Mercurial > hg > octave-lyh
annotate scripts/special-matrix/vander.m @ 9104:e0250e2b60ed
optimize vander
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Wed, 08 Apr 2009 13:16:23 +0200 |
| parents | 853f96e8008f |
| children | eebc7f8e7398 |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, |
| 8920 | 2 ## 2004, 2005, 2006, 2007, 2008, 2009 John W. Eaton |
| 9104 | 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} {} vander (@var{c}) | |
| 23 ## Return the Vandermonde matrix whose next to last column is @var{c}. | |
| 3426 | 24 ## |
| 5016 | 25 ## A Vandermonde matrix has the form: |
| 3369 | 26 ## @iftex |
| 27 ## @tex | |
| 28 ## $$ | |
| 5016 | 29 ## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr |
| 30 ## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr | |
| 31 ## \vdots & \ddots & \vdots & \vdots & \vdots \cr | |
| 32 ## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right] | |
| 3369 | 33 ## $$ |
| 34 ## @end tex | |
| 35 ## @end iftex | |
|
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36 ## @ifnottex |
| 3426 | 37 ## |
| 3369 | 38 ## @example |
| 39 ## @group | |
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Rik <rdrider0-list@yahoo.com>
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40 ## c(1)^(n-1) @dots{} c(1)^2 c(1) 1 |
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853f96e8008f
Cleanup documentation file matrix.texi
Rik <rdrider0-list@yahoo.com>
parents:
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changeset
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41 ## c(2)^(n-1) @dots{} c(2)^2 c(2) 1 |
| 5016 | 42 ## . . . . . |
| 43 ## . . . . . | |
| 44 ## . . . . . | |
|
9041
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Cleanup documentation file matrix.texi
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
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45 ## c(n)^(n-1) @dots{} c(n)^2 c(n) 1 |
| 3369 | 46 ## @end group |
| 47 ## @end example | |
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8517
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sh@sh-laptop
parents:
7411
diff
changeset
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48 ## @end ifnottex |
| 5642 | 49 ## @seealso{hankel, sylvester_matrix, hilb, invhilb, toeplitz} |
| 3369 | 50 ## @end deftypefn |
| 4 | 51 |
| 2314 | 52 ## Author: jwe |
| 53 | |
| 2311 | 54 function retval = vander (c) |
| 4 | 55 |
| 56 if (nargin != 1) | |
| 6046 | 57 print_usage (); |
| 4 | 58 endif |
| 59 | |
| 4030 | 60 if (isvector (c)) |
| 4 | 61 n = length (c); |
| 9104 | 62 retval = zeros (n, n, class (c)); |
| 63 ## avoiding many ^s appears to be faster for n >= 100. | |
| 64 d = 1; | |
| 65 c = c(:); | |
| 66 for i = n:-1:1 | |
| 67 retval(:,i) = d; | |
| 68 d = c .* d; | |
| 69 endfor | |
| 4 | 70 else |
| 71 error ("vander: argument must be a vector"); | |
| 72 endif | |
| 73 | |
| 74 endfunction | |
| 7387 | 75 |
| 76 %!test | |
| 77 %! c = [0,1,2,3]; | |
| 78 %! expect = [0,0,0,1; 1,1,1,1; 8,4,2,1; 27,9,3,1]; | |
| 79 %! result = vander(c); | |
| 80 %! assert(expect, result); | |
| 7411 | 81 |
| 82 %!assert((vander (1) == 1 && vander ([1, 2, 3]) == vander ([1; 2; 3]) | |
| 83 %! && vander ([1, 2, 3]) == [1, 1, 1; 4, 2, 1; 9, 3, 1] | |
| 84 %! && vander ([1, 2, 3]*i) == [-1, i, 1; -4, 2i, 1; -9, 3i, 1])); | |
| 85 | |
| 86 %!error vander ([1, 2; 3, 4]); | |
| 87 | |
| 88 %!error vander (); | |
| 89 | |
| 90 %!error vander (1, 2); | |
| 91 |