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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> |
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date | Wed, 06 May 2015 14:56:53 +0200 |
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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) |
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Create local repository for matrix toolboxes. Step #0 done.
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2 %LOGM_PADE_PF Evaluate Pade approximant to matrix log by partial fractions. |
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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 |
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Antonio Pino Robles <data.script93@gmail.com>
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4 % LOG(EYE(SIZE(A))+A) using a partial fraction expansion. |
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Antonio Pino Robles <data.script93@gmail.com>
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5 |
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6 [nodes,wts] = gauss_legendre(m); |
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7 % Convert from [-1,1] to [0,1]. |
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8 nodes = (nodes + 1)/2; |
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9 wts = wts/2; |
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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 |
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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 |
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18 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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19 function [x,w] = gauss_legendre(n) |
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20 %GAUSS_LEGENDRE Nodes and weights for Gauss-Legendre quadrature. |
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21 % [X,W] = GAUSS_LEGENDRE(N) computes the nodes X and weights W |
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22 % for N-point Gauss-Legendre quadrature. |
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23 |
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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 |
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28 i = 1:n-1; |
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29 v = i./sqrt((2*i).^2-1); |
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30 [V,D] = eig( diag(v,-1)+diag(v,1) ); |
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31 x = diag(D); |
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32 w = 2*(V(1,:)'.^2); |