Mercurial > octave-antonio
annotate scripts/special-matrix/vander.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> |
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date | Sun, 01 May 2011 08:55:15 -0700 |
parents | fd0a3ac60b0e |
children | da929884f51e |
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11523 | 1 ## Copyright (C) 1993-2011 John W. Eaton |
9104 | 2 ## Copyright (C) 2009 VZLU Prague |
2313 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
2313 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
245 | 19 |
3369 | 20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} vander (@var{c}) |
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22 ## @deftypefnx {Function File} {} vander (@var{c}, @var{n}) |
3369 | 23 ## Return the Vandermonde matrix whose next to last column is @var{c}. |
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24 ## If @var{n} is specified, it determines the number of columns; |
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25 ## otherwise, @var{n} is taken to be equal to the length of @var{c}. |
3426 | 26 ## |
5016 | 27 ## A Vandermonde matrix has the form: |
3369 | 28 ## @tex |
29 ## $$ | |
5016 | 30 ## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr |
31 ## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr | |
32 ## \vdots & \ddots & \vdots & \vdots & \vdots \cr | |
33 ## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right] | |
3369 | 34 ## $$ |
35 ## @end tex | |
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36 ## @ifnottex |
3426 | 37 ## |
3369 | 38 ## @example |
39 ## @group | |
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40 ## c(1)^(n-1) @dots{} c(1)^2 c(1) 1 |
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41 ## c(2)^(n-1) @dots{} c(2)^2 c(2) 1 |
5016 | 42 ## . . . . . |
43 ## . . . . . | |
44 ## . . . . . | |
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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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48 ## |
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49 ## @end ifnottex |
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50 ## @seealso{polyfit} |
3369 | 51 ## @end deftypefn |
4 | 52 |
2314 | 53 ## Author: jwe |
54 | |
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55 function retval = vander (c, n) |
4 | 56 |
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57 if (nargin == 1) |
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58 n = length (c); |
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59 elseif (nargin != 2) |
6046 | 60 print_usage (); |
4 | 61 endif |
62 | |
4030 | 63 if (isvector (c)) |
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64 retval = zeros (length (c), n, class (c)); |
9104 | 65 ## avoiding many ^s appears to be faster for n >= 100. |
66 d = 1; | |
67 c = c(:); | |
68 for i = n:-1:1 | |
69 retval(:,i) = d; | |
70 d = c .* d; | |
71 endfor | |
4 | 72 else |
73 error ("vander: argument must be a vector"); | |
74 endif | |
75 | |
76 endfunction | |
7387 | 77 |
78 %!test | |
79 %! c = [0,1,2,3]; | |
80 %! expect = [0,0,0,1; 1,1,1,1; 8,4,2,1; 27,9,3,1]; | |
81 %! result = vander(c); | |
82 %! assert(expect, result); | |
7411 | 83 |
84 %!assert((vander (1) == 1 && vander ([1, 2, 3]) == vander ([1; 2; 3]) | |
85 %! && vander ([1, 2, 3]) == [1, 1, 1; 4, 2, 1; 9, 3, 1] | |
86 %! && vander ([1, 2, 3]*i) == [-1, i, 1; -4, 2i, 1; -9, 3i, 1])); | |
87 | |
9140 | 88 %!assert(vander (2, 3), [4, 2, 1]) |
89 %!assert(vander ([2, 3], 3), [4, 2, 1; 9, 3, 1]) | |
90 | |
7411 | 91 %!error vander ([1, 2; 3, 4]); |
92 | |
93 %!error vander (); | |
94 | |
9140 | 95 %!error vander (1, 2, 3); |
7411 | 96 |