.TH IM_LU_DECOMP 3 "18 September 2006"
.SH NAME
 im_lu_decomp, im_lu_solve \- Solve SLEs by LU decomposition
.SH SYNOPSIS
.nf
.B #include <vips/vips.h>
.sp
.BI "DOUBLEMASK *im_lu_decomp( const DOUBLEMASK " "*mat" ", const char " "*name" " );
.br

.BI "int im_lu_solve( const DOUBLEMASK " "*lu" ", double " "*vec" " );
.fi
.SH DESCRIPTION
.B im_lu_decomp(3)
allocates a DOUBLEMASK representing the LU decomposition of the matrix in 
DOUBLEMASK 
.IR "*mat" ", 
and gives it the filename member
.IR "name" ".
.PP
.B im_lu_solve(3)
solves the system of linear equations (SLE) Ax=b, where matrix A has already
been decomposed into LU form in DOUBLEMASK 
.IR "*lu" ".
Input vector b is in
.I *vec
and is overwritten with output vector x. 
.PP
DOUBLEMASK 
.I *lu
is unaltered by 
.BR "im_matinv(3)" ",
and can be used again to solve a different SLE containing matrix A.
.SH NOTES
The scale and offset members of 
.I *mat
are ignored.  If they are not set to 1.0 and zero respectively, you must first
call 
.BR "im_norm_dmask(3)" ".
.PP
To understand the decomposition A=LU, see Press et al. (1992).  For the exact 
format used to represent the matrices L and U in 
.IR "*lu" ",
see the acompanying source code.
.SH ERRORS
If matrix
.I *mat
is singular (non-invertible), or close to singular then
.B im_lu_decomp(3)
will fail, calling
.BR "im_error(3)" ".
.SH RETURN VALUE
.B im_lu_decomp(3)
returns a pointer to the new DOUBLEMASK, or NULL on error.
.PP
.B im_lu_solve(3)
always returns zero, unless 
.I lu
was not returned by 
.BR "im_lu_decomp(3)" ",
when it returns -1.
.SH SEE ALSO
im_create_dmask(3), im_free_dmask(3), im_norm_dmask(3), im_matinv(3)
.SH REFERENCES
PRESS, W. et al, 1992.  Numerical Recipies in C; The Art of Scientific 
Computing, 2nd ed.  Cambridge: Cambridge University Press, pp. 43-50.
.PP
[Available online: 
http://www.library.cornell.edu/nr/bookcpdf.html accessed 2006-09-19]
.SH COPYRIGHT
.br
Copyright 2006, Tom Vajzovic.
.SH AUTHOR
Tom Vajzovic