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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 3 of the License, or (at |
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8 ## your option) 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} hankel (@var{c}, @var{r}) |
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21 ## Return the Hankel matrix constructed given the first column @var{c}, and |
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22 ## (optionally) the last row @var{r}. If the last element of @var{c} is |
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23 ## not the same as the first element of @var{r}, the last element of |
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24 ## @var{c} is used. If the second argument is omitted, it is assumed to |
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25 ## be a vector of zeros with the same size as @var{c}. |
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26 ## |
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27 ## A Hankel matrix formed from an m-vector @var{c}, and an n-vector |
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28 ## @var{r}, has the elements |
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29 ## @iftex |
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30 ## @tex |
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31 ## $$ |
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32 ## H (i, j) = \cases{c_{i+j-1},&$i+j-1\le m$;\cr r_{i+j-m},&otherwise.\cr} |
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33 ## $$ |
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34 ## @end tex |
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35 ## @end iftex |
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36 ## @ifinfo |
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37 ## |
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38 ## @example |
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39 ## @group |
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40 ## H(i,j) = c(i+j-1), i+j-1 <= m; |
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41 ## H(i,j) = r(i+j-m), otherwise |
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42 ## @end group |
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43 ## @end example |
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44 ## @end ifinfo |
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45 ## @seealso{vander, sylvester_matrix, hilb, invhilb, toeplitz} |
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46 ## @end deftypefn |
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47 |
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48 ## Author: jwe |
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49 |
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50 function retval = hankel (c, r) |
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51 |
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52 if (nargin == 1) |
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53 r = resize (resize (c, 0), size(c)); |
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54 elseif (nargin != 2) |
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55 print_usage (); |
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56 endif |
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57 |
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58 [c_nr, c_nc] = size (c); |
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59 [r_nr, r_nc] = size (r); |
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60 |
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61 if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1)) |
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62 error ("hankel: expecting vector arguments"); |
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63 endif |
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64 |
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65 if (nargin == 1) |
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66 r (1) = c (length (c)); |
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67 endif |
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68 |
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69 if (c_nc != 1) |
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70 c = c.'; |
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71 endif |
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72 |
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73 if (r_nr != 1) |
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74 r = r.'; |
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75 endif |
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76 |
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77 nc = length (r); |
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78 nr = length (c); |
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79 |
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80 if (r (1) != c (nr)) |
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81 warning ("hankel: column wins anti-diagonal conflict"); |
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82 endif |
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83 |
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84 ## This should probably be done with the colon operator... |
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85 |
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86 retval = resize (resize (c, 0), nr, nc); |
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87 |
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88 for i = 1:min (nr, nc) |
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89 retval (1:nr-i+1, i) = c (i:nr); |
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90 endfor |
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91 |
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92 tmp = 1; |
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93 if (nc <= nr) |
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94 tmp = nr - nc + 2; |
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95 endif |
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96 |
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97 for i = nr:-1:tmp |
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98 retval (i, 2+nr-i:nc) = r (2:nc-nr+i); |
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99 endfor |
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100 |
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101 endfunction |
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102 |
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103 %!assert(hankel(1:3),[1,2,3;2,3,0;3,0,0]) |
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104 %!assert(hankel(1),[1]); |
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105 %!assert(hankel(1:3,3:6),[1,2,3,4;2,3,4,5;3,4,5,6]); |
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106 %!assert(hankel(1:3,3:4),[1,2;2,3;3,4]); |
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107 %!assert(hankel(1:3,4:6),[1,2,3;2,3,5;3,5,6]); |
