--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc/interpreter/optim.txi	Tue Oct 19 10:08:42 1999 +0000
@@ -0,0 +1,128 @@
+@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
+
+@node Nonlinear Programming, Linear Least Squares, Quadratic Programming, Optimization
+@section Nonlinear Programming
+
+@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