# HG changeset patch
# User idamnjanovic
# Date 1269270385 0
# Node ID 207a6ae9a76fd4a65c5abb6374bc75bdfbfead0c
# Parent  28f2b5fe3483cdf50993a858fe749a9e3efb0542


diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/Pierre_Problem.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/Pierre_Problem.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,112 @@
+function data=Pierre_Problem(src, trg, blocksize, dictsize);
+%%% Generate Pierre Problem
+%   Ivan Damnjanovic 2010 
+%
+%   Pierre_Problem is a part of the SMALLbox and generates the problem
+%   suggested by Professor Pierre Vandergheynst on the SMALL meeting in 
+%   Villars.
+%   The function takes as an input:
+%   -   src - source image matrix (if not present function promts user for 
+%             an image file) ,
+%   -   trg - target image matrix (if not present function promts user for 
+%             an image file) ,
+%   -   blocksize - block (patch) vertical/horizontal dimension (default 8),
+%   -   dictsize - dictionary size (default - all patches from target
+%   image).
+%
+%   The output of the function is stucture with following fields:
+%   -   srcname - source image name,
+%   -   imageSrc - source image matrix,
+%   -   trgname - target image name,
+%   -   imageTrg - Target image matrix,
+%   -   A - dictonary with patches from the source image,
+%   -   b - measurement matrix (i.e. patches from target image to be
+%           represented in dictionary A,
+%   -   m - size of patches (default 25),
+%   -   n - number of patches to be represented,
+%   -   p - dictionary size,
+%   -   blocksize - block size (default [5 5]),
+%   -   maxval - maximum value (default - 255)
+%   -   sparse - if 1 SMALL_solve will keep solution matrix in sparse form,
+%                due to memory constrains.
+
+%% prompt user for images %%
+
+%ask for source file name
+
+TMPpath=pwd;
+FS=filesep;
+if ~ exist( 'src', 'var' ) || isempty(src)
+[pathstr1, name, ext, versn] = fileparts(which('SMALLboxSetup.m'));
+cd([pathstr1,FS,'data',FS,'images']);
+[filename,pathname] = uigetfile({'*.png;'},'Select a source image');
+[pathstr, name, ext, versn] = fileparts(filename);
+data.srcname=name;
+src = imread(filename);
+src = double(src);
+end;
+
+%ask for target file name
+
+if ~ exist( 'trg', 'var' ) || isempty(trg)
+[filename,pathname] = uigetfile({'*.png;'},'Select a target image');
+[pathstr, name, ext, versn] = fileparts(filename);
+data.trgname=name;
+trg = imread(filename);
+trg = double(trg);
+end;
+cd(TMPpath);
+
+%% set parameters %%
+
+maxval = 255;
+if ~ exist( 'blocksize', 'var' ) || isempty(blocksize),blocksize = 5;end
+
+if ~ exist( 'dictsize', 'var' ) || isempty(dictsize),
+    dictsize = (size(src,1)-blocksize+1)*(size(src,2)-blocksize+1);
+    patch_idx=1:dictsize;
+else  
+    num_blocks_src=(size(src,1)-blocksize+1)*(size(src,2)-blocksize+1);
+    patch_idx=1:floor(num_blocks_src/dictsize):dictsize*floor(num_blocks_src/dictsize);
+end
+
+p = ndims(src);
+if (p==2 && any(size(src)==1) && length(blocksize)==1)
+  p = 1;
+end
+
+
+% blocksize %
+if (numel(blocksize)==1)
+  blocksize = ones(1,p)*blocksize;
+end
+%%
+%% create dictionary data %%
+
+S=im2col(src,blocksize,'sliding');
+
+for j= 1:size(S,2)
+    S(:,j)=S(:,j)./norm(S(:,j));
+end
+
+%% create measurement matrix %%
+
+T=im2col(trg,blocksize, 'distinct');
+
+%% output structure %%
+
+data.imageSrc = src;
+data.imageTrg = trg;
+data.A = S(:,patch_idx);
+data.b = T;
+data.m = size(T,1);
+data.n = size(T,2);
+data.p = size(data.A,2);
+data.blocksize=blocksize;
+data.maxval=maxval;
+
+% geting around out of memory problem when converting big matrix from
+% sparse to full... (check SMALL_solve function)
+data.sparse=1;
+
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/generateAMT_Learning_Problem.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/generateAMT_Learning_Problem.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,84 @@
+function data = generateAMT_Learning_Problem(nfft, windowSize, overlap)
+%%% Generate Automatic Music Transcription Problem
+%   Ivan Damnjanovic 2010
+%   
+%
+%   generateAMT_Learning_Problem is a part of the SMALLbox and generates
+%   a problem that can be used for comparison of Dictionary Learning/Sparse
+%   Representation techniques in automatic music transcription scenario.
+%   The function prompts a user for an audio file (mid, wav, mat) reads it
+%   and generates a spectrogram given fft size (default nfft=4096), analysis
+%   window size (windowSize=2822), and analysis window overlap (overlap =
+%   0.5).
+%   
+%   The output of the function is stucture with following fields:
+%       b - matrix with magnitudes of the spectrogram
+%       f - vector of frequencies at wihch spectrogram is computed
+%       windowSize - analysis window size
+%       overlap - analysis window overlap
+%       fs - sampling frequency
+%       m - number of frequenciy points in spectrogram
+%       n - number of time points in the spectrogram
+%       p - number of dictionary elements to be learned (eg 88 for piano)
+%       notesOriginal - notes of the original audio to be used for
+%                       comparison (if midi of the original exists)
+%       name - name of the audio file to transcribe
+    
+%%
+FS=filesep;
+if ~ exist( 'nfft', 'var' ) || isempty(nfft), nfft = 4096; end
+if ~ exist( 'windowSize', 'var' ) || isempty(windowSize), windowSize = 2822; end
+if ~ exist( 'overlap', 'var' ) || isempty(overlap), overlap = 0.5; end
+
+%%
+%ask for file name
+TMPpath=pwd;
+[pathstr1, name, ext, versn] = fileparts(which('SMALLboxSetup.m'));
+cd([pathstr1,FS,'data',FS,'audio']);
+[filename,pathname] = uigetfile({'*.mat; *.mid; *.wav'},'Select a file to transcribe');
+[pathstr, name, ext, versn] = fileparts(filename);
+data.name=name;
+
+data.notesOriginal=[];
+
+if strcmp(ext,'.mid')
+    midi=readmidi(filename);
+    data.notesOriginal=midiInfo(midi);
+    y=midi2audio(midi);
+    wavwrite(y, 44100, 16, 'temp.wav');
+    [x.signal, x.fs, x.nbits]=wavread('temp.wav');
+    delete('temp.wav');
+elseif strcmp(ext,'.wav')
+    cd([pathstr1,FS, 'data', FS, 'audio', FS, 'midi']);
+    filename1=[name, '.mid'];
+    if exist(filename1, 'file')
+        midi=readmidi(filename1);
+        data.notesOriginal=midiInfo(midi);
+    end
+    cd([pathstr1,FS, 'data', FS, 'audio', FS, 'wav']);
+    [x.signal, x.fs, x.nbits]=wavread(filename);
+else
+    cd([pathstr1,FS, 'data', FS, 'audio', FS, 'midi']);
+    filename1=[name, '.mid'];
+    if exist(filename1, 'file')
+        midi=readmidi(filename1);
+        data.notesOriginal=midiInfo(midi);
+    end
+    cd([pathstr1,FS, 'data', FS, 'audio', FS, 'mat']);
+    x=load([pathname,filename]);
+end
+%%
+[X, frX]=spectrogram(x.signal, hanning(windowSize), overlap*windowSize, nfft, x.fs);
+%%
+data.b=abs(X);
+data.f=frX;
+data.windowSize=windowSize;
+data.overlap=overlap;
+data.fs=x.fs;
+data.m=size(X,1);
+data.n=size(X,2);
+
+data.p=88; %number of dictionary elements (ie notes to recover)
+cd(TMPpath);
+
+end
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/generateAudioDenoiseProblem.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/generateAudioDenoiseProblem.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,159 @@
+function data=generateAudioDenoiseProblem(au, trainnum, blocksize, dictsize, overlap, sigma, gain, maxval, initdict);
+
+%   Ivan Damnjanovic 2010 
+% 
+%
+%   generateAudioDenoiseProblem is part of the SMALLbox and generate a
+%   problem for comaprison of Dictionary Learning/Sparse Representation
+%   techniques in audio denoising scenario. It is based on KSVD image
+%   denoise demo by Ron Rubinstein (see bellow).
+%   The fuction takes as an optional input 
+%       au - audio samples to be denoised
+%       trainnum - number of frames for training 
+%       blocksize - 1D frame size (eg 512)
+%       dictsize - number of atoms to be trained
+%       overlap - ammount of overlaping frames between 0 and 1
+%   Ron Rubinstein
+%   Computer Science Department
+%   Technion, Haifa 32000 Israel
+%   ronrubin@cs
+%
+%   August 2009
+
+
+disp(' ');
+disp('  **********  Denoising Problem  **********');
+disp(' ');
+disp('  This function reads an audio, adds random Gaussian noise,');
+disp('  that can be later denoised by using dictionary learning techniques.');
+disp(' ');
+
+FS=filesep;
+if ~ exist( 'sigma', 'var' ) || isempty(sigma), sigma = 26.74; end
+if ~ exist( 'gain', 'var' ) || isempty(gain), gain = 1.15; end
+
+if ~ exist( 'initdict', 'var' ) || isempty(initdict), initdict = 'odct'; end
+if ~ exist( 'overlap', 'var' ) || isempty(overlap), overlap = 15/16; end
+%% prompt user for wav file %%
+%ask for file name
+
+TMPpath=pwd;
+if ~ exist( 'au', 'var' ) || isempty(au)
+    [pathstr1, name, ext, versn] = fileparts(which('SMALLboxSetup.m'));
+    cd([pathstr1,FS,'data',FS,'audio',FS,'wav']);
+    [filename,pathname] = uigetfile({'*.wav;'},'Select a wav file');
+    [pathstr, name, ext, versn] = fileparts(filename);
+    data.name=name;
+    
+    au = wavread(filename);
+    au = mean(au,2); % turn it into mono.
+end;
+if ~ exist( 'maxval', 'var' ) || isempty(maxval), maxval = max(au); end
+
+%% generate noisy audio %%
+
+disp(' ');
+disp('Generating noisy audio...');
+sigma = max(au)/10^(sigma/20); 
+n = randn(size(au)) .* sigma;
+aunoise = au + n;%  here we can load noise audio if available 
+                 %  for example: wavread('icassp06_x.wav');%
+
+
+
+%% set parameters %%
+
+x = aunoise;
+if ~ exist( 'blocksize', 'var' ) || isempty(blocksize),blocksize = 512;end
+if ~ exist( 'dictsize', 'var' ) || isempty(dictsize), dictsize = 2048;end
+
+if ~ exist( 'trainnum', 'var' ) || isempty(trainnum),trainnum = (size(x,1)-blocksize+1);end
+
+
+
+
+
+p=1;
+
+
+% 
+% msgdelta = 5;
+% 
+% verbose = 't';
+% if (msgdelta <= 0)
+%   verbose='';
+%   msgdelta = -1;
+% end
+% 
+% 
+% % initial dictionary %
+% 
+if (strcmpi(initdict,'odct'))
+    initdict = odctndict(blocksize,dictsize,p);
+elseif (strcmpi(initdict,'data'))
+    clear initdict;    % causes initialization using random examples
+else
+    error('Invalid initial dictionary specified.');
+end
+
+if exist( 'initdict', 'var' ) 
+  initdict = initdict(:,1:dictsize);
+end
+
+
+% noise mode %
+% if (isfield(params,'noisemode'))
+%   switch lower(params.noisemode)
+%     case 'psnr'
+%       sigma = maxval / 10^(params.psnr/20);
+%     case 'sigma'
+%       sigma = params.sigma;
+%     otherwise
+%       error('Invalid noise mode specified');
+%   end
+% elseif (isfield(params,'sigma'))
+%   sigma = params.sigma;
+% elseif (isfield(params,'psnr'))
+%   sigma = maxval / 10^(params.psnr/20);
+% else
+%   error('Noise strength not specified');
+% end
+
+% params.Edata = sqrt(prod(blocksize)) * sigma * gain;   % target error for omp
+% params.codemode = 'error';
+% 
+% params.sigma = sigma;
+% params.noisemode = 'sigma';
+% 
+% 
+% % make sure test data is not present in params
+% if (isfield(params,'testdata'))
+%   params = rmfield(params,'testdata');
+% end
+
+
+%%%% create training data %%%
+
+
+X = buffer( x(1:trainnum),blocksize, overlap*blocksize);
+
+% remove dc in blocks to conserve memory %
+% bsize = 2000;
+% for i = 1:bsize:size(X,2)
+%   blockids = i : min(i+bsize-1,size(X,2));
+%   X(:,blockids) = remove_dc(X(:,blockids),'columns');
+% end
+data.Original = au;
+data.Noisy = aunoise;
+data.b = X;
+data.m = size(X,1);
+data.n = size(X,2);
+data.p = dictsize;
+data.blocksize=blocksize;
+data.sigma = sigma;
+data.gain = gain;
+data.maxval = maxval;
+data.initdict= initdict;
+data.signalDim=1;
+cd(TMPpath);
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/generateImageDenoiseProblem.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/generateImageDenoiseProblem.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,144 @@
+function data=generateImageDenoiseProblem(im, trainnum, blocksize, dictsize, sigma, gain, maxval, initdict);
+%%% Generate Image Denoising Problem
+%   Ivan Damnjanovic 2010
+%
+%   generateImageDenoiseProblem is a part of the SMALLbox and generates
+%   a problem that can be used for comparison of Dictionary Learning/Sparse
+%   Representation techniques in image denoising scenario.
+%   The function takes as an input:
+%   -   im - image matrix (if not present function promts user for an
+%            image file) ,
+%   -   trainnum - number of training samples (default - 40000)
+%   -   blocksize - block (patch) vertical/horizontal dimension (default 8),
+%   -   dictsize - dictionary size (default - 256),
+%   -   sigma - noise level (default - 20),
+%   -   noise gain (default - 1.15),
+%   -   maxval - maximum value (default - 255)
+%   -   initdict - initial dictionary (default - 4x overcomlete dct)
+%
+%   The output of the function is stucture with following fields:
+%   -   name - name of the original image (if image is read inside of the
+%              function)
+%   -   Original - original image matrix,
+%   -   Noisy - image with added noise,
+%	-   b - training patches,
+%	-   m - size of training patches (default 64),
+%   -   n - number of training patches,
+%   -   p - number of dictionary elements to be learned,
+%   -   blocksize - block size (default [8 8]),
+%   -   sigma - noise level,
+%   -   noise gain (default - 1.15),
+%   -   maxval - maximum value (default - 255)
+%   -   initdict - initial dictionary (default - 4x overcomlete dct)
+%   -   signalDim - signal dimension (default - 2)
+%
+%   Based on KSVD denoise demo by Ron Rubinstein
+%   See also KSVDDENOISEDEMO and KSVDDEMO.
+%   Ron Rubinstein
+%   Computer Science Department
+%   Technion, Haifa 32000 Israel
+%   ronrubin@cs
+%   August 2009
+%%
+disp(' ');
+disp('  **********  Denoising Problem  **********');
+disp(' ');
+disp('  This function reads an image, adds random Gaussian noise,');
+disp('  that can be later denoised by using dictionary learning techniques.');
+disp(' ');
+
+
+%% prompt user for image %%
+%ask for file name
+FS=filesep;
+TMPpath=pwd;
+if ~ exist( 'im', 'var' ) || isempty(im)
+    [pathstr1, name, ext, versn] = fileparts(which('SMALLboxSetup.m'));
+    cd([pathstr1,FS,'data',FS,'images']);
+    [filename,pathname] = uigetfile({'*.png;'},'Select a file containin pre-calculated notes');
+    [pathstr, name, ext, versn] = fileparts(filename);
+    data.name=name;
+    im = imread(filename);
+    im = double(im);
+end;
+cd(TMPpath);
+
+%% check input parameters %%
+
+if ~ exist( 'blocksize', 'var' ) || isempty(blocksize),blocksize = 8;end
+if ~ exist( 'dictsize', 'var' ) || isempty(dictsize), dictsize = 256;end
+if ~ exist( 'trainnum', 'var' ) || isempty(trainnum),trainnum = 40000;end
+if ~ exist( 'sigma', 'var' ) || isempty(sigma), sigma = 20; end
+if ~ exist( 'gain', 'var' ) || isempty(gain), gain = 1.15; end
+if ~ exist( 'maxval', 'var' ) || isempty(maxval), maxval = 255; end
+if ~ exist( 'initdict', 'var' ) || isempty(initdict), initdict = 'odct'; end
+
+%% generate noisy image %%
+
+disp(' ');
+disp('Generating noisy image...');
+
+n = randn(size(im)) * sigma;
+imnoise = im + n;
+
+%% set parameters %%
+
+x = imnoise;
+p = ndims(x);
+
+if (p==2 && any(size(x)==1) && length(blocksize)==1)
+    p = 1;
+end
+
+% blocksize %
+
+if (numel(blocksize)==1)
+    blocksize = ones(1,p)*blocksize;
+end
+
+if (strcmpi(initdict,'odct'))
+    initdict = odctndict(blocksize,dictsize,p);
+elseif (strcmpi(initdict,'data'))
+    clear initdict;    % causes initialization using random examples
+else
+    error('Invalid initial dictionary specified.');
+end
+
+if exist( 'initdict', 'var' )
+    initdict = initdict(:,1:dictsize);
+end
+
+%%%% create training data %%%
+
+ids = cell(p,1);
+if (p==1)
+    ids{1} = reggrid(length(x)-blocksize+1, trainnum, 'eqdist');
+else
+    [ids{:}] = reggrid(size(x)-blocksize+1, trainnum, 'eqdist');
+end
+X = sampgrid(x,blocksize,ids{:});
+
+% remove dc in blocks to conserve memory %
+
+bsize = 2000;
+for i = 1:bsize:size(X,2)
+    blockids = i : min(i+bsize-1,size(X,2));
+    X(:,blockids) = remove_dc(X(:,blockids),'columns');
+end
+
+%% output structure %%
+
+data.Original = im;
+data.Noisy = imnoise;
+data.b = X;
+data.m = size(X,1);
+data.n = size(X,2);
+data.p = dictsize;
+data.blocksize=blocksize;
+data.sigma = sigma;
+data.gain = gain;
+data.maxval = maxval;
+data.initdict= initdict;
+data.signalDim=2;
+
+end %% end of function
\ No newline at end of file
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/add_dc.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/add_dc.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,33 @@
+function x = add_dc(y,dc,columns)
+%ADD_DC Add DC channel to signals.
+%   X = ADD_DC(Y,DC) adds the specified DC value to the (possibly
+%   multi-dimensional) signal Y, returning the result as X. DC should be a
+%   scalar value.
+%
+%   X = ADD_DC(Y,DC,'columns') where Y is a 2D matrix and DC is an array of
+%   length size(Y,2), treats the columns of Y as individual 1D signals, 
+%   adding to each one the corresponding DC value from the DC array. X is
+%   the same size as Y and contains the resulting signals.
+%
+%   See also REMOVE_DC.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2009
+
+
+if (nargin==3 && strcmpi(columns,'columns')), columns = 1;
+else columns = 0;
+end
+
+if (columns)
+  x = addtocols(y,dc);
+else
+  x = y + dc;
+end
+
+
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/addtocols.c
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/addtocols.c	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,85 @@
+/**************************************************************************
+ *
+ * File name: addtocols.c
+ *
+ * Ron Rubinstein
+ * Computer Science Department
+ * Technion, Haifa 32000 Israel
+ * ronrubin@cs
+ *
+ * Last Updated: 19.4.2009
+ *
+ *************************************************************************/
+
+
+#include "mex.h"
+
+
+/* Input Arguments */
+
+#define	X_IN	prhs[0]
+#define V_IN  prhs[1]
+
+
+/* Output Arguments */
+
+#define	Y_OUT	plhs[0]
+
+
+void mexFunction(int nlhs, mxArray *plhs[], 
+		             int nrhs, const mxArray*prhs[])
+     
+{ 
+    double *x, *y, *v, *xend;  
+    mwSize m,n,m1,n1;
+    mwIndex counter; 
+    
+    
+    /* Check for proper number of arguments */
+    
+    if (nrhs != 2) {
+      mexErrMsgTxt("Two input arguments required."); 
+    } else if (nlhs > 1) {
+      mexErrMsgTxt("Too many output arguments."); 
+    } 
+    
+    
+    /* Check the the input dimensions */ 
+    
+    m = mxGetM(X_IN);
+    n = mxGetN(X_IN);
+    if (!mxIsDouble(X_IN) || mxIsComplex(X_IN) || mxGetNumberOfDimensions(X_IN)>2) {
+      mexErrMsgTxt("ADDTOCOLS requires that X be a double matrix.");
+    }
+    m1 = mxGetM(V_IN);
+    n1 = mxGetN(V_IN);
+    if (!mxIsDouble(V_IN) || mxIsComplex(V_IN) || (m1!=1 && n1!=1)) {
+      mexErrMsgTxt("ADDTOCOLS requires that V be a double vector.");
+    }
+    if ((m1==1 && n1!=n) || (n1==1 && m1!=n)) {
+      mexErrMsgTxt("Error in ADDTOCOLS: dimensions of V and X must agree.");
+    }
+    
+    
+    /* Create a matrix for the return argument */ 
+    Y_OUT = mxCreateDoubleMatrix(m, n, mxREAL);
+         
+    
+    /* Assign pointers to the various parameters */ 
+    x = mxGetPr(X_IN); 
+    v = mxGetPr(V_IN);
+    y = mxGetPr(Y_OUT);
+            
+    
+    /* Do the actual computation */
+    
+    xend = x+(m*n);
+    counter = 0;
+    while (x<xend) {
+      (*y) = (*x) + (*v);
+      y++; x++; counter++;
+      if (counter==m) {v++; counter=0;}
+    }
+    
+    return;
+}
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/addtocols.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/addtocols.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,13 @@
+%ADDTOCOLS Add values to the columns of a matrix.
+%  Y=ADDTOCOLS(X,V) adds to each column of the MxN matrix X the
+%  corresponding value from the N-element vector V.
+%
+%  See also NORMCOLS.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  June 2005
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/collincomb.c
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/collincomb.c	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,165 @@
+/**************************************************************************
+ *
+ * File name: collincomb.c
+ *
+ * Ron Rubinstein
+ * Computer Science Department
+ * Technion, Haifa 32000 Israel
+ * ronrubin@cs
+ *
+ * Last Updated: 21.5.2009
+ *
+ *************************************************************************/
+
+
+#include "mex.h"
+
+
+/* Input Arguments */
+
+#define	A_IN	   prhs[0]
+#define ROWS_IN  prhs[1]
+#define COLS_IN1 prhs[1]
+#define COLS_IN2 prhs[2]
+#define X_IN1    prhs[2]
+#define X_IN2    prhs[3]
+
+
+/* Output Arguments */
+
+#define	Y_OUT	plhs[0]
+
+
+void mexFunction(int nlhs, mxArray *plhs[],
+int nrhs, const mxArray*prhs[])
+
+{
+  double *A, *x, *y, *rows, *cols;
+  mwSize m,n,m1,n1,m2,n2,rownum,colnum;
+  mwIndex col_id,*row_ids,i,j;
+  int rownumspecified=0;
+  
+  
+  /* Check for proper number of arguments */
+  
+  if (nrhs!=3 && nrhs!=4) {
+    mexErrMsgTxt("Invalid number of arguments.");
+  } else if (nlhs > 1) {
+    mexErrMsgTxt("Too many output arguments.");
+  }
+  
+  
+  /* Check the input dimensions */
+  
+  m = mxGetM(A_IN);
+  n = mxGetN(A_IN);
+  if (!mxIsDouble(A_IN) || mxIsComplex(A_IN) || mxGetNumberOfDimensions(A_IN)>2) {
+    mexErrMsgTxt("COLLINCOMB requires that A be a double matrix.");
+  }
+  
+  if (nrhs==3) {
+    
+    m1 = mxGetM(COLS_IN1);
+    n1 = mxGetN(COLS_IN1);
+    if (!mxIsDouble(COLS_IN1) || mxIsComplex(COLS_IN1) || (m1!=1 && n1!=1)) {
+      mexErrMsgTxt("COLLINCOMB requires that COLS be an index vector of type double.");
+    }
+    colnum = (m1 > n1) ? m1 : n1;   /* the number of columns in the linear combination */
+    
+    m2 = mxGetM(X_IN1);
+    n2 = mxGetN(X_IN1);
+    if (!mxIsDouble(X_IN1) || mxIsComplex(X_IN1) || (m2!=1 && n2!=1)) {
+      mexErrMsgTxt("COLLINCOMB requires that X be a double vector.");
+    }
+    
+    if (m2!=colnum && n2!=colnum) {
+      mexErrMsgTxt("The length of X does not match the number of columns in COLS.");
+    }
+    
+    rows = 0;
+    Y_OUT = mxCreateDoubleMatrix(m, 1, mxREAL);
+    cols = mxGetPr(COLS_IN1);
+    x = mxGetPr(X_IN1);
+  }
+  else {
+    
+    m1 = mxGetM(ROWS_IN);
+    n1 = mxGetN(ROWS_IN);
+    if (!mxIsDouble(ROWS_IN) || mxIsComplex(ROWS_IN) || (m1!=1 && n1!=1)) {
+      mexErrMsgTxt("COLLINCOMB requires that ROWS be an index vector of type double.");
+    }
+    rownum = (m1 > n1) ? m1 : n1;   /* the number of rows in the linear combination */
+    rownumspecified = 1;
+    rows = mxGetPr(ROWS_IN);
+    
+    m1 = mxGetM(COLS_IN2);
+    n1 = mxGetN(COLS_IN2);
+    if (!mxIsDouble(COLS_IN2) || mxIsComplex(COLS_IN2) || (m1!=1 && n1!=1)) {
+      mexErrMsgTxt("COLLINCOMB requires that COLS be an index vector of type double.");
+    }
+    colnum = (m1 > n1) ? m1 : n1;   /* the number of columns in the linear combination */
+    
+    m2 = mxGetM(X_IN2);
+    n2 = mxGetN(X_IN2);
+    if (!mxIsDouble(X_IN2) || mxIsComplex(X_IN2) || (m2!=1 && n2!=1)) {
+      mexErrMsgTxt("COLLINCOMB requires that X be a double vector.");
+    }
+    
+    if (m2!=colnum && n2!=colnum) {
+      mexErrMsgTxt("The length of X does not match the number of columns in COLS.");
+    }
+    
+    Y_OUT = mxCreateDoubleMatrix(rownum, 1, mxREAL);
+    cols = mxGetPr(COLS_IN2);
+    x = mxGetPr(X_IN2);
+  }
+  
+  
+  /* Assign pointers to the various parameters */
+  A = mxGetPr(A_IN);
+  y = mxGetPr(Y_OUT);
+  
+  
+  if (rownumspecified) {
+    
+     /* check row indices */
+    
+    row_ids = (mwIndex*)mxMalloc(rownum*sizeof(mwIndex));
+    
+    for (i=0; i<rownum; ++i) {
+      row_ids[i] = (mwIndex)(rows[i]+0.1)-1;
+      if (row_ids[i]<0 || row_ids[i]>=m) {
+        mexErrMsgTxt("Row index in ROWS is out of range.");
+      }
+    }
+    
+    /* Do the actual computation */
+    for (i=0; i<colnum; ++i) {
+      col_id = (mwIndex)(cols[i]+0.1)-1;
+      if (col_id<0 || col_id>=n) {
+        mexErrMsgTxt("Column index in COLS is out of range.");
+      }
+      for (j=0; j<rownum; ++j) {
+        y[j] += A[m*col_id+row_ids[j]]*x[i];
+      }
+    }
+    
+    mxFree(row_ids);
+  }
+  
+  else {
+    
+    /* Do the actual computation */
+    for (i=0; i<colnum; ++i) {
+      col_id = (mwIndex)(cols[i]+0.1)-1;
+      if (col_id<0 || col_id>=n) {
+        mexErrMsgTxt("Column index in COLS is out of range.");
+      }
+      for (j=0; j<m; ++j) {
+        y[j] += A[m*col_id+j]*x[i];
+      }
+    }
+  }
+  
+  return;
+}
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/collincomb.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/collincomb.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,27 @@
+%COLLINCOMB Linear combination of matrix columns.
+%  Y = COLLINCOMB(A,COLS,X) computes a linear combination of the columns of
+%  the matrix A. The column indices are specified in the vector COLS, and
+%  the correspoinding coefficients are specified in the vector X. The
+%  vectors COLS and X must be of the same length. 
+%  
+%  The call Y = COLLINCOMB(A,COLS,X) is essentially equivalent to
+%
+%         Y = A(:,COLS)*X .
+%
+%  However, it is implemented much more efficiently.
+%
+%  Y = COLLINCOMB(A,ROWS,COLS,X) only works on the rows of A specified
+%  in ROWS, returning a vector of length equal to ROWS. This call is
+%  essentially equivalent to the command
+%
+%         Y = A(ROWS,COLS)*X .
+%
+%  See also ROWLINCOMB.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2009
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/countcover.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/countcover.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,31 @@
+function cnt = countcover(sz,blocksize,stepsize)
+%COUNTCOVER Covering of signal samples by blocks
+%  CNT = COUNTCOVER(SZ,BLOCKSIZE,STEPSIZE) assumes a p-dimensional signal
+%  of size SZ=[N1 N2 ... Np] covered by (possibly overlapping) blocks of
+%  size BLOCKSIZE=[M1 M2 ... Mp]. The blocks start at position (1,1,..,1)
+%  and are shifted between them by steps of size STEPSIZE=[S1 S2 ... Sp].
+%  COUNTCOVER returns a matrix the same size as the signal, containing in
+%  each entry the number of blocks covering that sample.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  August 2008
+
+
+cnt = ones(sz);
+for k = 1:length(sz)
+  
+  % this code is modified from function NDGRID, so it computes one
+  % output argument of NDGRID at a time (to conserve memory)
+  ids = (1:sz(k))';
+  s = sz; s(k) = [];
+  ids = reshape(ids(:,ones(1,prod(s))),[length(ids) s]);
+  ids = permute(ids,[2:k 1 k+1:length(sz)]);
+  
+  cnt = cnt .* max( min(floor((ids-1)/stepsize(k)),floor((sz(k)-blocksize(k))/stepsize(k))) - ...
+                    max(ceil((ids-blocksize(k))/stepsize(k)),0) + 1 , 0 );
+end
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/diag_ids.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/diag_ids.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,30 @@
+function id = diag_ids(x,k)
+%DIAG_IDS Indices of matrix diagonal elements.
+%  ID = DIAG_IDS(X) returns the indices of the main diagonal of X.
+%
+%  ID = DIAG_IDS(X,K) returns the indices of the K-th diagonal. K=0
+%  represents the main diagonal, positive values are above the main
+%  diagonal and negative values are below the main diagonal.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  September 2006
+
+
+if (nargin==1), k=0; end
+
+[m,n] = size(x);
+l = max(m,n);
+
+if (k<=0)
+  id = (0:l-1)*m + (1:l) - k;
+else
+  id = (0:l-1)*m + (1:l) + k*m;
+end
+
+if (l-k>m), id = id(1:end-(l-k-m)); end
+if (l+k>n), id = id(1:end-(l+k-n)); end
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/dictdist.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/dictdist.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,61 @@
+function [dist,ratio] = dictdist(approxD,D,epsilon)
+%DICTDIST Distance between dictionaries.
+%  [DIST,RATIO] = DICTDIST(APPROXD,D) computes the distance between the
+%  approximate dictionary APPROXD and the true dictionary D, where APPROXD
+%  is NxK and D is NxM.
+%
+%  The distance between the dictionary APPROXD and a single atom A of D is
+%  defined as:
+%
+%      DIST(APPROXD,A) = min  { 1-abs(APPROXD(:,i)' * A) }
+%                         i
+%
+%  The distance between the dictionaries APPROXD and D is defined as:
+%
+%      DIST(APPROXD,D) = sum { dist(APPROXD, D(:,k)) } / M
+%                         k
+%
+%  Note that 0 <= DIST(APPROXD,D) <= 1, where 0 implies that all atoms in D
+%  appear in APPROXD, and 1 implies that the atoms of D are orthogonal to
+%  APPROXD.
+%
+%  The similarity ratio between APPROXD and D is defined as:
+%
+%      RATIO(APPROXD,D) = #(atoms in D that appear in APPROXD) / M
+%
+%  where two atoms are considered identical when DIST(A1,A2) < EPSILON with
+%  EPSILON=0.01 by default. Note that 0 <= RATIO(APPROXD,D) <= 1, where 0
+%  means APPROXD and D have no identical atoms, and 1 means that all atoms
+%  of D appear in APPROXD.
+%
+%  [DIST,RATIO] = DICTDIST(DICT1,DICT2,EPSILON) specifies a different value
+%  for EPSILON.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  October 2007
+
+
+if (nargin < 3), epsilon = 0.01; end
+
+[n,m] = size(D);
+
+approxD = normcols(approxD*spdiag(sign(approxD(1,:))));
+D = normcols(D*spdiag(sign(D(1,:))));
+
+identical_atoms = 0;
+dist = 0;
+
+for i = 1:m
+  atom = D(:,i);
+  distances = 1-abs(atom'*approxD);
+  mindist = min(distances);
+  dist = dist + mindist;
+  identical_atoms = identical_atoms + (mindist < epsilon);
+end
+
+dist = dist / m;
+ratio = identical_atoms / m;
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/imnormalize.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/imnormalize.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,19 @@
+function y = imnormalize(x)
+%IMNORMALIZE Normalize image values.
+%  Y = IMNORMALIZE(X) linearly transforms the intensity values of the image
+%  X to tightly cover the range [0,1]. If X has more than one channel, the
+%  channels are handled as one and normalized using the same transform.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  May 2004
+
+
+maxval = max(x(:));
+minval = min(x(:));
+
+y = (x-minval) / (maxval-minval);
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/iswhole.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/iswhole.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,17 @@
+function z = iswhole(x,epsilon)
+%ISWHOLE Determine whole numbers with finite precision.
+%  Z = ISWHOLE(X,EPSILON) returns a matrix the same size as X, containing
+%  1's where X is whole up to precision EPSILON, and 0's elsewhere. 
+%
+%  Z = ISWHOLE(X) uses the default value of EPSILON=1e-6.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  May 2005
+
+if (nargin<2), epsilon = 1e-6; end
+z = abs(round(x)-x) < epsilon;
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/make.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/make.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,40 @@
+function make
+%MAKE Build the KSVDBox MEX support files.
+%  MAKE compiles the KSVDBox supporting MEX functions, using Matlab's
+%  default MEX compiler. If the MEX compiler has not been set-up before,
+%  please run 
+%
+%    mex -setup
+%
+%  before using this MAKE file.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2009
+
+
+% detect platform 
+
+compstr = computer;
+is64bit = strcmp(compstr(end-1:end),'64');
+
+
+% compilation parameters
+
+compile_params = cell(0);
+if (is64bit)
+  compile_params{1} = '-largeArrayDims';
+end
+
+
+% Compile files %
+
+sourcefiles = {'addtocols.c','collincomb.c','rowlincomb.c'};
+
+for i = 1:length(sourcefiles)
+  printf('Compiling %s...', sourcefiles{i});
+  mex(sourcefiles{i},compile_params{:});
+end
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/normcols.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/normcols.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,17 @@
+function y = normcols(x)
+%NORMCOLS Normalize matrix columns.
+%  Y = NORMCOLS(X) normalizes the columns of X to unit length, returning
+%  the result as Y.
+%
+%  See also ADDTOCOLS.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2009
+
+
+y = x*spdiag(1./sqrt(sum(x.*x)));
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/printf.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/printf.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,26 @@
+function str = printf(varargin)
+%PRINTF Print formatted text to screen.
+%  PRINTF(FMT,VAL1,VAL2,...) formats the data in VAL1,VAL2,... according to
+%  the format string FMT, and prints the result to the screen.
+%
+%  The call to PRINTF(FMT,VAL1,VAL2,...) simply invokes the call
+%  DISP(SPRINTF(FMT,VAL1,VAL2,...)). For a complete description of the
+%  format string options see function SPRINTF.
+%
+%  STR = PRINTF(...) also returns the formatted string.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2008
+
+
+if (nargout>0)
+  str = sprintf(varargin{:});
+  disp(str);
+else
+  disp(sprintf(varargin{:}));
+end
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/reggrid.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/reggrid.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,136 @@
+function [varargout] = reggrid(sz,num,mode)
+%REGGRID Regular sampling grid.
+%  [I1,I2,...,Ip] = REGGRID([N1 N2 ... Np], NUM) returns the indices
+%  of a regular uniform sampling grid over a p-dimensional matrix with
+%  dimensions N1xN2x...xNp. NUM is the minimal number of required samples,
+%  and it is ensured that the actual number of samples, given by
+%  length(I1)xlength(I2)x...xlength(Ip), is at least as large as NUM.
+%
+%  [I1,I2,...,Ip] = REGGRID([N1 N2 ... Np], NUM,'MODE') specifies the
+%  method for distributing the samples along each dimension. Valid modes
+%  include 'eqdist' (the default mode) and 'eqnum'. 'eqdist' indicates an
+%  equal distance between the samples in each dimension, while 'eqnum'
+%  indicates an equal number of samples in each dimension.
+%
+%  Notes about MODE:
+%
+%    1. The 'eqnum' mode will generally fail when the p-th root of NUM
+%    (i.e. NUM^(1/p)) is larger than min([N1 N2 ... Np]). Thus 'eqdist' is
+%    the more useful choice for sampling an arbitrary number of samples
+%    from the matrix (up to the total number of matrix entries).
+%  
+%    2. In both modes, the equality (of the distance between samples, or
+%    the number of samples in each dimension) is only approximate. This is
+%    because REGGRID attempts to maintain the appropriate equality while at
+%    the same time find a sampling pattern where the total number of
+%    samples is as close as possible to NUM. In general, the larger {Ni}
+%    and NUM are, the tighter the equality.
+%
+%  Example: Sample a set of blocks uniformly from a 2D image.
+%
+%    n = 512; blocknum = 20000; blocksize = [8 8];
+%    im = rand(n,n);
+%    [i1,i2] = reggrid(size(im)-blocksize+1, blocknum);
+%    blocks = sampgrid(im, blocksize, i1, i2);
+%
+%  See also SAMPGRID.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  November 2007
+
+dim = length(sz);
+
+if (nargin<3)
+  mode = 'eqdist';
+end
+
+if (any(sz<1))
+  error(['Invalid matrix size : [' num2str(sz) ']']);
+end
+
+if (num > prod(sz))
+  warning(['Invalid number of samples, returning maximum number of samples.']);
+elseif (num <= 0)
+  if (num < 0)
+    warning('Invalid number of samples, assuming 0 samples.');
+  end
+  for i = 1:length(sz)
+    varargout{i} = [];
+  end
+  return;
+end
+
+
+if (strcmp(mode,'eqdist'))
+  
+  % approximate distance between samples: total volume divided by number of
+  % samples gives the average volume per sample. then, taking the p-th root
+  % gives the average distance between samples
+  d = (prod(sz)/num)^(1/dim);
+  
+  % compute the initial guess for number of samples in each dimension.
+  % then, while total number of samples is too large, decrese the number of
+  % samples by one in the dimension where the samples are the most crowded.
+  % finally, do the opposite process until just passing num, so the final
+  % number of samples is the closest to num from above.
+  
+  n = min(max(round(sz/d),1),sz);   % set n so that it saturates at 1 and sz
+  
+  active_dims = find(n>1);    % dimensions where the sample num can be reduced
+  while(prod(n)>num && ~isempty(active_dims))
+    [y,id] = min((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))-1;
+    if (n(active_dims(id)) < 2)
+      active_dims = find(n>1);
+    end
+  end
+
+  active_dims = find(n<sz);    % dimensions where the sample num can be increased
+  while(prod(n)<num && ~isempty(active_dims))
+    [y,id] = max((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))+1;
+    if (n(active_dims(id)) >= sz(active_dims(id)))
+      active_dims = find(n<sz);
+    end
+  end
+
+  for i = 1:dim
+    varargout{i} = round((1:n(i))/n(i)*sz(i));
+    varargout{i} = varargout{i} - floor((varargout{i}(1)-1)/2);
+  end
+  
+elseif (strcmp(mode,'eqnum'))
+  
+  % same idea as above
+  n = min(max( ones(size(sz)) * round(num^(1/dim)) ,1),sz);
+
+  active_dims = find(n>1);
+  while(prod(n)>num && ~isempty(active_dims))
+    [y,id] = min((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))-1;
+    if (n(active_dims(id)) < 2)
+      active_dims = find(n>1);
+    end
+  end
+  
+  active_dims = find(n<sz);
+  while(prod(n)<num && ~isempty(active_dims))
+    [y,id] = max((sz(active_dims)-1)./n(active_dims));
+    n(active_dims(id)) = n(active_dims(id))+1;
+    if (n(active_dims(id)) >= sz(active_dims(id)))
+      active_dims = find(n<sz);
+    end
+  end
+  
+  for i = 1:dim
+    varargout{i} = round((1:n(i))/n(i)*sz(i));
+    varargout{i} = varargout{i} - floor((varargout{i}(1)-1)/2);
+  end
+else
+  error('Invalid sampling mode');
+end
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/remove_dc.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/remove_dc.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,31 @@
+function [y,dc] = remove_dc(x,columns)
+%REMOVE_DC Remove DC channel from signals.
+%   [Y,DC] = REMOVE_DC(X) removes the DC channel (i.e. the mean) from the
+%   specified (possibly multi-dimensional) signal X. Y is the DC-free
+%   signal and is the same size as X. DC is a scalar containing the mean of
+%   the signal X.
+%
+%   [Y,DC] = REMOVE_DC(X,'columns') where X is a 2D matrix, treats the
+%   columns of X as a set of 1D signals, removing the DC channel from each
+%   one individually. Y is the same size as X and contains the DC-free
+%   signals. DC is a row vector of length size(X,2) containing the means of
+%   the signals in X.
+%
+%   See also ADD_DC.
+
+
+if (nargin==2 && strcmpi(columns,'columns')), columns = 1;
+else columns = 0;
+end
+
+if (columns)
+  dc = mean(x);
+  y = addtocols(x,-dc);
+else
+  if (ndims(x)==2)  % temporary, will remove in future
+    warning('Treating 2D matrix X as a single signal and not each column individually');
+  end
+  dc = mean(x(:));
+  y = x-dc;
+end
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/rowlincomb.c
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/rowlincomb.c	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,148 @@
+/**************************************************************************
+ *
+ * File name: rowlincomb.c
+ *
+ * Ron Rubinstein
+ * Computer Science Department
+ * Technion, Haifa 32000 Israel
+ * ronrubin@cs
+ *
+ * Last Updated: 21.5.2009
+ *
+ *************************************************************************/
+
+#include "mex.h"
+
+
+/* Input Arguments */
+
+#define	X_IN	   prhs[0]
+#define A_IN     prhs[1]
+#define ROWS_IN  prhs[2]
+#define COLS_IN  prhs[3]
+
+
+/* Output Arguments */
+
+#define	Y_OUT	plhs[0]
+
+
+void mexFunction(int nlhs, mxArray *plhs[],
+int nrhs, const mxArray*prhs[])
+
+{
+  double *A, *x, *y, *rows, *cols;
+  mwSize m,n,m1,n1,m2,n2,rownum,colnum;
+  mwIndex *row_ids,*col_ids,i,j;
+  int colnumspecified=0;
+  
+  
+  /* Check for proper number of arguments */
+  
+  if (nrhs!=3 && nrhs!=4) {
+    mexErrMsgTxt("Invalid number of input arguments.");
+  } else if (nlhs > 1) {
+    mexErrMsgTxt("Too many output arguments.");
+  }
+  
+  
+  /* Check the input dimensions */
+  
+  m = mxGetM(A_IN);
+  n = mxGetN(A_IN);
+  if (!mxIsDouble(A_IN) || mxIsComplex(A_IN) || mxGetNumberOfDimensions(A_IN)>2) {
+    mexErrMsgTxt("ROWLINCOMB requires that A be a double matrix.");
+  }
+  
+  m1 = mxGetM(ROWS_IN);
+  n1 = mxGetN(ROWS_IN);
+  if (!mxIsDouble(ROWS_IN) || mxIsComplex(ROWS_IN) || (m1!=1 && n1!=1)) {
+    mexErrMsgTxt("ROWLINCOMB requires that ROWS be an index vector of type double.");
+  }
+  rownum = (m1 > n1) ? m1 : n1;   /* the number of rows in the linear combination */
+  
+  m2 = mxGetM(X_IN);
+  n2 = mxGetN(X_IN);
+  if (!mxIsDouble(X_IN) || mxIsComplex(X_IN) || ((m2!=1) && (n2!=1))) {
+    mexErrMsgTxt("ROWLINCOMB requires that X be a double vector.");
+  }
+  
+  if (m2 != rownum && n2 != rownum) {
+    mexErrMsgTxt("The length of X does not match the number of rows in ROWS.");
+  }
+  
+  if (nrhs==4) {
+    m1 = mxGetM(COLS_IN);
+    n1 = mxGetN(COLS_IN);
+    if (!mxIsDouble(COLS_IN) || mxIsComplex(COLS_IN) || (m1!=1 && n1!=1)) {
+      mexErrMsgTxt("ROWLINCOMB requires that COLS be an index vector of type double.");
+    }
+    colnum = (m1 > n1) ? m1 : n1;   /* the number of columns */
+    colnumspecified = 1;
+    cols = mxGetPr(COLS_IN);
+    
+    Y_OUT = mxCreateDoubleMatrix(1, colnum, mxREAL);
+  }
+  else {
+    cols = 0;
+    Y_OUT = mxCreateDoubleMatrix(1, n, mxREAL);
+  }
+  
+  
+  /* Assign pointers to the various parameters */
+  A = mxGetPr(A_IN);
+  rows = mxGetPr(ROWS_IN);
+  x = mxGetPr(X_IN);
+  y = mxGetPr(Y_OUT);
+  
+  
+  /* check row indices */
+  
+  row_ids = (mwIndex*)mxMalloc(rownum*sizeof(mwIndex));
+  
+  for (i=0; i<rownum; ++i) {
+    row_ids[i] = (mwIndex)(rows[i]+0.1)-1;
+    if (row_ids[i]<0 || row_ids[i]>=m) {
+      mexErrMsgTxt("Row index in ROWS is out of range.");
+    }
+  }
+  
+  
+  
+  if (colnumspecified) {
+    
+    /* check column indices */
+    col_ids = (mwIndex*)mxMalloc(colnum*sizeof(mwIndex));
+    
+    for (i=0; i<colnum; ++i) {
+      col_ids[i] = (mwIndex)(cols[i]+0.1)-1;
+      if (col_ids[i]<0 || col_ids[i]>=n) {
+        mexErrMsgTxt("Column index in COLS is out of range.");
+      }
+    }
+    
+    /* Do the actual computation */
+    for (j=0; j<colnum; ++j) {
+      for (i=0; i<rownum; ++i) {
+        y[j] += A[m*col_ids[j]+row_ids[i]]*x[i];
+      }
+    }
+    
+    mxFree(col_ids);
+  }
+  
+  else {
+    
+    /* Do the actual computation */
+    for (j=0; j<n; ++j) {
+      for (i=0; i<rownum; ++i) {
+        y[j] += A[m*j+row_ids[i]]*x[i];
+      }
+    }
+  }
+  
+  
+  mxFree(row_ids);
+  
+  return;
+}
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/rowlincomb.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/rowlincomb.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,26 @@
+%ROWLINCOMB Linear combination of matrix rows.
+%  Y = ROWLINCOMB(X,A,ROWS) computes a linear combination of the rows of
+%  the matrix A. The row indices are specified in the vector ROWS, and the
+%  correspoinding coefficients are specified in the vector X. The vectors
+%  ROWS and X must be of the same length. The call Y = ROWLINCOMB(X,A,ROWS)
+%  is essentially equivalent to the command
+%
+%         Y = X'*A(ROWS,:) .
+%
+%  However, it is implemented much more efficiently.
+%
+%  Y = ROWLINCOMB(X,A,ROWS,COLS) only works on the columns of A specified
+%  in COLS, returning a vector of length equal to COLS. This call is
+%  essentially equivalent to the command
+%
+%         Y = X'*A(ROWS,COLS) .
+%
+%  See also COLLINCOMB.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2009
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/sampgrid.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/sampgrid.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,93 @@
+function y = sampgrid(x,blocksize,varargin)
+%SAMPGRID Sample a multi-dimensional matrix on a regular grid.
+%  Y = SAMPGRID(X,BLOCKSIZE,I1,I2,...,Ip) extracts block samples of size
+%  BLOCKSIZE from the p-dimensional matrix X, arranging the samples as the
+%  column vectors of the matrix Y. The locations of the (1,1,..,1)-th
+%  elements of each block are given in the index vectors I1,I2,..Ip. The
+%  total number of samples taken is length(I1)xlength(I2)x...xlength(Ip).
+%  BLOCKSIZE should either be a p-element vector of the form [N1,N2,...Np],
+%  or a scalar N which is shorthand for the square block size [N N ... N].
+%
+%  Example: Sample a set of blocks uniformly from a 2D image.
+%
+%    n = 512; blocknum = 20000; blocksize = [8 8];
+%    im = rand(n,n);
+%    [i1,i2] = reggrid(size(im)-blocksize+1, blocknum);
+%    blocks = sampgrid(im, blocksize, i1, i2);
+%
+%  See also REGGRID.
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  November 2007
+
+
+p = ndims(x);
+
+if (numel(blocksize)==1)
+  blocksize = ones(1,p)*blocksize;
+end
+
+n = zeros(1,p);
+for i = 1:p
+  n(i) = length(varargin{i});
+end
+
+nsamps = prod(n);
+
+% create y of the same class as x
+y = zeros(prod(blocksize),nsamps,class(x));
+
+% ids() contains the index of the current block in I1..Ip
+ids = ones(p,1);
+
+% block_ids contains the indices of the current block in X
+block_ids = cell(p,1);
+for j = 1:p
+  block_ids{j} = varargin{j}(1) : varargin{j}(1)+blocksize(j)-1;
+end
+
+for k = 1:nsamps
+  block = x(block_ids{:});
+  y(:,k) = block(:);
+  
+  % increment ids() and block_ids{}
+  if (k<nsamps)
+    j = 1;
+    while (ids(j) == n(j))
+      ids(j) = 1;
+      block_ids{j} = varargin{j}(1) : varargin{j}(1)+blocksize(j)-1;
+      j = j+1;
+    end
+    ids(j) = ids(j)+1;
+    block_ids{j} = varargin{j}(ids(j)) : varargin{j}(ids(j))+blocksize(j)-1;
+  end
+end
+
+
+% 
+% p = ndims(x);
+% 
+% n = zeros(1,p);
+% for i = 1:p
+%   n(i) = length(varargin{i});
+% end
+% 
+% nsamps = prod(n);
+% 
+% % create y of the same class as x
+% y = zeros(prod(blocksize),nsamps,class(x));
+% 
+% id = cell(p,1);
+% for k = 1:nsamps
+%   [id{:}] = ind2sub(n,k);
+%   for j = 1:p
+%     id{j} = varargin{j}(id{j}) : varargin{j}(id{j})+blocksize(j)-1;
+%   end
+%   block = x(id{:});
+%   y(:,k) = block(:);
+% end
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/secs2hms.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/secs2hms.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,28 @@
+function [h,m,s] = secs2hms(t)
+%SECS2HMS Convert seconds to hours, minutes and seconds.
+%  [H,M,S] = SECS2HMS(T) converts the specified number of seconds T to
+%  hours, minutes and seconds. H and M are whole numbers, and S is real.
+%
+%  Example: Estimate the remaining time of a loop
+%
+%    n = 10; tic;
+%    for i = 1:n
+%      pause(1);
+%      [h,m,s] = secs2hms( (n-i)*toc/i );
+%      printf('estimated remaining time: %02d:%02d:%05.2f',h,m,s);
+%    end
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  April 2008
+
+
+s = t;
+h = fix(s/3600);
+s = rem(s,3600);
+m = fix(s/60);
+s = rem(s,60);
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/spdiag.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/spdiag.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,38 @@
+function Y = spdiag(V,K)
+%SPDIAG Sparse diagonal matrices.
+%   SPDIAG(V,K) when V is a vector with N components is a sparse square
+%   matrix of order N+ABS(K) with the elements of V on the K-th diagonal. 
+%   K = 0 is the main diagonal, K > 0 is above the main diagonal and K < 0
+%   is below the main diagonal. 
+%
+%   SPDIAG(V) is the same as SPDIAG(V,0) and puts V on the main diagonal.
+%
+%   See also DIAG, SPDIAGS.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  June 2008
+
+
+if (nargin<2)
+  K = 0;
+end
+
+n = length(V) + abs(K);
+
+if (K>0)
+  i = 1:length(V);
+  j = K+1:n;
+elseif (K<0)
+  i = -K+1:n;
+  j = 1:length(V);
+else
+  i = 1:n;
+  j = 1:n;
+end
+
+Y = sparse(i,j,V(:),n,n);
\ No newline at end of file
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/timerclear.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/timerclear.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,37 @@
+function timerclear()
+%TIMERCLEAR Clear all timers.
+%   TIMERCLEAR clears all currenly registered timers, invalidating all
+%   timer ids.
+%
+%   Note: since registered timers do not consume CPU power except for when
+%   the TIMER<*> functions are called, this function is only useful in
+%   situations where a large number of timers have been initialized, and
+%   there is a need to reclaim memory.
+%
+%   See also TIMERINIT, TIMERETA.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  June 2008
+
+
+global utiltbx_timer_start_times    % start times
+global utiltbx_time_lastdisp        % last display times
+global utiltbx_timer_iternums       % iteration numbers
+global utiltbx_timer_lastiter       % last queried iteration numbers
+global utiltbx_timer_name           % timer names
+global utiltbx_timer_callfun        % timer calling functions
+
+
+% clear all timers %
+
+utiltbx_timer_start_times = [];
+utiltbx_time_lastdisp = [];
+utiltbx_timer_iternums = [];
+utiltbx_timer_lastiter = [];
+utiltbx_timer_name = [];
+utiltbx_timer_callfun = [];
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/timereta.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/timereta.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,98 @@
+function varargout = timereta(tid,iter,delay)
+%TIMERETA Estimated remaining time.
+%   S = TIMERETA(TID,ITER) returns the estimated remaining time (in
+%   seconds) for the process associated with timer TID, assuming the
+%   process has completed ITER iterations. Note: the function will exit
+%   with an error if the timer TID does not have an associated number of
+%   iterations (see function TIMERINIT).
+%
+%   [H,M,S] = TIMERETA(TID,ITER) returns the estimated remaining time in
+%   hours, minutes and seconds.
+%
+%   TIMERETA(TID,ITER), with no output arguments, prints the estimated
+%   remaining time to the screen. The time is displayed in the format
+%
+%     TIMERNAME: iteration ITER / ITERNUM, estimated remaining time: HH:MM:SS.SS
+%
+%   If the timer has no assigned name, the display format changes to
+%
+%     Iteration ITER / ITERNUM, estimated remaining time: HH:MM:SS.SS
+%
+%   TIMERETA(TID,ITER,DELAY) only displays the remaining time if the
+%   time elapsed since the previous printout is at least DELAY seconds.
+%
+%   See also TIMERINIT, TIMERCLEAR.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  June 2008
+
+
+global utiltbx_timer_start_times 
+global utiltbx_timer_iternums
+global utiltbx_timer_lastiter
+global utiltbx_time_lastdisp
+global utiltbx_timer_name
+
+
+if (tid<1 || tid>length(utiltbx_timer_iternums))
+  error('Unknown timer id');
+end
+
+if (utiltbx_timer_iternums(tid) < 0)
+  error('Specified timer does not have an associated number of iterations');
+end
+
+% update last reported iteration number
+utiltbx_timer_lastiter(tid) = iter;
+
+% compute elapsed time
+starttime = utiltbx_timer_start_times(tid,:);
+currtime = clock;
+timediff = etime(currtime, starttime);
+
+% total iteration number
+iternum = utiltbx_timer_iternums(tid);
+
+% compute eta
+timeremain = (iternum-iter)*timediff/iter;
+
+% return eta in seconds
+if (nargout==1)
+  varargout{1} = timeremain;
+  
+% return eta in hms
+elseif (nargout==3)
+  [varargout{1}, varargout{2}, varargout{3}] = secs2hms(timeremain);
+  
+  
+% print eta
+elseif (nargout==0)
+  
+  % check last display time
+  lastdisptime = utiltbx_time_lastdisp(tid,:);
+  if (nargin>2 && etime(currtime,lastdisptime) < delay)
+    return;
+  end
+  
+  % update last display time
+  utiltbx_time_lastdisp(tid,:) = currtime;
+
+  % display timer
+  [hrs,mins,secs] = secs2hms(timeremain);
+  if (isempty(utiltbx_timer_name{tid}))
+    printf('Iteration %d / %d, estimated remaining time: %02d:%02d:%05.2f', iter, iternum, hrs, mins, secs);
+  else
+    timername = utiltbx_timer_name{tid};
+    printf('%s: iteration %d / %d, estimated remaining time: %02d:%02d:%05.2f', timername, iter, iternum, hrs, mins, secs);
+  end
+   
+% invalid number of outputs
+else
+  error('Invalid number of output arguments');
+end
+
diff -r 28f2b5fe3483 -r 207a6ae9a76f Problems/private/timerinit.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/timerinit.m	Mon Mar 22 15:06:25 2010 +0000
@@ -0,0 +1,110 @@
+function tid = timerinit(par1,par2)
+%TIMERINIT Initialize a new timer.
+%   TID = TIMERINIT() initializes a new timer for counting elapsed time,
+%   and returns its id.
+%
+%   TID = TIMERINIT('TIMERNAME') sets the timer name to the specified
+%   string for display purposes.
+%
+%   TID = TIMERINIT(ITERNUM) initializes a new ETA timer for a process with
+%   ITERNUM iterations. An ETA timer can be used for both counting elapsed
+%   time and estimating remaining time.
+%
+%   TID = TIMERINIT('TIMERNAME',ITERNUM) sets the ETA timer name to the
+%   specified string for display purposes.
+%
+%   Example:
+%
+%     tid = timerinit(100); 
+%     for i = 1:100
+%       pause(0.07);
+%       timereta(tid,i,1);
+%     end
+%     timereta(tid,i);
+%
+%   See also TIMERETA, TIMERCLEAR.
+
+
+%  Ron Rubinstein
+%  Computer Science Department
+%  Technion, Haifa 32000 Israel
+%  ronrubin@cs
+%
+%  June 2008
+
+
+global utiltbx_timer_start_times    % start times
+global utiltbx_time_lastdisp        % last display times
+global utiltbx_timer_iternums       % iteration numbers
+global utiltbx_timer_lastiter       % last queried iteration numbers
+global utiltbx_timer_name           % timer names
+global utiltbx_timer_callfun        % timer calling functions
+
+
+% parse function arguments %
+
+if (nargin==0)
+
+  iternum = -1;
+  timername = '';
+
+elseif (nargin==1)
+
+  if (ischar(par1))
+    iternum = -1;
+    timername = par1;
+
+  elseif (isnumeric(par1) && numel(par1)==1 && par1>0)
+    iternum = par1;
+    timername = '';
+
+  else
+    error('Invalid number of iterations');
+  end
+
+elseif (nargin==2)
+
+  if (ischar(par1) && isnumeric(par2))
+    if (numel(par2)==1 && par2>0)
+      timername = par1;
+      iternum = par2;
+    else
+      error('Invalid number of iterations');
+    end
+  else
+    error('Invalid function syntax');
+  end
+
+else
+  error('Too many function parameters');
+end
+
+
+% register the timer %
+
+if (isempty(utiltbx_timer_start_times))
+  utiltbx_timer_start_times = clock;
+  utiltbx_time_lastdisp = utiltbx_timer_start_times;
+  utiltbx_timer_iternums = double(iternum);
+  utiltbx_timer_lastiter = 0;
+  utiltbx_timer_name = { timername };
+  utiltbx_timer_callfun = {};
+  tid = 1;
+else
+  utiltbx_timer_start_times(end+1,:) = clock;
+  utiltbx_time_lastdisp(end+1,:) = utiltbx_timer_start_times(end,:);
+  utiltbx_timer_iternums(end+1) = double(iternum);
+  utiltbx_timer_lastiter(end+1) = 0;
+  utiltbx_timer_name{end+1} = timername;
+  tid = size(utiltbx_timer_start_times,1);
+end
+
+
+% detect timer calling function %
+
+st = dbstack;
+if (length(dbstack) >= 2)
+  utiltbx_timer_callfun{end+1} = st(2).name;
+else
+  utiltbx_timer_callfun{end+1} = '';
+end