Mercurial > hg > octave-nkf
annotate scripts/special-matrix/toeplitz.m @ 8517:81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
| author | sh@sh-laptop |
|---|---|
| date | Wed, 14 Jan 2009 20:44:25 -0500 |
| parents | 83a8781b529d |
| children | eb63fbe60fab |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2004, |
| 2 ## 2005, 2006, 2007 John W. Eaton | |
| 2313 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 2313 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 245 | 19 |
| 3369 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} toeplitz (@var{c}, @var{r}) | |
| 22 ## Return the Toeplitz matrix constructed given the first column @var{c}, | |
| 23 ## and (optionally) the first row @var{r}. If the first element of @var{c} | |
| 24 ## is not the same as the first element of @var{r}, the first element of | |
| 25 ## @var{c} is used. If the second argument is omitted, the first row is | |
| 26 ## taken to be the same as the first column. | |
| 3426 | 27 ## |
| 5016 | 28 ## A square Toeplitz matrix has the form: |
| 3369 | 29 ## @iftex |
| 30 ## @tex | |
| 31 ## $$ | |
| 5016 | 32 ## \left[\matrix{c_0 & r_1 & r_2 & \cdots & r_n\cr |
| 33 ## c_1 & c_0 & r_1 & \cdots & r_{n-1}\cr | |
| 34 ## c_2 & c_1 & c_0 & \cdots & r_{n-2}\cr | |
| 35 ## \vdots & \vdots & \vdots & \ddots & \vdots\cr | |
| 36 ## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right] | |
| 3369 | 37 ## $$ |
| 38 ## @end tex | |
| 39 ## @end iftex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7411
diff
changeset
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40 ## @ifnottex |
| 3426 | 41 ## |
| 3369 | 42 ## @example |
| 43 ## @group | |
| 44 ## c(0) r(1) r(2) ... r(n) | |
| 5016 | 45 ## c(1) c(0) r(1) ... r(n-1) |
| 46 ## c(2) c(1) c(0) ... r(n-2) | |
| 47 ## . , , . . | |
| 48 ## . , , . . | |
| 49 ## . , , . . | |
| 3369 | 50 ## c(n) c(n-1) c(n-2) ... c(0) |
| 51 ## @end group | |
| 52 ## @end example | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7411
diff
changeset
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53 ## @end ifnottex |
| 5781 | 54 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb} |
| 3369 | 55 ## @end deftypefn |
| 4 | 56 |
| 2314 | 57 ## Author: jwe |
| 58 | |
| 2311 | 59 function retval = toeplitz (c, r) |
| 4 | 60 |
| 61 if (nargin == 1) | |
| 62 r = c; | |
| 63 elseif (nargin != 2) | |
| 6046 | 64 print_usage (); |
| 4 | 65 endif |
| 66 | |
| 67 [c_nr, c_nc] = size (c); | |
| 68 [r_nr, r_nc] = size (r); | |
| 69 | |
| 70 if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1)) | |
| 1518 | 71 error ("toeplitz: expecting vector arguments"); |
| 4 | 72 endif |
| 73 | |
| 74 if (c_nc != 1) | |
| 1015 | 75 c = c.'; |
| 4 | 76 endif |
| 77 | |
| 78 if (r_nr != 1) | |
| 1015 | 79 r = r.'; |
| 4 | 80 endif |
| 81 | |
| 82 if (r (1) != c (1)) | |
| 904 | 83 warning ("toeplitz: column wins diagonal conflict"); |
| 4 | 84 endif |
| 85 | |
| 2303 | 86 ## If we have a single complex argument, we want to return a |
| 87 ## Hermitian-symmetric matrix (actually, this will really only be | |
| 88 ## Hermitian-symmetric if the first element of the vector is real). | |
| 1016 | 89 |
| 90 if (nargin == 1) | |
| 91 c = conj (c); | |
| 92 c(1) = conj (c(1)); | |
| 93 endif | |
| 94 | |
| 2303 | 95 ## This should probably be done with the colon operator... |
| 4 | 96 |
| 97 nc = length (r); | |
| 98 nr = length (c); | |
| 99 | |
| 5731 | 100 retval = resize (resize (c, 0), nr, nc); |
| 4 | 101 |
| 102 for i = 1:min (nc, nr) | |
| 103 retval (i:nr, i) = c (1:nr-i+1); | |
| 104 endfor | |
| 105 | |
| 106 for i = 1:min (nr, nc-1) | |
| 107 retval (i, i+1:nc) = r (2:nc-i+1); | |
| 108 endfor | |
| 109 | |
| 110 endfunction | |
| 7411 | 111 |
| 112 %!assert((toeplitz (1) == 1 | |
| 113 %! && toeplitz ([1, 2, 3], [1; -3; -5]) == [1, -3, -5; 2, 1, -3; 3, 2, 1] | |
| 114 %! && toeplitz ([1, 2, 3], [1; -3i; -5i]) == [1, -3i, -5i; 2, 1, -3i; 3, 2, 1])); | |
| 115 | |
| 116 %!error toeplitz ([1, 2; 3, 4], 1); | |
| 117 | |
| 118 %!error toeplitz (); | |
| 119 | |
| 120 %!error toeplitz (1, 2, 3); | |
| 121 |