octave-nkf: scripts/statistics/base/ols.m annotate

annotate scripts/statistics/base/ols.m @ 14570:d07d96e53612 stable

seconds after the minute can be 0-60, not 0-61 * system.txi (Timing Utilities): Correct possible values for number of seconds in time structures. From Rafael Arndt <rafaelarndt@gmail.com>.

author	John W. Eaton <jwe@octave.org>
date	Tue, 17 Apr 2012 14:42:49 -0400
parents	2cd56a5e3a66
children	f3d52523cde1

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 13824 diff changeset	1 ## Copyright (C) 1996-2012 John W. Eaton
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	2 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	3 ## This file is part of Octave.
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	4 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	6 ## 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	7 ## 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	8 ## your option) any later version.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	9 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	13 ## General Public License for more details.
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	14 ##
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	15 ## 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	16 ## 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	17 ## <http://www.gnu.org/licenses/>.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	18
3458 d25bc039237b [project @ 2000-01-19 09:36:14 by jwe] jwe parents: 3456 diff changeset	19 ## -- texinfo --
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	20 ## @deftypefn {Function File} {[@var{beta}, @var{sigma}, @var{r}] =} ols (@var{y}, @var{x})
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	21 ## Ordinary least squares estimation for the multivariate model
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	22 ## @tex
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	23 ## $y = x b + e$
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	24 ## with
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	25 ## $\bar{e} = 0$, and cov(vec($e$)) = kron ($s, I$)
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	26 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	27 ## @ifnottex
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	28 ## @w{@math{y = x*b + e}} with
3499 3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3458 diff changeset	29 ## @math{mean (e) = 0} and @math{cov (vec (e)) = kron (s, I)}.
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	30 ## @end ifnottex
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	31 ## where
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	32 ## @tex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	33 ## $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix,
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	34 ## $b$ is a $k \times p$ matrix, and $e$ is a $t \times p$ matrix.
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	35 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	36 ## @ifnottex
3499 3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3458 diff changeset	37 ## @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by
3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3458 diff changeset	38 ## @math{k} matrix, @math{b} is a @math{k} by @math{p} matrix, and
3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3458 diff changeset	39 ## @math{e} is a @math{t} by @math{p} matrix.
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	40 ## @end ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	41 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	42 ## Each row of @var{y} and @var{x} is an observation and each column a
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	43 ## variable.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	44 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	45 ## The return values @var{beta}, @var{sigma}, and @var{r} are defined as
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	46 ## follows.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	47 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	48 ## @table @var
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	49 ## @item beta
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	50 ## The OLS estimator for @math{b}.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	51 ## @tex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	52 ## $beta$ is calculated directly via $(x^Tx)^{-1} x^T y$ if the matrix $x^Tx$ is
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	53 ## of full rank.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	54 ## @end tex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	55 ## @ifnottex
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	56 ## @var{beta} is calculated directly via @code{inv (x'x) x' * y} if the
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	57 ## matrix @code{x'*x} is of full rank.
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	58 ## @end ifnottex
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	59 ## Otherwise, @code{@var{beta} = pinv (@var{x}) * @var{y}} where
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	60 ## @code{pinv (@var{x})} denotes the pseudoinverse of @var{x}.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	61 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	62 ## @item sigma
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	63 ## The OLS estimator for the matrix @var{s},
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	64 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	65 ## @example
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	66 ## @group
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	67 ## @var{sigma} = (@var{y}-@var{x}*@var{beta})'
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	68 ## * (@var{y}-@var{x}*@var{beta})
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	69 ## / (@var{t}-rank(@var{x}))
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	70 ## @end group
a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	71 ## @end example
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3368 diff changeset	72 ##
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	73 ## @item r
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	74 ## The matrix of OLS residuals, @code{@var{r} = @var{y} - @var{x}*@var{beta}}.
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	75 ## @end table
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	76 ## @seealso{gls, pinv}
3368 a4cd1e9d9962 [project @ 1999-11-20 17:22:48 by jwe] jwe parents: 3200 diff changeset	77 ## @end deftypefn
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	78
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	79 ## Author: Teresa Twaroch <twaroch@ci.tuwien.ac.at>
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	80 ## Created: May 1993
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	81 ## Adapted-By: jwe
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	82
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	83 function [beta, sigma, r] = ols (y, x)
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	84
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	85 if (nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5307 diff changeset	86 print_usage ();
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	87 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	88
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	89 if (! (isnumeric (x) && isnumeric (y)))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	90 error ("ols: X and Y must be numeric matrices or vectors");
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	91 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	92
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	93 if (ndims (x) != 2 \|\| ndims (y) != 2)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	94 error ("ols: X and Y must be 2-D matrices or vectors");
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	95 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	96
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	97 [nr, nc] = size (x);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	98 [ry, cy] = size (y);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	99 if (nr != ry)
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	100 error ("ols: number of rows of X and Y must be equal");
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	101 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	102
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	103 if (isinteger (x))
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	104 x = double (x);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	105 endif
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	106 if (isinteger (y))
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	107 y = double (y);
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	108 endif
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	109
6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	110 ## Start of algorithm
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	111 z = x' * x;
13823 94a37dae80a9 Use a cheaper Cholesky decomposition than a rank() svd in ols.m Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 12656 diff changeset	112 [u, p] = chol (z);
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	113
13823 94a37dae80a9 Use a cheaper Cholesky decomposition than a rank() svd in ols.m Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 12656 diff changeset	114 if (p)
94a37dae80a9 Use a cheaper Cholesky decomposition than a rank() svd in ols.m Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 12656 diff changeset	115 beta = pinv (x) * y;
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	116 else
13824 aa0cba2256f4 Group the ols matrix operation in a smarter way Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 13823 diff changeset	117 beta = u \ (u' \ (x' * y));
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	118 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	119
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	120 if (isargout (2) \|\| isargout (3))
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	121 r = y - x * beta;
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	122 endif
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	123 if (isargout (2))
14341 71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	124
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	125 ## z is of full rank, avoid the SVD in rnk
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	126 if (p == 0)
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	127 rnk = columns (z);
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	128 else
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	129 rnk = rank (z);
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	130 endif
71efccec5936 * ols.m: Compute rank if needed. Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 14138 diff changeset	131
12547 17997376291b Fix variable name clash in ols.m Michael Creel <michael.creel@uab.es> parents: 11587 diff changeset	132 sigma = r' * r / (nr - rnk);
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	133 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	134
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	135 endfunction
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	136
12656 6b2f14af2360 Overhaul functions in statistics/base directory. Rik <octave@nomad.inbox5.com> parents: 12547 diff changeset	137
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	138 %!test
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	139 %! x = [1:5]';
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	140 %! y = 3*x + 2;
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	141 %! x = [x, ones(5,1)];
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	142 %! assert (ols(y,x), [3; 2], 50*eps)
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	143
14342 2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	144 %!test
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	145 %! x = [1, 2; 3, 4];
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	146 %! y = [1; 2];
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	147 %! [b, s, r] = ols (x, y);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	148 %! assert (b, [1.4, 2], 2*eps);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	149 %! assert (s, [0.2, 0; 0, 0], 2*eps);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	150 %! assert (r, [-0.4, 0; 0.2, 0], 2*eps);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	151
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	152 %!test
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	153 %! x = [1, 2; 3, 4];
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	154 %! y = [1; 2];
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	155 %! [b, s] = ols (x, y);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	156 %! assert (b, [1.4, 2], 2*eps);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	157 %! assert (s, [0.2, 0; 0, 0], 2*eps);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	158
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	159 %!test
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	160 %! x = [1, 2; 3, 4];
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	161 %! y = [1; 2];
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	162 %! b = ols (x, y);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	163 %! assert (b, [1.4, 2], 2*eps);
2cd56a5e3a66 new tests John W. Eaton <jwe@octave.org> parents: 14341 diff changeset	164
11436 e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	165 %% Test input validation
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	166 %!error ols ();
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	167 %!error ols (1);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	168 %!error ols (1, 2, 3);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	169 %!error ols ([true, true], [1, 2]);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	170 %!error ols ([1, 2], [true, true]);
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	171 %!error ols (ones (2,2,2), ones (2,2));
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	172 %!error ols (ones (2,2), ones (2,2,2));
e151e23f73bc Overhaul base statistics functions and documentation of same. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	173 %!error ols (ones(1,2), ones(2,2));

Mercurial > hg > octave-nkf

annotate scripts/statistics/base/ols.m @ 14570:d07d96e53612 stable