octave: scripts/specfun/expint.m annotate

annotate scripts/specfun/expint.m @ 25106:d7ad543255c5 stable

doc: Shorten very long first sentences of docstrings (bug #53388). * bsxfun.cc (Fbsxfun), daspk.cc (Fdaspk), dasrt.cc (Fdasrt), dassl.cc (Fdassl), gsvd.cc (Fgsvd), load-save.cc (Foctave_core_file_limit), qz.cc (Fqz), svd.cc (Fsvd), sylvester.cc (Fsylvester), utils.cc (Ferrno), bincoeff.m, bessel.m, krylov.m, expint.m, moment.m: Shorten very long first sentences.

author	Rik <rik@octave.org>
date	Tue, 03 Apr 2018 21:37:29 -0700
parents	baa7e37453b1
children	00f796120a6d

rev	line source
24923 40ab8be7d7ec Fixed style in specfun scripts Michele Ginesi <michele.ginesi@gmail.com> parents: 24922 diff changeset	1 ## Copyright (C) 2018 Michele Ginesi
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	2 ##
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	3 ## This file is part of Octave.
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	4 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	5 ## Octave is free software: you can redistribute it and/or modify it
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	6 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	7 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	8 ## (at your option) any later version.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	9 ##
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## GNU General Public License for more details.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	14 ##
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	15 ## You should have received a copy of the GNU General Public License
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	17 ## <https://www.gnu.org/licenses/>.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	18
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	19 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20162 diff changeset	20 ## @deftypefn {} {} expint (@var{x})
25106 d7ad543255c5 doc: Shorten very long first sentences of docstrings (bug #53388). Rik <rik@octave.org> parents: 25015 diff changeset	21 ## Compute the exponential integral.
d7ad543255c5 doc: Shorten very long first sentences of docstrings (bug #53388). Rik <rik@octave.org> parents: 25015 diff changeset	22 ##
d7ad543255c5 doc: Shorten very long first sentences of docstrings (bug #53388). Rik <rik@octave.org> parents: 25015 diff changeset	23 ## The exponential integral is defined as:
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	24 ##
16587 a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	25 ## @tex
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	26 ## $$
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	27 ## {\rm E_1} (x) = \int_x^\infty {e^{-t} \over t} dt
16587 a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	28 ## $$
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	29 ## @end tex
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	30 ## @ifnottex
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	31 ##
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	32 ## @example
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	33 ## @group
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	34 ## +oo
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	35 ## /
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	36 ## \| exp (-t)
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	37 ## E_1 (x) = \| -------- dt
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	38 ## \| t
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	39 ## /
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	40 ## x
16587 a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	41 ## @end group
a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	42 ## @end example
17513 fedcd3717ebc doc: grammarcheck of documentation before 3.8 release. Rik <rik@octave.org> parents: 17363 diff changeset	43 ##
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	44 ## @end ifnottex
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	45 ##
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	46 ## Note: For compatibility, this function uses the @sc{matlab} definition
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	47 ## of the exponential integral. Most other sources refer to this particular
20162 2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19593 diff changeset	48 ## value as @math{E_1 (x)}, and the exponential integral as
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	49 ## @tex
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	50 ## $$
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	51 ## {\rm Ei} (x) = - \int_{-x}^\infty {e^{-t} \over t} dt.
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	52 ## $$
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	53 ## @end tex
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	54 ## @ifnottex
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	55 ##
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	56 ## @example
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	57 ## @group
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	58 ## +oo
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	59 ## /
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	60 ## \| exp (-t)
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	61 ## Ei (x) = - \| -------- dt
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	62 ## \| t
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	63 ## /
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	64 ## -x
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	65 ## @end group
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	66 ## @end example
17513 fedcd3717ebc doc: grammarcheck of documentation before 3.8 release. Rik <rik@octave.org> parents: 17363 diff changeset	67 ##
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	68 ## @end ifnottex
17514 5b916efea542 doc: spellcheck of documentation before 3.8 release. Rik <rik@octave.org> parents: 17513 diff changeset	69 ## The two definitions are related, for positive real values of @var{x}, by
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	70 ## @tex
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	71 ## $
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	72 ## E_1 (-x) = -{\rm Ei} (x) - i\pi.
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	73 ## $
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	74 ## @end tex
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	75 ## @ifnottex
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	76 ## @w{@code{E_1 (-x) = -Ei (x) - i*pi}}.
16587 a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	77 ## @end ifnottex
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	78 ##
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	79 ## References:
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	80 ##
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	81 ## @nospell{M. Abramowitz and I.A. Stegun},
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	82 ## @cite{Handbook of Mathematical Functions}, 1964.
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	83 ##
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	84 ## @nospell{N. Bleistein and R.A. Handelsman},
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	85 ## @cite{Asymptotic expansions of integrals}, 1986.
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	86 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	87 ## @seealso{cosint, sinint, exp}
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	88 ## @end deftypefn
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	89
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	90 function E1 = expint (x)
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	91
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	92 if (nargin != 1)
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	93 print_usage ();
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	94 endif
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	95
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	96 if (! isnumeric (x))
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	97 error ("expint: X must be numeric");
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	98 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	99
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	100 ## Convert to floating point if necessary
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	101 if (isinteger (x))
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	102 x = double (x);
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	103 endif
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	104
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	105 orig_sparse = issparse (x);
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	106 orig_sz = size (x);
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	107 x = x(:); # convert to column vector
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	108
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	109 ## Initialize the result
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	110 if (isreal (x) && x >= 0)
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	111 E1 = zeros (size (x), class (x));
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	112 else
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	113 E1 = complex (zeros (size (x), class (x)));
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	114 endif
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	115 tol = eps (class (x));
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	116
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	117 ## Divide the input into 3 regions and apply a different algorithm for each.
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	118 ## s = series expansion, cf = continued fraction, a = asymptotic series
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	119 s_idx = (((real (x) + 19.5).^ 2 ./ (20.5^2) + ...
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	120 imag (x).^2 ./ (10^2)) <= 1) ...
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	121 \| (real (x) < 0 & abs (imag (x)) <= 1e-8);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	122 cf_idx = ((((real (x) + 1).^2 ./ (38^2) + ...
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	123 imag (x).^2 ./ (40^2)) <= 1) ...
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	124 & (! s_idx)) & (real (x) <= 35);
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	125 a_idx = (! s_idx) & (! cf_idx);
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	126 x_s = x(s_idx);
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	127 x_cf = x(cf_idx);
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	128 x_a = x(a_idx);
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	129
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	130 ## Series expansion
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	131 ## Abramowitz, Stegun, "Handbook of Mathematical Functions",
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	132 ## formula 5.1.11, p 229.
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	133 ## FIXME: Why so long? IEEE double doesn't have this much precision.
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	134 gm = 0.577215664901532860606512090082402431042159335;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	135 e1_s = -gm - log (x_s);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	136 res = -x_s;
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	137 ssum = res;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	138 k = 1;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	139 todo = true (size (res));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	140 while (k < 1e3 && any (todo))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	141 res(todo) .= (k (- x_s(todo)) / ((k + 1) ^ 2));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	142 ssum(todo) += res(todo);
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	143 k += 1;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	144 todo = (abs (res) > (tol * abs (ssum)));
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	145 endwhile
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	146 e1_s -= ssum;
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	147
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	148 ## Continued fraction expansion,
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	149 ## Abramowitz, Stegun, "Handbook of Mathematical Functions",
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	150 ## formula 5.1.22, p 229.
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	151 ## Modified Lentz's algorithm, from "Numerical recipes in Fortran 77" p.165.
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	152
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	153 e1_cf = exp (-x_cf) .* __expint__ (x_cf);
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	154
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	155 ## Remove spurious imaginary part if needed (__expint__ works automatically
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	156 ## with complex values)
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	157
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	158 if (isreal (x_cf) && x_cf >= 0)
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	159 e1_cf = real (e1_cf);
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	160 endif
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	161
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	162 ## Asymptotic series, from N. Bleistein and R.A. Handelsman
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	163 ## "Asymptotic expansion of integrals", pages 1-4.
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	164 e1_a = exp (-x_a) ./ x_a;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	165 ssum = res = ones (size (x_a), class (x_a));
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	166 k = 0;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	167 todo = true (size (x_a));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	168 while (k < 1e3 && any (todo))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	169 res(todo) ./= (- x_a(todo) / (k + 1));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	170 ssum(todo) += res(todo);
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	171 k += 1;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	172 todo = abs (x_a) > k;
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	173 endwhile
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	174 e1_a .*= ssum;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	175
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	176 ## Combine results from each region into final output
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	177 E1(s_idx) = e1_s;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	178 E1(cf_idx) = e1_cf;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	179 E1(a_idx) = e1_a;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	180
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	181 ## Restore shape and sparsity of input
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	182 E1 = reshape (E1, orig_sz);
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	183 if (orig_sparse)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	184 E1 = sparse (E1);
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	185 endif
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 20852 diff changeset	186
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	187 endfunction
16585 1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	188
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	189
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	190 ## The following values were computed with the Octave symbolic package
16585 1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	191 %!test
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	192 %! X = [-50 - 50i -30 - 50i -10 - 50i 5 - 50i 15 - 50i 25 - 50i
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	193 %! -50 - 30i -30 - 30i -10 - 30i 5 - 30i 15 - 30i 25 - 30i
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	194 %! -50 - 10i -30 - 10i -10 - 10i 5 - 10i 15 - 10i 25 - 10i
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	195 %! -50 + 5i -30 + 5i -10 + 5i 5 + 5i 15 + 5i 25 + 5i
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	196 %! -50 + 15i -30 + 15i -10 + 15i 5 + 15i 15 + 15i 25 + 15i
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	197 %! -50 + 25i -30 + 25i -10 + 25i 5 + 25i 15 + 25i 25 + 25i];
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	198 %! y_exp = [ -3.61285286166493e+19 + 6.46488018613387e+19i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	199 %! -4.74939752018180e+10 + 1.78647798300364e+11i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	200 %! 3.78788822381261e+01 + 4.31742823558278e+02i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	201 %! 5.02062497548626e-05 + 1.23967883532795e-04i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	202 %! 3.16785290137650e-09 + 4.88866651583182e-09i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	203 %! 1.66999261039533e-13 + 1.81161508735941e-13i;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	204 %! 3.47121527628275e+19 + 8.33104448629260e+19i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	205 %! 1.54596484273693e+11 + 2.04179357837414e+11i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	206 %! 6.33946547999647e+02 + 3.02965459323125e+02i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	207 %! 2.19834747595065e-04 - 9.25266900230165e-06i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	208 %! 8.49515487435091e-09 - 2.95133588338825e-09i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	209 %! 2.96635342439717e-13 - 1.85401806861382e-13i;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	210 %! 9.65535916388246e+19 + 3.78654062133933e+19i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	211 %! 3.38477774418380e+11 + 8.37063899960569e+10i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	212 %! 1.57615042657685e+03 - 4.33777639047543e+02i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	213 %! 2.36176542789578e-05 - 5.75861972980636e-04i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	214 %! -6.83624588479039e-09 - 1.47230889442175e-08i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	215 %! -2.93020801760942e-13 - 4.03912221595793e-13i;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	216 %! -1.94572937469407e+19 - 1.03494929263031e+20i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	217 %! -4.22385087573180e+10 - 3.61103191095041e+11i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	218 %! 4.89771220858552e+02 - 2.09175729060712e+03i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	219 %! 7.26650666035639e-04 + 4.71027801635222e-04i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	220 %! 1.02146578536128e-08 + 1.51813977370467e-08i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	221 %! 2.41628751621686e-13 + 4.66309048729523e-13i;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	222 %! 5.42351559144068e+19 + 8.54503231614651e+19i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	223 %! 1.22886461074544e+11 + 3.03555953589323e+11i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	224 %! -2.13050339387819e+02 + 1.23853666784218e+03i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	225 %! -3.68087391884738e-04 + 1.94003994408861e-04i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	226 %! -1.39355838231763e-08 + 6.57189276453356e-10i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	227 %! -4.55133112151501e-13 - 8.46035902535333e-14i;
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	228 %! -7.75482228205081e+19 - 5.36017490438329e+19i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	229 %! -1.85284579257329e+11 - 2.08761110392897e+11i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	230 %! -1.74210199269860e+02 - 8.09467914953486e+02i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	231 %! 9.40470496160143e-05 - 2.44265223110736e-04i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	232 %! 6.64487526601190e-09 - 7.87242868014498e-09i, ...
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	233 %! 3.10273337426175e-13 - 2.28030229776792e-13i];
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	234 %! assert (expint (X), y_exp, -1e-14);
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	235
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	236 ## Exceptional values (-Inf, Inf, NaN, 0, 0.37250741078)
19593 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	237 %!test
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	238 %! x = [-Inf; Inf; NaN; 0; -0.3725074107813668];
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	239 %! y_exp = [-Inf - ipi; 0; NaN; Inf; 0 - ipi];
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	240 %! y = expint (x);
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	241 %! assert (y, y_exp, 5*eps);
9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	242
25015 baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	243 %!test <53351>
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	244 %! assert (expint (32.5 + 1i),
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	245 %! 1.181108930758065e-16 - 1.966348533426658e-16i, -4*eps);
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	246 %! assert (expint (44 + 1i),
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	247 %! 9.018757389858152e-22 - 1.475771020004195e-21i, -4*eps);
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	248
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	249 %!test <47738>
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	250 %! assert (expint (10i), 0.0454564330044554 + 0.0875512674239774i, -4*eps);
baa7e37453b1 Added more tests for betainc and expint. Michele Ginesi <michele.ginesi@gmail.com> parents: 24927 diff changeset	251
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	252 ## Test preservation or conversion of the class
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	253 %!assert (class (expint (single (1))), "single")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	254 %!assert (class (expint (int8 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	255 %!assert (class (expint (int16 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	256 %!assert (class (expint (int32 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	257 %!assert (class (expint (int64 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	258 %!assert (class (expint (uint8 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	259 %!assert (class (expint (uint16 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	260 %!assert (class (expint (uint32 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	261 %!assert (class (expint (uint64 (1))), "double")
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	262 %!assert (issparse (expint (sparse (1))))
c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	263
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	264 ## Test on the correct Image set
6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	265 %!assert (isreal (expint (linspace (0, 100))))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24923 diff changeset	266 %!assert (! isreal (expint (-1)))
24908 6c082a43abd8 expint: moved the Lentz algorithm to .cc function. Michele Ginesi <michele.ginesi@gmail.com> parents: 24534 diff changeset	267
17363 9aca7020c89f expint.m: Overhaul function. Rik <rik@octave.org> parents: 17338 diff changeset	268 ## Test input validation
16585 1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	269 %!error expint ()
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	270 %!error expint (1,2)
23080 c56d30ea6cd4 expint.m: new strategies to compute the exponential integral (bug #47738). Michele Ginesi <michele.ginesi@gmail.com> parents: 22755 diff changeset	271 %!error <X must be numeric> expint ("1")

Mercurial > octave

annotate scripts/specfun/expint.m @ 25106:d7ad543255c5 stable