im_lu_decomp, im_lu_solve - Solve SLEs by LU decomposition
DOUBLEMASK *im_lu_decomp( const DOUBLEMASK *mat, const char *name );
int im_lu_solve( const DOUBLEMASK *lu, double *vec );
im_lu_decomp(3) allocates a DOUBLEMASK representing the LU
decomposition of the matrix in DOUBLEMASK *mat, and gives it the
filename member name.
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 *lu.
Input vector b is in *vec and is overwritten with output vector x.
DOUBLEMASK *lu is unaltered by im_matinv(3), and can be used again to
solve a different SLE containing matrix A.
The scale and offset members of *mat are ignored. If they are not set
to 1.0 and zero respectively, you must first call im_norm_dmask(3).
To understand the decomposition A=LU, see Press et al. (1992). For the
exact format used to represent the matrices L and U in *lu, see the
acompanying source code.
If matrix *mat is singular (non-invertible), or close to singular then
im_lu_decomp(3) will fail, calling im_error(3).
im_lu_decomp(3) returns a pointer to the new DOUBLEMASK, or NULL on
im_lu_solve(3) always returns zero, unless lu was not returned by
im_lu_decomp(3), when it returns -1.
im_create_dmask(3), im_free_dmask(3), im_norm_dmask(3), im_matinv(3)
PRESS, W. et al, 1992. Numerical Recipies in C; The Art of Scientific
Computing, 2nd ed. Cambridge: Cambridge University Press, pp. 43-50.
[Available online: http://www.library.cornell.edu/nr/bookcpdf.html
Copyright 2006, Tom Vajzovic.
18 September 2006