Mercurial > matrix-functions
annotate toolbox/signm.m @ 0:8f23314345f4 draft
Create local repository for matrix toolboxes. Step #0 done.
author | Antonio Pino Robles <data.script93@gmail.com> |
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date | Wed, 06 May 2015 14:56:53 +0200 |
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8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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1 function [S, N] = signm(A) |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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2 %SIGNM Matrix sign decomposition. |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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3 % [S, N] = SIGNM(A) is the matrix sign decomposition A = S*N, |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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4 % computed via the Schur decomposition. |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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5 % S is the matrix sign function, sign(A). |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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6 |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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7 % Reference: |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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8 % N.J. Higham, The matrix sign decomposition and its relation to the |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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9 % polar decomposition, Linear Algebra and Appl., 212/213:3-20, 1994. |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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10 |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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11 [Q, T] = schur(A); |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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12 [Q, T] = rsf2csf(Q, T); |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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13 S = Q * matsignt(T) * Q'; |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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14 |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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15 % Only problem with Schur method is possible nonzero imaginary part when |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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16 % A is real. Next line takes care of that. |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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17 if ~norm(imag(A),1), S = real(S); end |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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18 |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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19 if nargout == 2 |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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20 N = S*A; |
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Create local repository for matrix toolboxes. Step #0 done.
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21 end |