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view doc/interpreter/optim.texi @ 2689:8c7955a8d49f
[project @ 1997-02-18 09:06:10 by jwe]
author | jwe |
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date | Tue, 18 Feb 1997 09:09:12 +0000 |
parents | 18192eea4973 |
children | 91589ab98e37 |
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@c Copyright (C) 1996, 1997 John W. Eaton @c This is part of the Octave manual. @c For copying conditions, see the file gpl.texi. @node Optimization, Statistics, Differential Equations, Top @chapter Optimization @menu * Quadratic Programming:: * Nonlinear Programming:: * Linear Least Squares:: @end menu @c @cindex linear programming @cindex quadratic programming @cindex nonlinear programming @cindex optimization @cindex LP @cindex QP @cindex NLP @node Quadratic Programming, Nonlinear Programming, Optimization, Optimization @section Quadratic Programming @deftypefn {Loadable Function} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qpsol (@var{x}, @var{H}, @var{c}, @var{lb}, @var{ub}, @var{lb}, @var{A}, @var{ub}) Solve quadratic programs using Gill and Murray's @sc{Qpsol}. Because @sc{Qpsol} is not freely redistributable, this function is only available if you have obtained your own copy of @sc{Qpsol}. @xref{Installation}. @end deftypefn @deftypefn {Loadable Function} {} qpsol_options (@var{opt}, @var{val}) When called with two arguments, this function allows you set options parameters for the function @code{qpsol}. Given one argument, @code{qpsol_options} returns the value of the corresponding option. If no arguments are supplied, the names of all the available options and their current values are displayed. @end deftypefn @node Nonlinear Programming, Linear Least Squares, Quadratic Programming, Optimization @section Nonlinear Programming @ignore @deftypefn {Loadable Function} {} fsqp () @end deftypefn @deftypefn {Loadable Function} {} fsqp_options (@var{opt}, @var{val}) When called with two arguments, this function allows you set options parameters for the function @code{fsqp}. Given one argument, @code{fsqp_options} returns the value of the corresponding option. If no arguments are supplied, the names of all the available options and their current values are displayed. @end deftypefn Sorry, this hasn't been implemented yet. @end ignore @deftypefn {Loadable Function} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} npsol (@var{x}, @var{phi}, @var{lb}, @var{ub}, @var{lb}, @var{A}, @var{ub}, @var{lb}, @var{g}, @var{ub}) Solve nonlinear programs using Gill and Murray's @sc{Npsol}. Because @sc{Npsol} is not freely redistributable, this function is only available if you have obtained your own copy of @sc{Npsol}. @xref{Installation}. The second argument is a string containing the name of the objective function to call. The objective function must be of the form @example y = phi (x) @end example @noindent where x is a vector and y is a scalar. @end deftypefn @deftypefn {Loadable Function} {} npsol_options (@var{opt}, @var{val}) When called with two arguments, this function allows you set options parameters for the function @code{npsol}. Given one argument, @code{npsol_options} returns the value of the corresponding option. If no arguments are supplied, the names of all the available options and their current values are displayed. @end deftypefn @node Linear Least Squares, , Nonlinear Programming, Optimization @section Linear Least Squares @deftypefn {Function File} {[@var{beta}, @var{v}, @var{r}] =} gls (@var{y}, @var{x}, @var{o}) Generalized least squares estimation for the multivariate model @iftex @tex $y = x b + e$ with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$, @end tex @end iftex @ifinfo @code{@var{y} = @var{x} * @var{b} + @var{e}} with @code{mean (@var{e}) = 0} and @code{cov (vec (@var{e})) = (@var{s}^2)*@var{o}}, @end ifinfo where @iftex @tex $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, $b$ is a $k \times p$ matrix, $e$ is a $t \times p$ matrix, and $o$ is a $tp \times tp$ matrix. @end tex @end iftex @ifinfo @var{Y} is a @var{T} by @var{p} matrix, @var{X} is a @var{T} by @var{k} matrix, @var{B} is a @var{k} by @var{p} matrix, @var{E} is a @var{T} by @var{p} matrix, and @var{O} is a @var{T}@var{p} by @var{T}@var{p} matrix. @end ifinfo @noindent Each row of Y and X is an observation and each column a variable. The return values @var{beta}, @var{v}, and @var{r} are defined as follows. @table @var @item beta The GLS estimator for @var{b}. @item v The GLS estimator for @code{@var{s}^2}. @item r The matrix of GLS residuals, @code{@var{r} = @var{y} - @var{x} * @var{beta}}. @end table @end deftypefn @deftypefn {Function File} {[@var{beta}, @var{sigma}, @var{r}] =} ols (@var{y}, @var{x}) Ordinary least squares estimation for the multivariate model @iftex @tex $y = x b + e$ with $\bar{e} = 0$, and cov(vec($e$)) = kron ($s, I$) @end tex @end iftex @ifinfo @code{@var{y} = @var{x}*@var{b} + @var{e}} with @code{mean (@var{e}) = 0} and @code{cov (vec (@var{e})) = kron (@var{s}, @var{I})}. @end ifinfo where @iftex @tex $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, $b$ is a $k \times p$ matrix, and $e$ is a $t \times p$ matrix. @end tex @end iftex @ifinfo @var{y} is a @var{t} by @var{p} matrix, @var{X} is a @var{t} by @var{k} matrix, @var{B} is a @var{k} by @var{p} matrix, and @var{e} is a @var{t} by @var{p} matrix. @end ifinfo Each row of @var{y} and @var{x} is an observation and each column a variable. The return values @var{beta}, @var{sigma}, and @var{r} are defined as follows. @table @var @item beta The OLS estimator for @var{b}, @code{@var{beta} = pinv (@var{x}) * @var{y}}, where @code{pinv (@var{x})} denotes the pseudoinverse of @var{x}. @item sigma The OLS estimator for the matrix @var{s}, @example @group @var{sigma} = (@var{y}-@var{x}*@var{beta})' * (@var{y}-@var{x}*@var{beta}) / (@var{t}-rank(@var{x})) @end group @end example @item r The matrix of OLS residuals, @code{@var{r} = @var{y} - @var{x} * @var{beta}}. @end table @end deftypefn