137 lines
3.4 KiB
Matlab
137 lines
3.4 KiB
Matlab
function failed = trylusolve(A,b);
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% TRYLUSOLVE : Test the Matlab interface to lusolve.
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%
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% failed = trylusolve;
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% This runs several tests on lusolve, using a matrix with the
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% structure of "smallmesh". It returns a list of failed tests.
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%
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% failed = trylusolve(A);
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% failed = trylusolve(A,b);
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% This times the solution of a system with the given matrix,
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% both with lusolve and with Matlab's builtin "\" operator.
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% Usually, "\" will be faster for triangular or symmetric postive
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% definite matrices, and lusolve will be faster otherwise.
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%
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% Copyright (c) 1995 by Xerox Corporation. All rights reserved.
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% HELP COPYRIGHT for complete copyright and licensing notice.
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disp(' ');
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disp(['Testing LUSOLVE on ' time]);
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disp(' ');
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format compact
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resetrandoms;
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if nargin == 0
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A = hbo('smallmesh');
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end;
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[n,m] = size(A);
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if n~=m, error('matrix must be square'), end;
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failed = [];
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ntest = 0;
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tol = 100 * eps * n^2;
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if nargin >= 1 % Just try a solve with the given input matrix.
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ntest=ntest+1;
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v = spparms;
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spparms('spumoni',1);
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fprintf('Matrix size: %d by %d with %d nonzeros.\n',n,m,nnz(A));
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disp(' ');
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if nargin == 1
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b = rand(n,1);
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end;
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tic; x=A\b; t1=toc;
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fprintf('A\\b time = %d seconds.\n',t1);
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disp(' ');
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tic; x=lusolve(A,b); t2=toc;
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fprintf('LUSOLVE time = %d seconds.\n',t2);
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disp(' ');
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ratio = t1/t2;
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fprintf('Ratio = %d\n',ratio);
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residual_norm = norm(A*x-b,inf)/norm(A,inf)
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disp(' ');
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if residual_norm > tol
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disp('*** FAILED ***'); failed = [failed ntest];
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end;
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spparms(v);
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return;
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end;
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% With no inputs, try several tests on the small mesh.
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A = sprandn(A);
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p = randperm(n);
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I = speye(n);
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P = I(p,:);
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b = rand(n,2);
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ntest=ntest+1;
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fprintf('Test %d: Input perm 0.\n',ntest);
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x = lusolve(A,b,0);
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residual_norm = norm(A*x-b,inf)
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disp(' ');
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if residual_norm > tol
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disp('*** FAILED ***'), disp(' '), failed = [failed ntest];
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end;
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ntest=ntest+1;
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fprintf('Test %d: Input perm given as vector.\n',ntest);
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x = lusolve(A,b,p);
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residual_norm = norm(A*x-b,inf)
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disp(' ');
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if residual_norm > tol
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disp('*** FAILED ***^G'), disp(' '), failed = [failed ntest];
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end;
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ntest=ntest+1;
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fprintf('Test %d: Input perm given as matrix.\n',ntest);
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x = lusolve(A,b,P);
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residual_norm = norm(A*x-b,inf)
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disp(' ');
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if residual_norm > tol
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disp('*** FAILED ***'), disp(' '), failed = [failed ntest];
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end;
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ntest=ntest+1;
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fprintf('Test %d: No input perm (colamd done internally).\n',ntest);
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x = lusolve(A,b);
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residual_norm = norm(A*x-b,inf)
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disp(' ');
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if residual_norm > tol
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disp('*** FAILED ***'), disp(' '), failed = [failed ntest];
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end;
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ntest=ntest+1;
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fprintf('Test %d: Empty matrix.\n',ntest);
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x = lusolve([],[]);
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disp(' ');
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% if max(size(x))
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if length(x)
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x
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disp('*** FAILED ***^G'), disp(' ');
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failed = [failed ntest];
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end;
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ntest=ntest+1;
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fprintf('Test %d: Timing versus \\ on the 3-element airfoil matrix.\n',ntest);
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A = hbo('airfoil2');
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n = max(size(A));
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A = sprandn(A);
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b = rand(n,1);
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tic; x=A\b; t1=toc;
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fprintf('A\\b time = %d seconds.\n',t1);
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tic; x=lusolve(A,b); t2=toc;
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fprintf('LUSOLVE time = %d seconds.\n',t2);
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ratio = t1/t2;
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fprintf('Ratio = %d\n',ratio);
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disp(' ');
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if ratio < 1, disp('*** FAILED ***'), disp(' '), failed = [failed ntest]; end;
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nfailed = length(failed);
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if nfailed
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fprintf('\n%d tests failed.\n\n',nfailed);
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else
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fprintf('\nAll tests passed.\n\n',nfailed);
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end;
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