Mercurial > matrix-functions
comparison toolbox/tridiag.m @ 2:c124219d7bfa draft
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 |
| parents | 8f23314345f4 |
| children |
comparison
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| 1:e471a92d17be | 2:c124219d7bfa |
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| 1 function T = tridiag(n, x, y, z) | |
| 2 %TRIDIAG Tridiagonal matrix (sparse). | |
| 3 % TRIDIAG(X, Y, Z) is the tridiagonal matrix with subdiagonal X, | |
| 4 % diagonal Y, and superdiagonal Z. | |
| 5 % X and Z must be vectors of dimension one less than Y. | |
| 6 % Alternatively TRIDIAG(N, C, D, E), where C, D, and E are all | |
| 7 % scalars, yields the Toeplitz tridiagonal matrix of order N | |
| 8 % with subdiagonal elements C, diagonal elements D, and superdiagonal | |
| 9 % elements E. This matrix has eigenvalues (Todd 1977) | |
| 10 % D + 2*SQRT(C*E)*COS(k*PI/(N+1)), k=1:N. | |
| 11 % TRIDIAG(N) is the same as TRIDIAG(N,-1,2,-1), which is | |
| 12 % a symmetric positive definite M-matrix (the negative of the | |
| 13 % second difference matrix). | |
| 14 | |
| 15 % References: | |
| 16 % J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra, | |
| 17 % Birkhauser, Basel, and Academic Press, New York, 1977, p. 155. | |
| 18 % D.E. Rutherford, Some continuant determinants arising in physics and | |
| 19 % chemistry---II, Proc. Royal Soc. Edin., 63, A (1952), pp. 232-241. | |
| 20 | |
| 21 if nargin == 1, x = -1; y = 2; z = -1; end | |
| 22 if nargin == 3, z = y; y = x; x = n; end | |
| 23 | |
| 24 x = x(:); y = y(:); z = z(:); % Force column vectors. | |
| 25 | |
| 26 if max( [ size(x) size(y) size(z) ] ) == 1 | |
| 27 x = x*ones(n-1,1); | |
| 28 z = z*ones(n-1,1); | |
| 29 y = y*ones(n,1); | |
| 30 else | |
| 31 [nx, m] = size(x); | |
| 32 [ny, m] = size(y); | |
| 33 [nz, m] = size(z); | |
| 34 if (ny - nx - 1) | (ny - nz -1) | |
| 35 error('Dimensions of vector arguments are incorrect.') | |
| 36 end | |
| 37 end | |
| 38 | |
| 39 % T = diag(x, -1) + diag(y) + diag(z, 1); % For non-sparse matrix. | |
| 40 n = max(size(y)); | |
| 41 T = spdiags([ [x;0] y [0;z] ], -1:1, n, n); |