49 lines
1.3 KiB
Mathematica
49 lines
1.3 KiB
Mathematica
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%%****************************************************************
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%% orthbasis: Compute an orthonomal basis from
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%% the power basis {I,A,A^2, .... ,A^m}
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%% via an Arnoldi-type iteration.
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%%
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%% [Q,H,C] = orthbasis(A,m);
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%%
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%% Output: Q = a cell array containing the orthonormal basis
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%% obtained from {I,A,A^2, .... ,A^m}.
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%%
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%% use in chebymat.m, igmres.m
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [Q,H,C] = orthbasis(A,m);
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N = length(A);
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C(1,1) = 1/sqrt(N);
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Q = cell(1,m+1);
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Q{1} = eye(N)/sqrt(N);
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for k = 1:m
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V = A*Q{k};
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Vold = V;
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for j = 1:k
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H(j,k) = sum(sum(conj(Q{j}).*V));
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V = V - H(j,k)*Q{j};
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end;
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if (norm(V,'fro') < norm(Vold,'fro'));
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for j = 1:k
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s(j,1) = sum(sum(conj(Q{j}).*V));
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V = V - s(j)*Q{j};
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end;
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H(1:k,k) = H(1:k,k) + s;
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end;
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nrm = norm(V,'fro');
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H(k+1,k) = nrm;
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Q{k+1} = V/nrm;
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C(1:k+1,k+1) = ([0; C(1:k,k)] - [C(1:k,1:k)*H(1:k,k); 0])/nrm;
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end;
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%%*****************************************************************
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