octave: scripts/statistics/distributions/discrete

annotate scripts/statistics/distributions/discrete_inv.m @ 13171:19b9f17d22af

Overhaul of statistical distribution functions Support class "single" 75% reduction in memory usage More Matlab compatibility for corner cases * betacdf.m, betainv.m, betapdf.m, betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m, cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m, chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m, expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m, gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m, hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m, laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m, logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m, lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m, norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m, poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m, tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m, unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m, wblrnd.m: Return "single" outputs for "single" inputs, Use logical indexing rather than find() for 75% memory savings, Add tests for all functions, Use consistent documentation across all functions, More Matlab compatibilitcy for corner cases.

author	Rik <octave@nomad.inbox5.com>
date	Tue, 20 Sep 2011 12:13:13 -0700
parents	fd0a3ac60b0e
children	72c96de7a403

rev	line source
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	1 ## Copyright (C) 2011 Rik Wehbring
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 11472 diff changeset	2 ## Copyright (C) 1996-2011 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	3 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	4 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	5 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 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: 6046 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: 6046 diff changeset	9 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	10 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	14 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	15 ##
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 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: 6046 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: 6046 diff changeset	18 ## <http://www.gnu.org/licenses/>.
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	19
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	20 ## -- texinfo --
434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	21 ## @deftypefn {Function File} {} discrete_inv (@var{x}, @var{v}, @var{p})
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	22 ## For each element of @var{x}, compute the quantile (the inverse of
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	23 ## the CDF) at @var{x} of the univariate distribution which assumes the
434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	24 ## values in @var{v} with probabilities @var{p}.
434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	25 ## @end deftypefn
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	26
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	28 ## Description: Quantile function of a discrete distribution
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	29
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	30 function inv = discrete_inv (x, v, p)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	31
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	32 if (nargin != 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	33 print_usage ();
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	34 endif
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	35
4030 22bd65326ec1 [project @ 2002-08-09 18:58:13 by jwe] jwe parents: 3922 diff changeset	36 if (! isvector (v))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10524 diff changeset	37 error ("discrete_inv: V must be a vector");
4030 22bd65326ec1 [project @ 2002-08-09 18:58:13 by jwe] jwe parents: 3922 diff changeset	38 elseif (! isvector (p) \|\| (length (p) != length (v)))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10524 diff changeset	39 error ("discrete_inv: P must be a vector with length (V) elements");
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	40 elseif (any (isnan (p)))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	41 error ("discrete_rnd: P must not have any NaN elements");
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	42 elseif (! (all (p >= 0) && any (p)))
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	43 error ("discrete_inv: P must be a nonzero, non-negative vector");
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	44 endif
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	45
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	46 if (isa (x, "single") \|\| isa (v, "single") \|\| isa (p, "single"));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	47 inv = NaN (size (x), "single");
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	48 else
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	49 inv = NaN (size (x));
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	50 endif
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	51
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	52 ## FIXME: This isn't elegant. But cumsum and lookup together produce
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	53 ## different results when called with a single or a double.
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	54 if (isa (p, "single"));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	55 p = double (p);
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	56 endif
4778 567c8e2d2438 [project @ 2004-02-17 00:35:43 by jwe] jwe parents: 4030 diff changeset	57
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	58 [v, idx] = sort (v);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	59 p = cumsum (p(idx)(:)) / sum (p); # Reshape and normalize probability vector
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	60
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	61 k = (x == 0);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	62 inv(k) = v(1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	63
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	64 k = (x == 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	65 inv(k) = v(end);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	66
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	67 k = (x > 0) & (x < 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	68 inv(k) = v(length (p) - lookup (sort (p, "descend"), x(k)) + 1);
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	69
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	70 endfunction
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	71
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	72
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	73 %!shared x,v,p,y
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	74 %! x = [-1 0 0.1 0.5 1 2];
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	75 %! v = 0.1:0.2:1.9;
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	76 %! p = 1/length(v) * ones(1, length(v));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	77 %! y = [NaN v(1) v(1) v(end/2) v(end) NaN];
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	78 %!assert(discrete_inv ([x, NaN], v, p), [y, NaN], eps);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	79
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	80 %% Test class of input preserved
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	81 %!assert(discrete_inv (single([x, NaN]), v, p), single([y, NaN]), eps("single"));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	82 %!assert(discrete_inv ([x, NaN], single(v), p), single([y, NaN]), eps("single"));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	83 %!assert(discrete_inv ([x, NaN], v, single(p)), single([y, NaN]), eps("single"));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	84
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	85 %% Test input validation
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	86 %!error discrete_inv ()
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	87 %!error discrete_inv (1)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	88 %!error discrete_inv (1,2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	89 %!error discrete_inv (1,2,3,4)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	90 %!error discrete_inv (1, ones(2), ones(2,1))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	91 %!error discrete_inv (1, ones(2,1), ones(1,1))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	92 %!error discrete_inv (1, ones(2,1), [1 NaN])
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	93 %!error discrete_inv (1, ones(2,1), [1 -1])
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	94 %!error discrete_inv (1, ones(2,1), [0 0])
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	95

Mercurial > octave

annotate scripts/statistics/distributions/discrete_inv.m @ 13171:19b9f17d22af