testmextrdsdsmat

 TESTMEXTRDSDSMAT tests that the behaviour of mextrdsdsmat() is correct
 mextrdsdsmat was the first version which is now superseeded by
 mextrcolumn which computest the vector of traces, not just one
 element. Thus mextrdsdsmat can retire at some point.

 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 mextrdsdsmat, penlabtest, penlabstresstest

0001 function [status] = testmextrdsdsmat(verbose,tol)
0002 % TESTMEXTRDSDSMAT tests that the behaviour of mextrdsdsmat() is correct
0003 % mextrdsdsmat was the first version which is now superseeded by
0004 % mextrcolumn which computest the vector of traces, not just one
0005 % element. Thus mextrdsdsmat can retire at some point.
0006 %
0007 % RETURN
0008 %   status ...  0 failed, 1 all ok
0009 % INPUT
0010 %   verbose ... 0 print only what failed, 1 print progress,
0011 %               optional, default 1
0012 %   tol ....... tolerance when comparing the results
0013 %               optional, default 1e-8
0014 %
0015 % See also mextrdsdsmat, penlabtest, penlabstresstest
0016 %
0017 
0018 % This file is a part of PENLAB package distributed under GPLv3 license
0019 % Copyright (c) 2013 by  J. Fiala, M. Kocvara, M. Stingl
0020 % Last Modified: 5 Dec 2013
0021 
0022   if (nargin<2)
0023     tol = 1e-8;
0024   end
0025   if (nargin<1)
0026     verbose = 1;
0027   end
0028   status = 1;
0029 
0030   if (verbose)
0031     disp(' testing functionality of mextrdsdsmat()...')
0032   end
0033 
0034   % is it possible to call it?
0035   try
0036     mextrdsdsmat(1,sparse(1),1,sparse(1));
0037   catch
0038     disp(' Error: mextrdsdsmat - cannot call')
0039     status = 0;
0040     return;
0041   end
0042 
0043   status = status && onematrixtest(verbose,tol,'n=0, all empty', [],[],[],[],0);
0044   status = status && onematrixtest(verbose,tol,'n=1, all ones', 1,1,1,1,2);
0045   status = status && onematrixtest(verbose,tol,'n=1, all nonzeros', 2,3,-4,5,-120*2);
0046   status = status && onematrixtest(verbose,tol,'n=1, A=0', 0,3,-4,5,0);
0047   status = status && onematrixtest(verbose,tol,'n=1, S1=0', 2,0,-4,5,0);
0048   status = status && onematrixtest(verbose,tol,'n=1, B=0', 2,3,0,5,0);
0049   status = status && onematrixtest(verbose,tol,'n=1, S2=0', 2,3,-4,0,0);
0050   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]);
0051   % don't forget that magic() is not symmetric
0052   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);
0053   
0054   % build special examples with very sparse matrices
0055   n=5;
0056   A=diag(1:n);
0057   B=magic(n)+magic(n)';
0058   S1=sparse(n,n); S1(2,1)=2;
0059   S1=S1+S1';
0060   S2=sparse(n,n); S2(4,4)=9;
0061   status = status && onematrixtest(verbose,tol,'n=5, very sparse', A,S1,B,S2);
0062 
0063   n=5;
0064   A=diag(1:n);
0065   B=magic(n)+magic(n)';
0066   S1=sparse(n,n); S1(2,1)=2;
0067   S1=S1+S1';
0068   S2=sparse(n,n); S2(2,2)=9;
0069   status = status && onematrixtest(verbose,tol,'n=5, very sparse2', A,S1,B,S2);
0070 
0071   n=5;
0072   A=zeros(n,n);
0073   A(:)=[1:n^2]-10;
0074   A=A+A';
0075   B=magic(n)+magic(n)';
0076   S1=sparse(n,n); S1(2,1)=2;
0077   S1=S1+S1';
0078   S2=sparse(n,n); S2(2,2)=9;
0079   status = status && onematrixtest(verbose,tol,'n=5, very sparse3', A,S1,B,S2);
0080 
0081   n=5;
0082   A=zeros(n,n);
0083   A(:)=[1:n^2]-10;
0084   A=A+A';
0085   B=magic(n)+magic(n)';
0086   S1=sparse(n,n); S1(2,1)=2;
0087   S1=S1+S1';
0088   S2=sparse(diag([5:9]));
0089   status = status && onematrixtest(verbose,tol,'n=5, sparse, S2 spdiag', A,S1,B,S2);
0090 
0091   % random of different size
0092   for n=[5 5 5 10 10 10 100 100 101 101]
0093   %for n=[2 5 5]
0094     A=rand(n,n);
0095     A=A+A';
0096     B=rand(n,n);
0097     B=B+B';
0098     S1=sprandsym(n,0.2);
0099     S2=sprandsym(n,0.1);
0100     testname=sprintf('n=%i all random',n);
0101     status = status && onematrixtest(verbose,tol,testname, A,S1,B,S2);
0102   end
0103 
0104 end
0105 
0106 function [status] = onematrixtest(verbose,tol,testname,A,S1,B,S2,ref)
0107 % ONEMATRIXTEST - run one test with mextrdsdsmat(), S2 has just one element
0108 %   testname - string to print out
0109 %   A,B,S1,S2 - matrices for the test
0110 %   ref [optional] - reference result, if not present, computed in Matlab
0111 
0112   status = 1;
0113 
0114   if (~issparse(S1))
0115     S1=sparse(S1);
0116   end
0117   if (~issparse(S2))
0118     S2=sparse(S2);
0119   end
0120 
0121   if (nargin==7)
0122     %ref = trace(A*S1*B*S2);
0123     ref = trace(A*S1*B*S2) + trace(A*S2*B*S1);
0124   end
0125 
0126   try
0127     result = mextrdsdsmat(A,S1,B,S2);
0128     err = abs(result-ref);
0129   catch
0130     err = [];
0131   end
0132 
0133   if (isempty(err))
0134     fprintf(' test %-30s: HARD FAILED\n', testname);
0135     status = 0;
0136   elseif (err>tol*abs(ref))
0137     fprintf(' test %-30s: FAILED  %15.6e %15.6e\n', testname,err,ref);
0138     status = 0;
0139   elseif (verbose)
0140     fprintf(' test %-30s: ok (tol)  %15.6e %15.6e\n', testname,err,ref);
0141   end
0142 
0143 end
0144