = isave(15) + n endif l1 = isave(1) l2 = isave(2) l3 = isave(3) lws = isave(4) lwy = isave(5) lsy = isave(6) lss = isave(7) lwt = isave(9) lwn = isave(10) lsnd = isave(11) lz = isave(12) lr = isave(13) ld = isave(14) lt = isave(15) lwa = isave(16) call mainlb(n,m,x,l,u,nbd,f,g,factr,pgtol, + wa(lws),wa(lwy),wa(lsy),wa(lss),wa(lwt), + wa(lwn),wa(lsnd),wa(lz),wa(lr),wa(ld),wa(lt), + wa(lwa),iwa(1),iwa(n+1),iwa(2*n+1),task,iprint, + csave,lsave,isave(22),dsave) return end c======================= The end of setulb ============================= subroutine mainlb(n, m, x, l, u, nbd, f, g, factr, pgtol, ws, wy, + sy, ss, wt, wn, snd, z, r, d, t, wa, + index, iwhere, indx2, task, iprint, + csave, lsave, isave, dsave) character*60 task, csave logical lsave(4) integer n, m, iprint, nbd(n), index(n), + iwhere(n), indx2(n), isave(23) double precision f, factr, pgtol, + x(n), l(n), u(n), g(n), z(n), r(n), d(n), t(n), + wa(8*m), ws(n, m), wy(n, m), sy(m, m), ss(m, m), + wt(m, m), wn(2*m, 2*m), snd(2*m, 2*m), dsave(29) c ************ c c Subroutine mainlb c c This subroutine solves bound constrained optimization problems by c using the compact formula of the limited memory BFGS updates. c c n is an integer variable. c On entry n is the number of variables. c On exit n is unchanged. c c m is an integer variable. c On entry m is the maximum number of variable metric c corrections allowed in the limited memory matrix. c On exit m is unchanged. c c x is a double precision array of dimension n. c On entry x is an approximation to the solution. c On exit x is the current approximation. c c l is a double precision array of dimension n. c On entry l is the lower bound of x. c On exit l is unchanged. c c u is a double precision array of dimension n. c On entry u is the upper bound of x. c On exit u is unchanged. c c nbd is an integer array of dimension n. c On entry nbd represents the type of bounds imposed on the c variables, and must be specified as follows: c nbd(i)=0 if x(i) is unbounded, c 1 if x(i) has only a lower bound, c 2 if x(i) has both lower and upper bounds, c 3 if x(i) has only an upper bound. c On exit nbd is unchanged. c c f is a double precision variable. c On first entry f is unspecified. c On final exit f is the value of the function at x. c c g is a double precision array of dimension n. c On first entry g is unspecified. c On final exit g is the value of the gradient at x. c c factr is a double precision variable. c On entry factr >= 0 is specified by the user. The iteration c will stop when c c (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch c c where epsmch is the machine precision, which is automatically c generated by the code. c On exit factr is unchanged. c c pgtol is a double precision variable. c On entry pgtol >= 0 is specified by the user. The iteration c will stop when c c max{|proj g_i | i = 1, ..., n} <= pgtol c c where pg_i is the ith component of the projected gradient. c On exit pgtol is unchanged. c c ws, wy, sy, and wt are double precision working arrays used to c store the following information defining the limited memory c BFGS matrix: c ws, of dimension n x m, stores S, the matrix of s-vectors; c wy, of dimension n x m, stores Y, the matrix of y-vectors; c sy, of dimension m x m, stores S'Y; c ss, of dimension m x m, stores S'S; c wt, of dimension m x m, stores the Cholesky factorization c of (theta*S'S+LD^(-1)L'); see eq. c (2.26) in [3]. c c wn is a double precision working array of dimension 2m x 2m c used to store the LEL^T factorization of the indefinite matrix c K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] c [L_a -R_z theta*S'AA'S ] c c where E = [-I 0] c [ 0 I] c c snd is a double precision working array of dimension 2m x 2m c used to store the lower triangular part of c N = [Y' ZZ'Y L_a'+R_z'] c [L_a +R_z S'AA'S ] c c z(n),r(n),d(n),t(n),wa(8*m) are double precision working arrays. c z is used at different times to store the Cauchy point and c the Newton point. c c c index is an integer working array of dimension n. c In subroutine freev, index is used to store the free and fixed c variables at the Generalized Cauchy Point (GCP). c c iwhere is an integer working array of dimension n used to record c the status of the vector x for GCP computation. c iwhere(i)=0 or -3 if x(i) is free and has bounds, c 1 if x(i) is fixed at l(i), and l(i) .ne. u(i) c 2 if x(i) is fixed at u(i), and u(i) .ne. l(i) c 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i) c -1 if x(i) is always free, i.e., no bounds on it. c c indx2 is an integer working array of dimension n. c Within subroutine cauchy, indx2 corresponds to the array iorder. c In subroutine freev, a list of variables entering and leaving c the free set is stored in indx2, and it is passed on to c subroutine formk with this information. c c task is a working string of characters of length 60 indicating c the current job when entering and leaving this subroutine. c c iprint is an INTEGER variable that must be set by the user. c It controls the frequency and type of output generated: c iprint<0 no output is generated; c iprint=0 print only one line at the last iteration; c 0100 print details of every iteration including x and g; c When iprint > 0, the file iterate.dat will be created to c summarize the iteration. c c csave is a working string of characters of length 60. c c lsave is a logical working array of dimension 4. c c isave is an integer working array of dimension 23. c c dsave is a double precision working array of dimension 29. c c c Subprograms called c c L-BFGS-B Library ... cauchy, subsm, lnsrlb, formk, c c errclb, prn1lb, prn2lb, prn3lb, active, projgr, c c freev, cmprlb, matupd, formt. c c Minpack2 Library ... timer, dpmeps. c c Linpack Library ... dcopy, ddot. c c c References: c c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited c memory algorithm for bound constrained optimization'', c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. c c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN c Subroutines for Large Scale Bound Constrained Optimization'' c Tech. Report, NAM-11, EECS Department, Northwestern University, c 1994. c c [3] R. Byrd, J. Nocedal and R. Schnabel "Representations of c Quasi-Newton Matrices and their use in Limited Memory Methods'', c Mathematical Programming 63 (1994), no. 4, pp. 129-156. c c (Postscript files of these papers are available via anonymous c ftp to ece.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ logical prjctd,cnstnd,boxed,updatd,wrk character*3 word integer i,k,nintol,itfile,iback,nskip, + head,col,iter,itail,iupdat, + nint,nfgv,info,ifun, + iword,nfree,nact,ileave,nenter double precision theta,fold,ddot,dr,rr,tol,dpmeps, + xstep,sbgnrm,ddum,dnorm,dtd,epsmch, + cpu1,cpu2,cachyt,sbtime,lnscht,time1,time2, + gd,gdold,stp,stpmx,time double precision one,zero parameter (one=1.0d0,zero=0.0d0) if (task .eq. 'START') then call timer(time1) c Generate the current machine precision. epsmch = dpmeps() fold = 0.0d0 dnorm = 0.0d0 cpu1 = 0.0d0 gd = 0.0d0 sbgnrm = 0.0d0 stp = 0.0d0 stpmx = 0.0d0 gdold = 0.0d0 dtd = 0.0d0 c Initialize counters and scalars when task='START'. c for the limited memory BFGS matrices: col = 0 head = 1 theta = one iupdat = 0 updatd = .false. iback = 0 itail = 0 ifun = 0 iword = 0 nact = 0 ileave = 0 nenter = 0 c for operation counts: iter = 0 nfgv = 0 nint = 0 nintol = 0 nskip = 0 nfree = n c for stopping tolerance: tol = factr*epsmch c for measuring running time: cachyt = 0 sbtime = 0 lnscht = 0 c 'word' records the status of subspace solutions. word = '---' c 'info' records the termination information. info = 0 itfile = 0 if (iprint .ge. 1) then c open a summary file 'iterate.dat' open (8, file = 'iterate.dat', status = 'unknown') itfile = 8 endif c Check the input arguments for errors. call errclb(n,m,factr,l,u,nbd,task,info,k) if (task(1:5) .eq. 'ERROR') then call prn3lb(n,x,f,task,iprint,info,itfile, + iter,nfgv,nintol,nskip,nact,sbgnrm, + zero,nint,word,iback,stp,xstep,k, + cachyt,sbtime,lnscht) return endif call prn1lb(n,m,l,u,x,iprint,itfile,epsmch) c Initialize iwhere & project x onto the feasible set. call active(n,l,u,nbd,x,iwhere,iprint,prjctd,cnstnd,boxed) c The end of the initialization. else c restore local variables. prjctd = lsave(1) cnstnd = lsave(2) boxed = lsave(3) updatd = lsave(4) nintol = isave(1) itfile = isave(3) iback = isave(4) nskip = isave(5) head = isave(6) col = isave(7) itail = isave(8) iter = isave(9) iupdat = isave(10) nint = isave(12) nfgv = isave(13) info = isave(14) ifun = isave(15) iword = isave(16) nfree = isave(17) nact = isave(18) ileave = isave(19) nenter = isave(20) theta = dsave(1) fold = dsave(2) tol = dsave(3) dnorm = dsave(4) epsmch = dsave(5) cpu1 = dsave(6) cachyt = dsave(7) sbtime = dsave(8) lnscht = dsave(9) time1 = dsave(10) gd = dsave(11) stpmx = dsave(12) sbgnrm = dsave(13) stp = dsave(14) gdold = dsave(15) dtd = dsave(16) c After returning from the driver go to the point where execution c is to resume. if (task(1:5) .eq. 'FG_LN') goto 666 if (task(1:5) .eq. 'NEW_X') goto 777 if (task(1:5) .eq. 'FG_ST') goto 111 if (task(1:4) .eq. 'STOP') then if (task(7:9) .eq. 'CPU') then c restore the previous iterate. call dcopy(n,t,1,x,1) call dcopy(n,r,1,g,1) f = fold endif goto 999 endif endif c Compute f0 and g0. task = 'FG_START' c return to the driver to calculate f and g; reenter at 111. goto 1000 111 continue nfgv = 1 c Compute the infinity norm of the (-) projected gradient. call projgr(n,l,u,nbd,x,g,sbgnrm) if (iprint .ge. 1) then write (6,1002) iter,f,sbgnrm write (itfile,1003) iter,nfgv,sbgnrm,f endif if (sbgnrm .le. pgtol) then c terminate the algorithm. task = 'CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL' goto 999 endif c ----------------- the beginning of the loop -------------------------- 222 continue if (iprint .ge. 99) write (6,1001) iter + 1 iword = -1 c if (.not. cnstnd .and. col .gt. 0) then c skip the search for GCP. call dcopy(n,x,1,z,1) wrk = updatd nint = 0 goto 333 endif cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Compute the Generalized Cauchy Point (GCP). c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc call timer(cpu1) call cauchy(n,x,l,u,nbd,g,indx2,iwhere,t,d,z, + m,wy,ws,sy,wt,theta,col,head, + wa(1),wa(2*m+1),wa(4*m+1),wa(6*m+1),nint, + iprint,sbgnrm,info,epsmch) if (info .ne. 0) then c singular triangular system detected; refresh the lbfgs memory. if(iprint .ge. 1) write (6, 1005) info = 0 col = 0 head = 1 theta = one iupdat = 0 updatd = .false. call timer(cpu2) cachyt = cachyt + cpu2 - cpu1 goto 222 endif call timer(cpu2) cachyt = cachyt + cpu2 - cpu1 nintol = nintol + nint c Count the entering and leaving variables for iter > 0; c find the index set of free and active variables at the GCP. call freev(n,nfree,index,nenter,ileave,indx2, + iwhere,wrk,updatd,cnstnd,iprint,iter) nact = n - nfree 333 continue c If there are no free variables or B=theta*I, then c skip the subspace minimization. if (nfree .eq. 0 .or. col .eq. 0) goto 555 cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Subspace minimization. c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc call timer(cpu1) c Form the LEL^T factorization of the indefinite c matrix K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] c [L_a -R_z theta*S'AA'S ] c where E = [-I 0] c [ 0 I] if (wrk) call formk(n,nfree,index,nenter,ileave,indx2,iupdat, + updatd,wn,snd,m,ws,wy,sy,theta,col,head,info) if (info .ne. 0) then c nonpositive definiteness in Cholesky factorization; c refresh the lbfgs memory and restart the iteration. if(iprint .ge. 1) write (6, 1006) info = 0 col = 0 head = 1 theta = one iupdat = 0 updatd = .false. call timer(cpu2) sbtime = sbtime + cpu2 - cpu1 goto 222 endif c compute r=-Z'B(xcp-xk)-Z'g (using wa(2m+1)=W'(xcp-x) c from 'cauchy'). call cmprlb(n,m,x,g,ws,wy,sy,wt,z,r,wa,index, + theta,col,head,nfree,cnstnd,info) if (info .ne. 0) goto 444 c call the direct method. call subsm(n,m,nfree,index,l,u,nbd,z,r,ws,wy,theta, + col,head,iword,wa,wn,iprint,info) 444 continue if (info .ne. 0) then c singular triangular system detected; c refresh the lbfgs memory and restart the iteration. if(iprint .ge. 1) write (6, 1005) info = 0 col = 0 head = 1 theta = one iupdat = 0 updatd = .false. call timer(cpu2) sbtime = sbtime + cpu2 - cpu1 goto 222 endif call timer(cpu2) sbtime = sbtime + cpu2 - cpu1 555 continue cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Line search and optimality tests. c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Generate the search direction d:=z-x. do 40 i = 1, n d(i) = z(i) - x(i) 40 continue call timer(cpu1) 666 continue call lnsrlb(n,l,u,nbd,x,f,fold,gd,gdold,g,d,r,t,z,stp,dnorm, + dtd,xstep,stpmx,iter,ifun,iback,nfgv,info,task, + boxed,cnstnd,csave,isave(22),dsave(17)) if (info .ne. 0 .or. iback .ge. 20) then c restore the previous iterate. call dcopy(n,t,1,x,1) call dcopy(n,r,1,g,1) f = fold if (col .eq. 0) then c abnormal termination. if (info .eq. 0) then info = -9 c restore the actual number of f and g evaluations etc. nfgv = nfgv - 1 ifun = ifun - 1 iback = iback - 1 endif task = 'ABNORMAL_TERMINATION_IN_LNSRCH' iter = iter + 1 goto 999 else c refresh the lbfgs memory and restart the iteration. if(iprint .ge. 1) write (6, 1008) if (info .eq. 0) nfgv = nfgv - 1 info = 0 col = 0 head = 1 theta = one iupdat = 0 updatd = .false. task = 'RESTART_FROM_LNSRCH' call timer(cpu2) lnscht = lnscht + cpu2 - cpu1 goto 222 endif else if (task(1:5) .eq. 'FG_LN') then c return to the driver for calculating f and g; reenter at 666. goto 1000 else c calculate and print out the quantities related to the new X. call timer(cpu2) lnscht = lnscht + cpu2 - cpu1 iter = iter + 1 c Compute the infinity norm of the projected (-)gradient. call projgr(n,l,u,nbd,x,g,sbgnrm) c Print iteration information. call prn2lb(n,x,f,g,iprint,itfile,iter,nfgv,nact, + sbgnrm,nint,word,iword,iback,stp,xstep) goto 1000 endif 777 continue c Test for termination. if (sbgnrm .le. pgtol) then c terminate the algorithm. task = 'CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL' goto 999 endif ddum = max(abs(fold), abs(f), one) if ((fold - f) .le. tol*ddum) then c terminate the algorithm. task = 'CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH' if (iback .ge. 10) info = -5 c i.e., to issue a warning if iback>10 in the line search. goto 999 endif c Compute d=newx-oldx, r=newg-oldg, rr=y'y and dr=y's. do 42 i = 1, n r(i) = g(i) - r(i) 42 continue rr = ddot(n,r,1,r,1) if (stp .eq. one) then dr = gd - gdold ddum = -gdold else dr = (gd - gdold)*stp call dscal(n,stp,d,1) ddum = -gdold*stp endif if (dr .le. epsmch*ddum) then c skip the L-BFGS update. nskip = nskip + 1 updatd = .false. if (iprint .ge. 1) write (6,1004) dr, ddum goto 888 endif cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Update the L-BFGS matrix. c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc updatd = .true. iupdat = iupdat + 1 c Update matrices WS and WY and form the middle matrix in B. call matupd(n,m,ws,wy,sy,ss,d,r,itail, + iupdat,col,head,theta,rr,dr,stp,dtd) c Form the upper half of the pds T = theta*SS + L*D^(-1)*L'; c Store T in the upper triangular of the array wt; c Cholesky factorize T to J*J' with c J' stored in the upper triangular of wt. call formt(m,wt,sy,ss,col,theta,info) if (info .ne. 0) then c nonpositive definiteness in Cholesky factorization; c refresh the lbfgs memory and restart the iteration. if(iprint .ge. 1) write (6, 1007) info = 0 col = 0 head = 1 theta = one iupdat = 0 updatd = .false. goto 222 endif c Now the inverse of the middle matrix in B is c [ D^(1/2) O ] [ -D^(1/2) D^(-1/2)*L' ] c [ -L*D^(-1/2) J ] [ 0 J' ] 888 continue c -------------------- the end of the loop ----------------------------- goto 222 999 continue call timer(time2) time = time2 - time1 call prn3lb(n,x,f,task,iprint,info,itfile, + iter,nfgv,nintol,nskip,nact,sbgnrm, + time,nint,word,iback,stp,xstep,k, + cachyt,sbtime,lnscht) 1000 continue c Save local variables. lsave(1) = prjctd lsave(2) = cnstnd lsave(3) = boxed lsave(4) = updatd isave(1) = nintol isave(3) = itfile isave(4) = iback isave(5) = nskip isave(6) = head isave(7) = col isave(8) = itail isave(9) = iter isave(10) = iupdat isave(12) = nint isave(13) = nfgv isave(14) = info isave(15) = ifun isave(16) = iword isave(17) = nfree isave(18) = nact isave(19) = ileave isave(20) = nenter dsave(1) = theta dsave(2) = fold dsave(3) = tol dsave(4) = dnorm dsave(5) = epsmch dsave(6) = cpu1 dsave(7) = cachyt dsave(8) = sbtime dsave(9) = lnscht dsave(10) = time1 dsave(11) = gd dsave(12) = stpmx dsave(13) = sbgnrm dsave(14) = stp dsave(15) = gdold dsave(16) = dtd 1001 format (//,'ITERATION ',i5) 1002 format + (/,'At iterate',i5,4x,'f= ',1p,d12.5,4x,'|proj g|= ',1p,d12.5) 1003 format (2(1x,i4),5x,'-',5x,'-',3x,'-',5x,'-',5x,'-',8x,'-',3x, + 1p,2(1x,d10.3)) 1004 format (' ys=',1p,e10.3,' -gs=',1p,e10.3,' BFGS update SKIPPED') 1005 format (/, +' Singular triangular system detected;',/, +' refresh the lbfgs memory and restart the iteration.') 1006 format (/, +' Nonpositive definiteness in Cholesky factorization in formk;',/, +' refresh the lbfgs memory and restart the iteration.') 1007 format (/, +' Nonpositive definiteness in Cholesky factorization in formt;',/, +' refresh the lbfgs memory and restart the iteration.') 1008 format (/, +' Bad direction in the line search;',/, +' refresh the lbfgs memory and restart the iteration.') return end c======================= The end of mainlb ============================= subroutine active(n, l, u, nbd, x, iwhere, iprint, + prjctd, cnstnd, boxed) logical prjctd, cnstnd, boxed integer n, iprint, nbd(n), iwhere(n) double precision x(n), l(n), u(n) c ************ c c Subroutine active c c This subroutine initializes iwhere and projects the initial x to c the feasible set if necessary. c c iwhere is an integer array of dimension n. c On entry iwhere is unspecified. c On exit iwhere(i)=-1 if x(i) has no bounds c 3 if l(i)=u(i) c 0 otherwise. c In cauchy, iwhere is given finer gradations. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer nbdd,i double precision zero parameter (zero=0.0d0) c Initialize nbdd, prjctd, cnstnd and boxed. nbdd = 0 prjctd = .false. cnstnd = .false. boxed = .true. c Project the initial x to the easible set if necessary. do 10 i = 1, n if (nbd(i) .gt. 0) then if (nbd(i) .le. 2 .and. x(i) .le. l(i)) then if (x(i) .lt. l(i)) then prjctd = .true. x(i) = l(i) endif nbdd = nbdd + 1 else if (nbd(i) .ge. 2 .and. x(i) .ge. u(i)) then if (x(i) .gt. u(i)) then prjctd = .true. x(i) = u(i) endif nbdd = nbdd + 1 endif endif 10 continue c Initialize iwhere and assign values to cnstnd and boxed. do 20 i = 1, n if (nbd(i) .ne. 2) boxed = .false. if (nbd(i) .eq. 0) then c this variable is always free iwhere(i) = -1 c otherwise set x(i)=mid(x(i), u(i), l(i)). else cnstnd = .true. if (nbd(i) .eq. 2 .and. u(i) - l(i) .le. zero) then c this variable is always fixed iwhere(i) = 3 else iwhere(i) = 0 endif endif 20 continue if (iprint .ge. 0) then if (prjctd) write (6,*) + 'The initial X is infeasible. Restart with its projection.' if (.not. cnstnd) + write (6,*) 'This problem is unconstrained.' endif if (iprint .gt. 0) write (6,1001) nbdd 1001 format (/,'At X0 ',i9,' variables are exactly at the bounds') return end c======================= The end of active ============================= subroutine bmv(m, sy, wt, col, v, p, info) integer m, col, info double precision sy(m, m), wt(m, m), v(2*col), p(2*col) c ************ c c Subroutine bmv c c This subroutine computes the product of the 2m x 2m middle matrix c in the compact L-BFGS formula of B and a 2m vector v; c it returns the product in p. c c m is an integer variable. c On entry m is the maximum number of variable metric corrections c used to define the limited memory matrix. c On exit m is unchanged. c c sy is a double precision array of dimension m x m. c On entry sy specifies the matrix S'Y. c On exit sy is unchanged. c c wt is a double precision array of dimension m x m. c On entry wt specifies the upper triangular matrix J' which is c the Cholesky factor of (thetaS'S+LD^(-1)L'). c On exit wt is unchanged. c c col is an integer variable. c On entry col specifies the number of s-vectors (or y-vectors) c stored in the compact L-BFGS formula. c On exit col is unchanged. c c v is a double precision array of dimension 2col. c On entry v specifies vector v. c On exit v is unchanged. c c p is a double precision array of dimension 2col. c On entry p is unspecified. c On exit p is the product Mv. c c info is an integer variable. c On entry info is unspecified. c On exit info = 0 for normal return, c = nonzero for abnormal return when the system c to be solved by dtrsl is singular. c c Subprograms called: c c Linpack ... dtrsl. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i,k,i2 double precision sum if (col .eq. 0) return c PART I: solve [ D^(1/2) O ] [ p1 ] = [ v1 ] c [ -L*D^(-1/2) J ] [ p2 ] [ v2 ]. c solve Jp2=v2+LD^(-1)v1. p(col + 1) = v(col + 1) do 20 i = 2, col i2 = col + i sum = 0.0d0 do 10 k = 1, i - 1 sum = sum + sy(i,k)*v(k)/sy(k,k) 10 continue p(i2) = v(i2) + sum 20 continue c Solve the triangular system call dtrsl(wt,m,col,p(col+1),11,info) if (info .ne. 0) return c solve D^(1/2)p1=v1. cc do 30 i = 1, col cc p(i) = v(i)/sqrt(sy(i,i)) cc30 continue c PART II: solve [ -D^(1/2) D^(-1/2)*L' ] [ p1 ] = [ p1 ] c [ 0 J' ] [ p2 ] [ p2 ]. c solve J^Tp2=p2. call dtrsl(wt,m,col,p(col+1),01,info) if (info .ne. 0) return c compute p1=-D^(-1/2)(p1-D^(-1/2)L'p2) c =-D^(-1/2)p1+D^(-1)L'p2. do 40 i = 1, col cc p(i) = -p(i)/sqrt(sy(i,i)) combined with do 30 loop cc into the next line p(i) = -v(i)/sy(i,i) 40 continue do 60 i = 1, col sum = 0.d0 do 50 k = i + 1, col sum = sum + sy(k,i)*p(col+k)/sy(i,i) 50 continue p(i) = p(i) + sum 60 continue return end c======================== The end of bmv =============================== subroutine cauchy(n, x, l, u, nbd, g, iorder, iwhere, t, d, xcp, + m, wy, ws, sy, wt, theta, col, head, p, c, wbp, + v, nint, iprint, sbgnrm, info, epsmch) integer n, m, head, col, nint, iprint, info, + nbd(n), iorder(n), iwhere(n) double precision theta, epsmch, + x(n), l(n), u(n), g(n), t(n), d(n), xcp(n), + wy(n, col), ws(n, col), sy(m, m), + wt(m, m), p(2*m), c(2*m), wbp(2*m), v(2*m) c ************ c c Subroutine cauchy c c For given x, l, u, g (with sbgnrm > 0), and a limited memory c BFGS matrix B defined in terms of matrices WY, WS, WT, and c scalars head, col, and theta, this subroutine computes the c generalized Cauchy point (GCP), defined as the first local c minimizer of the quadratic c c Q(x + s) = g's + 1/2 s'Bs c c along the projected gradient direction P(x-tg,l,u). c The routine returns the GCP in xcp. c c n is an integer variable. c On entry n is the dimension of the problem. c On exit n is unchanged. c c x is a double precision array of dimension n. c On entry x is the starting point for the GCP computation. c On exit x is unchanged. c c l is a double precision array of dimension n. c On entry l is the lower bound of x. c On exit l is unchanged. c c u is a double precision array of dimension n. c On entry u is the upper bound of x. c On exit u is unchanged. c c nbd is an integer array of dimension n. c On entry nbd represents the type of bounds imposed on the c variables, and must be specified as follows: c nbd(i)=0 if x(i) is unbounded, c 1 if x(i) has only a lower bound, c 2 if x(i) has both lower and upper bounds, and c 3 if x(i) has only an upper bound. c On exit nbd is unchanged. c c g is a double precision array of dimension n. c On entry g is the gradient of f(x). g must be a nonzero vector. c On exit g is unchanged. c c iorder is an integer working array of dimension n. c iorder will be used to store the breakpoints in the piecewise c linear path and free variables encountered. On exit, c iorder(1),...,iorder(nleft) are indices of breakpoints c which have not been encountered; c iorder(nleft+1),...,iorder(nbreak) are indices of c encountered breakpoints; and c iorder(nfree),...,iorder(n) are indices of variables which c have no bound constraits along the search direction. c c iwhere is an integer array of dimension n. c On entry iwhere indicates only the permanently fixed (iwhere=3) c or free (iwhere= -1) components of x. c On exit iwhere records the status of the current x variables. c iwhere(i)=-3 if x(i) is free and has bounds, but is not moved c 0 if x(i) is free and has bounds, and is moved c 1 if x(i) is fixed at l(i), and l(i) .ne. u(i) c 2 if x(i) is fixed at u(i), and u(i) .ne. l(i) c 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i) c -1 if x(i) is always free, i.e., it has no bounds. c c t is a double precision working array of dimension n. c t will be used to store the break points. c c d is a double precision array of dimension n used to store c the Cauchy direction P(x-tg)-x. c c xcp is a double precision array of dimension n used to return the c GCP on exit. c c m is an integer variable. c On entry m is the maximum number of variable metric corrections c used to define the limited memory matrix. c On exit m is unchanged. c c ws, wy, sy, and wt are double precision arrays. c On entry they store information that defines the c limited memory BFGS matrix: c ws(n,m) stores S, a set of s-vectors; c wy(n,m) stores Y, a set of y-vectors; c sy(m,m) stores S'Y; c wt(m,m) stores the c Cholesky factorization of (theta*S'S+LD^(-1)L'). c On exit these arrays are unchanged. c c theta is a double precision variable. c On entry theta is the scaling factor specifying B_0 = theta I. c On exit theta is unchanged. c c col is an integer variable. c On entry col is the actual number of variable metric c corrections stored so far. c On exit col is unchanged. c c head is an integer variable. c On entry head is the location of the first s-vector c (or y-vector) in S (or Y). c On exit col is unchanged. c c p is a double precision working array of dimension 2m. c p will be used to store the vector p = W^(T)d. c c c is a double precision working array of dimension 2m. c c will be used to store the vector c = W^(T)(xcp-x). c c wbp is a double precision working array of dimension 2m. c wbp will be used to store the row of W corresponding c to a breakpoint. c c v is a double precision working array of dimension 2m. c c nint is an integer variable. c On exit nint records the number of quadratic segments explored c in searching for the GCP. c c iprint is an INTEGER variable that must be set by the user. c It controls the frequency and type of output generated: c iprint<0 no output is generated; c iprint=0 print only one line at the last iteration; c 0100 print details of every iteration including x and g; c When iprint > 0, the file iterate.dat will be created to c summarize the iteration. c c sbgnrm is a double precision variable. c On entry sbgnrm is the norm of the projected gradient at x. c On exit sbgnrm is unchanged. c c info is an integer variable. c On entry info is 0. c On exit info = 0 for normal return, c = nonzero for abnormal return when the the system c used in routine bmv is singular. c c Subprograms called: c c L-BFGS-B Library ... hpsolb, bmv. c c Linpack ... dscal dcopy, daxpy. c c c References: c c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited c memory algorithm for bound constrained optimization'', c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. c c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN c Subroutines for Large Scale Bound Constrained Optimization'' c Tech. Report, NAM-11, EECS Department, Northwestern University, c 1994. c c (Postscript files of these papers are available via anonymous c ftp to ece.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ logical xlower,xupper,bnded integer i,j,col2,nfree,nbreak,pointr, + ibp,nleft,ibkmin,iter double precision f1,f2,dt,dtm,tsum,dibp,zibp,dibp2,bkmin, + tu,tl,wmc,wmp,wmw,ddot,tj,tj0,neggi,sbgnrm, + f2_org double precision one,zero parameter (one=1.0d0,zero=0.0d0) c Check the status of the variables, reset iwhere(i) if necessary; c compute the Cauchy direction d and the breakpoints t; initialize c the derivative f1 and the vector p = W'd (for theta = 1). if (sbgnrm .le. zero) then if (iprint .ge. 0) write (6,*) 'Subgnorm = 0. GCP = X.' call dcopy(n,x,1,xcp,1) return endif bnded = .true. nfree = n + 1 nbreak = 0 ibkmin = 0 bkmin = zero col2 = 2*col f1 = zero if (iprint .ge. 99) write (6,3010) c We set p to zero and build it up as we determine d. do 20 i = 1, col2 p(i) = zero 20 continue c In the following loop we determine for each variable its bound c status and its breakpoint, and update p accordingly. c Smallest breakpoint is identified. do 50 i = 1, n neggi = -g(i) if (iwhere(i) .ne. 3 .and. iwhere(i) .ne. -1) then c if x(i) is not a constant and has bounds, c compute the difference between x(i) and its bounds. if (nbd(i) .le. 2) tl = x(i) - l(i) if (nbd(i) .ge. 2) tu = u(i) - x(i) c If a variable is close enough to a bound c we treat it as at bound. xlower = nbd(i) .le. 2 .and. tl .le. zero xupper = nbd(i) .ge. 2 .and. tu .le. zero c reset iwhere(i). iwhere(i) = 0 if (xlower) then if (neggi .le. zero) iwhere(i) = 1 else if (xupper) then if (neggi .ge. zero) iwhere(i) = 2 else if (abs(neggi) .le. zero) iwhere(i) = -3 endif endif pointr = head if (iwhere(i) .ne. 0 .and. iwhere(i) .ne. -1) then d(i) = zero else d(i) = neggi f1 = f1 - neggi*neggi c calculate p := p - W'e_i* (g_i). do 40 j = 1, col p(j) = p(j) + wy(i,pointr)* neggi p(col + j) = p(col + j) + ws(i,pointr)*neggi pointr = mod(pointr,m) + 1 40 continue if (nbd(i) .le. 2 .and. nbd(i) .ne. 0 + .and. neggi .lt. zero) then c x(i) + d(i) is bounded; compute t(i). nbreak = nbreak + 1 iorder(nbreak) = i t(nbreak) = tl/(-neggi) if (nbreak .eq. 1 .or. t(nbreak) .lt. bkmin) then bkmin = t(nbreak) ibkmin = nbreak endif else if (nbd(i) .ge. 2 .and. neggi .gt. zero) then c x(i) + d(i) is bounded; compute t(i). nbreak = nbreak + 1 iorder(nbreak) = i t(nbreak) = tu/neggi if (nbreak .eq. 1 .or. t(nbreak) .lt. bkmin) then bkmin = t(nbreak) ibkmin = nbreak endif else c x(i) + d(i) is not bounded. nfree = nfree - 1 iorder(nfree) = i if (abs(neggi) .gt. zero) bnded = .false. endif endif 50 continue c The indices of the nonzero components of d are now stored c in iorder(1),...,iorder(nbreak) and iorder(nfree),...,iorder(n). c The smallest of the nbreak breakpoints is in t(ibkmin)=bkmin. if (theta .ne. one) then c complete the initialization of p for theta not= one. call dscal(col,theta,p(col+1),1) endif c Initialize GCP xcp = x. call dcopy(n,x,1,xcp,1) if (nbreak .eq. 0 .and. nfree .eq. n + 1) then c is a zero vector, return with the initial xcp as GCP. if (iprint .gt. 100) write (6,1010) (xcp(i), i = 1, n) return endif c Initialize c = W'(xcp - x) = 0. do 60 j = 1, col2 c(j) = zero 60 continue c Initialize derivative f2. f2 = -theta*f1 f2_org = f2 if (col .gt. 0) then call bmv(m,sy,wt,col,p,v,info) if (info .ne. 0) return f2 = f2 - ddot(col2,v,1,p,1) endif dtm = -f1/f2 tsum = zero nint = 1 if (iprint .ge. 99) + write (6,*) 'There are ',nbreak,' breakpoints ' c If there are no breakpoints, locate the GCP and return. if (nbreak .eq. 0) goto 888 nleft = nbreak iter = 1 tj = zero c------------------- the beginning of the loop ------------------------- 777 continue c Find the next smallest breakpoint; c compute dt = t(nleft) - t(nleft + 1). tj0 = tj if (iter .eq. 1) then c Since we already have the smallest breakpoint we need not do c heapsort yet. Often only one breakpoint is used and the c cost of heapsort is avoided. tj = bkmin ibp = iorder(ibkmin) else if (iter .eq. 2) then c Replace the already used smallest breakpoint with the c breakpoint numbered nbreak > nlast, before heapsort call. if (ibkmin .ne. nbreak) then t(ibkmin) = t(nbreak) iorder(ibkmin) = iorder(nbreak) endif c Update heap structure of breakpoints c (if iter=2, initialize heap). endif call hpsolb(nleft,t,iorder,iter-2) tj = t(nleft) ibp = iorder(nleft) endif dt = tj - tj0 if (dt .ne. zero .and. iprint .ge. 100) then write (6,4011) nint,f1,f2 write (6,5010) dt write (6,6010) dtm endif c If a minimizer is within this interval, c locate the GCP and return. if (dtm .lt. dt) goto 888 c Otherwise fix one variable and c reset the corresponding component of d to zero. tsum = tsum + dt nleft = nleft - 1 iter = iter + 1 dibp = d(ibp) d(ibp) = zero if (dibp .gt. zero) then zibp = u(ibp) - x(ibp) xcp(ibp) = u(ibp) iwhere(ibp) = 2 else zibp = l(ibp) - x(ibp) xcp(ibp) = l(ibp) iwhere(ibp) = 1 endif if (iprint .ge. 100) write (6,*) 'Variable ',ibp,' is fixed.' if (nleft .eq. 0 .and. nbreak .eq. n) then c all n variables are fixed, c return with xcp as GCP. dtm = dt goto 999 endif c Update the derivative information. nint = nint + 1 dibp2 = dibp**2 c Update f1 and f2. c temporarily set f1 and f2 for col=0. f1 = f1 + dt*f2 + dibp2 - theta*dibp*zibp f2 = f2 - theta*dibp2 if (col .gt. 0) then c update c = c + dt*p. call daxpy(col2,dt,p,1,c,1) c choose wbp, c the row of W corresponding to the breakpoint encountered. pointr = head do 70 j = 1,col wbp(j) = wy(ibp,pointr) wbp(col + j) = theta*ws(ibp,pointr) pointr = mod(pointr,m) + 1 70 continue c compute (wbp)Mc, (wbp)Mp, and (wbp)M(wbp)'. call bmv(m,sy,wt,col,wbp,v,info) if (info .ne. 0) return wmc = ddot(col2,c,1,v,1) wmp = ddot(col2,p,1,v,1) wmw = ddot(col2,wbp,1,v,1) c update p = p - dibp*wbp. call daxpy(col2,-dibp,wbp,1,p,1) c complete updating f1 and f2 while col > 0. f1 = f1 + dibp*wmc f2 = f2 + 2.0d0*dibp*wmp - dibp2*wmw endif f2 = max(epsmch*f2_org,f2) if (nleft .gt. 0) then dtm = -f1/f2 goto 777 c to repeat the loop for unsearched intervals. else if(bnded) then f1 = zero f2 = zero dtm = zero else dtm = -f1/f2 endif c------------------- the end of the loop ------------------------------- 888 continue if (iprint .ge. 99) then write (6,*) write (6,*) 'GCP found in this segment' write (6,4010) nint,f1,f2 write (6,6010) dtm endif if (dtm .le. zero) dtm = zero tsum = tsum + dtm c Move free variables (i.e., the ones w/o breakpoints) and c the variables whose breakpoints haven't been reached. call daxpy(n,tsum,d,1,xcp,1) 999 continue c Update c = c + dtm*p = W'(x^c - x) c which will be used in computing r = Z'(B(x^c - x) + g). if (col .gt. 0) call daxpy(col2,dtm,p,1,c,1) if (iprint .gt. 100) write (6,1010) (xcp(i),i = 1,n) if (iprint .ge. 99) write (6,2010) 1010 format ('Cauchy X = ',/,(4x,1p,6(1x,d11.4))) 2010 format (/,'---------------- exit CAUCHY----------------------',/) 3010 format (/,'---------------- CAUCHY entered-------------------') 4010 format ('Piece ',i3,' --f1, f2 at start point ',1p,2(1x,d11.4)) 4011 format (/,'Piece ',i3,' --f1, f2 at start point ', + 1p,2(1x,d11.4)) 5010 format ('Distance to the next break point = ',1p,d11.4) 6010 format ('Distance to the stationary point = ',1p,d11.4) return end c====================== The end of cauchy ============================== subroutine cmprlb(n, m, x, g, ws, wy, sy, wt, z, r, wa, index, + theta, col, head, nfree, cnstnd, info) logical cnstnd integer n, m, col, head, nfree, info, index(n) double precision theta, + x(n), g(n), z(n), r(n), wa(4*m), + ws(n, m), wy(n, m), sy(m, m), wt(m, m) c ************ c c Subroutine cmprlb c c This subroutine computes r=-Z'B(xcp-xk)-Z'g by using c wa(2m+1)=W'(xcp-x) from subroutine cauchy. c c Subprograms called: c c L-BFGS-B Library ... bmv. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i,j,k,pointr double precision a1,a2 if (.not. cnstnd .and. col .gt. 0) then do 26 i = 1, n r(i) = -g(i) 26 continue else do 30 i = 1, nfree k = index(i) r(i) = -theta*(z(k) - x(k)) - g(k) 30 continue call bmv(m,sy,wt,col,wa(2*m+1),wa(1),info) if (info .ne. 0) then info = -8 return endif pointr = head do 34 j = 1, col a1 = wa(j) a2 = theta*wa(col + j) do 32 i = 1, nfree k = index(i) r(i) = r(i) + wy(k,pointr)*a1 + ws(k,pointr)*a2 32 continue pointr = mod(pointr,m) + 1 34 continue endif return end c======================= The end of cmprlb ============================= subroutine errclb(n, m, factr, l, u, nbd, task, info, k) character*60 task integer n, m, info, k, nbd(n) double precision factr, l(n), u(n) c ************ c c Subroutine errclb c c This subroutine checks the validity of the input data. c c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i double precision zero parameter (zero=0.0d0) c Check the input arguments for errors. if (n .le. 0) task = 'ERROR: N .LE. 0' if (m .le. 0) task = 'ERROR: M .LE. 0' if (factr .lt. zero) task = 'ERROR: FACTR .LT. 0' c Check the validity of the arrays nbd(i), u(i), and l(i). do 10 i = 1, n if (nbd(i) .lt. 0 .or. nbd(i) .gt. 3) then c return task = 'ERROR: INVALID NBD' info = -6 k = i endif if (nbd(i) .eq. 2) then if (l(i) .gt. u(i)) then c return task = 'ERROR: NO FEASIBLE SOLUTION' info = -7 k = i endif endif 10 continue return end c======================= The end of errclb ============================= subroutine formk(n, nsub, ind, nenter, ileave, indx2, iupdat, + updatd, wn, wn1, m, ws, wy, sy, theta, col, + head, info) integer n, nsub, m, col, head, nenter, ileave, iupdat, + info, ind(n), indx2(n) double precision theta, wn(2*m, 2*m), wn1(2*m, 2*m), + ws(n, m), wy(n, m), sy(m, m) logical updatd c ************ c c Subroutine formk c c This subroutine forms the LEL^T factorization of the indefinite c c matrix K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] c [L_a -R_z theta*S'AA'S ] c where E = [-I 0] c [ 0 I] c The matrix K can be shown to be equal to the matrix M^[-1]N c occurring in section 5.1 of [1], as well as to the matrix c Mbar^[-1] Nbar in section 5.3. c c n is an integer variable. c On entry n is the dimension of the problem. c On exit n is unchanged. c c nsub is an integer variable c On entry nsub is the number of subspace variables in free set. c On exit nsub is not changed. c c ind is an integer array of dimension nsub. c On entry ind specifies the indices of subspace variables. c On exit ind is unchanged. c c nenter is an integer variable. c On entry nenter is the number of variables entering the c free set. c On exit nenter is unchanged. c c ileave is an integer variable. c On entry indx2(ileave),...,indx2(n) are the variables leaving c the free set. c On exit ileave is unchanged. c c indx2 is an integer array of dimension n. c On entry indx2(1),...,indx2(nenter) are the variables entering c the free set, while indx2(ileave),...,indx2(n) are the c variables leaving the free set. c On exit indx2 is unchanged. c c iupdat is an integer variable. c On entry iupdat is the total number of BFGS updates made so far. c On exit iupdat is unchanged. c c updatd is a logical variable. c On entry 'updatd' is true if the L-BFGS matrix is updatd. c On exit 'updatd' is unchanged. c c wn is a double precision array of dimension 2m x 2m. c On entry wn is unspecified. c On exit the upper triangle of wn stores the LEL^T factorization c of the 2*col x 2*col indefinite matrix c [-D -Y'ZZ'Y/theta L_a'-R_z' ] c [L_a -R_z theta*S'AA'S ] c c wn1 is a double precision array of dimension 2m x 2m. c On entry wn1 stores the lower triangular part of c [Y' ZZ'Y L_a'+R_z'] c [L_a+R_z S'AA'S ] c in the previous iteration. c On exit wn1 stores the corresponding updated matrices. c The purpose of wn1 is just to store these inner products c so they can be easily updated and inserted into wn. c c m is an integer variable. c On entry m is the maximum number of variable metric corrections c used to define the limited memory matrix. c On exit m is unchanged. c c ws, wy, sy, and wtyy are double precision arrays; c theta is a double precision variable; c col is an integer variable; c head is an integer variable. c On entry they store the information defining the c limited memory BFGS matrix: c ws(n,m) stores S, a set of s-vectors; c wy(n,m) stores Y, a set of y-vectors; c sy(m,m) stores S'Y; c wtyy(m,m) stores the Cholesky factorization c of (theta*S'S+LD^(-1)L') c theta is the scaling factor specifying B_0 = theta I; c col is the number of variable metric corrections stored; c head is the location of the 1st s- (or y-) vector in S (or Y). c On exit they are unchanged. c c info is an integer variable. c On entry info is unspecified. c On exit info = 0 for normal return; c = -1 when the 1st Cholesky factorization failed; c = -2 when the 2st Cholesky factorization failed. c c Subprograms called: c c Linpack ... dcopy, dpofa, dtrsl. c c c References: c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited c memory algorithm for bound constrained optimization'', c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. c c [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: a c limited memory FORTRAN code for solving bound constrained c optimization problems'', Tech. Report, NAM-11, EECS Department, c Northwestern University, 1994. c c (Postscript files of these papers are available via anonymous c ftp to ece.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer m2,ipntr,jpntr,iy,is,jy,js,is1,js1,k1,i,k, + col2,pbegin,pend,dbegin,dend,upcl double precision ddot,temp1,temp2,temp3,temp4 double precision zero parameter (zero=0.0d0) c Form the lower triangular part of c WN1 = [Y' ZZ'Y L_a'+R_z'] c [L_a+R_z S'AA'S ] c where L_a is the strictly lower triangular part of S'AA'Y c R_z is the upper triangular part of S'ZZ'Y. if (updatd) then if (iupdat .gt. m) then c shift old part of WN1. do 10 jy = 1, m - 1 js = m + jy call dcopy(m-jy,wn1(jy+1,jy+1),1,wn1(jy,jy),1) call dcopy(m-jy,wn1(js+1,js+1),1,wn1(js,js),1) call dcopy(m-1,wn1(m+2,jy+1),1,wn1(m+1,jy),1) 10 continue endif c put new rows in blocks (1,1), (2,1) and (2,2). pbegin = 1 pend = nsub dbegin = nsub + 1 dend = n iy = col is = m + col ipntr = head + col - 1 if (ipntr .gt. m) ipntr = ipntr - m jpntr = head do 20 jy = 1, col js = m + jy temp1 = zero temp2 = zero temp3 = zero c compute element jy of row 'col' of Y'ZZ'Y do 15 k = pbegin, pend k1 = ind(k) temp1 = temp1 + wy(k1,ipntr)*wy(k1,jpntr) 15 continue c compute elements jy of row 'col' of L_a and S'AA'S do 16 k = dbegin, dend k1 = ind(k) temp2 = temp2 + ws(k1,ipntr)*ws(k1,jpntr) temp3 = temp3 + ws(k1,ipntr)*wy(k1,jpntr) 16 continue wn1(iy,jy) = temp1 wn1(is,js) = temp2 wn1(is,jy) = temp3 jpntr = mod(jpntr,m) + 1 20 continue c put new column in block (2,1). jy = col jpntr = head + col - 1 if (jpntr .gt. m) jpntr = jpntr - m ipntr = head do 30 i = 1, col is = m + i temp3 = zero c compute element i of column 'col' of R_z do 25 k = pbegin, pend k1 = ind(k) temp3 = temp3 + ws(k1,ipntr)*wy(k1,jpntr) 25 continue ipntr = mod(ipntr,m) + 1 wn1(is,jy) = temp3 30 continue upcl = col - 1 else upcl = col endif c modify the old parts in blocks (1,1) and (2,2) due to changes c in the set of free variables. ipntr = head do 45 iy = 1, upcl is = m + iy jpntr = head do 40 jy = 1, iy js = m + jy temp1 = zero temp2 = zero temp3 = zero temp4 = zero do 35 k = 1, nenter k1 = indx2(k) temp1 = temp1 + wy(k1,ipntr)*wy(k1,jpntr) temp2 = temp2 + ws(k1,ipntr)*ws(k1,jpntr) 35 continue do 36 k = ileave, n k1 = indx2(k) temp3 = temp3 + wy(k1,ipntr)*wy(k1,jpntr) temp4 = temp4 + ws(k1,ipntr)*ws(k1,jpntr) 36 continue wn1(iy,jy) = wn1(iy,jy) + temp1 - temp3 wn1(is,js) = wn1(is,js) - temp2 + temp4 jpntr = mod(jpntr,m) + 1 40 continue ipntr = mod(ipntr,m) + 1 45 continue c modify the old parts in block (2,1). ipntr = head do 60 is = m + 1, m + upcl jpntr = head do 55 jy = 1, upcl temp1 = zero temp3 = zero do 50 k = 1, nenter k1 = indx2(k) temp1 = temp1 + ws(k1,ipntr)*wy(k1,jpntr) 50 continue do 51 k = ileave, n k1 = indx2(k) temp3 = temp3 + ws(k1,ipntr)*wy(k1,jpntr) 51 continue if (is .le. jy + m) then wn1(is,jy) = wn1(is,jy) + temp1 - temp3 else wn1(is,jy) = wn1(is,jy) - temp1 + temp3 endif jpntr = mod(jpntr,m) + 1 55 continue ipntr = mod(ipntr,m) + 1 60 continue c Form the upper triangle of WN = [D+Y' ZZ'Y/theta -L_a'+R_z' ] c [-L_a +R_z S'AA'S*theta] m2 = 2*m do 70 iy = 1, col is = col + iy is1 = m + iy do 65 jy = 1, iy js = col + jy js1 = m + jy wn(jy,iy) = wn1(iy,jy)/theta wn(js,is) = wn1(is1,js1)*theta 65 continue do 66 jy = 1, iy - 1 wn(jy,is) = -wn1(is1,jy) 66 continue do 67 jy = iy, col wn(jy,is) = wn1(is1,jy) 67 continue wn(iy,iy) = wn(iy,iy) + sy(iy,iy) 70 continue c Form the upper triangle of c WN= [ LL' L^-1(-L_a'+R_z')] c [(-L_a +R_z)L'^-1 S'AA'S*theta ] c first Cholesky factor (1,1) block of wn to get LL' c with L' stored in the upper triangle of wn. call dpofa(wn,m2,col,info) if (info .ne. 0) then info = -1 return endif c then form L^-1(-L_a'+R_z') in the (1,2) block. col2 = 2*col do 71 js = col+1 ,col2 call dtrsl(wn,m2,col,wn(1,js),11,info) 71 continue c Form S'AA'S*theta + (L^-1(-L_a'+R_z'))'L^-1(-L_a'+R_z') in the c upper triangle of (2,2) block of wn. do 72 is = col+1, col2 do 74 js = is, col2 wn(is,js) = wn(is,js) + ddot(col,wn(1,is),1,wn(1,js),1) 74 continue 72 continue c Cholesky factorization of (2,2) block of wn. call dpofa(wn(col+1,col+1),m2,col,info) if (info .ne. 0) then info = -2 return endif return end c======================= The end of formk ============================== subroutine formt(m, wt, sy, ss, col, theta, info) integer m, col, info double precision theta, wt(m, m), sy(m, m), ss(m, m) c ************ c c Subroutine formt c c This subroutine forms the upper half of the pos. def. and symm. c T = theta*SS + L*D^(-1)*L', stores T in the upper triangle c of the array wt, and performs the Cholesky factorization of T c to produce J*J', with J' stored in the upper triangle of wt. c c Subprograms called: c c Linpack ... dpofa. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i,j,k,k1 double precision ddum double precision zero parameter (zero=0.0d0) c Form the upper half of T = theta*SS + L*D^(-1)*L', c store T in the upper triangle of the array wt. do 52 j = 1, col wt(1,j) = theta*ss(1,j) 52 continue do 55 i = 2, col do 54 j = i, col k1 = min(i,j) - 1 ddum = zero do 53 k = 1, k1 ddum = ddum + sy(i,k)*sy(j,k)/sy(k,k) 53 continue wt(i,j) = ddum + theta*ss(i,j) 54 continue 55 continue c Cholesky factorize T to J*J' with c J' stored in the upper triangle of wt. call dpofa(wt,m,col,info) if (info .ne. 0) then info = -3 endif return end c======================= The end of formt ============================== subroutine freev(n, nfree, index, nenter, ileave, indx2, + iwhere, wrk, updatd, cnstnd, iprint, iter) integer n, nfree, nenter, ileave, iprint, iter, + index(n), indx2(n), iwhere(n) logical wrk, updatd, cnstnd c ************ c c Subroutine freev c c This subroutine counts the entering and leaving variables when c iter > 0, and finds the index set of free and active variables c at the GCP. c c cnstnd is a logical variable indicating whether bounds are present c c index is an integer array of dimension n c for i=1,...,nfree, index(i) are the indices of free variables c for i=nfree+1,...,n, index(i) are the indices of bound variables c On entry after the first iteration, index gives c the free variables at the previous iteration. c On exit it gives the free variables based on the determination c in cauchy using the array iwhere. c c indx2 is an integer array of dimension n c On entry indx2 is unspecified. c On exit with iter>0, indx2 indicates which variables c have changed status since the previous iteration. c For i= 1,...,nenter, indx2(i) have changed from bound to free. c For i= ileave+1,...,n, indx2(i) have changed from free to bound. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer iact,i,k nenter = 0 ileave = n + 1 if (iter .gt. 0 .and. cnstnd) then c count the entering and leaving variables. do 20 i = 1, nfree k = index(i) if (iwhere(k) .gt. 0) then ileave = ileave - 1 indx2(ileave) = k if (iprint .ge. 100) write (6,*) + 'Variable ',k,' leaves the set of free variables' endif 20 continue do 22 i = 1 + nfree, n k = index(i) if (iwhere(k) .le. 0) then nenter = nenter + 1 indx2(nenter) = k if (iprint .ge. 100) write (6,*) + 'Variable ',k,' enters the set of free variables' endif 22 continue if (iprint .ge. 99) write (6,*) + n+1-ileave,' variables leave; ',nenter,' variables enter' endif wrk = (ileave .lt. n+1) .or. (nenter .gt. 0) .or. updatd c Find the index set of free and active variables at the GCP. nfree = 0 iact = n + 1 do 24 i = 1, n if (iwhere(i) .le. 0) then nfree = nfree + 1 index(nfree) = i else iact = iact - 1 index(iact) = i endif 24 continue if (iprint .ge. 99) write (6,*) + nfree,' variables are free at GCP ',iter + 1 return end c======================= The end of freev ============================== subroutine hpsolb(n, t, iorder, iheap) integer iheap, n, iorder(n) double precision t(n) c ************ c c Subroutine hpsolb c c This subroutine sorts out the least element of t, and puts the c remaining elements of t in a heap. c c n is an integer variable. c On entry n is the dimension of the arrays t and iorder. c On exit n is unchanged. c c t is a double precision array of dimension n. c On entry t stores the elements to be sorted, c On exit t(n) stores the least elements of t, and t(1) to t(n-1) c stores the remaining elements in the form of a heap. c c iorder is an integer array of dimension n. c On entry iorder(i) is the index of t(i). c On exit iorder(i) is still the index of t(i), but iorder may be c permuted in accordance with t. c c iheap is an integer variable specifying the task. c On entry iheap should be set as follows: c iheap .eq. 0 if t(1) to t(n) is not in the form of a heap, c iheap .ne. 0 if otherwise. c On exit iheap is unchanged. c c c References: c Algorithm 232 of CACM (J. W. J. Williams): HEAPSORT. c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c ************ integer i,j,k,indxin,indxou double precision ddum,out if (iheap .eq. 0) then c Rearrange the elements t(1) to t(n) to form a heap. do 20 k = 2, n ddum = t(k) indxin = iorder(k) c Add ddum to the heap. i = k 10 continue if (i.gt.1) then j = i/2 if (ddum .lt. t(j)) then t(i) = t(j) iorder(i) = iorder(j) i = j goto 10 endif endif t(i) = ddum iorder(i) = indxin 20 continue endif c Assign to 'out' the value of t(1), the least member of the heap, c and rearrange the remaining members to form a heap as c elements 1 to n-1 of t. if (n .gt. 1) then i = 1 out = t(1) indxou = iorder(1) ddum = t(n) indxin = iorder(n) c Restore the heap 30 continue j = i+i if (j .le. n-1) then if (t(j+1) .lt. t(j)) j = j+1 if (t(j) .lt. ddum ) then t(i) = t(j) iorder(i) = iorder(j) i = j goto 30 endif endif t(i) = ddum iorder(i) = indxin c Put the least member in t(n). t(n) = out iorder(n) = indxou endif return end c====================== The end of hpsolb ============================== subroutine lnsrlb(n, l, u, nbd, x, f, fold, gd, gdold, g, d, r, t, + z, stp, dnorm, dtd, xstep, stpmx, iter, ifun, + iback, nfgv, info, task, boxed, cnstnd, csave, + isave, dsave) character*60 task, csave logical boxed, cnstnd integer n, iter, ifun, iback, nfgv, info, + nbd(n), isave(2) double precision f, fold, gd, gdold, stp, dnorm, dtd, xstep, + stpmx, x(n), l(n), u(n), g(n), d(n), r(n), t(n), + z(n), dsave(13) c ********** c c Subroutine lnsrlb c c This subroutine calls subroutine dcsrch from the Minpack2 library c to perform the line search. Subroutine dscrch is safeguarded so c that all trial points lie within the feasible region. c c Subprograms called: c c Minpack2 Library ... dcsrch. c c Linpack ... dtrsl, ddot. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ********** integer i double precision ddot,a1,a2 double precision one,zero,big parameter (one=1.0d0,zero=0.0d0,big=1.0d+10) double precision ftol,gtol,xtol parameter (ftol=1.0d-3,gtol=0.9d0,xtol=0.1d0) if (task(1:5) .eq. 'FG_LN') goto 556 dtd = ddot(n,d,1,d,1) dnorm = sqrt(dtd) c Determine the maximum step length. stpmx = big if (cnstnd) then if (iter .eq. 0) then stpmx = one else do 43 i = 1, n a1 = d(i) if (nbd(i) .ne. 0) then if (a1 .lt. zero .and. nbd(i) .le. 2) then a2 = l(i) - x(i) if (a2 .ge. zero) then stpmx = zero else if (a1*stpmx .lt. a2) then stpmx = a2/a1 endif else if (a1 .gt. zero .and. nbd(i) .ge. 2) then a2 = u(i) - x(i) if (a2 .le. zero) then stpmx = zero else if (a1*stpmx .gt. a2) then stpmx = a2/a1 endif endif endif 43 continue endif endif if (iter .eq. 0 .and. .not. boxed) then stp = min(one/dnorm, stpmx) else stp = one endif call dcopy(n,x,1,t,1) call dcopy(n,g,1,r,1) fold = f ifun = 0 iback = 0 csave = 'START' 556 continue gd = ddot(n,g,1,d,1) if (ifun .eq. 0) then gdold=gd if (gd .ge. zero) then c the directional derivative >=0. c Line search is impossible. info = -4 return endif endif call dcsrch(f,gd,stp,ftol,gtol,xtol,zero,stpmx,csave,isave,dsave) xstep = stp*dnorm if (csave(1:4) .ne. 'CONV' .and. csave(1:4) .ne. 'WARN') then task = 'FG_LNSRCH' ifun = ifun + 1 nfgv = nfgv + 1 iback = ifun - 1 if (stp .eq. one) then call dcopy(n,z,1,x,1) else do 41 i = 1, n x(i) = stp*d(i) + t(i) 41 continue endif else task = 'NEW_X' endif return end c======================= The end of lnsrlb ============================= subroutine matupd(n, m, ws, wy, sy, ss, d, r, itail, + iupdat, col, head, theta, rr, dr, stp, dtd) integer n, m, itail, iupdat, col, head double precision theta, rr, dr, stp, dtd, d(n), r(n), + ws(n, m), wy(n, m), sy(m, m), ss(m, m) c ************ c c Subroutine matupd c c This subroutine updates matrices WS and WY, and forms the c middle matrix in B. c c Subprograms called: c c Linpack ... dcopy, ddot. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer j,pointr double precision ddot double precision one parameter (one=1.0d0) c Set pointers for matrices WS and WY. if (iupdat .le. m) then col = iupdat itail = mod(head+iupdat-2,m) + 1 else itail = mod(itail,m) + 1 head = mod(head,m) + 1 endif c Update matrices WS and WY. call dcopy(n,d,1,ws(1,itail),1) call dcopy(n,r,1,wy(1,itail),1) c Set theta=yy/ys. theta = rr/dr c Form the middle matrix in B. c update the upper triangle of SS, c and the lower triangle of SY: if (iupdat .gt. m) then c move old information do 50 j = 1, col - 1 call dcopy(j,ss(2,j+1),1,ss(1,j),1) call dcopy(col-j,sy(j+1,j+1),1,sy(j,j),1) 50 continue endif c add new information: the last row of SY c and the last column of SS: pointr = head do 51 j = 1, col - 1 sy(col,j) = ddot(n,d,1,wy(1,pointr),1) ss(j,col) = ddot(n,ws(1,pointr),1,d,1) pointr = mod(pointr,m) + 1 51 continue if (stp .eq. one) then ss(col,col) = dtd else ss(col,col) = stp*stp*dtd endif sy(col,col) = dr return end c======================= The end of matupd ============================= subroutine prn1lb(n, m, l, u, x, iprint, itfile, epsmch) integer n, m, iprint, itfile double precision epsmch, x(n), l(n), u(n) c ************ c c Subroutine prn1lb c c This subroutine prints the input data, initial point, upper and c lower bounds of each variable, machine precision, as well as c the headings of the output. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i if (iprint .ge. 0) then write (6,7001) epsmch write (6,*) 'N = ',n,' M = ',m if (iprint .ge. 1) then write (itfile,2001) epsmch write (itfile,*)'N = ',n,' M = ',m write (itfile,9001) if (iprint .gt. 100) then write (6,1004) 'L =',(l(i),i = 1,n) write (6,1004) 'X0 =',(x(i),i = 1,n) write (6,1004) 'U =',(u(i),i = 1,n) endif endif endif 1004 format (/,a4, 1p, 6(1x,d11.4),/,(4x,1p,6(1x,d11.4))) 2001 format ('RUNNING THE L-BFGS-B CODE',/,/, + 'it = iteration number',/, + 'nf = number of function evaluations',/, + 'nint = number of segments explored during the Cauchy search',/, + 'nact = number of active bounds at the generalized Cauchy point' + ,/, + 'sub = manner in which the subspace minimization terminated:' + ,/,' con = converged, bnd = a bound was reached',/, + 'itls = number of iterations performed in the line search',/, + 'stepl = step length used',/, + 'tstep = norm of the displacement (total step)',/, + 'projg = norm of the projected gradient',/, + 'f = function value',/,/, + ' * * *',/,/, + 'Machine precision =',1p,d10.3) 7001 format ('RUNNING THE L-BFGS-B CODE',/,/, + ' * * *',/,/, + 'Machine precision =',1p,d10.3) 9001 format (/,3x,'it',3x,'nf',2x,'nint',2x,'nact',2x,'sub',2x,'itls', + 2x,'stepl',4x,'tstep',5x,'projg',8x,'f') return end c======================= The end of prn1lb ============================= subroutine prn2lb(n, x, f, g, iprint, itfile, iter, nfgv, nact, + sbgnrm, nint, word, iword, iback, stp, xstep) character*3 word integer n, iprint, itfile, iter, nfgv, nact, nint, + iword, iback double precision f, sbgnrm, stp, xstep, x(n), g(n) c ************ c c Subroutine prn2lb c c This subroutine prints out new information after a successful c line search. c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i,imod c 'word' records the status of subspace solutions. if (iword .eq. 0) then c the subspace minimization converged. word = 'con' else if (iword .eq. 1) then c the subspace minimization stopped at a bound. word = 'bnd' else if (iword .eq. 5) then c the truncated Newton step has been used. word = 'TNT' else word = '---' endif if (iprint .ge. 99) then write (6,*) 'LINE SEARCH',iback,' times; norm of step = ',xstep write (6,2001) iter,f,sbgnrm if (iprint .gt. 100) then write (6,1004) 'X =',(x(i), i = 1, n) write (6,1004) 'G =',(g(i), i = 1, n) endif else if (iprint .gt. 0) then imod = mod(iter,iprint) if (imod .eq. 0) write (6,2001) iter,f,sbgnrm endif if (iprint .ge. 1) write (itfile,3001) + iter,nfgv,nint,nact,word,iback,stp,xstep,sbgnrm,f 1004 format (/,a4, 1p, 6(1x,d11.4),/,(4x,1p,6(1x,d11.4))) 2001 format + (/,'At iterate',i5,4x,'f= ',1p,d12.5,4x,'|proj g|= ',1p,d12.5) 3001 format(2(1x,i4),2(1x,i5),2x,a3,1x,i4,1p,2(2x,d7.1),1p,2(1x,d10.3)) return end c======================= The end of prn2lb ============================= subroutine prn3lb(n, x, f, task, iprint, info, itfile, + iter, nfgv, nintol, nskip, nact, sbgnrm, + time, nint, word, iback, stp, xstep, k, + cachyt, sbtime, lnscht) character*60 task character*3 word integer n, iprint, info, itfile, iter, nfgv, nintol, + nskip, nact, nint, iback, k double precision f, sbgnrm, time, stp, xstep, cachyt, sbtime, + lnscht, x(n) c ************ c c Subroutine prn3lb c c This subroutine prints out information when either a built-in c convergence test is satisfied or when an error message is c generated. c c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i if (task(1:5) .eq. 'ERROR') goto 999 if (iprint .ge. 0) then write (6,3003) write (6,3004) write(6,3005) n,iter,nfgv,nintol,nskip,nact,sbgnrm,f if (iprint .ge. 100) then write (6,1004) 'X =',(x(i),i = 1,n) endif if (iprint .ge. 1) write (6,*) ' F =',f endif 999 continue if (iprint .ge. 0) then write (6,3009) task if (info .ne. 0) then if (info .eq. -1) write (6,9011) if (info .eq. -2) write (6,9012) if (info .eq. -3) write (6,9013) if (info .eq. -4) write (6,9014) if (info .eq. -5) write (6,9015) if (info .eq. -6) write (6,*)' Input nbd(',k,') is invalid.' if (info .eq. -7) + write (6,*)' l(',k,') > u(',k,'). No feasible solution.' if (info .eq. -8) write (6,9018) if (info .eq. -9) write (6,9019) endif if (iprint .ge. 1) write (6,3007) cachyt,sbtime,lnscht write (6,3008) time if (iprint .ge. 1) then if (info .eq. -4 .or. info .eq. -9) then write (itfile,3002) + iter,nfgv,nint,nact,word,iback,stp,xstep endif write (itfile,3009) task if (info .ne. 0) then if (info .eq. -1) write (itfile,9011) if (info .eq. -2) write (itfile,9012) if (info .eq. -3) write (itfile,9013) if (info .eq. -4) write (itfile,9014) if (info .eq. -5) write (itfile,9015) if (info .eq. -8) write (itfile,9018) if (info .eq. -9) write (itfile,9019) endif write (itfile,3008) time endif endif 1004 format (/,a4, 1p, 6(1x,d11.4),/,(4x,1p,6(1x,d11.4))) 3002 format(2(1x,i4),2(1x,i5),2x,a3,1x,i4,1p,2(2x,d7.1),6x,'-',10x,'-') 3003 format (/, + ' * * *',/,/, + 'Tit = total number of iterations',/, + 'Tnf = total number of function evaluations',/, + 'Tnint = total number of segments explored during', + ' Cauchy searches',/, + 'Skip = number of BFGS updates skipped',/, + 'Nact = number of active bounds at final generalized', + ' Cauchy point',/, + 'Projg = norm of the final projected gradient',/, + 'F = final function value',/,/, + ' * * *') 3004 format (/,3x,'N',3x,'Tit',2x,'Tnf',2x,'Tnint',2x, + 'Skip',2x,'Nact',5x,'Projg',8x,'F') 3005 format (i5,2(1x,i4),(1x,i6),(2x,i4),(1x,i5),1p,2(2x,d10.3)) 3007 format (/,' Cauchy time',1p,e10.3,' seconds.',/ + ' Subspace minimization time',1p,e10.3,' seconds.',/ + ' Line search time',1p,e10.3,' seconds.') 3008 format (/,' Total User time',1p,e10.3,' seconds.',/) 3009 format (/,a60) 9011 format (/, +' Matrix in 1st Cholesky factorization in formk is not Pos. Def.') 9012 format (/, +' Matrix in 2st Cholesky factorization in formk is not Pos. Def.') 9013 format (/, +' Matrix in the Cholesky factorization in formt is not Pos. Def.') 9014 format (/, +' Derivative >= 0, backtracking line search impossible.',/, +' Previous x, f and g restored.',/, +' Possible causes: 1 error in function or gradient evaluation;',/, +' 2 rounding errors dominate computation.') 9015 format (/, +' Warning: more than 10 function and gradient',/, +' evaluations in the last line search. Termination',/, +' may possibly be caused by a bad search direction.') 9018 format (/,' The triangular system is singular.') 9019 format (/, +' Line search cannot locate an adequate point after 20 function',/ +,' and gradient evaluations. Previous x, f and g restored.',/, +' Possible causes: 1 error in function or gradient evaluation;',/, +' 2 rounding error dominate computation.') return end c======================= The end of prn3lb ============================= subroutine projgr(n, l, u, nbd, x, g, sbgnrm) integer n, nbd(n) double precision sbgnrm, x(n), l(n), u(n), g(n) c ************ c c Subroutine projgr c c This subroutine computes the infinity norm of the projected c gradient. c c c * * * c c NEOS, November 1994. (Latest revision April 1997.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ integer i double precision gi double precision zero parameter (zero=0.0d0) sbgnrm = zero do 15 i = 1, n gi = g(i) if (nbd(i) .ne. 0) then if (gi .lt. zero) then if (nbd(i) .ge. 2) gi = max((x(i)-u(i)),gi) else if (nbd(i) .le. 2) gi = min((x(i)-l(i)),gi) endif endif sbgnrm = max(sbgnrm,abs(gi)) 15 continue return end c======================= The end of projgr ============================= subroutine subsm(n, m, nsub, ind, l, u, nbd, x, d, ws, wy, theta, + col, head, iword, wv, wn, iprint, info) integer n, m, nsub, col, head, iword, iprint, info, + ind(nsub), nbd(n) double precision theta, + l(n), u(n), x(n), d(n), + ws(n, m), wy(n, m), + wv(2*m), wn(2*m, 2*m) c ************ c c Subroutine subsm c c Given xcp, l, u, r, an index set that specifies c the active set at xcp, and an l-BFGS matrix B c (in terms of WY, WS, SY, WT, head, col, and theta), c this subroutine computes an approximate solution c of the subspace problem c c (P) min Q(x) = r'(x-xcp) + 1/2 (x-xcp)' B (x-xcp) c c subject to l<=x<=u c x_i=xcp_i for all i in A(xcp) c c along the subspace unconstrained Newton direction c c d = -(Z'BZ)^(-1) r. c c The formula for the Newton direction, given the L-BFGS matrix c and the Sherman-Morrison formula, is c c d = (1/theta)r + (1/theta*2) Z'WK^(-1)W'Z r. c c where c K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] c [L_a -R_z theta*S'AA'S ] c c Note that this procedure for computing d differs c from that described in [1]. One can show that the matrix K is c equal to the matrix M^[-1]N in that paper. c c n is an integer variable. c On entry n is the dimension of the problem. c On exit n is unchanged. c c m is an integer variable. c On entry m is the maximum number of variable metric corrections c used to define the limited memory matrix. c On exit m is unchanged. c c nsub is an integer variable. c On entry nsub is the number of free variables. c On exit nsub is unchanged. c c ind is an integer array of dimension nsub. c On entry ind specifies the coordinate indices of free variables. c On exit ind is unchanged. c c l is a double precision array of dimension n. c On entry l is the lower bound of x. c On exit l is unchanged. c c u is a double precision array of dimension n. c On entry u is the upper bound of x. c On exit u is unchanged. c c nbd is a integer array of dimension n. c On entry nbd represents the type of bounds imposed on the c variables, and must be specified as follows: c nbd(i)=0 if x(i) is unbounded, c 1 if x(i) has only a lower bound, c 2 if x(i) has both lower and upper bounds, and c 3 if x(i) has only an upper bound. c On exit nbd is unchanged. c c x is a double precision array of dimension n. c On entry x specifies the Cauchy point xcp. c On exit x(i) is the minimizer of Q over the subspace of c free variables. c c d is a double precision array of dimension n. c On entry d is the reduced gradient of Q at xcp. c On exit d is the Newton direction of Q. c c ws and wy are double precision arrays; c theta is a double precision variable; c col is an integer variable; c head is an integer variable. c On entry they store the information defining the c limited memory BFGS matrix: c ws(n,m) stores S, a set of s-vectors; c wy(n,m) stores Y, a set of y-vectors; c theta is the scaling factor specifying B_0 = theta I; c col is the number of variable metric corrections stored; c head is the location of the 1st s- (or y-) vector in S (or Y). c On exit they are unchanged. c c iword is an integer variable. c On entry iword is unspecified. c On exit iword specifies the status of the subspace solution. c iword = 0 if the solution is in the box, c 1 if some bound is encountered. c c wv is a double precision working array of dimension 2m. c c wn is a double precision array of dimension 2m x 2m. c On entry the upper triangle of wn stores the LEL^T factorization c of the indefinite matrix c c K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] c [L_a -R_z theta*S'AA'S ] c where E = [-I 0] c [ 0 I] c On exit wn is unchanged. c c iprint is an INTEGER variable that must be set by the user. c It controls the frequency and type of output generated: c iprint<0 no output is generated; c iprint=0 print only one line at the last iteration; c 0100 print details of every iteration including x and g; c When iprint > 0, the file iterate.dat will be created to c summarize the iteration. c c info is an integer variable. c On entry info is unspecified. c On exit info = 0 for normal return, c = nonzero for abnormal return c when the matrix K is ill-conditioned. c c Subprograms called: c c Linpack dtrsl. c c c References: c c [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited c memory algorithm for bound constrained optimization'', c SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. c c c c * * * c c NEOS, November 1994. (Latest revision June 1996.) c Optimization Technology Center. c Argonne National Laboratory and Northwestern University. c Written by c Ciyou Zhu c in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. c c c ************ logical temp1_updated integer pointr,m2,col2,ibd,jy,js,i,j,k double precision alpha,dk,temp1,temp2 double precision one,zero parameter (one=1.0d0,zero=0.0d0) if (nsub .le. 0) return if (iprint .ge. 99) write (6,1001) c Compute wv = W'Zd. pointr = head do 20 i = 1, col temp1 = zero temp2 = zero do 10 j = 1, nsub k = ind(j) temp1 = temp1 + wy(k,pointr)*d(j) temp2 = temp2 + ws(k,pointr)*d(j) 10 continue wv(i) = temp1 wv(col + i) = theta*temp2 pointr = mod(pointr,m) + 1 20 continue c Compute wv:=K^(-1)wv. m2 = 2*m col2 = 2*col call dtrsl(wn,m2,col2,wv,11,info) if (info .ne. 0) return do 25 i = 1, col wv(i) = -wv(i) 25 continue call dtrsl(wn,m2,col2,wv,01,info) if (info .ne. 0) return c Compute d = (1/theta)d + (1/theta**2)Z'W wv. pointr = head do 40 jy = 1, col js = col + jy do 30 i = 1, nsub k = ind(i) d(i) = d(i) + wy(k,pointr)*wv(jy)/theta + + ws(k,pointr)*wv(js) 30 continue pointr = mod(pointr,m) + 1 40 continue do 50 i = 1, nsub d(i) = d(i)/theta 50 continue c Backtrack to the feasible region. alpha = one temp1 = alpha do 60 i = 1, nsub k = ind(i) dk = d(i) if (nbd(k) .ne. 0) then temp1_updated = .false. if (dk .lt. zero .and. nbd(k) .le. 2) then temp2 = l(k) - x(k) if (temp2 .ge. zero) then temp1 = zero temp1_updated = .true. else if (dk*alpha .lt. temp2) then temp1 = temp2/dk temp1_updated = .true. endif else if (dk .gt. zero .and. nbd(k) .ge. 2) then temp2 = u(k) - x(k) if (temp2 .le. zero) then temp1 = zero temp1_updated = .true. else if (dk*alpha .gt. temp2) then temp1 = temp2/dk temp1_updated = .true. endif endif cc logical variable temp1_updated added to eliminate unexpected cc trigger of the if statement due to possible difference between cc hardware precision and double precision. if (temp1_updated .and. temp1 .lt. alpha) then alpha = temp1 ibd = i endif endif 60 continue if (alpha .lt. one) then dk = d(ibd) k = ind(ibd) if (dk .gt. zero) then x(k) = u(k) d(ibd) = zero else if (dk .lt. zero) then x(k) = l(k) d(ibd) = zero endif endif do 70 i = 1, nsub k = ind(i) x(k) = x(k) + alpha*d(i) 70 continue if (iprint .ge. 99) then if (alpha .lt. one) then write (6,1002) alpha else write (6,*) 'SM solution inside the box' end if if (iprint .gt.100) write (6,1003) (x(i),i=1,n) endif if (alpha .lt. one) then iword = 1 else iword = 0 endif if (iprint .ge. 99) write (6,1004) 1001 format (/,'----------------SUBSM entered-----------------',/) 1002 format ( 'ALPHA = ',f7.5,' backtrack to the BOX') 1003 format ('Subspace solution X = ',/,(4x,1p,6(1x,d11.4))) 1004 format (/,'----------------exit SUBSM --------------------',/) return end c====================== The end of subsm =============================== subroutine dcsrch(f,g,stp,ftol,gtol,xtol,stpmin,stpmax, + task,isave,dsave) character*(*) task integer isave(2) double precision f,g,stp,ftol,gtol,xtol,stpmin,stpmax double precision dsave(13) c ********** c c Subroutine dcsrch c c This subroutine finds a step that satisfies a sufficient c decrease condition and a curvature condition. c c Each call of the subroutine updates an interval with c endpoints stx and sty. The interval is initially chosen c so that it contains a minimizer of the modified function c c psi(stp) = f(stp) - f(0) - ftol*stp*f'(0). c c If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the c interval is chosen so that it contains a minimizer of f. c c The algorithm is designed to find a step that satisfies c the sufficient decrease condition c c f(stp) <= f(0) + ftol*stp*f'(0), c c and the curvature condition c c abs(f'(stp)) <= gtol*abs(f'(0)). c c If ftol is less than gtol and if, for example, the function c is bounded below, then there is always a step which satisfies c both conditions. c c If no step can be found that satisfies both conditions, then c the algorithm stops with a warning. In this case stp only c satisfies the sufficient decrease condition. c c A typical invocation of dcsrch has the following outline: c c task = 'START' c 10 continue c call dcsrch( ... ) c if (task .eq. 'FG') then c Evaluate the function and the gradient at stp c goto 10 c end if c c NOTE: The user must no alter work arrays between calls. c c The subroutine statement is c c subroutine dcsrch(f,g,stp,ftol,gtol,xtol,stpmin,stpmax, c task,isave,dsave) c where c c f is a double precision variable. c On initial entry f is the value of the function at 0. c On subsequent entries f is the value of the c function at stp. c On exit f is the value of the function at stp. c c g is a double precision variable. c On initial entry g is the derivative of the function at 0. c On subsequent entries g is the derivative of the c function at stp. c On exit g is the derivative of the function at stp. c c stp is a double precision variable. c On entry stp is the current estimate of a satisfactory c step. On initial entry, a positive initial estimate c must be provided. c On exit stp is the current estimate of a satisfactory step c if task = 'FG'. If task = 'CONV' then stp satisfies c the sufficient decrease and curvature condition. c c ftol is a double precision variable. c On entry ftol specifies a nonnegative tolerance for the c sufficient decrease condition. c On exit ftol is unchanged. c c gtol is a double precision variable. c On entry gtol specifies a nonnegative tolerance for the c curvature condition. c On exit gtol is unchanged. c c xtol is a double precision variable. c On entry xtol specifies a nonnegative relative tolerance c for an acceptable step. The subroutine exits with a c warning if the relative difference between sty and stx c is less than xtol. c On exit xtol is unchanged. c c stpmin is a double precision variable. c On entry stpmin is a nonnegative lower bound for the step. c On exit stpmin is unchanged. c c stpmax is a double precision variable. c On entry stpmax is a nonnegative upper bound for the step. c On exit stpmax is unchanged. c c task is a character variable of length at least 60. c On initial entry task must be set to 'START'. c On exit task indicates the required action: c c If task(1:2) = 'FG' then evaluate the function and c derivative at stp and call dcsrch again. c c If task(1:4) = 'CONV' then the search is successful. c c If task(1:4) = 'WARN' then the subroutine is not able c to satisfy the convergence conditions. The exit value of c stp contains the best point found during the search. c c If task(1:5) = 'ERROR' then there is an error in the c input arguments. c c On exit with convergence, a warning or an error, the c variable task contains additional information. c c isave is an integer work array of dimension 2. c c dsave is a double precision work array of dimension 13. c c Subprograms called c c MINPACK-2 ... dcstep c c MINPACK-1 Project. June 1983. c Argonne National Laboratory. c Jorge J. More' and David J. Thuente. c c MINPACK-2 Project. October 1993. c Argonne National Laboratory and University of Minnesota. c Brett M. Averick, Richard G. Carter, and Jorge J. More'. c c ********** double precision zero,p5,p66 parameter(zero=0.0d0,p5=0.5d0,p66=0.66d0) double precision xtrapl,xtrapu parameter(xtrapl=1.1d0,xtrapu=4.0d0) logical brackt integer stage double precision finit,ftest,fm,fx,fxm,fy,fym,ginit,gtest, + gm,gx,gxm,gy,gym,stx,sty,stmin,stmax,width,width1 c Initialization block. if (task(1:5) .eq. 'START') then c Check the input arguments for errors. if (stp .lt. stpmin) task = 'ERROR: STP .LT. STPMIN' if (stp .gt. stpmax) task = 'ERROR: STP .GT. STPMAX' if (g .ge. zero) task = 'ERROR: INITIAL G .GE. ZERO' if (ftol .lt. zero) task = 'ERROR: FTOL .LT. ZERO' if (gtol .lt. zero) task = 'ERROR: GTOL .LT. ZERO' if (xtol .lt. zero) task = 'ERROR: XTOL .LT. ZERO' if (stpmin .lt. zero) task = 'ERROR: STPMIN .LT. ZERO' if (stpmax .lt. stpmin) task = 'ERROR: STPMAX .LT. STPMIN' c Exit if there are errors on input. if (task(1:5) .eq. 'ERROR') return c Initialize local variables. brackt = .false. stage = 1 finit = f ginit = g gtest = ftol*ginit width = stpmax - stpmin width1 = width/p5 c The variables stx, fx, gx contain the values of the step, c function, and derivative at the best step. c The variables sty, fy, gy contain the value of the step, c function, and derivative at sty. c The variables stp, f, g contain the values of the step, c function, and derivative at stp. stx = zero fx = finit gx = ginit sty = zero fy = finit gy = ginit stmin = zero stmax = stp + xtrapu*stp task = 'FG' goto 1000 else c Restore local variables. if (isave(1) .eq. 1) then brackt = .true. else brackt = .false. endif stage = isave(2) ginit = dsave(1) gtest = dsave(2) gx = dsave(3) gy = dsave(4) finit = dsave(5) fx = dsave(6) fy = dsave(7) stx = dsave(8) sty = dsave(9) stmin = dsave(10) stmax = dsave(11) width = dsave(12) width1 = dsave(13) endif c If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the c algorithm enters the second stage. ftest = finit + stp*gtest if (stage .eq. 1 .and. f .le. ftest .and. g .ge. zero) + stage = 2 c Test for warnings. if (brackt .and. (stp .le. stmin .or. stp .ge. stmax)) + task = 'WARNING: ROUNDING ERRORS PREVENT PROGRESS' if (brackt .and. stmax - stmin .le. xtol*stmax) + task = 'WARNING: XTOL TEST SATISFIED' if (stp .eq. stpmax .and. f .le. ftest .and. g .le. gtest) + task = 'WARNING: STP = STPMAX' if (stp .eq. stpmin .and. (f .gt. ftest .or. g .ge. gtest)) + task = 'WARNING: STP = STPMIN' cc New warning statement added to eliminate the unexpected case cc of stp=stx due to possible difference between hardware precision cc and double precision. if (stp .eq. stx) + task = 'WARNING: STP = STX' c Test for convergence. if (f .le. ftest .and. abs(g) .le. gtol*(-ginit)) + task = 'CONVERGENCE' c Test for termination. if (task(1:4) .eq. 'WARN' .or. task(1:4) .eq. 'CONV') goto 1000 c A modified function is used to predict the step during the c first stage if a lower function value has been obtained but c the decrease is not sufficient. if (stage .eq. 1 .and. f .le. fx .and. f .gt. ftest) then c Define the modified function and derivative values. fm = f - stp*gtest fxm = fx - stx*gtest fym = fy - sty*gtest gm = g - gtest gxm = gx - gtest gym = gy - gtest c Call dcstep to update stx, sty, and to compute the new step. call dcstep(stx,fxm,gxm,sty,fym,gym,stp,fm,gm, + brackt,stmin,stmax) c Reset the function and derivative values for f. fx = fxm + stx*gtest fy = fym + sty*gtest gx = gxm + gtest gy = gym + gtest else c Call dcstep to update stx, sty, and to compute the new step. call dcstep(stx,fx,gx,sty,fy,gy,stp,f,g, + brackt,stmin,stmax) endif c Decide if a bisection step is needed. if (brackt) then if (abs(sty-stx) .ge. p66*width1) stp = stx + p5*(sty - stx) width1 = width width = abs(sty-stx) endif c Set the minimum and maximum steps allowed for stp. if (brackt) then stmin = min(stx,sty) stmax = max(stx,sty) else stmin = stp + xtrapl*(stp - stx) stmax = stp + xtrapu*(stp - stx) endif c Force the step to be within the bounds stpmax and stpmin. stp = max(stp,stpmin) stp = min(stp,stpmax) c If further progress is not possible, let stp be the best c point obtained during the search. if (brackt .and. (stp .le. stmin .or. stp .ge. stmax) + .or. (brackt .and. stmax-stmin .le. xtol*stmax)) stp = stx c Obtain another function and derivative. task = 'FG' 1000 continue c Save local variables. if (brackt) then isave(1) = 1 else isave(1) = 0 endif isave(2) = stage dsave(1) = ginit dsave(2) = gtest dsave(3) = gx dsave(4) = gy dsave(5) = finit dsave(6) = fx dsave(7) = fy dsave(8) = stx dsave(9) = sty dsave(10) = stmin dsave(11) = stmax dsave(12) = width dsave(13) = width1 end c====================== The end of dcsrch ============================== subroutine dcstep(stx,fx,dx,sty,fy,dy,stp,fp,dp,brackt, + stpmin,stpmax) logical brackt double precision stx,fx,dx,sty,fy,dy,stp,fp,dp,stpmin,stpmax c ********** c c Subroutine dcstep c c This subroutine computes a safeguarded step for a search c procedure and updates an interval that contains a step that c satisfies a sufficient decrease and a curvature condition. c c The parameter stx contains the step with the least function c value. If brackt is set to .true. then a minimizer has c been bracketed in an interval with endpoints stx and sty. c The parameter stp contains the current step. c The subroutine assumes that if brackt is set to .true. then c c min(stx,sty) < stp < max(stx,sty), c c and that the derivative at stx is negative in the direction c of the step. c c The subroutine statement is c c subroutine dcstep(stx,fx,dx,sty,fy,dy,stp,fp,dp,brackt, c stpmin,stpmax) c c where c c stx is a double precision variable. c On entry stx is the best step obtained so far and is an c endpoint of the interval that contains the minimizer. c On exit stx is the updated best step. c c fx is a double precision variable. c On entry fx is the function at stx. c On exit fx is the function at stx. c c dx is a double precision variable. c On entry dx is the derivative of the function at c stx. The derivative must be negative in the direction of c the step, that is, dx and stp - stx must have opposite c signs. c On exit dx is the derivative of the function at stx. c c sty is a double precision variable. c On entry sty is the second endpoint of the interval that c contains the minimizer. c On exit sty is the updated endpoint of the interval that c contains the minimizer. c c fy is a double precision variable. c On entry fy is the function at sty. c On exit fy is the function at sty. c c dy is a double precision variable. c On entry dy is the derivative of the function at sty. c On exit dy is the derivative of the function at the exit sty. c c stp is a double precision variable. c On entry stp is the current step. If brackt is set to .true. c then on input stp must be between stx and sty. c On exit stp is a new trial step. c c fp is a double precision variable. c On entry fp is the function at stp c On exit fp is unchanged. c c dp is a double precision variable. c On entry dp is the the derivative of the function at stp. c On exit dp is unchanged. c c brackt is an logical variable. c On entry brackt specifies if a minimizer has been bracketed. c Initially brackt must be set to .false. c On exit brackt specifies if a minimizer has been bracketed. c When a minimizer is bracketed brackt is set to .true. c c stpmin is a double precision variable. c On entry stpmin is a lower bound for the step. c On exit stpmin is unchanged. c c stpmax is a double precision variable. c On entry stpmax is an upper bound for the step. c On exit stpmax is unchanged. c c MINPACK-1 Project. June 1983 c Argonne National Laboratory. c Jorge J. More' and David J. Thuente. c c MINPACK-2 Project. October 1993. c Argonne National Laboratory and University of Minnesota. c Brett M. Averick and Jorge J. More'. c c ********** double precision zero,p66,two,three parameter(zero=0.0d0,p66=0.66d0,two=2.0d0,three=3.0d0) double precision gamma,p,q,r,s,sgnd,stpc,stpf,stpq,theta sgnd = dp*(dx/abs(dx)) c First case: A higher function value. The minimum is bracketed. c If the cubic step is closer to stx than the quadratic step, the c cubic step is taken, otherwise the average of the cubic and c quadratic steps is taken. if (fp .gt. fx) then theta = three*(fx - fp)/(stp - stx) + dx + dp s = max(abs(theta),abs(dx),abs(dp)) gamma = s*sqrt((theta/s)**2 - (dx/s)*(dp/s)) if (stp .lt. stx) gamma = -gamma p = (gamma - dx) + theta q = ((gamma - dx) + gamma) + dp r = p/q stpc = stx + r*(stp - stx) stpq = stx + ((dx/((fx - fp)/(stp - stx) + dx))/two)* + (stp - stx) if (abs(stpc-stx) .lt. abs(stpq-stx)) then stpf = stpc else stpf = stpc + (stpq - stpc)/two endif brackt = .true. c Second case: A lower function value and derivatives of opposite c sign. The minimum is bracketed. If the cubic step is farther from c stp than the secant step, the cubic step is taken, otherwise the c secant step is taken. else if (sgnd .lt. zero) then theta = three*(fx - fp)/(stp - stx) + dx + dp s = max(abs(theta),abs(dx),abs(dp)) gamma = s*sqrt((theta/s)**2 - (dx/s)*(dp/s)) if (stp .gt. stx) gamma = -gamma p = (gamma - dp) + theta q = ((gamma - dp) + gamma) + dx r = p/q stpc = stp + r*(stx - stp) stpq = stp + (dp/(dp - dx))*(stx - stp) if (abs(stpc-stp) .gt. abs(stpq-stp)) then stpf = stpc else stpf = stpq endif brackt = .true. c Third case: A lower function value, derivatives of the same sign, c and the magnitude of the derivative decreases. else if (abs(dp) .lt. abs(dx)) then c The cubic step is computed only if the cubic tends to infinity c in the direction of the step or if the minimum of the cubic c is beyond stp. Otherwise the cubic step is defined to be the c secant step. theta = three*(fx - fp)/(stp - stx) + dx + dp s = max(abs(theta),abs(dx),abs(dp)) c The case gamma = 0 only arises if the cubic does not tend c to infinity in the direction of the step. gamma = s*sqrt(max(zero,(theta/s)**2-(dx/s)*(dp/s))) if (stp .gt. stx) gamma = -gamma p = (gamma - dp) + theta q = (gamma + (dx - dp)) + gamma r = p/q if (r .lt. zero .and. gamma .ne. zero) then stpc = stp + r*(stx - stp) else if (stp .gt. stx) then stpc = stpmax else stpc = stpmin endif stpq = stp + (dp/(dp - dx))*(stx - stp) if (brackt) then c A minimizer has been bracketed. If the cubic step is c closer to stp than the secant step, the cubic step is c taken, otherwise the secant step is taken. if (abs(stpc-stp) .lt. abs(stpq-stp)) then stpf = stpc else stpf = stpq endif if (stp .gt. stx) then stpf = min(stp+p66*(sty-stp),stpf) else stpf = max(stp+p66*(sty-stp),stpf) endif else c A minimizer has not been bracketed. If the cubic step is c farther from stp than the secant step, the cubic step is c taken, otherwise the secant step is taken. if (abs(stpc-stp) .gt. abs(stpq-stp)) then stpf = stpc else stpf = stpq endif stpf = min(stpmax,stpf) stpf = max(stpmin,stpf) endif c Fourth case: A lower function value, derivatives of the c same sign, and the magnitude of the derivative does not c decrease. If the minimum is not bracketed, the step is either c stpmin or stpmax, otherwise the cubic step is taken. else if (brackt) then theta = three*(fp - fy)/(sty - stp) + dy + dp s = max(abs(theta),abs(dy),abs(dp)) gamma = s*sqrt((theta/s)**2 - (dy/s)*(dp/s)) if (stp .gt. sty) gamma = -gamma p = (gamma - dp) + theta q = ((gamma - dp) + gamma) + dy r = p/q stpc = stp + r*(sty - stp) stpf = stpc else if (stp .gt. stx) then stpf = stpmax else stpf = stpmin endif endif c Update the interval which contains a minimizer. if (fp .gt. fx) then sty = stp fy = fp dy = dp else if (sgnd .lt. zero) then sty = stx fy = fx dy = dx endif stx = stp fx = fp dx = dp endif c Compute the new step. stp = stpf end c====================== The end of dcstep ============================== subroutine timer(ttime) double precision ttime c ********* c c Subroutine timer c c This subroutine is used to determine user time. In a typical c application, the user time for a code segment requires calls c to subroutine timer to determine the initial and final time. c c The subroutine statement is c c subroutine timer(ttime) c c where c c ttime is an output variable which specifies the user time. c c Argonne National Laboratory and University of Minnesota. c MINPACK-2 Project. c c Modified October 1990 by Brett M. Averick. c c ********** real temp real tarray(2) real etime c The first element of the array tarray specifies user time temp = etime(tarray) ttime = dble(tarray(1)) return end c====================== The end of timer =============================== double precision function dnrm2(n,x,incx) integer n,incx double precision x(n) c ********** c c Function dnrm2 c c Given a vector x of length n, this function calculates the c Euclidean norm of x with stride incx. c c The function statement is c c double precision function dnrm2(n,x,incx) c c where c c n is a positive integer input variable. c c x is an input array of length n. c c incx is a positive integer variable that specifies the c stride of the vector. c c Subprograms called c c FORTRAN-supplied ... abs, max, sqrt c c MINPACK-2 Project. February 1991. c Argonne National Laboratory. c Brett M. Averick. c c ********** integer i double precision scale dnrm2 = 0.0d0 scale = 0.0d0 do 10 i = 1, n, incx scale = max(scale, abs(x(i))) 10 continue if (scale .eq. 0.0d0) return do 20 i = 1, n, incx dnrm2 = dnrm2 + (x(i)/scale)**2 20 continue dnrm2 = scale*sqrt(dnrm2) return end c====================== The end of dnrm2 =============================== double precision function dpmeps() c ********** c c Subroutine dpeps c c This subroutine computes the machine precision parameter c dpmeps as the smallest floating point number such that c 1 + dpmeps differs from 1. c c This subroutine is based on the subroutine machar described in c c W. J. Cody, c MACHAR: A subroutine to dynamically determine machine parameters, c ACM Trans. Math. Soft., 14, 1988, pages 303-311. c c The subroutine statement is: c c subroutine dpeps(dpmeps) c c where c c dpmeps is a double precision variable. c On entry dpmeps need not be specified. c On exit dpmeps is the machine precision. c c MINPACK-2 Project. February 1991. c Argonne National Laboratory and University of Minnesota. c Brett M. Averick. c c ******* integer i,ibeta,irnd,it,itemp,negep double precision a,b,beta,betain,betah,temp,tempa,temp1, + zero,one,two data zero,one,two /0.0d0,1.0d0,2.0d0/ c determine ibeta, beta ala malcolm. a = one b = one 10 continue a = a + a temp = a + one temp1 = temp - a if (temp1 - one .eq. zero) go to 10 20 continue b = b + b temp = a + b itemp = int(temp - a) if (itemp .eq. 0) go to 20 ibeta = itemp beta = dble(ibeta) c determine it, irnd. it = 0 b = one 30 continue it = it + 1 b = b * beta temp = b + one temp1 = temp - b if (temp1 - one .eq. zero) go to 30 irnd = 0 betah = beta/two temp = a + betah if (temp - a .ne. zero) irnd = 1 tempa = a + beta temp = tempa + betah if ((irnd .eq. 0) .and. (temp - tempa .ne. zero)) irnd = 2 c determine dpmeps. negep = it + 3 betain = one/beta a = one do 40 i = 1, negep a = a*betain 40 continue 50 continue temp = one + a if (temp - one .ne. zero) go to 60 a = a*beta go to 50 60 continue dpmeps = a if ((ibeta .eq. 2) .or. (irnd .eq. 0)) go to 70 a = (a*(one + a))/two temp = one + a if (temp - one .ne. zero) dpmeps = a 70 return end c====================== The end of dpmeps ============================== subroutine daxpy(n,da,dx,incx,dy,incy) c c constant times a vector plus a vector. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dy(*),da integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if (da .eq. 0.0d0) return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dy(iy) = dy(iy) + da*dx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,4) if( m .eq. 0 ) go to 40 do 30 i = 1,m dy(i) = dy(i) + da*dx(i) 30 continue if( n .lt. 4 ) return 40 mp1 = m + 1 do 50 i = mp1,n,4 dy(i) = dy(i) + da*dx(i) dy(i + 1) = dy(i + 1) + da*dx(i + 1) dy(i + 2) = dy(i + 2) + da*dx(i + 2) dy(i + 3) = dy(i + 3) + da*dx(i + 3) 50 continue return end c====================== The end of daxpy =============================== subroutine dcopy(n,dx,incx,dy,incy) c c copies a vector, x, to a vector, y. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dy(*) integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dy(iy) = dx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,7) if( m .eq. 0 ) go to 40 do 30 i = 1,m dy(i) = dx(i) 30 continue if( n .lt. 7 ) return 40 mp1 = m + 1 do 50 i = mp1,n,7 dy(i) = dx(i) dy(i + 1) = dx(i + 1) dy(i + 2) = dx(i + 2) dy(i + 3) = dx(i + 3) dy(i + 4) = dx(i + 4) dy(i + 5) = dx(i + 5) dy(i + 6) = dx(i + 6) 50 continue return end c====================== The end of dcopy =============================== double precision function ddot(n,dx,incx,dy,incy) c c forms the dot product of two vectors. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dy(*),dtemp integer i,incx,incy,ix,iy,m,mp1,n c ddot = 0.0d0 dtemp = 0.0d0 if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = dtemp + dx(ix)*dy(iy) ix = ix + incx iy = iy + incy 10 continue ddot = dtemp return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dtemp + dx(i)*dy(i) 30 continue if( n .lt. 5 ) go to 60 40 mp1 = m + 1 do 50 i = mp1,n,5 dtemp = dtemp + dx(i)*dy(i) + dx(i + 1)*dy(i + 1) + * dx(i + 2)*dy(i + 2) + dx(i + 3)*dy(i + 3) + dx(i + 4)*dy(i + 4) 50 continue 60 ddot = dtemp return end c====================== The end of ddot ================================ subroutine dpofa(a,lda,n,info) integer lda,n,info double precision a(lda,*) c c dpofa factors a double precision symmetric positive definite c matrix. c c dpofa is usually called by dpoco, but it can be called c directly with a saving in time if rcond is not needed. c (time for dpoco) = (1 + 18/n)*(time for dpofa) . c c on entry c c a double precision(lda, n) c the symmetric matrix to be factored. only the c diagonal and upper triangle are used. c c lda integer c the leading dimension of the array a . c c n integer c the order of the matrix a . c c on return c c a an upper triangular matrix r so that a = trans(r)*r c where trans(r) is the transpose. c the strict lower triangle is unaltered. c if info .ne. 0 , the factorization is not complete. c c info integer c = 0 for normal return. c = k signals an error condition. the leading minor c of order k is not positive definite. c c linpack. this version dated 08/14/78 . c cleve moler, university of new mexico, argonne national lab. c c subroutines and functions c c blas ddot c fortran sqrt c c internal variables c double precision ddot,t double precision s integer j,jm1,k c begin block with ...exits to 40 c c do 30 j = 1, n info = j s = 0.0d0 jm1 = j - 1 if (jm1 .lt. 1) go to 20 do 10 k = 1, jm1 t = a(k,j) - ddot(k-1,a(1,k),1,a(1,j),1) t = t/a(k,k) a(k,j) = t s = s + t*t 10 continue 20 continue s = a(j,j) - s c ......exit if (s .le. 0.0d0) go to 40 a(j,j) = sqrt(s) 30 continue info = 0 40 continue return end c====================== The end of dpofa =============================== subroutine dscal(n,da,dx,incx) c c scales a vector by a constant. c uses unrolled loops for increment equal to one. c jack dongarra, linpack, 3/11/78. c modified 3/93 to return if incx .le. 0. c double precision da,dx(*) integer i,incx,m,mp1,n,nincx c if( n.le.0 .or. incx.le.0 )return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c nincx = n*incx do 10 i = 1,nincx,incx dx(i) = da*dx(i) 10 continue return c c code for increment equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dx(i) = da*dx(i) 30 continue if( n .lt. 5 ) return 40 mp1 = m + 1 do 50 i = mp1,n,5 dx(i) = da*dx(i) dx(i + 1) = da*dx(i + 1) dx(i + 2) = da*dx(i + 2) dx(i + 3) = da*dx(i + 3) dx(i + 4) = da*dx(i + 4) 50 continue return end c====================== The end of dscal =============================== subroutine dtrsl(t,ldt,n,b,job,info) integer ldt,n,job,info double precision t(ldt,*),b(*) c c c dtrsl solves systems of the form c c t * x = b c or c trans(t) * x = b c c where t is a triangular matrix of order n. here trans(t) c denotes the transpose of the matrix t. c c on entry c c t double precision(ldt,n) c t contains the matrix of the system. the zero c elements of the matrix are not referenced, and c the corresponding elements of the array can be c used to store other information. c c ldt integer c ldt is the leading dimension of the array t. c c n integer c n is the order of the system. c c b double precision(n). c b contains the right hand side of the system. c c job integer c job specifies what kind of system is to be solved. c if job is c c 00 solve t*x=b, t lower triangular, c 01 solve t*x=b, t upper triangular, c 10 solve trans(t)*x=b, t lower triangular, c 11 solve trans(t)*x=b, t upper triangular. c c on return c c b b contains the solution, if info .eq. 0. c otherwise b is unaltered. c c info integer c info contains zero if the system is nonsingular. c otherwise info contains the index of c the first zero diagonal element of t. c c linpack. this version dated 08/14/78 . c g. w. stewart, university of maryland, argonne national lab. c c subroutines and functions c c blas daxpy,ddot c fortran mod c c internal variables c double precision ddot,temp integer case,j,jj c c begin block permitting ...exits to 150 c c check for zero diagonal elements. c do 10 info = 1, n c ......exit if (t(info,info) .eq. 0.0d0) go to 150 10 continue info = 0 c c determine the task and go to it. c case = 1 if (mod(job,10) .ne. 0) case = 2 if (mod(job,100)/10 .ne. 0) case = case + 2 go to (20,50,80,110), case c c solve t*x=b for t lower triangular c 20 continue b(1) = b(1)/t(1,1) if (n .lt. 2) go to 40 do 30 j = 2, n temp = -b(j-1) call daxpy(n-j+1,temp,t(j,j-1),1,b(j),1) b(j) = b(j)/t(j,j) 30 continue 40 continue go to 140 c c solve t*x=b for t upper triangular. c 50 continue b(n) = b(n)/t(n,n) if (n .lt. 2) go to 70 do 60 jj = 2, n j = n - jj + 1 temp = -b(j+1) call daxpy(j,temp,t(1,j+1),1,b(1),1) b(j) = b(j)/t(j,j) 60 continue 70 continue go to 140 c c solve trans(t)*x=b for t lower triangular. c 80 continue b(n) = b(n)/t(n,n) if (n .lt. 2) go to 100 do 90 jj = 2, n j = n - jj + 1 b(j) = b(j) - ddot(jj-1,t(j+1,j),1,b(j+1),1) b(j) = b(j)/t(j,j) 90 continue 100 continue go to 140 c c solve trans(t)*x=b for t upper triangular. c 110 continue b(1) = b(1)/t(1,1) if (n .lt. 2) go to 130 do 120 j = 2, n b(j) = b(j) - ddot(j-1,t(1,j),1,b(1),1) b(j) = b(j)/t(j,j) 120 continue 130 continue 140 continue 150 continue return end c====================== The end of dtrsl =============================== glm-ie_v1.4/pls/lbfgsb/matlabexception.h0000644000175000017500000000154511455163061016170 0ustar hnhn#ifndef INCLUDE_MATLABEXCEPTION #define INCLUDE_MATLABEXCEPTION #include // Class MatlabException // ----------------------------------------------------------------- // This class just makes it easier for me to throw exceptions. Its // functionality really has nothing to do with MATLAB. class MatlabException : public std::exception { public: MatlabException (const char* message) throw(); ~MatlabException() throw() { }; // The copy constructor makes a shallow copy. MatlabException (const MatlabException& source) throw(); // The copy assignment operator makes a shallow copy as well. MatlabException& operator= (const MatlabException& source); // Return the message string. virtual const char* what () const throw() { return message; }; private: const char* message; // The error message. }; #endif glm-ie_v1.4/pls/lbfgsb/license.txt0000644000175000017500000000302711455163061015020 0ustar hnhnCopyright (c) 2009, Peter Carbonetto All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution * Neither the name of the University of British Columbia nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. glm-ie_v1.4/pls/brentmin.m0000755000175000017500000000730311455163066013403 0ustar hnhnfunction [xmin,fmin,funccount] = brentmin(xlow,xupp,Nitmax,tol,f,varargin) % BRENT Brent's minimization method in one dimension taken from: % § 10.2 Parabolic Interpolation and Brent's Method in One Dimension % Press, Teukolsky, Vetterling & Flannery % Numerical Recipes in C, Cambridge University Press, 2002 % % [xmin,fmin] = BRENTMIN(xlow,xupp,Nit,tol,f,varargin) % Given a function f, and given a search interval this routine isolates % the minimum of fractional precision of about tol using Brent's method. % % INPUT % xlow,xupp: search interval such that xlow<=xmin<=xupp % Nitmax: maximum number of function evaluations made by the routine % tol: fractional precision % f, varargin: f(x,varargin{:}) is the function % % OUTPUT % fmin: minimal function value % xmin: corresponding abscissa-value % funccount: number of function evaluations made % % Hannes Nickisch % revised 10/04/2006 % version 1.0.2 % tolerance is no smaller than machine's floating point precision tol = max(tol,eps); % Evaluate endpoints fa = f(xlow,varargin{:}); fb = f(xupp,varargin{:}); funccount = 2; % number of function evaluations % Compute the start point seps = sqrt(eps); c = 0.5*(3.0 - sqrt(5.0));% golden ratio a = xlow; b = xupp; v = a + c*(b-a); w = v; xf = v; d = 0.0; e = 0.0; x= xf; fx = f(x,varargin{:}); funccount = funccount + 1; fv = fx; fw = fx; xm = 0.5*(a+b); tol1 = seps*abs(xf) + tol/3.0; tol2 = 2.0*tol1; % Main loop while ( abs(xf-xm) > (tol2 - 0.5*(b-a)) ) gs = 1; % Is a parabolic fit possible if abs(e) > tol1 % Yes, so fit parabola gs = 0; r = (xf-w)*(fx-fv); q = (xf-v)*(fx-fw); p = (xf-v)*q-(xf-w)*r; q = 2.0*(q-r); if q > 0.0, p = -p; end q = abs(q); r = e; e = d; % Is the parabola acceptable if ( (abs(p)q*(a-xf)) && (p= xm, e = a-xf; else e = b-xf; end d = c*e; end % The function must not be evaluated too close to xf si = sign(d) + (d == 0); x = xf + si * max( abs(d), tol1 ); fu = f(x,varargin{:}); funccount = funccount + 1; % Update a, b, v, w, x, xm, tol1, tol2 if fu <= fx if x >= xf, a = xf; else b = xf; end v = w; fv = fw; w = xf; fw = fx; xf = x; fx = fu; else % fu > fx if x < xf, a = x; else b = x; end if ( (fu <= fw) || (w == xf) ) v = w; fv = fw; w = x; fw = fu; elseif ( (fu <= fv) || (v == xf) || (v == w) ) v = x; fv = fu; end end xm = 0.5*(a+b); tol1 = seps*abs(xf) + tol/3.0; tol2 = 2.0*tol1; if funccount >= Nitmax % BREAK fmin = fx; xmin = xf; % typically we should not get here % warning(sprintf('Maximum number of iterations (%d) exceeded: precision is not guaranteed',Nitmax)) % fprintf('[%1.3f,%1.3f,%1.3f]\n',xlow,xf,xupp) break end end % while % check that endpoints are less than the minimum found if ( (fa < fx) && (fa <= fb) ) xf = xlow; fx = fa; elseif fb < fx xf = xupp; fx = fb; end fmin = fx; xmin = xf; glm-ie_v1.4/pls/lbfgsb.m0000644000175000017500000001160111473273375013022 0ustar hnhn% LBFGSB Call the nonlinear bound-constrained solver that uses % limited-memory BFGS quasi-Newton updates. % % The basic function call is % % LBFGSB(x0,lb,ub,objfunc,gradfunc) % % The first input argument x0 is either a matrix or a cell array of % matrices. It declares the starting point for the solver. % % The second and third input arguments lb and ub must be of the exact same % structure as x0. They declare the lower and upper bounds on the % variables, respectively. Set an entry to Inf to declare no bound. % % The next two input arguments must be the names of MATLAB routines % (M-files): % % objfunc Calculates the objective function at the current % point. The routine must accept as many inputs as cell % entry in x0 (or one input if x0 is a matrix). The % output must be a scalar representing the objective % evaluated at the current point. % % gradfunc Computes the gradient of the objective at the current % point. The input is the same as objfunc, but it must % return as many outputs as there are inputs, and each % of the outputs have the same matrix structure as its % corresponding input. % % Optionally, one may choose to pass additional auxiliary data to the % MATLAB callback routines listed above through the function call % LBFGSB(...,auxdata). If auxdata is the empty matrix, no extra % information is passed. It is important to observe that the auxiliary % data MAY NOT CHANGE through the course of the L-BFGS optimization! The % auxiliary data keep the same values as they possessed in the initial % call. If you need variables that change over time, you may want to % consider global variables (type HELP GLOBAL). % % LBFGSB(...,auxdata,iterfunc) specifies an additional callback routine % which is called once per algorithm iteration. The callback routine must % take the form ITERFUNC(T,F,X1,X2,...,AUXDATA). T is the current % iteration of the algorithm. F is the current value of the objective. The % inputs X1, X2,... are exactly the same as the ones passed to objfunc and % gradfunc. Finally, extra information may be passed through the input % AUXDATA. No outputs are expected from iterfunc. If iterfunc is the empty % string, no routine is called. % % These inputs may be followed by parameter/value pairs to modify the % default algorithm options. The algorithm option 'maxiter' sets the % maximum number of iterations. The rest of the options 'm', 'factr' and % 'pgtol' are described in the L-BFGS-B documentation. Note that in this % implementation we divide factr by the machine precision, so that the % convergence condition is satisfied when it is less than factr, not less % than factr times the machine precision. % % Interface has been written by Peter Carbonetto. % Compilation instructions by Hannes Nickisch, 2010-07-19 function x = lbfgsb(x,varargin) fprintf('\n\n\n') fprintf('##########################################################################\n') fprintf('In order to use the L-BFGS minimiser you have to compile Peter Carbonetto''s\n') fprintf('"Matlab interface for L-BFGS-B" [1]. The challenge here is the Fortran 77 code.\n') fprintf('We provide a Makefile suitable for Linux 32/64 bit and Mac whenever you have g77\n') fprintf('properly installed.Under Ubuntu, you can achieve this by installing the package\n') fprintf('fort77, for example.\n\n') fprintf('Compilation is done by editing lbfgsb/Makefile. In any case, you need to\n') fprintf('provide MATLAB_HOME which can be found by the commands ''locate matlab'' or \n') fprintf('''find / -name "matlab"''. You can choose between two compilation modes:\n') fprintf('a) using the mex utility by Matlab [default]\n') fprintf(' provide MEX, then type ''make mex''\n\n') fprintf('b) without mex utility by Matlab\n') fprintf(' provide MEX_SUFFIX and MATLAB_LIB, then type ''make nomex''\n\n') fprintf('In Ubuntu 10.04 LTS, the libg2c library needed for both a) and b) is not\n') fprintf('included per default. If ''ls /usr/lib/libg2c.*'' does not list anything\n') fprintf('this is the case on your machine. You then whant to install the packages\n') fprintf('gcc-3.4-base and libg2c0 e.g. from\n') fprintf('http://packages.ubuntu.com/hardy/gcc-3.4-base and\n') fprintf('http://packages.ubuntu.com/hardy/libg2c0.\n') fprintf('After installation, you have to create a symbolic link by ''cd /usr/lib'' and\n') fprintf('''ln -s libg2c.so.0 libg2c.so''.\n\n') fprintf('[1] http://www.cs.ubc.ca/~pcarbo/lbfgsb-for-matlab.html\n') fprintf('[2] http://www.mathworks.com/support/compilers/R2010a\n') fprintf('##########################################################################\n') fprintf('\n\n\n') error glm-ie_v1.4/pls/solve_quartic.m0000644000175000017500000000253311455163066014442 0ustar hnhn% X = SOLVE_QUARTIC(a,b,c,d) % % Solve the quartic equation % % x^4 + a*x^3 + b*x^2 + c*x + d = 0 % % with real-valued coefficients a, b, c, d analytically using Ferrari's method. % % ARGUMENTS % a [n,1] coefficient vector % or [1,1] coefficient scalar % b [n,1] coefficient vector % or [1,1] coefficient scalar % c [n,1] coefficient vector % or [1,1] coefficient scalar % d [n,1] coefficient vector % or [1,1] coefficient scalar % % RESULTS % X [n,4] result matrix, each column contains a solution % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 11 function X = solve_quartic(a,b,c,d) n = max([numel(a),numel(b),numel(c),numel(d)]); X = zeros(n,4);% allocate memory p = b(:) - a(:).*a(:)*(3/8); % y^4 + p*y^2 + r*y + q = 0, substitute x = y-a/4 q = c(:) - a(:).*b(:)/2 + a(:).*a(:).*a(:)/8; r = d(:) - a(:).*c(:)/4 + a(:).*a(:).*b(:)/16 - a(:).*a(:).*a(:).*a(:)*(3/256); Z = solve_cubic(2*p, p.*p-4*r, -q.*q); % resolvent Z = sort(Z,2,'descend'); % bring smallest solution to the right id = min(abs(Z(:,1:2)),[],2)>1e-12; % nonzero entries W = sqrt(Z); W(id,3) = -q(id)./(W(id,1).*W(id,2)); X = W * [1,1,-1,-1; 1,-1,1,-1; 1,-1,-1,1]; for i=1:4, X(:,i) = X(:,i)/2 - a(:)/4; end % backsubstituteglm-ie_v1.4/pls/phi.m0000644000175000017500000000231611465520303012331 0ustar hnhn% Penalised least squares objective function and derivatives % phi(u) = 1/lambda * ||X*u-y||_2^2 + 2*sum( pen(s) ), s=B*u % % [f,df,d2f] = phi(u,X,y,B,lam,pen,varargin) where the penaliser is evaluated % by feval(pen,s,varargin{:}) % % The return arguments have the following meaning: % f = phi(u), [1,1] scalar % df = d phi(u) / du, and [n,1] gradient vector (same size as u) % d2f = d^2 phi(u) / du^2. [n,n] Hessian matrix % % See also PLSALGORITHMS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 07 function [f,df,d2f] = phi(u,X,y,B,lam,pen,varargin) s = B*u; r = X*u-y; if nargout==1 p = feval(pen,s,varargin{:}); elseif nargout==2 [p,dp] = feval(pen,s,varargin{:}); else [p,dp,d2p] = feval(pen,s,varargin{:}); end f = norm(r,2)^2/lam + 2*sum(p); if nargout>1 df = 2*([X']*r/lam + [B']*dp); if nargout>2 % evaluation of the Hessian is dangerous for large n if numel(dp)==numel(d2p) d2f = 2*(X'*X/lam + B'*diag(d2p)*B); % d2p is a vector else d2f = 2*(X'*X/lam + B'*d2p*B); % d2p is a scalar or a full matrix end end endglm-ie_v1.4/pls/solve_cubic.m0000644000175000017500000000276711455163066014070 0ustar hnhn% X = SOLVE_CUBIC(a,b,c) % % Solve the cubic equation % % x^3 + a*x^2 + b*x + c = 0 % % with real-valued coefficients a, b, c analytically using Cardano's method. % % ARGUMENTS % a [n,1] coefficient vector % or [1,1] coefficient scalar % b [n,1] coefficient vector % or [1,1] coefficient scalar % c [n,1] coefficient vector % or [1,1] coefficient scalar % % RESULTS % X [n,3] result matrix, each column contains a solution; the real one % comes first % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 October 11 function X = solve_cubic(a,b,c) n = max([numel(a),numel(b),numel(c)]); X = zeros(n,3); % allocate memory p = (3*b(:)-a(:).*a(:))/3; % y^3 + p*y + q = 0, substitute x = y-a/3 q = 2*a(:).*a(:).*a(:)/27 - a(:).*b(:)/3 + c(:); D = p.*p.*p/27 + q.*q/4; d = sqrt(D); % discriminant id = D(:)>=0; % nonnegative discriminant u = -q(id)/2+d(id); u = sign(u).*abs(u).^(1/3); v = -q(id)/2-d(id); v = sign(v).*abs(v).^(1/3); r1 = (-1+1i*sqrt(3))/2; r2 = (-1-1i*sqrt(3))/2; X(id,1) = u+v; X(id,2) = r1*u+r2*v; X(id,3) = r2*u+r1*v; id = D(:)<0; % negative discriminant r = sqrt(-p(id).*p(id).*p(id)/27); phi = acos(-q(id)./(2*r)); al = 2*r.^(1/3); X(id,1) = al.*cos(phi/3); X(id,2) = al.*cos(phi/3+2*pi/3); X(id,3) = al.*cos(phi/3+4*pi/3); for i=1:3, X(:,i) = X(:,i) - a(:)/3; end % backsubstituteglm-ie_v1.4/startup.m0000644000175000017500000000152511472707141012463 0ustar hnhn% startup script to make Octave/Matlab aware of the glm-ie package % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 August 25 disp(['executing glm-ie startup script...']); OCT = exist('OCTAVE_VERSION') ~= 0; % check if we run Matlab or Octave me = mfilename; % what is my filename mydir = which(me); mydir = mydir(1:end-2-numel(me)); % where am I located if OCT && numel(mydir)==2 if strcmp(mydir,'./'), mydir = [pwd,mydir(2:end)]; end end % OCTAVE 3.0.x relative, MATLAB and newer have absolute path addpath(mydir(1:end-1)) addpath([mydir,'inf']) addpath([mydir,'mat']) if OCT, addpath([mydir,'mat/@matWav/private']), end addpath([mydir,'mat']) addpath([mydir,'pen']) addpath([mydir,'pls']) addpath([mydir,'pot']) addpath([mydir,'doc']) clear me mydir glm-ie_v1.4/index.html0000644000175000017500000000102611453154140012566 0ustar hnhn User Documentation of the Generalised Linear Models: Inference and Estimation Toolbox (glm-ie) glm-ie_v1.4/plsSolvers.m0000644000175000017500000000417711646246166013153 0ustar hnhn% A PLS (penalised least squares) solver is a program solving the % minimisation problem % phi(u) = 1/lambda * ||X*u-y||_2^2 + 2*sum( pen(s) ), s = B*u, % where pen(s) is a penalty function. % % [u,phi] = pls(u0,X,y,B,opt,lam,pen,varargin) % % INPUT % ===== % u0 [nx1] initial vector % X [mxn] matrix or operator % y [mx1] vector % B [qxn] matrix or operator % opt. optimisation parameters % nMVM maximal number of steps = matrix vector multiplications ... % with A=X'*X/lam+B'*D*B, D diagonal, [default 100] % output flag saying whether something is printed [default false] % the function will show the current iteration number, the actual % function value phi and the current length of the step % in the format: 13, phi=8.6063e-01; du=2.325e-04 % lam [1x1] (positive) weight of the penaliser, can be Inf % pen penaliser function handle or function name % [p,dp,d2p] = feval(pen,Bu,varargin{:}) % varargin additional parameters for pen % % OUTPUT % ====== % u [nx1] optimal solution % phi [1x1] optimal function value % % Currently, we have implemented in pls/pls.m % LBFGS: LIMITED memory BROYDEN-FLETCHER-GOLDFARB-SHANNO % quasi Newton or variable metric method % TN: TRUNCATED NEWTON % optimisation with CG approximated Newton steps % CGBT: CONJUGATE GRADIENTS with BACKTRACKING line search % optimisation using the Armijo rule % CG: CONJUGATE GRADIENTS % optimisation with CG code minimize.m by Carl E. Rasmussen % SB: SPLIT BREGMAN % optimisation using an augmented Lagrangian approach % BB: BARZILAI/BORWEIN % stepsize adjusted gradient method without descent guarantee % % Examples: % >> lam=1; plsLBFGS(u,X,y,B,opt,lam,'penQuad') % >> lam=1; tau=2; z=1.3; plsCG(u,X,y,B,opt,lam,'penVB','potLaplace',tau,z) % % See also PENFUNCTIONS.M, POTFUNCTIONS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 20 glm-ie_v1.4/Copyright0000644000175000017500000000274611530563514012503 0ustar hnhnCopyright 2010, 2011 Hannes Nickisch. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY HANNES NICKISCH ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL HANNES NICKISCH OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. The views and conclusions contained in the software and documentation are those of the authors and should not be interpreted as representing official policies, either expressed or implied, of Hannes Nickisch. glm-ie_v1.4/penFunctions.m0000644000175000017500000000323411466250654013440 0ustar hnhn% A penalty function pen(s) is a function IR^q -> IR. % % [p,dp,d2p] = pen(s,psi) where psi contains additional parameters % % The return arguments have the following meaning: % p = pen(s), % dp = d pen(s) / ds, % d2p = d^2 pen(s) / ds^2, % and the following dimensions: % p function value [1x1] or vector of individual function values [qx1], % dp gradient vector [qx1], % d2p Hessian diagonal [qx1] or full matrix [qxq]. % % Currently, we have implemented in pen/pen.m % Absolute value: penAbs(s) = abs(s), => potLaplace % Smoothed absolute value: penAbsSmooth(s,ep) = sqrt(s^2+ep), % Linear pen. on negative: penNegLin(s) = max(-s,0), % Logarithmic: penLogSmooth(s,nu) = log(s^2+nu),=> potT % Power: penPow(s,d) = abs(s)^d, => potExpPow % Smoothed power: penPowSmooth(s,d,ep) = sqrt(s^2+ep)^d, % Quadratic: penQuad(s) = s^2/2, => potGauss % Quadr. pen on negative: penNegQuad(s) = min(s,0)^2/2, % Zero: penZero(s) = 0, and % % Derived from a potential for use with Variational bounding (VB) inference: % penVB(s,pot,tau,z) = tau*b*(r-s) -log(pot(tau*r)), r=sign(s)*sqrt(s^2+z) % Norm penalty derived from symmetric potential to be used with VB inference: % penVBNorm(s,pot,tau,z,G) = -log( pot(tau*r) ), r=sqrt( G*(s^2+z) ) % % Examples: % >> s=0.3; d=1.5; penPow(s,d) % >> s=-4; pot='potLaplace'; tau=2; z=1.3; penVB(s,pot,tau,z) % % See also POTFUNCTIONS.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 09glm-ie_v1.4/inf/0000755000175000017500000000000011755435662011366 5ustar hnhnglm-ie_v1.4/inf/linsolve_lcg.m0000644000175000017500000001065111650201643014207 0ustar hnhn% [c,k,res,mvmMfun,prec] = LINSOLVE_LCG(X,R,B,P,b,kmax,c,tol,prec) % % Computes c = A\b with A = X'*R*X + B'*P*B by Linear Conjugate Gradients (LCG) % as described in § 10.2.6 of Golub, van Loan, Matrix Computations with at most % kmax MVMs. % % ARGUMENTS % X [m,n] matrix or operator, m can be zero % R [m,m] square matrix % or [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % B [q,n] matrix or operator % P [n,n] square matrix % or [m,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % b [n,1] vector % kmax [1,1] scalar, default value is n % c [n,1] vector, default is zeros(n,1) % tol [1,1] scalar, residual relative tolerance |r|/|b| < tol % prec [1,1] flag, try and use preconditioner % % RESULTS % c [n,1] vector c = A\b, A = X'*R*X + B'*P*B % k [1,1] number of commited iterations % res [k+1,1] residual norm % prec [1,1] flag whether preconditioning is possible at all % % (c) by Hannes Nickisch, MPI for Biological Cybernetics and % George Papandreou, University of California, LA, 2011 October 20 function [c,k,res,mvmMfun,prec] = linsolve_lcg(X,R,B,P,b,kmax,c,tol,prec) if nargin<6, kmax=length(b); end if nargin<7 || isempty(c), c=zeros(size(b)); end if nargin<8 || isempty(tol), tol=1e-10; end if nargin<9, prec=[]; end % If |b|=0, no need to iterate nb = norm(b,'fro'); % |b| if nb==0 c = zeros(size(b)); k = 0; res = 0; return end % Check if fast Jacobi-DFT preconditioner is possible. % If it is, then we use as preconditioner the circulant matrix % M = mean(R)*X'*X + mean(P)*B'*B % Then M\r is implemented as pointwise division in the DFT domain. if isempty(prec) || prec fftdiag = ~isnumeric(X) && ~isnumeric(B); if fftdiag dX = diagFAtAFt(X,'cheap'); dB = diagFAtAFt(B,'cheap'); fftdiag = numel(dX)>0 && numel(dB)>0; end if fftdiag R_mean = meandiag(R); P_mean = meandiag(P); d = R_mean*dX + P_mean*dB; F = matFFTNmask(true(size(d))); d = d(:); % DFT matrix prec = 1; else if prec error('linsolve_lcg: requested preconditioning is not possible'); end prec = 0; end end res = zeros(kmax+1,1); mvmAfun = @(c) mvmA(X,R,B,P, c); if prec mvmMinvfun = @(r) mvmMinv(F,d, r); end % See Shewchuk, pp. 50 and 51 for the algorithm r = b - mvmAfun(c); % r = b-A*c; res(1) = norm(r,'fro')^2; if ~prec % proceed without preconditioner z = r; for k=1:kmax w = mvmAfun(z); alpha = res(k)/(z(:)'*w(:)); c = c + alpha*z; r = r - alpha*w; res(k+1) = norm(r,'fro')^2; beta = res(k+1)/res(k); z = r + beta*z; if sqrt(res(k+1))=4 if ~prec mvmMfun = @(x) mvmI(x); else mvmMfun = @(x) mvmM(F,d,x); end end function v = mvmA(X,R,B,P, w) % MVM with A where A = X'*R*X + B'*P*B Xw = X*w; if numel(R)==numel(Xw), RXw = R(:).*Xw; else RXw = R*Xw; end Bw = B*w; if numel(P)==numel(Bw), PBw = P(:).*Bw; else PBw = P*Bw; end v = [X']*RXw + [B']*PBw; % the [] around the transpose is needed by Octave function z = mvmMinv(F,d, r) % M\r in the DFT domain if numel(r)>numel(d) z = cx2re([F']*((F*re2cx(r))./d)); else z = [F']*((F*r)./d); end function [z,d] = mvmM(F,d, x) % M*x in the DFT domain if numel(x)>numel(d) z = cx2re([F']*((F*re2cx(x)).*d)); else z = [F']*((F*x).*d); end function [x,d] = mvmI(x) % M*x when M=I d = 1; function J_mean = meandiag(J) % Compute mean(diag(J)) [m n] = size(J); if isempty(J) J_mean = []; elseif m==1 || n==1, J_mean = mean(J); elseif m==n J_mean = mean(diag(J)); else error('meandiag: wrong J'); end glm-ie_v1.4/inf/diaginv_factorial.m0000644000175000017500000000363011704110625015172 0ustar hnhn% [z,zu,ldA,Q,T] = DIAGINV_FULL(X,R,B,P) % % Approximates diag( B*inv(A)*B' ) with A = X'*R*X + B'*P*B by making a diagonal % approximation to A: % % ARGUMENTS % X [m,n] matrix or operator, m can be zero % R [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % B [q,n] matrix or operator % P [q,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % RESULTS % z [q,1] vector z = diag(B*inv(A)*B'), A = X'*R*X + B'*P*B % zu [n,1] vector zu = diag( inv(A) ), A = X'*R*X + B'*P*B % ldA [1,1] log determinant of A % Q [n,n] orthogonal matrix of Lanczos vectors, Q'*Q = I % T [n,n] diagonal matrix, T = Q'*A*Q % % A is given by Q*T*Q', Q'*Q = I. As a result, inv(A) equals Q*inv(T)*Q'. % % The matrices X and B can be given implicitely through their multiplication. % % (c) by Hannes Nickisch, Philips Research, 2012 January 13 function [z,zu,ldA,Q,T] = diaginv_factorial(X,R,B,P) n = max(size(X,2),size(B,2)); m = size(X,1); q = size(B,1); dgA = zeros(n,1); if isnumeric(X) if numel(R)==m dgA = dgA + diag( X'*(repmat(R(:),1,n).*X) ); else dgA = dgA + diag( X'*(R*X) ); end else dgA = dgA + reshape(mvmAA(X,R.*ones(m,1),true),[],1); end if isnumeric(B) if numel(B)==1 if numel(P)==n dgA = dgA + diag( (B*B)*diag(P(:)) ); elseif numel(P)==1 dgA = dgA + diag( (B*B*P)*eye(n) ); else dgA = dgA + diag( (B*B)*P ); end elseif numel(P)==q dgA = dgA + diag( B'*(repmat(P(:),1,n).*B) ); else dgA = dgA + diag( B'*(P*B) ); end else dgA = dgA + reshape(mvmAA(B,P.*ones(q,1),true),[],1); end zu = 1./dgA; if nargout>1 if isnumeric(B) z = diag(B*diag(zu)*B'); else z = mvmAA(B,zu); end end if nargout>2, ldA = sum(log(dgA)); end if nargout>3, Q = speye(n); end if nargout>4, T = sparse(1:n,1:n,dgA); end glm-ie_v1.4/inf/linsolve_woodbury.m0000644000175000017500000000560511466734126015333 0ustar hnhn% c = LINSOLVE_WOODBURY(X,R,P,b) % % Computes c = A\b with A = X'*R*X + P positive definite where X is an % m-by-n matrix and both R and P are positive semi-definite. % % We use the Woodbury matrix identity % inv(X'*R*X + P) = inv(P) - inv(P)*X'*inv( inv(R)+X*inv(P)*X' )*X*inv(P) % whenever mO(M^3) where N=max(m,n) and M=min(m,n) % due to the Cholesky decomposition on a matrix of size MxM and a matrix-matrix % multiplication X'*X or X*X'. % % ARGUMENTS % X [m,n] full or sparse matrix, no operator allowed % % R [m,m] square matrix % or [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % P [n,n] square matrix % or [m,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % b [n,1] vector % % RESULTS % c [n,1] vector c = A\b, A = X'*R*X + P % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 November 11 function c = linsolve_woodbury(X,R,P,b) [m,n] = size(X); if m1, ldT = 0; end v = zeros(n,1); b = 1; k = 0; Q = zeros(n,kmax); z = 0; zu = 0; % memory for the Lanczos and results while abs(b)>1e-10 && k0, t = w; w = v/b; v = -b*t; end w(:) = w(:) - Q*(Q'*w(:)); % Gram-Schmidt orthogonalisation v = v + mvmA(X,R,B,P, w); % MVM with A: v = v + A*w k = k+1; a = real(w(:)'*v(:)); alpha(k) = a; % needed for T v = v - a*w; if k==1 Lkk = sqrt(a); % L(k,k), L = chol(T)' <=> L*L' = T p = w/Lkk; % Q(:,k) = w else Lkk1 = b/Lkk; % L(k,k-1) Lkk = sqrt( a - Lkk1*Lkk1 ); % L(k,k) p = (w-Lkk1*p)/Lkk; end if nargout>1 && k>0, ldT = ldT + 2*log(Lkk); end b = norm(v,'fro'); if k4, T = diag(alpha)+diag(beta,+1)+diag(beta,-1); end function v = mvmA(X,R,B,P, w) % MVM with A where A = X'*R*X + B'*P*B Xw = X*w; if numel(R)==numel(Xw), RXw = R(:).*Xw; else RXw = R*Xw; end Bw = B*w; if numel(P)==numel(Bw), PBw = P(:).*Bw; else PBw = P*Bw; end v = [X']*RXw + [B']*PBw; % the [] around the transpose is needed by Octaveglm-ie_v1.4/inf/dli.m0000644000175000017500000002643711704075600012312 0ustar hnhn% [m,ga,b,z,zu,nlZ,Q,T] = DLI(X,y,s2,B,pot,tau,opts,G) % % DLI - Double Loop Inference - Bayesian Inference using a Double Loop algorithm % The variational criterion whose stationary point is found has the form % phi(ga,b) = ln|A| + h(ga,b) + \min_u R(u,ga,b), where % A = X'*X/s2 + B'*diag(1./ga)*B, s=B*u, % h(ga,b) = \sum_{j=1}^q h_j(ga_j,b_j) % R(u,ga,b) = (1/s2) * ||X*u-y||^2 + s'*diag(1./ga)*s - 2*b'*s. % % The methods differ in the scalar function h_j(ga_j,b_j). We drop the % subindex j in the following. % % In the case of the variational bounding technique (VB), we have: % h(ga) = max_x -x/ga - 2 \ln pot(sqrt(x)), x = s*s % % Expectation propagation (EP) yields % h(ga,b) = -2/eta * ( \ln E[pot(s)^eta] % - \ln E[exp(b*s-pi*s^2/2)^eta] ) % where E[#] = \int Q_(s) # ds, and Q_(s) = N(s|mu_,rho_) is the cavity % distribution with mu_ = (mu-eta*b*rho)/(1-eta*pi*rho) and % rho_ = rho/(1-eta*pi*rho). % Here, mu and rho are the marginal moments of the Gaussian % approximation N(u|m,V) to the posterior % % See also INFENGINE.M. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 21 function [m,ga,b,z,zu,nlZ,Q,T] = dli(X,y,s2,B,pot,tau, opts,G) if nargin<6, error('We need at least 6 input arguments'), end if nargin==6, opts = 1; end if nargin<8, G = 1; else if numel(G)==0, G = 1; end, end % set default % set default values if isfield(opts,'outerZinit') % initial value for upper bound z0 = opts.outerZinit; else z0 = 0.05; end if isfield(opts,'outerGainit') % initial value for variational parameter pi = 1./opts.outerGainit; else pi = 1; end if isfield(opts,'outerNiter') % number of outer loop iterations nout = opts.outerNiter; else nout = 10; end if isfield(opts,'outerVarOpts') % extra params for approx variance computation varOpts = opts.outerVarOpts; else varOpts = []; end if isfield(opts,'outerMethod') % method for computing marginal variances outerMethod = opts.outerMethod; else outerMethod = 'lanczos'; % default end switch outerMethod case 'woodbury' if ~(isnumeric(B) && numel(B)==1 && B==1 && isnumeric(X)) error('dli: woodbury is not possible'); end case {'full','factorial'} case 'lanczos' if ~isfield(varOpts,'MVM') if isfield(opts,'outerMVM') varOpts.MVM = opts.outerMVM; else varOpts.MVM = 50; end end case 'sample' if ~isfield(varOpts,'outerNSamples') varOpts.NSamples = 10; end if ~isfield(varOpts,'outerNcg') varOpts.Ncg = 20; end otherwise error('dli: unknown outer method'); end if isfield(opts,'innerExact') % Solve inner problem approximately or exactly innerExact = opts.innerExact; else innerExact = 0; end if isfield(opts,'innerMVM') % number of inner loop MVMs or CG steps ninMVM = opts.innerMVM; else ninMVM = 50; end if isfield(opts,'innerType') innerType = opts.innerType; else innerType = 'VB'; end % information parameters if isfield(opts,'outerOutput') % flag saying whether some output is shown output = opts.outerOutput; else output = false; end if ~isfield(opts,'innerOutput') % flag saying whether some output is shown opts.innerOutput = false; end n = max(size(X,2),size(B,2)); u = zeros(n,1); q = numel(B*u); z = z0(:).*ones(q,1); ldA = 0; nlZ = inf(nout,1); b = feval(pot,zeros(q,1)); b = b(:,4); PI = 2*acos(0); % this is the usual pi which is used by the natural parameters if output, tic, end for i = 1:nout if output, fprintf('BEGIN loop %d/%d\n',i,nout), end pi_old = pi; b_old = b; % 1) INNER loop(u,ga,b) if output, fprintf('INNER: %s\n',innerType), end it = ['inner',innerType(1:2)]; opts.innerType = innerType; % phi0 = phi[z=0] = h(pi,ga) + min_u R(u), R=||X*u-y||^2/s2+s'*(pi.*s)-2*b'*s [u,pi,b,phi0] = feval(it,u,pi,b,z,X,y,s2,B,pot,tau,G,innerExact,ninMVM,opts); % 2) NEGATIVE LOG MARGINAL LIKELIHOOD % -2 log(Z_Q) = min_u R(u,b,pi) + log(det(A)) - C1 C1 = n*log(2*PI) - size(X,1)*log(2*PI*s2); nlZ(i) = ( phi0 + ldA - C1 )/2; if output, fprintf('NLZ(%s): %1.4e\n',innerType,nlZ(i)), end % 3) OUTER loop: compute marginal variances z from X, s2, B, pi if i3 if output, fprintf('OUTER: %s\n',outerMethod), end switch outerMethod case 'woodbury' args = {X,1/s2,pi}; case {'full','factorial'} args = {X,1/s2,B,pi}; case 'lanczos' args = {X,1/s2,B,pi,varOpts.MVM,output}; case 'sample' args = {X,1/s2,B,pi,varOpts.NSamples,varOpts.Ncg}; end if nargout>6 [z,zu,ldA,Q,T] = feval(['diaginv_',outerMethod],args{:}); else [z,zu,ldA] = feval(['diaginv_',outerMethod],args{:}); end clear diaginv end % 4) FINISH: recompute the mean and check convergence dpi = dev(pi_old,pi); db = dev(b_old,b); cvg = dpi+db<1e-6; if output fprintf('END loop %d/%d: db=%1.4e, dpi=%1.4e [%1.1fs]\n',i,nout,db,dpi,toc) end if cvg || i==nout % converged or last loop if output && cvg, fprintf(' Converged\n'), end m = postmean(X,s2,B,pi,y,b,innerExact,ninMVM,u,output); ga = 1./pi; break end end nlZ = nlZ(1:i); % Inner Loop: Variational Bayesian: penalised least squares function [u,pi,b,phi0] = innerVB(u,pi,b,z,X,y,s2,B,pot,tau,G,exact,ninMVM,opts) if isfield(opts,'innerVBpls') % method for solving the PLS inner loop problem pls = opts.innerVBpls; else OCT = exist('OCTAVE_VERSION') ~= 0; % check if we run Matlab or Octave if OCT, pls = 'plsCG'; else pls = 'plsLBFGS'; end % LBFGS and Octave is hard end pls_opts.output = opts.innerOutput; if pls_opts.output, fprintf(' Use %s solver.\n',pls), end pls_opts.nMVM = ninMVM; if isfield(opts,'innerIt') % number of inner Newton loops for plsTN pls_opts.nit = opts.innerIt; else pls_opts.nit = 15; end if strcmp(pls,'plsTN'), pls_opts.exactNewt = exact; end if G==1 % PLS, no ga dependence since implicitely minimised [u,phi_z] = feval(pls,u,X,y,B,pls_opts,s2,'penVB',pot,tau,z); else [u,phi_z] = feval(pls,u,X,y,B,pls_opts,s2,'penVBNorm',pot,tau,z,G); end phi0 = phi_z - sum(z.*pi); % phi0 = phi_[z=0] at the optimum (pi,u) if G==1 [junk,junk,junk,b,pi] = penVB(B*u,pot,tau,z); else s = B*u; r = sqrt(G*(s.*s+z)); [lp,dlp] = cols( feval(pot,tau.*r) ); dlp = tau.*dlp; pi = G'*abs(-dlp./r); b = zeros(size(pi)); end % Inner Loop: Expectation Propagation: mean computation + moment matching function [u,pi,b,phi0] = innerEP(u,pi,b,z,X,y,s2,B,pot,tau,G,exact,ninMVM,opts) nsweep = 8; % maximum number of sweeps with fixed z = rho directeffect = 1; if directeffect, pi0 = pi; end % take direct effect of pi into account if isfield(opts,'innerEPeta') % fractional pot{Laplace,Gauss}, eta \in (0,1] eta = opts.innerEPeta; [eta,tau] = fracEPpar(pot,eta,tau,opts.innerOutput); else eta = 1; end for jj=1:nsweep pi_old = pi; b_old = b; if opts.innerOutput str = sprintf(' %0*d/%d',floor(log(nsweep)/log(10)+1),jj,nsweep); fprintf(str) end u = postmean(X,s2,B,pi,y,b,exact,ninMVM,u,opts.innerOutput); s = B*u; % mean irho = 1./z; if directeffect, irho = irho + (pi-pi0); end pi_n = irho - eta.*pi; b_n = s.*irho - eta.*b; % cavity parameters P = feval(pot, tau.*b_n./pi_n, 'EP', (tau.*tau)./pi_n); % compute criterion i.e. EP free energy lZh = P(:,1); % lZh = \int_s N(s|b_n/pi_n,1/pi_n) pot(s)^eta ds % lZ = \int_s N(s|b_n/pi_n,1/pi_n) exp(b*s-pi*s^2/2)^eta ds aa = 1-eta.*pi./irho; bb = s-eta.*b./irho; lZ = ( (s.*s - bb.*bb./aa).*irho + log(aa) )/2; h = -2*sum( (lZh-lZ)./eta ); minR = norm(X*u-y)^2/s2 + s'*(pi.*s) - 2*b'*s; phi0 = minR + h; phi_z = phi0+sum(z.*pi); % beta = dlZ = d lZ / d mu, nu = d2lZ = -d^2 lZ / d mu^2 dlZ = tau.*P(:,2); d2lZ = tau.*tau.*P(:,3); pi = (1-eta).*pi - d2lZ ./(1+d2lZ./pi_n); pi(pi<0) = 0; % enforce positivity i.e. lower bound pi by zero b = (1-eta).*b + ( dlZ - (b_n./pi_n).*d2lZ )./(1+d2lZ./pi_n); if opts.innerOutput % display some information dd = [dev(pi_old,pi), dev(b_old,b)]; spc = repmat(' ',[1,length(str)]); fprintf('%s phi=%4.4e; Block moment match.\n',spc,phi_z) fprintf('%s dpi=%1.2e, db=%1.2e\n',spc,dd) end if dev(pi_old,pi)+dev(b_old,b)<1e-6, break, end % converged? end % set parameters for fractional EP function [eta,tau] = fracEPpar(pot,eta,tau,output) if ischar(pot), pot_str = pot; else pot_str = func2str(pot); end % make string eta = min(1,eta); eta = max(eta,1e-5); % maxe sure, eta is between 0 and 1 if strfind(pot_str,'potCat') P = feval(pot,[]); % which potentials have been concatenated q = 0; for i=1:length(P.pots), q = max(q,max(P.ids{i})); end e0 = eta; eta = e0*ones(q,1); if output, fprintf(' fractional Cat:'), end for i=1:length(P.pots) poi = P.pots{i}; if ~ischar(poi), poi = func2str(poi); end, id = P.ids{i}; if strfind(poi,'potLaplace') tau(id) = tau(id).*eta(id); % Laplace: tau <- tau*eta if output, fprintf(', Lap[%d] eta=%1.2f',numel(id),e0), end elseif strfind(poi,'potGauss') tau(id) = tau(id).*sqrt(eta(id)); % Gauss: tau <- tau*sqrt(eta) if output, fprintf(', Gau[%d] eta=%1.2f',numel(id),e0), end else eta(id) = 1; if output, fprintf(', Oth[%d] eta=1',numel(id)), end end end if output, fprintf('\n'), end else if strfind(pot_str,'potLaplace') tau = tau*eta; % Laplace: tau <- tau*eta if output, fprintf(' fractional Lap, eta=%1.2f\n',eta), end elseif strfind(pot_str,'potGauss') tau = tau*sqrt(eta); % Gauss: tau <- tau*sqrt(eta) if output, fprintf(' fractional Gau, eta=%1.2f\n',eta), end else eta = 1; % no support for fractional other than Gaussian or Laplacian if output, fprintf(' full, eta=%1.2f\n',eta), end end end function m = postmean(X,s2,B,pi,y,b,exact,nMVM,u,output) % posterior mean if nargin<10, output = false; end woodbury = isnumeric(B) && numel(B)==1 && isnumeric(X); if woodbury, woodbury = woodbury && B==1; end % Is Woodbury possible? if exact if woodbury if output, fprintf(' Compute exact mean using Woodbury\n'), end m = linsolve_woodbury(X,1/s2,pi,X'*y/s2+B'*b); % Woodbury formula else if output, fprintf(' Compute exact mean using dense matrices\n'), end m = linsolve_full(X,1/s2,B,pi,X'*y/s2+B'*b); % use the full matrix end else if output, fprintf(' Approximate mean using LCG\n'), end m = linsolve_lcg(X,1/s2,B,pi,[X']*y/s2+[B']*b,nMVM,u); end function d = dev(a,b) % relative deviation d = norm(a-b)/max([1,norm(a),norm(b)]); function varargout = cols(A) % split a matrix into its columns ncol = size(A,2); varargout = cell(1,nargout); for n=1:nargout, if n>ncol, varargout{n}=[]; else varargout{n}=A(:,n); end, endglm-ie_v1.4/inf/linsolve_full.m0000644000175000017500000000265311453154140014407 0ustar hnhn% c = LINSOLVE_FULL(X,R,B,P,b) % % Computes c = A\b with A = X'*R*X + B*P*B by % % ARGUMENTS % X [m,n] matrix or operator, m can be zero % R [m,m] square matrix % or [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % B [q,n] matrix or operator % P [n,n] square matrix % or [m,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % b [n,1] vector % % RESULTS % c [n,1] vector c = A\b, A = X'*X/s2 + B*diag(pi)*B % % The matrices X and B can be given implicitely through their multiplication. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2010 September 25 function c = linsolve_full(X,R,B,P,b) n = max(size(X,2),size(B,2)); A = zeros(n); ei = zeros(n,1); if isnumeric(X) if numel(R)==size(X,1) A = A + X'*(repmat(R(:),1,n).*X); else A = A + X'*(R*X); end else for i=1:n, ei(i)=1; A(:,i) = A(:,i) + mvm(X,R,ei); ei(i)=0; end end if isnumeric(B) if numel(P)==size(B,1) A = A + B'*(repmat(P(:),1,n).*B); else A = A + B'*(P*B); end else for i=1:n, ei(i)=1; A(:,i) = A(:,i) + mvm(B,P,ei); ei(i)=0; end end c = A\b; function v = mvm(X,R, w) % MVM with X'*R*X Xw = X*w; if numel(R)==numel(Xw), RXw = R(:).*Xw; else RXw = R*Xw; end v = [X']*RXw; % the [] around the transpose is needed by Octaveglm-ie_v1.4/inf/diaginv_woodbury.m0000644000175000017500000000761611650326014015111 0ustar hnhn% [z,zu,ldA,Q,T] = DIAGINV_WOODBURY(X,R,P) % % Computes z = diag(inv(A)) with A = X'*R*X + P positive definite where X is an % m-by-n matrix and both R and P are positive semi-definite. % % We use the Woodbury matrix identity % inv(X'*R*X + P) = inv(P) - inv(P)*X'*inv( inv(R)+X*inv(P)*X' )*X*inv(P) % whenever mO(M^3) where N=max(m,n) and M=min(m,n) % due to the Cholesky decomposition on a matrix of size MxM and a matrix-matrix % multiplication X'*X or X*X'. % % ARGUMENTS % X [m,n] full or sparse matrix, no operator allowed % % R [m,m] square matrix % or [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % P [n,n] square matrix % or [m,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % RESULTS % z [q,1] vector z = diag(B*inv(A)*B'), A = X'*R*X + B'*P*B, B = I % zu [n,1] vector zu = diag( inv(A) ), A = X'*R*X + B'*P*B, B = I % ldA [1,1] log determinant of A % Q [n,n] orthogonal matrix of Lanczos vectors, Q'*Q = I (for n1, ldP = n*log(P+ep); end elseif numel(P)==n C = X*diag(1./(P(:)+ep))*X'; % P is a vector if nargout>1, ldP = sum(log(P(:)+ep)); end else C = X*((P+ep*eye(n))\X'); % P is a matrix if nargout>1, L = chol(P+ep*eye(n)); ldP = 2*sum(log(diag(L))); end end ep = 1e-9*max(R(:)); % stabilise inversion of R if numel(R)==1 C = C + eye(m)/(R+ep); % R is a scalar if nargout>1, ldR = m*log(R+ep); end elseif numel(R)==m C = C + diag(1./(R(:)+ep)); % R is a vector if nargout>1, ldR = sum(log(R(:)+ep)); end else C = C + (R+ep*eye(m))\eye(m); % R is a matrix if nargout>1, L = chol(R+ep*eye(m)); ldR = 2*sum(log(diag(L))); end end L = chol(C); V = XiP'/L; z = z - sum(V.*V,2); if nargout>1, zu = z; end if nargout>2, ldA = ldP + ldR + 2*sum(log(diag(L))); end Q = []; T = []; % there is no canonical output else % do direct computation if numel(R)==m A = X'*diag(R(:))*X; % R is a vector else A = X'*R*X; % R is a scalar or a matrix end if numel(P)==1 A = A + P*eye(n); % P is a scalar elseif numel(P)==n A = A + diag(P(:)); % P is a vector else A = A + P; % P is a matrix end L = chol(A); iL = L \ eye(n); z = sum(iL.*iL,2); if nargout>1, zu = z; end if nargout>2, ldA = 2*sum(log(diag(L))); end if nargout>3, [Q,T] = eig(A); end endglm-ie_v1.4/inf/diaginv_sample.m0000644000175000017500000001373711650333262014524 0ustar hnhn% [z,zu,ldA,Q,T] = DIAGINV_SAMPLE(X,R,B,P,Ns,Ncg) % % Approximates diag( B*inv(A)*B' ) with A = X'*R*X + B'*P*B as % Monte-Carlo sample-average. Note that R and P correspond to inverse % covariance matrices. % % Specifically, we generate Ns samples from a zero-mean Gaussian with % information matrix A by repeatedly solving the linear system % A*x_s = b_s, s=1:Ns, % with % b_s = X'*R*mu_rs + B'*P*mu_ps % and % mu_rs ~ Gauss(0,inv(R)), mu_ps ~ Gauss(0,inv(P)) % % Then % z \approx 1/Ns*sum_s (B*x_s).^2 % % ARGUMENTS % X [m,n] matrix or operator, m can be zero % R [m,m] square SPD inverse covariance matrix % or [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % B [q,n] matrix or operator % P [q,q] square SPD inverse covariance matrix % or [q,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % Ns [1,1] number of samples [default 20] % Ncg [1,1] number of LCG iterations [default 100] % % RESULTS % z [q,1] Unbiased Monte-Carlo estimate of diag(B*inv(A)*B'), % A = X'*R*X + B'*P*B. The estimator has rank-Ns and its relative % error drops as 1/sqrt(Ns) % It also enforces the constraint that z <= diag(inv(P)) % zu [n,1] Unbiased Monte-Carlo estimate of diag(inv(A)), % A = X'*R*X + B'*P*B. The estimator has rank-Ns and its relative % error drops as 1/sqrt(Ns) % ldA [1,1] Monte-Carlo estimate of the log determinant of A. It works % by comparing the logdet(A) with the logdet(M), where M is % the circular preconditioner used in diaginv_sample. It is % reliable when the preconditioner is reasonably close to A. % Q, T Empty output arguments to obey the interface of diaginv_*.m % % The matrices X and B can be given implicitly through their multiplication. % % G. Papandreou and A. Yuille, Gaussian sampling by local perturbations, NIPS-10 % % (c) by George Papandreou, CIVS@UCLA, 2011 October 21 function [z,zu,ldA,Q,T] = diaginv_sample(X,R,B,P,Ns,Ncg) if nargin<5, Ns = 100; end % number of samples if nargin<6, Ncg = 100; end Rsqrt = info_sqrt(R); Psqrt = info_sqrt(P); % Find sizes n = max(size(X,2),size(B,2)); if isempty(X) m = 0; elseif isscalar(X) m = max(size(R)); else m = size(X,1); end if isempty(B) error('diaginv_sample: B cannot be empty'); elseif isscalar(B) q = max(size(P)); else q = size(B,1); end z = zeros([q 1]); Es = zeros(Ns,1); comp_zu = nargout>1; comp_ldA = nargout>2; if comp_zu zu = zeros(n,1); else zu = []; end % logdet(M) has the same value at each iteration, but parfor complains ldM = zeros(Ns,1); % in this loop most of the expensive computation takes place % if you are using a recent version of Matlab, you can replace "for" by "parfor" % to take advantage of your multiprocessor infrastructure for s=1:Ns k_s = genks(X,Rsqrt,m) + genks(B,Psqrt,q); [x_s,cg_done,cg_res,mvmMfun,prec] = linsolve_lcg(X,R,B,P,k_s,Ncg); z = z + (B*x_s).^2; if comp_zu zu = zu + x_s.^2; end % Es(s) = 0.5*(x_s'*(k_s-x_s)); % energy if M=I [mx_s d] = mvmMfun(x_s); % mx_s=M*x_s, M=F'*diag(d)*F ldM(s) = sum(log(d)); Es(s) = 0.5*(x_s'*(k_s-mx_s)); end z = 1/Ns*z; z = cov_constraint(P,z); if comp_ldA ldA = ldM(1) + ... % logdet(M), with M being the preconditioner LSum(Es,1) - log(Ns); % term comparing the proximity of A to M if ~prec, warning(['diaginv_sample: ldA, the estimate of the log ', ... 'determinant of A is probably unreliable since no ', ... 'preconditioning is possible']) end end if comp_zu zu = 1/Ns*zu; end if nargout>3, Q=[]; end, if nargout>4, T=[]; end % J [m,m] square SPD inverse covariance matrix % or [m,1] vector of diagonal J = diag(J(:)) % or [1,1] scalar multiple of identity J = J*eye(m) function Jsqrt = info_sqrt(J) [m n] = size(J); if isempty(J) Jsqrt = []; elseif m==1 || n==1, Jsqrt = sqrt(J); elseif m==n Jsqrt = chol(J,'lower'); else error('diaginv_sample: wrong J'); end % generates k_s = F'*C*mu_s = F'*C*C^(-0.5)*n_s = F'*C^(0.5)*n_s, % with mu_s ~ Gauss(0,inv(C)) and n_s = Gauss(0,I) function k_s = genks(F,Csqrt,d) if isempty(F) k_s = 0; return; end n_s = randn([d 1]); [m n] = size(Csqrt); if m==1 || n==1, z = Csqrt.*n_s; elseif m==n z = Csqrt*n_s; else error('diaginv_sample: wrong Csqrt'); end k_s = [F']*z; % Enforce the constraint that z <= diag(inv(P)), whenever this is cheap to % do, i.e., J is spherical or diagonal function z = cov_constraint(J,z) [m n] = size(J); if m==1 && n==1 z = min(z,1/J); elseif m==1 || n==1, z = min(z,1./reshape(J,size(z))); end % returns log(exp(x1)+exp(x2)+...+exp(xn)) with precautions. % the equivalent of sum, but replaces addition with LAdd % useful for properly adding log probs function ls = LSum(x,dim) if nargin<2, dim=1; end LZERO = -1e10; sz = size(x); sz1 = [sz(1:dim-1), sz(dim+1:end)]; if length(sz1) ~= length(sz) sz1 = [sz1(:)', 1]; end sz2 = [sz(1:dim-1), 1, sz(dim+1:end)]; ls = reshape(LZERO*ones(sz1),sz2); x_ndims = ndims(x); switch x_ndims case 1 colons = {':'}; case 2 colons = {':' ':'}; case 3 colons = {':' ':' ':'}; case 4 colons = {':' ':' ':' ':'}; otherwise colons = repmat({':'}, [1, x_ndims]); end for i = 1:size(x,dim) colons{dim} = i; ls = LAdd(ls,x(colons{:})); end % returns log(exp(x)+exp(y)) with precautions. % used to properly add log-probabilities function res = LAdd(x,y) LZERO = -1e10; LSMALL = -0.5e10; minLogExp = -23.0259; % = -log(-LZERO); I = x=minLogExp; z = exp(diff(I2)); z = x(I2)+log(1+z); res = zeros(size(x)); res(I1) = x(I1); res(I2) = z;glm-ie_v1.4/inf/diaginv_full.m0000644000175000017500000000407611701663177014211 0ustar hnhn% [z,zu,ldA,Q,T] = DIAGINV_FULL(X,R,B,P) % % Computes diag( B*inv(A)*B' ) with A = X'*R*X + B'*P*B. % % ARGUMENTS % X [m,n] matrix or operator, m can be zero % R [m,m] square matrix % or [m,1] vector of diagonal R = diag(R(:)) % or [1,1] scalar multiple of identity R = R*eye(n) % % B [q,n] matrix or operator % P [q,q] square matrix % or [q,1] vector of diagonal P = diag(P(:)) % or [1,1] scalar multiple of identity P = P*eye(n) % % RESULTS % z [q,1] vector z = diag(B*inv(A)*B'), A = X'*R*X + B'*P*B % zu [n,1] vector zu = diag( inv(A) ), A = X'*R*X + B'*P*B % ldA [1,1] log determinant of A % Q [n,n] orthogonal matrix of Lanczos vectors, Q'*Q = I % T [n,n] diagonal matrix, T = Q'*A*Q % % A is given by Q*T*Q', Q'*Q = I. As a result, inv(A) equals Q*inv(T)*Q'. % % The matrices X and B can be given implicitely through their multiplication. % % (c) by Hannes Nickisch, MPI for Biological Cybernetics, 2011 October 21 function [z,zu,ldA,Q,T] = diaginv_full(X,R,B,P) n = max(size(X,2),size(B,2)); A = zeros(n); ei = zeros(n,1); if isnumeric(X) if numel(R)==size(X,1) A = A + X'*(repmat(R(:),1,n).*X); else A = A + X'*(R*X); end else for i=1:n, ei(i)=1; A(:,i) = A(:,i) + mvm(X,R,ei); ei(i)=0; end end if isnumeric(B) if numel(B)==1 if numel(P)==size(A,1) A = A + (B*B)*diag(P(:)); elseif numel(P)==1 A = A + (B*B*P)*eye(n); else A = A + (B*B)*P; end elseif numel(P)==size(B,1) A = A + B'*(repmat(P(:),1,n).*B); else A = A + B'*(P*B); end else for i=1:n, ei(i)=1; A(:,i) = A(:,i) + mvm(B,P,ei); ei(i)=0; end end L = chol((A+A')/2); z = 0; zu = 0; for i=1:n, ei(i)=1; w=L\ei; zu=zu+w.*conj(w); v=B*w; z=z+v.*conj(v); ei(i)=0;end if nargout>2, ldA = 2*sum(log(diag(L))); end if nargout>3, [Q,T] = eig(A); end function v = mvm(X,R,w) % MVM with X'*R*X Xw = X*w; if numel(R)==numel(Xw), RXw = R(:).*Xw; else RXw = R*Xw; end v = [X']*RXw; % the [] around the transpose is needed by Octave