76 lines
1.9 KiB
Groff
76 lines
1.9 KiB
Groff
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.TH IM_LU_DECOMP 3 "18 September 2006"
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.SH NAME
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im_lu_decomp, im_lu_solve \- Solve SLEs by LU decomposition
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.SH SYNOPSIS
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.nf
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.B #include <vips/vips.h>
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.sp
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.BI "DOUBLEMASK *im_lu_decomp( const DOUBLEMASK " "*mat" ", const char " "*name" " );
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.br
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.BI "int im_lu_solve( const DOUBLEMASK " "*lu" ", double " "*vec" " );
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.fi
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.SH DESCRIPTION
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.B im_lu_decomp(3)
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allocates a DOUBLEMASK representing the LU decomposition of the matrix in
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DOUBLEMASK
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.IR "*mat" ",
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and gives it the filename member
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.IR "name" ".
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.PP
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.B im_lu_solve(3)
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solves the system of linear equations (SLE) Ax=b, where matrix A has already
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been decomposed into LU form in DOUBLEMASK
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.IR "*lu" ".
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Input vector b is in
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.I *vec
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and is overwritten with output vector x.
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.PP
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DOUBLEMASK
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.I *lu
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is unaltered by
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.BR "im_matinv(3)" ",
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and can be used again to solve a different SLE containing matrix A.
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.SH NOTES
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The scale and offset members of
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.I *mat
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are ignored. If they are not set to 1.0 and zero respectively, you must first
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call
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.BR "im_norm_dmask(3)" ".
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.PP
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To understand the decomposition A=LU, see Press et al. (1992). For the exact
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format used to represent the matrices L and U in
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.IR "*lu" ",
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see the acompanying source code.
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.SH ERRORS
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If matrix
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.I *mat
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is singular (non-invertible), or close to singular then
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.B im_lu_decomp(3)
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will fail, calling
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.BR "im_error(3)" ".
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.SH RETURN VALUE
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.B im_lu_decomp(3)
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returns a pointer to the new DOUBLEMASK, or NULL on error.
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.PP
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.B im_lu_solve(3)
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always returns zero, unless
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.I lu
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was not returned by
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.BR "im_lu_decomp(3)" ",
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when it returns -1.
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.SH SEE ALSO
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im_create_dmask(3), im_free_dmask(3), im_norm_dmask(3), im_matinv(3)
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.SH REFERENCES
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PRESS, W. et al, 1992. Numerical Recipies in C; The Art of Scientific
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Computing, 2nd ed. Cambridge: Cambridge University Press, pp. 43-50.
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.PP
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[Available online:
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http://www.library.cornell.edu/nr/bookcpdf.html accessed 2006-09-19]
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.SH COPYRIGHT
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.br
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Copyright 2006, Tom Vajzovic.
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.SH AUTHOR
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Tom Vajzovic
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