Mercurial > hg > octave-nkf

annotate scripts/general/cart2sph.m @ 20818:9d2023d1a63c

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
binoinv.m: Implement binary search algorithm for 28X performance increase (bug #34363). * binoinv.m: Call new functions scalar_binoinv or vector_binoinv to calculate binoinv. If there are still uncalculated values then call bin_search_binoinv to perform binary search for remaining values. Add more BIST tests. * binoinv.m (scalar_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000. * binoinv.m (vector_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000.
author Lachlan Andrew <lachlanbis@gmail.com>
date Sun, 11 Oct 2015 19:49:40 -0700
parents aa36fb998a4d
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
19898
4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
parents: 17744
diff changeset
1 ## Copyright (C) 2000-2015 Kai Habel
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
2 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
3 ## This file is part of Octave.
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
4 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
6 ## 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: 6786
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6786
diff changeset
8 ## your option) any later version.
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
9 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
13 ## General Public License for more details.
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
14 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
15 ## 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: 6786
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6786
diff changeset
17 ## <http://www.gnu.org/licenses/>.
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
18
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
19 ## -*- texinfo -*-
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
20 ## @deftypefn {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
21 ## @deftypefnx {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{C})
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
22 ## @deftypefnx {Function File} {@var{S} =} cart2sph (@dots{})
20368
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
23 ## Transform Cartesian coordinates to spherical coordinates.
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
24 ##
20368
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
25 ## The inputs @var{x}, @var{y}, and @var{z} must be the same shape, or scalar.
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
26 ## If called with a single matrix argument then each row of @var{C} represents
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
27 ## the Cartesian coordinate (@var{x}, @var{y}, @var{z}).
20391
aa36fb998a4d maint: Remove unnecessary whitespace at end of lines.
Rik <rik@octave.org>
parents: 20368
diff changeset
28 ##
9168
742cf6388a8f Update section 17.7 (Coordinate Transformations) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
29 ## @var{theta} describes the angle relative to the positive x-axis.
20368
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
30 ##
8491
aaff46fef256 [docs] fix hypenation: x - axis => x-axis, etc
Brian Gough <bjg@gnu.org>
parents: 7017
diff changeset
31 ## @var{phi} is the angle relative to the xy-plane.
20368
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
32 ##
10687
a8ce6bdecce5 Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
33 ## @var{r} is the distance to the origin @w{(0, 0, 0)}.
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
34 ##
20368
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
35 ## If only a single return argument is requested then return a matrix @var{S}
7503499a252b doc: Update docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19898
diff changeset
36 ## where each row represents one spherical coordinate
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
37 ## (@var{theta}, @var{phi}, @var{r}).
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
38 ## @seealso{sph2cart, cart2pol, pol2cart}
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
39 ## @end deftypefn
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
40
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
41 ## Author: Kai Habel <kai.habel@gmx.de>
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
42 ## Adapted-by: jwe
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
43
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
44 function [theta, phi, r] = cart2sph (x, y, z)
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
45
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
46 if (nargin != 1 && nargin != 3)
6046
34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe]
jwe
parents: 5642
diff changeset
47 print_usage ();
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
48 endif
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
49
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
50 if (nargin == 1)
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
51 if (ismatrix (x) && columns (x) == 3)
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
52 z = x(:,3);
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
53 y = x(:,2);
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
54 x = x(:,1);
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
55 else
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
56 error ("cart2sph: matrix input must have 3 columns [X, Y, Z]");
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
57 endif
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
58 elseif (nargin == 3)
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
59 if (! ((ismatrix (x) && ismatrix (y) && ismatrix (z))
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
60 && (size_equal (x, y) || isscalar (x) || isscalar (y))
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
61 && (size_equal (x, z) || isscalar (x) || isscalar (z))
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
62 && (size_equal (y, z) || isscalar (y) || isscalar (z))))
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
63 error ("cart2sph: X, Y, Z must be matrices of the same size, or scalar");
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
64 endif
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
65 endif
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
66
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
67 theta = atan2 (y, x);
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
68 phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
69 r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
70
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
71 if (nargout <= 1)
17585
36b9fa789d8e Overhaul polar, spherical, cartesian conversion routiens when nargout == 1.
Rik <rik@octave.org>
parents: 14363
diff changeset
72 theta = [theta(:), phi(:), r(:)];
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
73 endif
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
74
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
75 endfunction
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
76
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
77
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
78 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
79 %! x = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
80 %! y = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
81 %! z = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
82 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
83 %! assert (t, [0, pi/4, pi/4], eps);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
84 %! assert (p, [0, 1, 1]*atan (sqrt (0.5)), eps);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
85 %! assert (r, [0, 1, 2]*sqrt (3), eps);
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
86
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
87 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
88 %! x = 0;
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
89 %! y = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
90 %! z = [0, 1, 2];
17585
36b9fa789d8e Overhaul polar, spherical, cartesian conversion routiens when nargout == 1.
Rik <rik@octave.org>
parents: 14363
diff changeset
91 %! S = cart2sph (x, y, z);
36b9fa789d8e Overhaul polar, spherical, cartesian conversion routiens when nargout == 1.
Rik <rik@octave.org>
parents: 14363
diff changeset
92 %! assert (S(:,1), [0; 1; 1] * pi/2, eps);
36b9fa789d8e Overhaul polar, spherical, cartesian conversion routiens when nargout == 1.
Rik <rik@octave.org>
parents: 14363
diff changeset
93 %! assert (S(:,2), [0; 1; 1] * pi/4, eps);
36b9fa789d8e Overhaul polar, spherical, cartesian conversion routiens when nargout == 1.
Rik <rik@octave.org>
parents: 14363
diff changeset
94 %! assert (S(:,3), [0; 1; 2] * sqrt (2), eps);
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
95
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
96 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
97 %! x = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
98 %! y = 0;
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
99 %! z = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
100 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
101 %! assert (t, [0, 0, 0]);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
102 %! assert (p, [0, 1, 1] * pi/4);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
103 %! assert (r, [0, 1, 2] * sqrt (2));
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
104
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
105 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
106 %! x = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
107 %! y = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
108 %! z = 0;
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
109 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
110 %! assert (t, [0, 1, 1] * pi/4);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
111 %! assert (p, [0, 0, 0]);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
112 %! assert (r, [0, 1, 2] * sqrt (2));
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
113
10688
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
114 %!test
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
115 %! C = [0, 0, 0; 1, 0, 1; 2, 0, 2];
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
diff changeset
116 %! S = [0, 0, 0; 0, pi/4, sqrt(2); 0, pi/4, 2*sqrt(2)];
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
117 %! assert (cart2sph (C), S, eps);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
118