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annotate toolbox/tridiag.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 = tridiag(n, x, y, z)
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2 %TRIDIAG Tridiagonal matrix (sparse).
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3 % TRIDIAG(X, Y, Z) is the tridiagonal matrix with subdiagonal X,
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4 % diagonal Y, and superdiagonal Z.
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5 % X and Z must be vectors of dimension one less than Y.
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6 % Alternatively TRIDIAG(N, C, D, E), where C, D, and E are all
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7 % scalars, yields the Toeplitz tridiagonal matrix of order N
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8 % with subdiagonal elements C, diagonal elements D, and superdiagonal
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9 % elements E. This matrix has eigenvalues (Todd 1977)
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10 % D + 2*SQRT(C*E)*COS(k*PI/(N+1)), k=1:N.
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11 % TRIDIAG(N) is the same as TRIDIAG(N,-1,2,-1), which is
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12 % a symmetric positive definite M-matrix (the negative of the
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13 % second difference matrix).
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14
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15 % References:
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16 % J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra,
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17 % Birkhauser, Basel, and Academic Press, New York, 1977, p. 155.
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18 % D.E. Rutherford, Some continuant determinants arising in physics and
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19 % chemistry---II, Proc. Royal Soc. Edin., 63, A (1952), pp. 232-241.
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20
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21 if nargin == 1, x = -1; y = 2; z = -1; end
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22 if nargin == 3, z = y; y = x; x = n; end
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23
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24 x = x(:); y = y(:); z = z(:); % Force column vectors.
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26 if max( [ size(x) size(y) size(z) ] ) == 1
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27 x = x*ones(n-1,1);
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28 z = z*ones(n-1,1);
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29 y = y*ones(n,1);
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30 else
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31 [nx, m] = size(x);
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32 [ny, m] = size(y);
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33 [nz, m] = size(z);
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34 if (ny - nx - 1) | (ny - nz -1)
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35 error('Dimensions of vector arguments are incorrect.')
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36 end
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37 end
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38
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39 % T = diag(x, -1) + diag(y) + diag(z, 1); % For non-sparse matrix.
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40 n = max(size(y));
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41 T = spdiags([ [x;0] y [0;z] ], -1:1, n, n);