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annotate scripts/special-matrix/toeplitz.m @ 10549:95c3e38098bf
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| author | Rik <code@nomad.inbox5.com> |
|---|---|
| date | Fri, 23 Apr 2010 11:28:50 -0700 |
| parents | f0c3d3fc4903 |
| children | 3140cb7a05a1 |
| rev | line source |
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| 7017 | 1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2004, |
| 8920 | 2 ## 2005, 2006, 2007, 2008, 2009 John W. Eaton |
| 9092 | 3 ## Copyright (C) 2009 VZLU Prague |
| 2313 | 4 ## |
| 5 ## This file is part of Octave. | |
| 6 ## | |
| 7 ## Octave is free software; you can redistribute it and/or modify it | |
| 8 ## under the terms of the GNU General Public License as published by | |
| 7016 | 9 ## the Free Software Foundation; either version 3 of the License, or (at |
| 10 ## your option) any later version. | |
| 2313 | 11 ## |
| 12 ## Octave is distributed in the hope that it will be useful, but | |
| 13 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 15 ## General Public License for more details. | |
| 16 ## | |
| 17 ## You should have received a copy of the GNU General Public License | |
| 7016 | 18 ## along with Octave; see the file COPYING. If not, see |
| 19 ## <http://www.gnu.org/licenses/>. | |
| 245 | 20 |
| 3369 | 21 ## -*- texinfo -*- |
| 22 ## @deftypefn {Function File} {} toeplitz (@var{c}, @var{r}) | |
| 23 ## Return the Toeplitz matrix constructed given the first column @var{c}, | |
| 24 ## and (optionally) the first row @var{r}. If the first element of @var{c} | |
| 25 ## is not the same as the first element of @var{r}, the first element of | |
| 26 ## @var{c} is used. If the second argument is omitted, the first row is | |
| 27 ## taken to be the same as the first column. | |
| 3426 | 28 ## |
| 5016 | 29 ## A square Toeplitz matrix has the form: |
| 3369 | 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 | |
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39 ## @ifnottex |
| 3426 | 40 ## |
| 3369 | 41 ## @example |
| 42 ## @group | |
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43 ## c(0) r(1) r(2) @dots{} r(n) |
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44 ## c(1) c(0) r(1) @dots{} r(n-1) |
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45 ## c(2) c(1) c(0) @dots{} r(n-2) |
| 5016 | 46 ## . , , . . |
| 47 ## . , , . . | |
| 48 ## . , , . . | |
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49 ## c(n) c(n-1) c(n-2) @dots{} c(0) |
| 3369 | 50 ## @end group |
| 51 ## @end example | |
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52 ## @end ifnottex |
| 5781 | 53 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb} |
| 3369 | 54 ## @end deftypefn |
| 4 | 55 |
| 9092 | 56 ## Author: jwe && jh |
| 2314 | 57 |
| 2311 | 58 function retval = toeplitz (c, r) |
| 4 | 59 |
| 60 if (nargin == 1) | |
| 61 r = c; | |
| 62 elseif (nargin != 2) | |
| 6046 | 63 print_usage (); |
| 4 | 64 endif |
| 65 | |
| 9092 | 66 if (! (isvector (c) && isvector (r))) |
| 1518 | 67 error ("toeplitz: expecting vector arguments"); |
| 4 | 68 endif |
| 69 | |
| 9092 | 70 nc = length (r); |
| 71 nr = length (c); | |
| 4 | 72 |
| 9092 | 73 if (nr == 0 || nc == 0) |
| 74 ## Empty matrix. | |
| 75 retval = zeros (nr, nc, class (c)); | |
| 76 return; | |
| 4 | 77 endif |
| 78 | |
| 79 if (r (1) != c (1)) | |
| 904 | 80 warning ("toeplitz: column wins diagonal conflict"); |
| 4 | 81 endif |
| 82 | |
| 2303 | 83 ## If we have a single complex argument, we want to return a |
| 84 ## Hermitian-symmetric matrix (actually, this will really only be | |
| 85 ## Hermitian-symmetric if the first element of the vector is real). | |
| 1016 | 86 |
| 9092 | 87 if (nargin == 1 && iscomplex (c)) |
| 1016 | 88 c = conj (c); |
| 89 c(1) = conj (c(1)); | |
| 90 endif | |
| 91 | |
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92 if (issparse(c) && issparse(r)) |
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93 c = c(:).'; |
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94 r = r(:).'; |
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95 cidx = find(c); |
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96 ridx = find(r); |
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97 |
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98 ## Ignore the first element in r. |
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99 ridx = ridx(ridx > 1); |
| 4 | 100 |
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101 ## Form matrix. |
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102 retval = spdiags(repmat(c(cidx),nr,1),1-cidx,nr,nc)+... |
| 10549 | 103 spdiags(repmat(r(ridx),nr,1),ridx-1,nr,nc); |
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104 else |
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105 ## Concatenate data into a single column vector. |
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106 data = [r(end:-1:2)(:); c(:)]; |
| 4 | 107 |
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108 ## Get slices. |
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109 slices = cellslices (data, nc:-1:1, nc+nr-1:-1:nr); |
| 4 | 110 |
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111 ## Form matrix. |
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112 retval = horzcat (slices{:}); |
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113 endif |
| 4 | 114 endfunction |
| 7411 | 115 |
| 116 %!assert((toeplitz (1) == 1 | |
| 117 %! && toeplitz ([1, 2, 3], [1; -3; -5]) == [1, -3, -5; 2, 1, -3; 3, 2, 1] | |
| 118 %! && toeplitz ([1, 2, 3], [1; -3i; -5i]) == [1, -3i, -5i; 2, 1, -3i; 3, 2, 1])); | |
| 119 | |
| 120 %!error toeplitz ([1, 2; 3, 4], 1); | |
| 121 | |
| 122 %!error toeplitz (); | |
| 123 | |
| 124 %!error toeplitz (1, 2, 3); | |
| 125 |