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1 ## Copyright (C) 1996, 1997 John W. Eaton |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} toeplitz (@var{c}, @var{r}) |
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22 ## Return the Toeplitz matrix constructed given the first column @var{c}, |
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23 ## and (optionally) the first row @var{r}. If the first element of @var{c} |
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24 ## is not the same as the first element of @var{r}, the first element of |
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25 ## @var{c} is used. If the second argument is omitted, the first row is |
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26 ## taken to be the same as the first column. |
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27 ## |
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28 ## A square Toeplitz matrix has the form: |
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29 ## @iftex |
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30 ## @tex |
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31 ## $$ |
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32 ## \left[\matrix{c_0 & r_1 & r_2 & \cdots & r_n\cr |
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33 ## c_1 & c_0 & r_1 & \cdots & r_{n-1}\cr |
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34 ## c_2 & c_1 & c_0 & \cdots & r_{n-2}\cr |
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35 ## \vdots & \vdots & \vdots & \ddots & \vdots\cr |
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36 ## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right] |
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37 ## $$ |
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38 ## @end tex |
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39 ## @end iftex |
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40 ## @ifinfo |
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41 ## |
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42 ## @example |
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43 ## @group |
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44 ## c(0) r(1) r(2) ... r(n) |
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45 ## c(1) c(0) r(1) ... r(n-1) |
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46 ## c(2) c(1) c(0) ... r(n-2) |
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47 ## . , , . . |
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48 ## . , , . . |
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49 ## . , , . . |
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50 ## c(n) c(n-1) c(n-2) ... c(0) |
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51 ## @end group |
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52 ## @end example |
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53 ## @end ifinfo |
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54 ## @end deftypefn |
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55 ## |
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56 ## @seealso{hankel, vander, sylvester_matrix, hilb, and invhib} |
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57 |
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58 ## Author: jwe |
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59 |
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60 function retval = toeplitz (c, r) |
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61 |
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62 if (nargin == 1) |
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63 r = c; |
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64 elseif (nargin != 2) |
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65 usage ("toeplitz (c, r)"); |
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66 endif |
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67 |
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68 [c_nr, c_nc] = size (c); |
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69 [r_nr, r_nc] = size (r); |
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70 |
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71 if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1)) |
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72 error ("toeplitz: expecting vector arguments"); |
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73 endif |
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74 |
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75 if (c_nc != 1) |
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76 c = c.'; |
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77 endif |
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78 |
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79 if (r_nr != 1) |
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80 r = r.'; |
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81 endif |
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82 |
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83 if (r (1) != c (1)) |
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84 warning ("toeplitz: column wins diagonal conflict"); |
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85 endif |
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86 |
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87 ## If we have a single complex argument, we want to return a |
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88 ## Hermitian-symmetric matrix (actually, this will really only be |
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89 ## Hermitian-symmetric if the first element of the vector is real). |
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90 |
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91 if (nargin == 1) |
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92 c = conj (c); |
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93 c(1) = conj (c(1)); |
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94 endif |
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95 |
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96 ## This should probably be done with the colon operator... |
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97 |
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98 nc = length (r); |
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99 nr = length (c); |
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100 |
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101 retval = zeros (nr, nc); |
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102 |
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103 for i = 1:min (nc, nr) |
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104 retval (i:nr, i) = c (1:nr-i+1); |
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105 endfor |
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106 |
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107 for i = 1:min (nr, nc-1) |
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108 retval (i, i+1:nc) = r (2:nc-i+1); |
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109 endfor |
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110 |
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111 endfunction |
