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1 ### Copyright (C) 1996 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 ## usage: hankel (c, r) |
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21 ## |
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22 ## Return the Hankel matrix constructed given the first column |
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23 ## c, and (optionally) the last row r. |
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24 ## |
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25 ## If the second argument is omitted, zeros are inserted below the main |
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26 ## anti-diagonal. If the last element of c is not the same as the first |
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27 ## element of r, the last element of c is used. |
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28 ## |
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29 ## See also: vander, hadamard, hilb, invhilb, toeplitz |
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30 |
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31 function retval = hankel (c, r) |
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32 |
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33 if (nargin == 1) |
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34 r = zeros (size (c)); |
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35 elseif (nargin != 2) |
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36 usage ("hankel (c, r)"); |
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37 endif |
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38 |
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39 [c_nr, c_nc] = size (c); |
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40 [r_nr, r_nc] = size (r); |
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41 |
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42 if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1)) |
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43 error ("hankel: expecting vector arguments"); |
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44 endif |
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45 |
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46 if (nargin == 1) |
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47 r (1) = c (length (c)); |
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48 endif |
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49 |
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50 if (c_nc != 1) |
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51 c = c.'; |
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52 endif |
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53 |
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54 if (r_nr != 1) |
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55 r = r.'; |
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56 endif |
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57 |
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58 nc = length (r); |
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59 nr = length (c); |
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60 |
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61 if (r (1) != c (nr)) |
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62 warning ("hankel: column wins anti-diagonal conflict"); |
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63 endif |
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64 |
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65 ## This should probably be done with the colon operator... |
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66 |
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67 retval = zeros (nr, nc); |
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68 |
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69 for i = 1:min (nr, nc) |
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70 retval (1:nr-i+1, i) = c (i:nr); |
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71 endfor |
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72 |
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73 tmp = 1; |
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74 if (nc <= nr) |
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75 tmp = nr - nc + 2; |
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76 endif |
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77 |
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78 for i = nr:-1:tmp |
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79 retval (i, 2+nr-i:nc) = r (2:nc-nr+i); |
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80 endfor |
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81 |
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82 endfunction |
