octave-nkf: scripts/specfun/isprime.m annotate

annotate scripts/specfun/isprime.m @ 20828:a3b9ee5c040a

Replace bsxfun with broadcasting for performance with complex inputs (bug #38628). cumtrapz.m, quadgk.m, trapz.m, center.m, zscore.m: Replace bsxfun with broadcasting for performance where inputs might be complex.

author	Rik <rik@octave.org>
date	Mon, 12 Oct 2015 21:28:32 -0700
parents	2645f9ef8c88
children

rev	line source
19898 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19794 diff changeset	1 ## Copyright (C) 2000-2015 Paul Kienzle
10664 faff5367cc05 second isprime rewrite Jaroslav Hajek <highegg@gmail.com> parents: 10657 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 ## -- texinfo --
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	21 ## @deftypefn {Function File} {} isprime (@var{x})
20372 2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	22 ## Return a logical array which is true where the elements of @var{x} are prime
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 20038 diff changeset	23 ## numbers and false where they are not.
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	24 ##
19244 bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19242 diff changeset	25 ## A prime number is conventionally defined as a positive integer greater than
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19242 diff changeset	26 ## 1 (e.g., 2, 3, @dots{}) which is divisible only by itself and 1. Octave
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19242 diff changeset	27 ## extends this definition to include both negative integers and complex
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19242 diff changeset	28 ## values. A negative integer is prime if its positive counterpart is prime.
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19242 diff changeset	29 ## This is equivalent to @code{isprime (abs (x))}.
19794 db92e7e28e1f strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 19244 diff changeset	30 ##
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	31 ## If @code{class (@var{x})} is complex, then primality is tested in the domain
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	32 ## of Gaussian integers (@url{http://en.wikipedia.org/wiki/Gaussian_integer}).
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	33 ## Some non-complex integers are prime in the ordinary sense, but not in the
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	34 ## domain of Gaussian integers. For example, @math{5 = (1+2i)*(1-2i)} shows
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	35 ## that 5 is not prime because it has a factor other than itself and 1.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	36 ## Exercise caution when testing complex and real values together in the same
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	37 ## matrix.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	38 ##
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	39 ## Examples:
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	40 ##
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	41 ## @example
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	42 ## @group
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	43 ## isprime (1:6)
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	44 ## @result{} [0, 1, 1, 0, 1, 0]
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	45 ## @end group
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	46 ## @end example
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	47 ##
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	48 ## @example
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	49 ## @group
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	50 ## isprime ([i, 2, 3, 5])
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	51 ## @result{} [0, 0, 1, 0]
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	52 ## @end group
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	53 ## @end example
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	54 ##
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	55 ## Programming Note: @code{isprime} is appropriate if the maximum value in
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	56 ## @var{x} is not too large (< 1e15). For larger values special purpose
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	57 ## factorization code should be used.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	58 ##
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	59 ## Compatibility Note: @var{matlab} does not extend the definition of prime
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	60 ## numbers and will produce an error if given negative or complex inputs.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	61 ## @seealso{primes, factor, gcd, lcm}
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	62 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	63
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 11431 diff changeset	64 function t = isprime (x)
7125 f084ba47812b [project @ 2007-11-08 02:29:23 by jwe] jwe parents: 7017 diff changeset	65
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	66 if (nargin != 1)
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	67 print_usage ();
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	68 elseif (any (fix (x) != x))
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	69 error ("isprime: X contains non-integer entries");
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	70 endif
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	71
19237 920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19233 diff changeset	72 if (isempty (x))
920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19233 diff changeset	73 t = x;
920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19233 diff changeset	74 return;
920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19233 diff changeset	75 endif
920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19233 diff changeset	76
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	77 if (iscomplex (x))
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	78 t = isgaussianprime (x);
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	79 return;
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	80 endif
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	81
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	82 ## Code strategy is to build a table with the list of possible primes
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	83 ## and then quickly compare entries in x with the table of primes using
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	84 ## lookup(). The table size is limited to save memory and computation
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	85 ## time during its creation. All entries larger than the maximum in the
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	86 ## table are checked by straightforward division.
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	87
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	88 x = abs (x); # handle negative entries
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	89 maxn = max (x(:));
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	90 ## generate prime table of suitable length.
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	91 ## 1e7 threshold requires ~0.15 seconds of computation, 1e8 requires 1.8.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	92 maxp = min (maxn, max (sqrt (maxn), 1e7));
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	93 pr = primes (maxp);
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	94 t = lookup (pr, x, "b"); # quick search for table matches.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	95
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	96 ## process any remaining large entries
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	97 m = x(x > maxp);
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	98 if (! isempty (m))
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	99 if (maxn <= intmax ("uint32"))
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	100 m = uint32 (m);
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	101 elseif (maxn <= intmax ("uint64"))
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	102 m = uint64 (m);
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	103 else
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	104 warning ("isprime: X contains integers too large to be tested");
10664 faff5367cc05 second isprime rewrite Jaroslav Hajek <highegg@gmail.com> parents: 10657 diff changeset	105 endif
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	106
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	107 ## Start by dividing through by the small primes until the remaining
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	108 ## list of entries is small (and most likely prime themselves).
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	109 pr = cast (pr(pr <= sqrt (maxn)), class (m));
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	110 for p = pr
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	111 m = m(rem (m, p) != 0);
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	112 if (numel (m) < numel (pr) / 10)
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	113 break;
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	114 endif
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	115 endfor
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	116
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	117 ## Check the remaining list of possible primes against the
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	118 ## remaining prime factors which were not tested in the for loop.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	119 ## This is just an optimization to use arrayfun over for loo
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	120 pr = pr(pr > p);
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	121 mm = arrayfun (@(x) all (rem (x, pr)), m);
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	122 m = m(mm);
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	123
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	124 ## Add any remaining entries, which are truly prime, to the results.
10664 faff5367cc05 second isprime rewrite Jaroslav Hajek <highegg@gmail.com> parents: 10657 diff changeset	125 if (! isempty (m))
19233 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	126 m = cast (sort (m), class (x));
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	127 t \|= lookup (m, x, "b");
10664 faff5367cc05 second isprime rewrite Jaroslav Hajek <highegg@gmail.com> parents: 10657 diff changeset	128 endif
7125 f084ba47812b [project @ 2007-11-08 02:29:23 by jwe] jwe parents: 7017 diff changeset	129 endif
f084ba47812b [project @ 2007-11-08 02:29:23 by jwe] jwe parents: 7017 diff changeset	130
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	131 endfunction
9984 d1cc2e0ddf55 isprime: produce logical result John W. Eaton <jwe@octave.org> parents: 7125 diff changeset	132
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	133 function t = isgaussianprime (z)
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	134 ## Assume prime unless proven otherwise
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	135 t = true (size (z));
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	136
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	137 x = real (z);
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	138 y = imag (z);
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	139
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	140 ## If purely real or purely imaginary, ordinary prime test for
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	141 ## that complex part if that part is 3 mod 4.
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	142 xidx = y==0 & mod (x, 4) == 3;
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	143 yidx = x==0 & mod (y, 4) == 3;
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	144
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	145 t(xidx) &= isprime (x(xidx));
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	146 t(yidx) &= isprime (y(yidx));
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	147
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	148 ## Otherwise, prime if x^2 + y^2 is prime
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	149 zidx = ! (xidx \| yidx); # Skip entries that were already evaluated
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	150 zabs = x(zidx).^2 + y(zidx).^2;
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	151 t(zidx) &= isprime (zabs);
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	152 endfunction
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	153
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	154
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	155 %!assert (isprime (3), true)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	156 %!assert (isprime (4), false)
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	157 %!assert (isprime (5i), false)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	158 %!assert (isprime (7i), true)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	159 %!assert (isprime ([1+2i, (2+3i)*(-1+2i)]), [true, false])
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	160 %!assert (isprime (-2), true)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	161 %!assert (isprime (complex (-2)), false)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	162 %!assert (isprime (2i), false)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	163 %!assert (isprime ([i, 2, 3, 5]), [false, false, true, false])
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	164 %!assert (isprime (0), false)
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	165 %!assert (isprime (magic (3)), logical ([0, 0, 0; 1, 1, 1; 0, 0, 1]))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	166
20038 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19898 diff changeset	167 ## Test input validation
9984 d1cc2e0ddf55 isprime: produce logical result John W. Eaton <jwe@octave.org> parents: 7125 diff changeset	168 %!error isprime ()
d1cc2e0ddf55 isprime: produce logical result John W. Eaton <jwe@octave.org> parents: 7125 diff changeset	169 %!error isprime (1, 2)
19238 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	170 %!error <X contains non-integer entries> isprime (0.5i)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19237 diff changeset	171 %!error <X contains non-integer entries> isprime (0.5)
19242 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19238 diff changeset	172

Mercurial > hg > octave-nkf

annotate scripts/specfun/isprime.m @ 20828:a3b9ee5c040a