testmextrcolumn

 TESTMEXTRCOLUMN tests that the behaviour of mextrcolumn() is correct

 RETURN
   status ...  0 failed, 1 all ok
 INPUT
   verbose ... 0 print only what failed, 1 print progress,
               optional, default 1
   tol ....... tolerance when comparing the results
               optional, default 1e-8

 See also mextrcolumn, penlabtest, penlabstresstest

0001 function [status] = testmextrcolumn(verbose,tol)
0002 % TESTMEXTRCOLUMN tests that the behaviour of mextrcolumn() is correct
0003 %
0004 % RETURN
0005 %   status ...  0 failed, 1 all ok
0006 % INPUT
0007 %   verbose ... 0 print only what failed, 1 print progress,
0008 %               optional, default 1
0009 %   tol ....... tolerance when comparing the results
0010 %               optional, default 1e-8
0011 %
0012 % See also mextrcolumn, penlabtest, penlabstresstest
0013 %
0014 
0015 % This file is a part of PENLAB package distributed under GPLv3 license
0016 % Copyright (c) 2013 by  J. Fiala, M. Kocvara, M. Stingl
0017 % Last Modified: 5 Dec 2013
0018 
0019   if (nargin<2)
0020     tol = 1e-8;
0021   end
0022   if (nargin<1)
0023     verbose = 1;
0024   end
0025   status = 1;
0026 
0027   if (verbose)
0028     disp(' testing functionality of mextrcolumn()...')
0029   end
0030 
0031   % is it possible to call it?
0032   try
0033     mextrcolumn(1,sparse(1),1,{sparse(1)});
0034   catch
0035     disp(' Error: mextrcolumn - cannot call')
0036     status = 0;
0037     return;
0038   end
0039 
0040   status = status && onematrixtest(verbose,tol,'n=0, all empty', [],[],[],[],0);
0041   status = status && onematrixtest(verbose,tol,'n=1, all ones', 1,1,1,1,2);
0042   status = status && onematrixtest(verbose,tol,'n=1, all nonzeros', 2,3,-4,5,-120*2);
0043   status = status && onematrixtest(verbose,tol,'n=1, A=0', 0,3,-4,5,0);
0044   status = status && onematrixtest(verbose,tol,'n=1, S1=0', 2,0,-4,5,0);
0045   status = status && onematrixtest(verbose,tol,'n=1, B=0', 2,3,0,5,0);
0046   status = status && onematrixtest(verbose,tol,'n=1, S2=0', 2,3,-4,0,0);
0047   status = status && onematrixtest(verbose,tol,'n=2, all numbers, A diag', diag([2 3]),[-2.1,3.2;3.2,4.4],[4,6;6,5],[-13,-9;-9,-16]);
0048   % don't forget that magic() is not symmetric
0049   status = status && onematrixtest(verbose,tol,'n=2, all numbers, A diag, B=[]', diag([2 3]),[-2.1,3.2;3.2,4.4],magic(2)+magic(2)'+3,sparse(2,2),0);
0050   
0051   % build special examples with very sparse matrices
0052   n=5;
0053   A=diag(1:n);
0054   B=magic(n)+magic(n)';
0055   S1=sparse(n,n); S1(2,1)=2;
0056   S1=S1+S1';
0057   S2=sparse(n,n); S2(4,4)=9;
0058   status = status && onematrixtest(verbose,tol,'n=5, very sparse', A,S1,B,S2);
0059 
0060   n=5;
0061   A=diag(1:n);
0062   B=magic(n)+magic(n)';
0063   S1=sparse(n,n); S1(2,1)=2;
0064   S1=S1+S1';
0065   S2=sparse(n,n); S2(2,2)=9;
0066   status = status && onematrixtest(verbose,tol,'n=5, very sparse2', A,S1,B,S2);
0067 
0068   n=5;
0069   A=zeros(n,n);
0070   A(:)=[1:n^2]-10;
0071   A=A+A';
0072   B=magic(n)+magic(n)';
0073   S1=sparse(n,n); S1(2,1)=2;
0074   S1=S1+S1';
0075   S2=sparse(n,n); S2(2,2)=9;
0076   status = status && onematrixtest(verbose,tol,'n=5, very sparse3', A,S1,B,S2);
0077 
0078   n=5;
0079   A=zeros(n,n);
0080   A(:)=[1:n^2]-10;
0081   A=A+A';
0082   B=magic(n)+magic(n)';
0083   S1=sparse(n,n); S1(2,1)=2;
0084   S1=S1+S1';
0085   S2=sparse(diag([5:9]));
0086   status = status && onematrixtest(verbose,tol,'n=5, sparse, S2 spdiag', A,S1,B,S2);
0087 
0088   % random of different size
0089   for n=[5 5 5 10 10 10 100 100 999 1000]
0090   %for n=[2 5 5]
0091     A=rand(n,n);
0092     A=A+A';
0093     B=rand(n,n);
0094     B=B+B';
0095     S1=sprandsym(n,0.2);
0096     S2=sprandsym(n,0.1);
0097     testname=sprintf('n=%i all random',n);
0098     status = status && onematrixtest(verbose,tol,testname, A,S1,B,S2);
0099   end
0100 
0101   % test mex on the vector of matrices S2, random data
0102   %[A,S1,B,Si] = vecmatrixdata(n,nmat,dS1,dSi);
0103   [A,S1,B,Si] = vecmatrixdata(7,1,0.2,0.9); testname='n=7 * 1 mat';
0104   status = status && vecmatrixtest(verbose,tol,testname,A,S1,B,Si);
0105   [A,S1,B,Si] = vecmatrixdata(7,31,0.8,rand(31,1)); testname='n=7 * 31 mat';
0106   status = status && vecmatrixtest(verbose,tol,testname,A,S1,B,Si);
0107   [A,S1,B,Si] = vecmatrixdata(8,17,0.5,[17:-1:1]/20); testname='n=8 * 17 mat';
0108   status = status && vecmatrixtest(verbose,tol,testname,A,S1,B,Si);
0109   [A,S1,B,Si] = vecmatrixdata(20,10,0.2,ones(10,1)*0.8); testname='n=20 * 10 mat (0.8)';
0110   status = status && vecmatrixtest(verbose,tol,testname,A,S1,B,Si);
0111   [A,S1,B,Si] = vecmatrixdata(3,99,0.9,ones(99,1)*0.9); testname='n=3 * 99 mat (0.9)';
0112   status = status && vecmatrixtest(verbose,tol,testname,A,S1,B,Si);
0113 
0114 end
0115 
0116 function [status] = onematrixtest(verbose,tol,testname,A,S1,B,S2,ref)
0117 % ONEMATRIXTEST - run one test with mextrcolumn(), S2 has just one element
0118 %   testname - string to print out
0119 %   A,B,S1,S2 - matrices for the test
0120 %   ref [optional] - reference result, if not present, computed in Matlab
0121 
0122   status = 1;
0123 
0124   if (~issparse(S1))
0125     S1=sparse(S1);
0126   end
0127   if (~issparse(S2))
0128     S2=sparse(S2);
0129   end
0130 
0131   % compute reference result if not provided
0132   if (nargin==7)
0133     %ref = trace(A*S1*B*S2);
0134     ref = trace(A*S1*B*S2) + trace(A*S2*B*S1);
0135   end
0136 
0137   try
0138     result = mextrcolumn(A,S1,B,{S2});
0139     err = abs(result-ref);
0140   catch
0141     err = [];
0142   end
0143 
0144   if (isempty(err))
0145     fprintf(' test %-30s: HARD FAILED\n', testname);
0146     status = 0;
0147   elseif (err>tol*abs(ref))
0148     fprintf(' test %-30s: FAILED  %15.6e %15.6e\n', testname,err,ref);
0149     status = 0;
0150   elseif (verbose)
0151     fprintf(' test %-30s: ok (tol)  %15.6e %15.6e\n', testname,err,ref);
0152   end
0153 
0154 end
0155 
0156 function [A,S1,B,Si] = vecmatrixdata(n,nmat,dS1,dSi)
0157 % VECMATRIXDATA - generate random dataset for vecmatrixtest
0158 %   n - dimension of the matrices
0159 %   nmat - the number of the cell array Si
0160 %   dS1 - density of S1
0161 %   dSi - vector of densities (of length nmat) for Si
0162 
0163   A = rand(n,n);
0164   A = A+A';
0165   B = rand(n,n);
0166   B = B+B';
0167   S1 = sprandsym(n,dS1);
0168   Si = cell(nmat,1);
0169   for i = 1:nmat
0170     Si{i} = sprandsym(n,dSi(i));
0171   end
0172 
0173 end
0174 
0175 function [status] = vecmatrixtest(verbose,tol,testname,A,S1,B,Si,ref)
0176 % VECMATRIXTEST - run one test with mextrcolumn() on vector Si
0177 %   testname - string to print out
0178 %   A,B,S1,Si{:} - matrices for the test, (Si is a cell array of matrices),
0179 %      all symmetric, S1, Si{:} must be sparse
0180 %   ref [optional] - reference result, if not present, computed in Matlab
0181 
0182   status = 1;
0183 
0184   % compute reference results if not provided
0185   if (nargin==7)
0186     nmat = length(Si);
0187     ref = zeros(nmat,1);
0188     for i = 1:nmat
0189       ref(i) = trace(A*S1*B*Si{i}) + trace(A*Si{i}*B*S1);
0190     end
0191   end
0192   nrm = norm(ref);
0193 
0194   try
0195     result = mextrcolumn(A,S1,B,Si);
0196     err = norm(result-ref);
0197   catch
0198     err = [];
0199   end
0200 
0201   if (isempty(err))
0202     fprintf(' test (vec) %-24s: HARD FAILED\n', testname);
0203     status = 0;
0204   elseif (err>tol*nrm)
0205     fprintf(' test (vec) %-24s: FAILED  %15.6e %15.6e\n', testname,err,nrm);
0206     status = 0;
0207   elseif (verbose)
0208     fprintf(' test (vec) %-24s: ok (tol)  %15.6e %15.6e\n', testname,err,nrm);
0209   end
0210 
0211 end
0212