Mercurial > octave
view libinterp/corefcn/psi.cc @ 30889:3a15bf04cb7f
maint: Remove ancient unused function __sort_rows_idx__.
* data.cc (F__sort_rows_idx__): Delete function.
author | Rik <rik@octave.org> |
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date | Mon, 04 Apr 2022 10:50:26 -0700 |
parents | 32d2b6604a9f |
children | e88a07dec498 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2016-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "ov.h" #include "defun.h" #include "error.h" #include "dNDArray.h" #include "fNDArray.h" #include "lo-specfun.h" OCTAVE_NAMESPACE_BEGIN DEFUN (psi, args, , doc: /* -*- texinfo -*- @deftypefn {} {@var{y} =} psi (@var{z}) @deftypefnx {} {@var{y} =} psi (@var{k}, @var{z}) Compute the psi (polygamma) function. The polygamma functions are the @var{k}th derivative of the logarithm of the gamma function. If unspecified, @var{k} defaults to zero. A value of zero computes the digamma function, a value of 1, the trigamma function, and so on. The digamma function is defined: @tex $$ \Psi (z) = {d (log (\Gamma (z))) \over dx} $$ @end tex @ifnottex @example @group psi (z) = d (log (gamma (z))) / dx @end group @end example @end ifnottex When computing the digamma function (when @var{k} equals zero), @var{z} can have any value real or complex value. However, for polygamma functions (@var{k} higher than 0), @var{z} must be real and non-negative. @seealso{gamma, gammainc, gammaln} @end deftypefn */) { int nargin = args.length (); if (nargin < 1 || nargin > 2) print_usage (); const octave_value oct_z = (nargin == 1) ? args(0) : args(1); const octave_idx_type k = (nargin == 1) ? 0 : args(0).xidx_type_value ("psi: K must be an integer"); if (k < 0) error ("psi: K must be non-negative"); octave_value retval; if (k == 0) { #define FLOAT_BRANCH(T, A, M, E) \ if (oct_z.is_ ## T ##_type ()) \ { \ const A ## NDArray z = oct_z.M ## array_value (); \ A ## NDArray psi_z (z.dims ()); \ \ const E *zv = z.data (); \ E *psi_zv = psi_z.fortran_vec (); \ const octave_idx_type n = z.numel (); \ for (octave_idx_type i = 0; i < n; i++) \ *psi_zv++ = math::psi (*zv++); \ \ retval = psi_z; \ } if (oct_z.iscomplex ()) { FLOAT_BRANCH(double, Complex, complex_, Complex) else FLOAT_BRANCH(single, FloatComplex, float_complex_, FloatComplex) else error ("psi: Z must be a floating point"); } else { FLOAT_BRANCH(double, , , double) else FLOAT_BRANCH(single, Float, float_, float) else error ("psi: Z must be a floating point"); } #undef FLOAT_BRANCH } else { if (! oct_z.isreal ()) error ("psi: Z must be real value for polygamma (K > 0)"); #define FLOAT_BRANCH(T, A, M, E) \ if (oct_z.is_ ## T ##_type ()) \ { \ const A ## NDArray z = oct_z.M ## array_value (); \ A ## NDArray psi_z (z.dims ()); \ \ const E *zv = z.data (); \ E *psi_zv = psi_z.fortran_vec (); \ const octave_idx_type n = z.numel (); \ for (octave_idx_type i = 0; i < n; i++) \ { \ if (*zv < 0) \ error ("psi: Z must be non-negative for polygamma (K > 0)"); \ \ *psi_zv++ = math::psi (k, *zv++); \ } \ retval = psi_z; \ } FLOAT_BRANCH(double, , , double) else FLOAT_BRANCH(single, Float, float_, float) else error ("psi: Z must be a floating point for polygamma (K > 0)"); #undef FLOAT_BRANCH } return retval; } /* %!shared em %! em = 0.577215664901532860606512090082402431042; # Euler-Mascheroni Constant %!assert (psi (ones (7, 3, 5)), repmat (-em, [7 3 5])) %!assert (psi ([0 1]), [-Inf -em]) %!assert (psi ([-20:1]), [repmat(-Inf, [1 21]) -em]) %!assert (psi (single ([0 1])), single ([-Inf -em])) ## Abramowitz and Stegun, page 258, eq 6.3.5 %!test %! z = [-100:-1 1:200] ./ 10; # drop the 0 %! assert (psi (z + 1), psi (z) + 1 ./ z, eps*1000); ## Abramowitz and Stegun, page 258, eq 6.3.2 %!assert (psi (1), -em) ## Abramowitz and Stegun, page 258, eq 6.3.3 %!assert (psi (1/2), -em - 2 * log (2)) ## The following tests are from Pascal Sebah and Xavier Gourdon (2002) ## "Introduction to the Gamma Function" ## Interesting identities of the digamma function, in section of 5.1.3 %!assert (psi (1/3), - em - (3/2) * log (3) - ((sqrt (3) / 6) * pi), eps*10) %!assert (psi (1/4), - em -3 * log (2) - pi/2, eps*10) %!assert (psi (1/6), %! - em -2 * log (2) - (3/2) * log (3) - ((sqrt (3) / 2) * pi), eps*10) ## First 6 zeros of the digamma function, in section of 5.1.5 (and also on ## Abramowitz and Stegun, page 258, eq 6.3.19) %!assert (psi ( 1.46163214496836234126265954232572132846819620400644), 0, eps) %!assert (psi (-0.504083008264455409258269304533302498955385182368579), 0, eps*2) %!assert (psi (-1.573498473162390458778286043690434612655040859116846), 0, eps*2) %!assert (psi (-2.610720868444144650001537715718724207951074010873480), 0, eps*10) %!assert (psi (-3.635293366436901097839181566946017713948423861193530), 0, eps*10) %!assert (psi (-4.653237761743142441714598151148207363719069416133868), 0, eps*100) ## Tests for complex values %!shared z %! z = [-100:-1 1:200] ./ 10; # drop the 0 ## Abramowitz and Stegun, page 259 eq 6.3.10 %!assert (real (psi (i*z)), real (psi (1 - i*z))) ## Abramowitz and Stegun, page 259 eq 6.3.11 %!assert (imag (psi (i*z)), 1/2 .* 1./z + 1/2 * pi * coth (pi * z), eps *10) ## Abramowitz and Stegun, page 259 eq 6.3.12 %!assert (imag (psi (1/2 + i*z)), 1/2 * pi * tanh (pi * z), eps*10) ## Abramowitz and Stegun, page 259 eq 6.3.13 %!assert (imag (psi (1 + i*z)), - 1./(2*z) + 1/2 * pi * coth (pi * z), eps*10) ## Abramowitz and Stegun, page 260 eq 6.4.5 %!test %! for z = 0:20 %! assert (psi (1, z + 0.5), %! 0.5 * (pi^2) - 4 * sum ((2*(1:z) -1) .^(-2)), %! eps*10); %! endfor ## Abramowitz and Stegun, page 260 eq 6.4.6 %!test %! z = 0.1:0.1:20; %! for n = 0:8 %! ## our precision goes down really quick when computing n is too high. %! assert (psi (n, z+1), %! psi (n, z) + ((-1)^n) * factorial (n) * (z.^(-n-1)), 0.1); %! endfor ## Test input validation %!error psi () %!error psi (1, 2, 3) %!error <Z must be> psi ("non numeric") %!error <K must be an integer> psi ({5.3}, 1) %!error <K must be non-negative> psi (-5, 1) %!error <Z must be non-negative for polygamma> psi (5, -1) %!error <Z must be a floating point> psi (5, uint8 (-1)) %!error <Z must be real value for polygamma> psi (5, 5i) */ OCTAVE_NAMESPACE_END