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/* PSPP - a program for statistical analysis.
Copyright (C) 2005 Free Software Foundation, Inc.
This program 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.
This program 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 this program. If not, see <http://www.gnu.org/licenses/>. */
#ifndef SWEEP_H
#define SWEEP_H
/*
Find the least-squares estimate of b for the linear model:
Y = Xb + Z
where Y is an n-by-1 column vector, X is an n-by-p matrix of
independent variables, b is a p-by-1 vector of regression coefficients,
and Z is an n-by-1 normally-distributed random vector with independent
identically distributed components with mean 0.
This estimate is found via the sweep operator, which is a modification
of Gauss-Jordan pivoting.
References:
Matrix Computations, third edition. GH Golub and CF Van Loan.
The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
Numerical Analysis for Statisticians. K Lange. Springer. 1999.
ISBN 0-387-94979-8.
Numerical Linear Algebra for Applications in Statistics. JE Gentle.
Springer. 1998. ISBN 0-387-98542-5.
*/
/*
The matrix A will be overwritten. In ordinary uses of the sweep
operator, A will be the matrix
__ __
|X'X X'Y|
| |
|Y'X Y'Y|
-- --
X refers to the design matrix and Y to the vector of dependent
observations. reg_sweep sweeps on the diagonal elements of
X'X.
The matrix A is assumed to be symmetric, so the sweep operation is
performed only for the upper triangle of A.
*/
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_math.h>
int reg_sweep (gsl_matrix *, int);
#endif
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