Mercurial > hg > octave-jordi

annotate scripts/specfun/nthroot.m @ 20851:516bb87ea72e

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
2015 Code Sprint: remove class of function from docstring for all m-files.
author Rik <rik@octave.org>
date Sat, 12 Dec 2015 07:31:00 -0800
parents 9fc020886ae9
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
19696
4197fc428c7d maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
parents: 19291
diff changeset
1 ## Copyright (C) 2004-2015 Paul Kienzle
10415
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
2 ## Copyright (C) 2010 VZLU Prague
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
3 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
4 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
5 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
6 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
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: 5827
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: 5827
diff changeset
9 ## your option) any later version.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
10 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
11 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
14 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
15 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
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: 5827
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: 5827
diff changeset
18 ## <http://www.gnu.org/licenses/>.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
19 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
20 ## Original version by Paul Kienzle distributed as free software in the
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
21 ## public domain.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
22
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
23 ## -*- texinfo -*-
20851
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files.
Rik <rik@octave.org>
parents: 19832
diff changeset
24 ## @deftypefn {} {} nthroot (@var{x}, @var{n})
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
25 ##
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
26 ## Compute the real (non-complex) @var{n}-th root of @var{x}.
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
27 ##
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
28 ## @var{x} must have all real entries and @var{n} must be a scalar.
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
29 ## If @var{n} is an even integer and @var{x} has negative entries then
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
30 ## @code{nthroot} aborts and issues an error.
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
31 ##
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
32 ## Example:
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
33 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
34 ## @example
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
35 ## @group
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
36 ## nthroot (-1, 3)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
37 ## @result{} -1
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
38 ## (-1) ^ (1 / 3)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
39 ## @result{} 0.50000 - 0.86603i
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
40 ## @end group
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
41 ## @end example
11532
34bb8d38f19f Add undocumented function cbrt to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
42 ## @seealso{realsqrt, sqrt, cbrt}
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
43 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
44
10415
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
45 function y = nthroot (x, n)
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
46
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
47 if (nargin != 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
48 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
49 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
50
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
51 if (iscomplex (x))
12628
619fbc98a7eb nthroot.m: Fix input validation to disallow complex values (bug #33135)
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
52 error ("nthroot: X must not contain complex values");
619fbc98a7eb nthroot.m: Fix input validation to disallow complex values (bug #33135)
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
53 endif
619fbc98a7eb nthroot.m: Fix input validation to disallow complex values (bug #33135)
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
54
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
55 if (! isreal (n) || ! isscalar (n) || n == 0)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
56 error ("nthroot: N must be a real nonzero scalar");
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
57 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
58
10415
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
59 if (n == 3)
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
60 y = cbrt (x);
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
61 elseif (n == -3)
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
62 y = 1 ./ cbrt (x);
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
63 elseif (n < 0)
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
64 y = 1 ./ nthroot (x, -n);
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
65 else
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
66 ## Compute using power.
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
67 integer_n = n == fix (n);
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
68 if (integer_n && mod (n, 2) == 1)
10415
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
69 y = abs (x) .^ (1/n) .* sign (x);
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
70 elseif (any (x(:) < 0))
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
71 error ("nthroot: N must be an odd integer if X contains negative values");
10415
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
72 else
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
73 y = x .^ (1/n);
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
74 endif
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
75
19116
a4c226a963c5 Deprecate finite in favor of isfinite.
Rik <rik@octave.org>
parents: 19101
diff changeset
76 if (integer_n && n > 0 && isfinite (n))
19291
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
77 if (isscalar (y) && y == 0)
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
78 ## Don't apply correction which leads to division by zero (bug #43492)
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
79 else
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
80 ## FIXME: What is this correction for?
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
81 y = ((n-1)*y + x ./ (y.^(n-1))) / n;
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
82 y = merge (isfinite (y), y, x);
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
83 endif
10415
976e76b77fa0 rewrite nth_root, move to specfun
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
84 endif
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
85 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
86
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
87 endfunction
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
88
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
89
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
90 %!assert (nthroot (-32, 5), -2)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
91 %!assert (nthroot (81, 4), 3)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
92 %!assert (nthroot (Inf, 4), Inf)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
93 %!assert (nthroot (-Inf, 7), -Inf)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
94 %!assert (nthroot (-Inf, -7), 0)
12628
619fbc98a7eb nthroot.m: Fix input validation to disallow complex values (bug #33135)
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
95
19291
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
96 ## Bug #43492. This should not generate a division by zero warning
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
97 %!test
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
98 %! warnmsg = lastwarn ();
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
99 %! assert (nthroot (0, 2), 0);
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
100 %! assert (lastwarn (), warnmsg);
238522618904 nthroot.m: Fix division by zero warning when input x is 0 (bug #43492).
Rik <rik@octave.org>
parents: 19116
diff changeset
101
19832
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19696
diff changeset
102 ## Test input validation
19101
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
103 %!error nthroot ()
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
104 %!error nthroot (1)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
105 %!error nthroot (1,2,3)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
106 %!error <X must not contain complex values> nthroot (1+j, 2)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
107 %!error <N must be a real nonzero scalar> nthroot (1, i)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
108 %!error <N must be a real nonzero scalar> nthroot (1, [1 2])
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
109 %!error <N must be a real nonzero scalar> nthroot (1, 0)
bb20384acf7b doc: Overhaul documentation for some functions in specfun/ dir.
Rik <rik@octave.org>
parents: 17744
diff changeset
110 %!error <N must be an odd integer> nthroot (-1, 2)
12628
619fbc98a7eb nthroot.m: Fix input validation to disallow complex values (bug #33135)
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
111