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fvn_sparse/UMFPACK/MATLAB/umfpack_test.m 3.6 KB
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422234dc3   daniau   git-svn-id: https... 
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  %UMFPACK_TEST for testing umfpack2 (requires UFget)
  %
  % Example:
  %   umfpack_test
  % See also umfpack2
  
  % Copyright 1995-2007 by Timothy A. Davis.
  
  index = UFget ;
  
  f = find (index.nrows == index.ncols) ;
  [ignore, i] = sort (index.nrows (f)) ;
  f = f (i) ;
  
  Control = umfpack2 ;
  Control (1) = 0 ;
  
  figure (1)
  clf
  
  
  for i = f
  
      fprintf ('
  matrix: %s %s %d
  ', index.Group{i}, index.Name{i}, index.nrows(i)) ;
  
      Prob = UFget (i) ;
      A = Prob.A ;
      n = size (A,1) ;
  
      b = rand (1,n) ;
      c = b' ;
  
      try
  
  	%-----------------------------------------------------------------------
  	% symbolic factorization
  	%-----------------------------------------------------------------------
  
  	[P1, Q1, Fr, Ch, Info] = umfpack2 (A, 'symbolic') ;
  	subplot (2,2,1)
  	spy (A)
  	title ('A')
  
  	subplot (2,2,2)
  	treeplot (Fr (1:end-1,2)') ;
  	title ('supercolumn etree')
  
  	%-----------------------------------------------------------------------
  	% P(R\A)Q = LU
  	%-----------------------------------------------------------------------
  
  	[L,U,P,Q,R,Info] = umfpack2 (A) ;
  	err = lu_normest (P*(R\A)*Q, L, U) ;
  	fprintf ('norm est PR\\AQ-LU: %g relative: %g
  ', ...
  	    err, err / norm (A,1)) ;
  
  	subplot (2,2,3)
  	spy (P*A*Q)
  	title ('PAQ') ;
  
  	cs = Info (57) ;
  	rs = Info (58) ;
  
  	subplot (2,2,4)
  	hold off
  	spy (L|U)
  	hold on
  	if (cs > 0)
  	    plot ([0 cs n n 0] + .5, [0 cs cs 0 0]+.5, 'c') ;
  	end
  	if (rs > 0)
  	    plot ([0 rs rs 0 0] + cs +.5, [cs cs+rs n n cs]+.5, 'r') ;
  	end
  
  	title ('LU factors')
  	drawnow
  
  	%-----------------------------------------------------------------------
  	% PAQ = LU
  	%-----------------------------------------------------------------------
  
  	[L,U,P,Q] = umfpack2 (A) ;
  	err = lu_normest (P*A*Q, L, U) ;
  	fprintf ('norm est PAQ-LU:   %g relative: %g
  ', ...
  	    err, err / norm (A,1)) ;
  
  	%-----------------------------------------------------------------------
  	% solve
  	%-----------------------------------------------------------------------
  
  	x1 = b/A ;
  	y1 = A\c ;
  	m1 = norm (b-x1*A) ;
  	m2 = norm (A*y1-c) ;
  
  	% factor the transpose
  	Control (8) = 2 ;
  	[x, info] = umfpack2 (A', '\', c, Control) ;
  	lunz0 = info (44) + info (45) - info (67) ;
  	r = norm (A'*x-c) ;
  
  	fprintf (':: %8.2e  matlab: %8.2e %8.2e
  ',  r, m1, m2) ;
  
  	% factor the original matrix and solve xA=b
  	for ir = 0:4
  	    Control (8) = ir ;
  	    [x, info] = umfpack2 (b, '/', A, Control) ;
  	    r = norm (b-x*A) ;
  	    if (ir == 0)
  		lunz1 = info (44) + info (45) - info (67) ;
  	    end
  	    fprintf ('%d: %8.2e %d %d
  ', ir, r, info (81), info (82)) ;
  	end
  
  	% factor the original matrix and solve Ax=b
  	for ir = 0:4
  	    Control (8) = ir ;
  	    [x, info] = umfpack2 (A, '\', c, Control) ;
  	    r = norm (A*x-c) ;
  	    fprintf ('%d: %8.2e %d %d
  ', ir, r, info (81), info (82)) ;
  	end
  
  	fprintf (...
  	    'lunz trans %12d    no trans: %12d  trans/notrans: %10.4f
  ', ...
  	    lunz0, lunz1, lunz0 / lunz1) ;
  
  	%-----------------------------------------------------------------------
  	% get the determinant
  	%-----------------------------------------------------------------------
  
  	det1 = det (A) ;
  	det2 = umfpack2 (A, 'det') ;
  	[det3 dexp3] = umfpack2 (A, 'det') ;
  	err = abs (det1-det2) ;
  	err3 = abs (det1 - (det3 * 10^dexp3)) ;
  	denom = det1 ;
  	if (denom == 0)
  	    denom = 1 ;
  	end
  	err = err / denom ;
  	err3 = err3 / denom ;
  	fprintf ('det:  %20.12e + (%20.12e)i MATLAB
  ', ...
  	    real(det1), imag(det1)) ;
  	fprintf ('det:  %20.12e + (%20.12e)i umfpack2
  ', ...
  	    real(det2), imag(det2)) ;
  	fprintf ('det: (%20.12e + (%20.12e)i) * 10^(%g) umfpack2
  ', ...
  	    real(det3), imag(det3), dexp3) ;
  	fprintf ('diff %g %g
  ', err, err3) ;
  
      catch
  	fprintf ('failed
  ') ;
      end
  end