annotate mftoolbox/logm_pade_pf.m @ 0:8f23314345f4 draft

Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
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>
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1 function S = logm_pade_pf(A,m)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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2 %LOGM_PADE_PF Evaluate Pade approximant to matrix log by partial fractions.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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3 % Y = LOGM_PADE_PF(A,M) evaluates the [M/M] Pade approximation to
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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4 % LOG(EYE(SIZE(A))+A) using a partial fraction expansion.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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6 [nodes,wts] = gauss_legendre(m);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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7 % Convert from [-1,1] to [0,1].
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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8 nodes = (nodes + 1)/2;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 wts = wts/2;
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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10
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11 n = length(A);
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12 S = zeros(n);
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13
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14 for j=1:m
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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15 S = S + wts(j)*(A/(eye(n) + nodes(j)*A));
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16 end
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17
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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19 function [x,w] = gauss_legendre(n)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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20 %GAUSS_LEGENDRE Nodes and weights for Gauss-Legendre quadrature.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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21 % [X,W] = GAUSS_LEGENDRE(N) computes the nodes X and weights W
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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22 % for N-point Gauss-Legendre quadrature.
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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23
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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24 % Reference:
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25 % G. H. Golub and J. H. Welsch, Calculation of Gauss quadrature
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26 % rules, Math. Comp., 23(106):221-230, 1969.
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27
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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28 i = 1:n-1;
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29 v = i./sqrt((2*i).^2-1);
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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30 [V,D] = eig( diag(v,-1)+diag(v,1) );
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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31 x = diag(D);
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32 w = 2*(V(1,:)'.^2);