Mercurial > hg > octave-nkf
annotate scripts/special-matrix/hankel.m @ 12639:4d777e05d47c stable
doc: Review and update documentation for "Matrix Manipulation" chapter.
* matrix.txi, arrayfun.m, blkdiag.m, fliplr.m, flipud.m, logspace.m,
postpad.m, prepad.m, randi.m, repmat.m, rot90.m, rotdim.m, shiftdim.m,
sortrows.m, vech.m, xor.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m,
pascal.m, rosser.m, sylvester_matrix.m, toeplitz.m, vander.m, wilkinson.m,
bsxfun.cc, find.cc, lookup.cc, rand.cc, tril.cc, data.cc, arrayfun.m,
blkdiag.m, fliplr.m, flipud.m, logspace.m, postpad.m, prepad.m, randi.m,
repmat.m, rot90.m, rotdim.m, shiftdim.m, sortrows.m, vech.m, xor.m, hadamard.m,
hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, sylvester_matrix.m,
toeplitz.m, vander.m, wilkinson.m, bsxfun.cc (bsxfun), find.cc (find),
lookup.cc (lookup), rand.cc (rand, randn, rande, randg, randp),
tril.cc (triu), data.cc (all, any, horzcat, vertcat, cat, permute, ipermute,
ones, zeros, eye, linspace, resize, reshape, issorted, diff):
Improve docstrings
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 01 May 2011 08:55:15 -0700 |
| parents | fd0a3ac60b0e |
| children | c78ac846fcbc |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 1993-2011 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 245 | 18 |
| 3369 | 19 ## -*- texinfo -*- |
|
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20 ## @deftypefn {Function File} {} hankel (@var{c}) |
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21 ## @deftypefnx {Function File} {} hankel (@var{c}, @var{r}) |
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22 ## Return the Hankel matrix constructed from the first column @var{c}, and |
| 3369 | 23 ## (optionally) the last row @var{r}. If the last element of @var{c} is |
| 24 ## not the same as the first element of @var{r}, the last element of | |
| 4922 | 25 ## @var{c} is used. If the second argument is omitted, it is assumed to |
| 26 ## be a vector of zeros with the same size as @var{c}. | |
| 3426 | 27 ## |
| 3369 | 28 ## A Hankel matrix formed from an m-vector @var{c}, and an n-vector |
| 29 ## @var{r}, has the elements | |
| 30 ## @tex | |
| 31 ## $$ | |
| 32 ## H (i, j) = \cases{c_{i+j-1},&$i+j-1\le m$;\cr r_{i+j-m},&otherwise.\cr} | |
| 33 ## $$ | |
| 34 ## @end tex | |
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35 ## @ifnottex |
| 3426 | 36 ## |
| 3369 | 37 ## @example |
| 38 ## @group | |
| 4922 | 39 ## H(i,j) = c(i+j-1), i+j-1 <= m; |
| 40 ## H(i,j) = r(i+j-m), otherwise | |
| 3369 | 41 ## @end group |
| 42 ## @end example | |
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43 ## |
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44 ## @end ifnottex |
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45 ## @seealso{hadamard, toeplitz} |
| 3369 | 46 ## @end deftypefn |
| 4 | 47 |
| 2314 | 48 ## Author: jwe |
| 49 | |
| 2311 | 50 function retval = hankel (c, r) |
| 4 | 51 |
| 52 if (nargin == 1) | |
| 5731 | 53 r = resize (resize (c, 0), size(c)); |
| 4 | 54 elseif (nargin != 2) |
| 6046 | 55 print_usage (); |
| 4 | 56 endif |
| 57 | |
| 58 [c_nr, c_nc] = size (c); | |
| 59 [r_nr, r_nc] = size (r); | |
| 60 | |
| 61 if ((c_nr != 1 && c_nc != 1) || (r_nr != 1 && r_nc != 1)) | |
| 1518 | 62 error ("hankel: expecting vector arguments"); |
| 4 | 63 endif |
| 64 | |
| 2325 | 65 if (nargin == 1) |
| 1396 | 66 r (1) = c (length (c)); |
| 67 endif | |
| 68 | |
| 4 | 69 if (c_nc != 1) |
| 1035 | 70 c = c.'; |
| 4 | 71 endif |
| 72 | |
| 73 if (r_nr != 1) | |
| 1035 | 74 r = r.'; |
| 4 | 75 endif |
| 76 | |
| 1396 | 77 nc = length (r); |
| 78 nr = length (c); | |
| 79 | |
| 80 if (r (1) != c (nr)) | |
| 904 | 81 warning ("hankel: column wins anti-diagonal conflict"); |
| 4 | 82 endif |
| 83 | |
| 2303 | 84 ## This should probably be done with the colon operator... |
| 4 | 85 |
| 5731 | 86 retval = resize (resize (c, 0), nr, nc); |
| 4 | 87 |
| 88 for i = 1:min (nr, nc) | |
| 89 retval (1:nr-i+1, i) = c (i:nr); | |
| 90 endfor | |
| 91 | |
| 92 tmp = 1; | |
| 93 if (nc <= nr) | |
| 94 tmp = nr - nc + 2; | |
| 95 endif | |
| 96 | |
| 97 for i = nr:-1:tmp | |
| 98 retval (i, 2+nr-i:nc) = r (2:nc-nr+i); | |
| 99 endfor | |
| 100 | |
| 101 endfunction | |
| 5731 | 102 |
| 103 %!assert(hankel(1:3),[1,2,3;2,3,0;3,0,0]) | |
| 104 %!assert(hankel(1),[1]); | |
| 105 %!assert(hankel(1:3,3:6),[1,2,3,4;2,3,4,5;3,4,5,6]); | |
| 106 %!assert(hankel(1:3,3:4),[1,2;2,3;3,4]); | |
| 107 %!assert(hankel(1:3,4:6),[1,2,3;2,3,5;3,5,6]); | |
| 7411 | 108 |
| 109 %!assert((hankel (1) == 1 && hankel ([1, 2]) == [1, 2; 2, 0] | |
| 110 %! && hankel ([1, 2], [2; -1; -3]) == [1, 2, -1; 2, -1, -3])); | |
| 111 | |
| 112 %!error hankel ([1, 2; 3, 4], [1, 2; 3, 4]); | |
| 113 | |
| 114 %!error hankel (); | |
| 115 | |
| 116 %!error hankel (1, 2, 3); | |
| 117 |