octave-antonio: scripts/special-matrix/toeplitz.m annotate

annotate scripts/special-matrix/toeplitz.m @ 20162:2645f9ef8c88 stable

doc: Update more docstrings to have one sentence summary as first line. Reviewed specfun, special-matrix, testfun, and time script directories. * scripts/specfun/expint.m, scripts/specfun/isprime.m, scripts/specfun/legendre.m, scripts/specfun/primes.m, scripts/specfun/reallog.m, scripts/specfun/realsqrt.m, scripts/special-matrix/gallery.m, scripts/special-matrix/hadamard.m, scripts/special-matrix/hankel.m, scripts/special-matrix/hilb.m, scripts/special-matrix/invhilb.m, scripts/special-matrix/magic.m, scripts/special-matrix/pascal.m, scripts/special-matrix/rosser.m, scripts/special-matrix/toeplitz.m, scripts/special-matrix/vander.m, scripts/special-matrix/wilkinson.m, scripts/testfun/assert.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/fail.m, scripts/testfun/rundemos.m, scripts/testfun/runtests.m, scripts/testfun/speed.m, scripts/time/asctime.m, scripts/time/calendar.m, scripts/time/clock.m, scripts/time/ctime.m, scripts/time/datenum.m, scripts/time/datestr.m, scripts/time/datevec.m, scripts/time/etime.m, scripts/time/is_leap_year.m, scripts/time/now.m, scripts/time/weekday.m: Update more docstrings to have one sentence summary as first line.

author	Rik <rik@octave.org>
date	Sun, 03 May 2015 17:00:11 -0700
parents	9fc020886ae9
children

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19593 diff changeset	1 ## Copyright (C) 1993-2015 John W. Eaton
9092 38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	2 ## Copyright (C) 2009 VZLU Prague
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	3 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	4 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	5 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	9 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	10 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	14 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	15 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	18 ## <http://www.gnu.org/licenses/>.
245 16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe] jwe parents: 4 diff changeset	19
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	20 ## -- texinfo --
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	21 ## @deftypefn {Function File} {} toeplitz (@var{c})
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	22 ## @deftypefnx {Function File} {} toeplitz (@var{c}, @var{r})
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	23 ## Return the Toeplitz matrix constructed from the first column @var{c},
20162 2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	24 ## and (optionally) the first row @var{r}.
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	25 ##
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	26 ## If the first element of @var{r} is not the same as the first element of
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	27 ## @var{c}, the first element of @var{c} is used. If the second argument is
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	28 ## omitted, the first row is taken to be the same as the first column.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3408 diff changeset	29 ##
5016 bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 3426 diff changeset	30 ## A square Toeplitz matrix has the form:
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	31 ## @tex
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	32 ## $$
5016 bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 3426 diff changeset	33 ## \left[\matrix{c_0 & r_1 & r_2 & \cdots & r_n\cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 3426 diff changeset	34 ## c_1 & c_0 & r_1 & \cdots & r_{n-1}\cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 3426 diff changeset	35 ## c_2 & c_1 & c_0 & \cdots & r_{n-2}\cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 3426 diff changeset	36 ## \vdots & \vdots & \vdots & \ddots & \vdots\cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe] jwe parents: 3426 diff changeset	37 ## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right]
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	38 ## $$
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	39 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	40 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3408 diff changeset	41 ##
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	42 ## @example
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	43 ## @group
9041 853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	44 ## c(0) r(1) r(2) @dots{} r(n)
853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	45 ## c(1) c(0) r(1) @dots{} r(n-1)
853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	46 ## c(2) c(1) c(0) @dots{} r(n-2)
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	47 ## . . . . .
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	48 ## . . . . .
693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	49 ## . . . . .
9041 853f96e8008f Cleanup documentation file matrix.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	50 ## c(n) c(n-1) c(n-2) @dots{} c(0)
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	51 ## @end group
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	52 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10791 diff changeset	53 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7411 diff changeset	54 ## @end ifnottex
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	55 ## @seealso{hankel}
3369 f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe] jwe parents: 3140 diff changeset	56 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	57
9092 38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	58 ## Author: jwe && jh
2314 949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	59
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	60 function retval = toeplitz (c, r)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	61
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	62 if (nargin < 1 \|\| nargin > 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5781 diff changeset	63 print_usage ();
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	64 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	65
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	66 if (nargin == 1)
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	67 if (! isvector (c))
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	68 error ("toeplitz: C must be a vector");
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	69 endif
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	70
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	71 r = c;
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	72 nr = length (c);
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	73 nc = nr;
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	74 else
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 18984 diff changeset	75 if (! (isvector (c) && isvector (r)))
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	76 error ("toeplitz: C and R must be vectors");
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	77 elseif (r(1) != c(1))
18984 1197f04eec09 doc: minor typo fixes and copy-paste error. Colin Macdonald <cbm@m.fsf.org> parents: 17744 diff changeset	78 warning ("toeplitz: column wins diagonal conflict");
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	79 endif
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	80
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	81 nr = length (c);
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	82 nc = length (r);
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	83 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	84
9092 38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	85 if (nr == 0 \|\| nc == 0)
38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	86 ## Empty matrix.
38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	87 retval = zeros (nr, nc, class (c));
38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	88 return;
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	89 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	90
2303 5cffc4b8de57 [project @ 1996-06-24 09:15:24 by jwe] jwe parents: 1887 diff changeset	91 ## If we have a single complex argument, we want to return a
5cffc4b8de57 [project @ 1996-06-24 09:15:24 by jwe] jwe parents: 1887 diff changeset	92 ## Hermitian-symmetric matrix (actually, this will really only be
5cffc4b8de57 [project @ 1996-06-24 09:15:24 by jwe] jwe parents: 1887 diff changeset	93 ## Hermitian-symmetric if the first element of the vector is real).
9092 38c3a0f8c6d0 optimize toeplitz Jaroslav Hajek <highegg@gmail.com> parents: 9041 diff changeset	94 if (nargin == 1 && iscomplex (c))
1016 58ce441b5426 [project @ 1995-01-06 19:18:43 by jwe] jwe parents: 1015 diff changeset	95 c = conj (c);
58ce441b5426 [project @ 1995-01-06 19:18:43 by jwe] jwe parents: 1015 diff changeset	96 c(1) = conj (c(1));
58ce441b5426 [project @ 1995-01-06 19:18:43 by jwe] jwe parents: 1015 diff changeset	97 endif
58ce441b5426 [project @ 1995-01-06 19:18:43 by jwe] jwe parents: 1015 diff changeset	98
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	99 if (issparse (c) && issparse (r))
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	100 c = c(:).'; # enforce row vector
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 14868 diff changeset	101 r = r(:).'; # enforce row vector
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	102 cidx = find (c);
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	103 ridx = find (r);
9126 5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	104
5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	105 ## Ignore the first element in r.
5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	106 ridx = ridx(ridx > 1);
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	107
9126 5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	108 ## Form matrix.
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	109 retval = spdiags (repmat (c(cidx),nr,1),1-cidx,nr,nc) + ...
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	110 spdiags (repmat (r(ridx),nr,1),ridx-1,nr,nc);
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	111 else
9126 5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	112 ## Concatenate data into a single column vector.
5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	113 data = [r(end:-1:2)(:); c(:)];
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	114
9126 5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	115 ## Get slices.
5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	116 slices = cellslices (data, nc:-1:1, nc+nr-1:-1:nr);
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	117
9126 5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	118 ## Form matrix.
5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	119 retval = horzcat (slices{:});
5780b3b80425 optimize toeplitz for sparse args Jaroslav Hajek <highegg@gmail.com> parents: 9092 diff changeset	120 endif
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	121
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	122 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	123
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	124
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	125 %!assert (toeplitz (1), [1])
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	126 %!assert (toeplitz ([1, 2, 3], [1; -3; -5]), [1, -3, -5; 2, 1, -3; 3, 2, 1])
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	127 %!assert (toeplitz ([1, 2, 3], [1; -3i; -5i]), [1, -3i, -5i; 2, 1, -3i; 3, 2, 1])
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	128
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	129 ## Test input validation
13889 aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	130 %!error toeplitz ()
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	131 %!error toeplitz (1, 2, 3)
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	132 %!error <C must be a vector> toeplitz ([1, 2; 3, 4])
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	133 %!error <C and R must be vectors> toeplitz ([1, 2; 3, 4], 1)
aaefd6b28188 toeplitz.m: Update coding style Rik <octave@nomad.inbox5.com> parents: 12639 diff changeset	134 %!error <C and R must be vectors> toeplitz (1, [1, 2; 3, 4])
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	135

Mercurial > octave-antonio

annotate scripts/special-matrix/toeplitz.m @ 20162:2645f9ef8c88 stable