Mercurial > octave
view libinterp/corefcn/psi.cc @ 20232:a9574e3c6e9e
Deprecate Array::length() and Sparse::length() in favour of ::numel().
* liboctave/array/Array.h (Array::length): deprecate for ::numel.
* liboctave/array/Sparse.h (Sparse::length): deprecate for ::numel.
* libgui/graphics/QtHandlesUtils.cc, libgui/src/octave-qt-link.cc,
libinterp/corefcn/Cell.cc, libinterp/corefcn/__contourc__.cc,
libinterp/corefcn/__pchip_deriv__.cc, libinterp/corefcn/__qp__.cc,
libinterp/corefcn/cellfun.cc, libinterp/corefcn/daspk.cc,
libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc,
libinterp/corefcn/data.cc, libinterp/corefcn/filter.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/gl-render.h, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.h, libinterp/corefcn/lsode.cc,
libinterp/corefcn/matrix_type.cc, libinterp/corefcn/oct-hist.cc,
libinterp/corefcn/oct-map.cc, libinterp/corefcn/oct-map.h,
libinterp/corefcn/oct-obj.h, libinterp/corefcn/oct-stream.cc,
libinterp/corefcn/oct-stream.h, libinterp/corefcn/pr-output.cc,
libinterp/corefcn/quadcc.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/strfns.cc,
libinterp/corefcn/sub2ind.cc, libinterp/corefcn/symtab.h,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/tsearch.cc,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc,
libinterp/corefcn/variables.cc, libinterp/corefcn/xdiv.cc,
libinterp/corefcn/xpow.cc, libinterp/dldfcn/__glpk__.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/__magick_read__.cc,
libinterp/dldfcn/audiodevinfo.cc, libinterp/dldfcn/ccolamd.cc,
libinterp/dldfcn/colamd.cc, libinterp/octave-value/ov-cell.cc,
libinterp/octave-value/ov-class.cc, libinterp/octave-value/ov-class.h,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-perm.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov.cc,
libinterp/operators/op-int.h, libinterp/parse-tree/pt-pr-code.cc,
liboctave/array/Array-util.cc, liboctave/array/Array.cc,
liboctave/array/CColVector.cc, liboctave/array/CDiagMatrix.cc,
liboctave/array/CMatrix.cc, liboctave/array/CRowVector.cc,
liboctave/array/DiagArray2.cc, liboctave/array/DiagArray2.h,
liboctave/array/MArray.cc, liboctave/array/PermMatrix.cc,
liboctave/array/PermMatrix.h, liboctave/array/Sparse.cc,
liboctave/array/boolMatrix.cc, liboctave/array/chMatrix.cc,
liboctave/array/chNDArray.cc, liboctave/array/dColVector.cc,
liboctave/array/dDiagMatrix.cc, liboctave/array/dMatrix.cc,
liboctave/array/dRowVector.cc, liboctave/array/fCColVector.cc,
liboctave/array/fCDiagMatrix.cc, liboctave/array/fCMatrix.cc,
liboctave/array/fCRowVector.cc, liboctave/array/fColVector.cc,
liboctave/array/fDiagMatrix.cc, liboctave/array/fMatrix.cc,
liboctave/array/fRowVector.cc, liboctave/array/idx-vector.cc,
liboctave/array/intNDArray.cc, liboctave/numeric/CmplxCHOL.cc,
liboctave/numeric/CmplxLU.cc, liboctave/numeric/CmplxQR.cc,
liboctave/numeric/DASPK.cc, liboctave/numeric/DASRT.cc,
liboctave/numeric/DASSL.cc, liboctave/numeric/LSODE.cc,
liboctave/numeric/ODES.cc, liboctave/numeric/ODES.h,
liboctave/numeric/base-dae.h, liboctave/numeric/base-lu.cc,
liboctave/numeric/dbleCHOL.cc, liboctave/numeric/dbleLU.cc,
liboctave/numeric/dbleQR.cc, liboctave/numeric/eigs-base.cc,
liboctave/numeric/fCmplxCHOL.cc, liboctave/numeric/fCmplxLU.cc,
liboctave/numeric/fCmplxQR.cc, liboctave/numeric/floatCHOL.cc,
liboctave/numeric/floatLU.cc, liboctave/numeric/floatQR.cc,
liboctave/numeric/lo-specfun.cc, liboctave/numeric/oct-rand.cc,
liboctave/numeric/oct-spparms.cc, liboctave/numeric/sparse-base-chol.cc,
liboctave/operators/mx-inlines.cc, liboctave/system/file-ops.cc,
liboctave/util/glob-match.h, liboctave/util/kpse.cc,
liboctave/util/lo-regexp.cc, liboctave/util/oct-glob.cc,
liboctave/util/pathsearch.cc, liboctave/util/str-vec.cc,
liboctave/util/str-vec.h, liboctave/util/url-transfer.cc: replace all usage
of Array::length() and Sparse::length() with ::numel().
author | Carnë Draug <carandraug@octave.org> |
---|---|
date | Sat, 30 May 2015 03:14:07 +0100 |
parents | 65e22ba879f0 |
children | 099bdf98f724 |
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/* Copyright (C) 2015 Carnë Draug 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 <http://www.gnu.org/licenses/>. */ #ifdef 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" DEFUN (psi, args, , "-*- texinfo -*-\n\ @deftypefn {Function File} {} psi (@var{z})\n\ @deftypefnx {Function File} {} psi (@var{k}, @var{z})\n\ Compute the psi (polygamma) function.\n\ \n\ The polygamma functions are the @var{k}th derivative of the logarithm\n\ of the gamma function. If unspecified, @var{k} defaults to zero. A value\n\ of zero computes the digamma function, a value of 1, the trigamma function,\n\ and so on.\n\ \n\ The digamma function is defined:\n\ \n\ @tex\n\ $$\n\ \\Psi (z) = {d (log (\\Gamma (z))) \\over dx}\n\ $$\n\ @end tex\n\ @ifnottex\n\ @example\n\ @group\n\ psi (z) = d (log (gamma (z))) / dx\n\ @end group\n\ @end example\n\ @end ifnottex\n\ \n\ When computing the digamma function (when @var{k} equals zero), @var{z}\n\ can have any value real or complex value. However, for polygamma functions\n\ (@var{k} higher than 0), @var{z} must be real and non-negative.\n\ \n\ @seealso{gamma, gammainc, gammaln}\n\ @end deftypefn") { octave_value retval; const octave_idx_type nargin = args.length (); if (nargin < 1 || nargin > 2) { print_usage (); return retval; } const octave_value oct_z = (nargin == 1) ? args(0) : args(1); const octave_idx_type k = (nargin == 1) ? 0 : args(0).idx_type_value (); if (error_state || k < 0) { error ("psi: K must be a non-negative integer"); return retval; } else 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++ = psi (*zv++); \ \ retval = psi_z; \ } if (oct_z.is_complex_type ()) { 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.is_real_type ()) { error ("psi: Z must be real value for polygamma (K > 0)"); return retval; } #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)"); \ return retval; \ } \ *psi_zv++ = 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 = [-10:.1:-.1 .1:.1:20]; # 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) %!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) %!assert (psi (-1.573498473162390458778286043690434612655040859116846), 0, eps) %!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 = [-10:.1:-.1 .1:.1:20]; # 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) ## 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 a non-negative integer> 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) */