| .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 |
| |
