qccmatrixorthogonalize.3

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.TH QCCMATRIXORTHOGONALIZE 3 "QCCPACK" ""
.SH NAME
QccMatrixOrthogonalize
\- generate orthonormal basis for range of matrix
.SH SYNOPSIS
.B #include "libQccPack.h"
.sp
.BI "int QccMatrixOrthogonalize(const QccMatrix " matrix1 ", int " num_rows ", i " num_cols ", QccMatrix " matrix2 ", int *" num_cols2 );
.SH DESCRIPTION
.B QccMatrixOrthogonalize()
creates an orthonormal basis for the range of
.IR matrix1
which is a matrix of size
.IR num_rows
x
.IR num_cols .
This orthonormal basis is returned as the columns of
.IR matrix2 ;
that is, the columns of
.IR matrix2
span the same space as the columns of
.IR matrix1 .
.IR matrix2
must be allocated to be of size
.IR num_rows
x
.IR num_cols
prior to calling
.BR QccMatrixOrthogonalize() .
.LP
The number of basis vectors in the orthogonal basis is returned as
.IR num_cols2 .
If
.IR matrix1
is rank-deficient, then 
.IR num_cols2
will be less than
.IR num_cols .
In this case,
.IR num_cols " - " num_cols2
columns of
.IR matrix2
will be zero.
.LP
.BR QccMatrixOrthogonalize()
is implemented via a call to
.BR QccMatrixSVD (3)
to generate the singular value decomposition of
.IR matrix1 .
Then,
the left singular vectors corresponding to nonzero
singular values are returned in
.IR matrix2 .
.SH "SEE ALSO"
.BR QccMatrixSVD (3),
.BR QccMatrix (3),
.BR QccPack (3)
.SH AUTHOR
Copyright (C) 1997-2009  James E. Fowler
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