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annotate toolbox/signm.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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1 function [S, N] = signm(A)
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2 %SIGNM Matrix sign decomposition.
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3 % [S, N] = SIGNM(A) is the matrix sign decomposition A = S*N,
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4 % computed via the Schur decomposition.
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5 % S is the matrix sign function, sign(A).
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6
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7 % Reference:
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8 % N.J. Higham, The matrix sign decomposition and its relation to the
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9 % polar decomposition, Linear Algebra and Appl., 212/213:3-20, 1994.
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11 [Q, T] = schur(A);
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12 [Q, T] = rsf2csf(Q, T);
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13 S = Q * matsignt(T) * Q';
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15 % Only problem with Schur method is possible nonzero imaginary part when
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16 % A is real. Next line takes care of that.
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17 if ~norm(imag(A),1), S = real(S); end
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19 if nargout == 2
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20 N = S*A;
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21 end