Mercurial > matrix-functions
comparison toolbox/pdtoep.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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| -1:000000000000 | 0:8f23314345f4 |
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| 1 function T = pdtoep(n, m, w, theta) | |
| 2 %PDTOEP Symmetric positive definite Toeplitz matrix. | |
| 3 % PDTOEP(N, M, W, THETA) is an N-by-N symmetric positive (semi-) | |
| 4 % definite (SPD) Toeplitz matrix, comprised of the sum of M rank 2 | |
| 5 % (or, for certain THETA, rank 1) SPD Toeplitz matrices. | |
| 6 % Specifically, | |
| 7 % T = W(1)*T(THETA(1)) + ... + W(M)*T(THETA(M)), | |
| 8 % where T(THETA(k)) has (i,j) element COS(2*PI*THETA(k)*(i-j)). | |
| 9 % Defaults: M = N, W = RAND(M,1), THETA = RAND(M,1). | |
| 10 | |
| 11 % Reference: | |
| 12 % G. Cybenko and C.F. Van Loan, Computing the minimum eigenvalue of | |
| 13 % a symmetric positive definite Toeplitz matrix, SIAM J. Sci. Stat. | |
| 14 % Comput., 7 (1986), pp. 123-131. | |
| 15 | |
| 16 if nargin < 2, m = n; end | |
| 17 if nargin < 3, w = rand(m,1); end | |
| 18 if nargin < 4, theta = rand(m,1); end | |
| 19 | |
| 20 if max(size(w)) ~= m | max(size(theta)) ~= m | |
| 21 error('Arguments W and THETA must be vectors of length M.') | |
| 22 end | |
| 23 | |
| 24 T = zeros(n); | |
| 25 E = 2*pi*( (1:n)'*ones(1,n) - ones(n,1)*(1:n) ); | |
| 26 | |
| 27 for i=1:m | |
| 28 T = T + w(i) * cos( theta(i)*E ); | |
| 29 end |