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annotate toolbox/pdtoep.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.
Antonio Pino Robles <data.script93@gmail.com>
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1 function T = pdtoep(n, m, w, theta)
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2 %PDTOEP Symmetric positive definite Toeplitz matrix.
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3 % PDTOEP(N, M, W, THETA) is an N-by-N symmetric positive (semi-)
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4 % definite (SPD) Toeplitz matrix, comprised of the sum of M rank 2
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5 % (or, for certain THETA, rank 1) SPD Toeplitz matrices.
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6 % Specifically,
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7 % T = W(1)*T(THETA(1)) + ... + W(M)*T(THETA(M)),
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8 % where T(THETA(k)) has (i,j) element COS(2*PI*THETA(k)*(i-j)).
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9 % Defaults: M = N, W = RAND(M,1), THETA = RAND(M,1).
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10
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11 % Reference:
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12 % G. Cybenko and C.F. Van Loan, Computing the minimum eigenvalue of
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13 % a symmetric positive definite Toeplitz matrix, SIAM J. Sci. Stat.
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14 % Comput., 7 (1986), pp. 123-131.
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16 if nargin < 2, m = n; end
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17 if nargin < 3, w = rand(m,1); end
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18 if nargin < 4, theta = rand(m,1); end
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20 if max(size(w)) ~= m | max(size(theta)) ~= m
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21 error('Arguments W and THETA must be vectors of length M.')
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22 end
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24 T = zeros(n);
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25 E = 2*pi*( (1:n)'*ones(1,n) - ones(n,1)*(1:n) );
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27 for i=1:m
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28 T = T + w(i) * cos( theta(i)*E );
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29 end