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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/LU-decomposition/Maxima/lu-decomposition.maxima Normal file
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/* LU decomposition is built-in */
a: hilbert_matrix(4)$
/* LU in "packed" form */
lup: lu_factor(a);
/* [matrix([1, 1/2, 1/3, 1/4 ],
[1/2, 1/12, 1/12, 3/40 ],
[1/3, 1, 1/180, 1/120 ],
[1/4, 9/10, 3/2, 1/2800]),
[1, 2, 3, 4], generalring] */
/* extract actual factors */
get_lu_factors(lup);
/* [matrix([1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]),
matrix([1, 0, 0, 0],
[1/2, 1, 0, 0],
[1/3, 1, 1, 0],
[1/4, 9/10, 3/2, 1]),
matrix([1, 1/2, 1/3, 1/4 ],
[0, 1/12, 1/12, 3/40 ],
[0, 0, 1/180, 1/120 ],
[0, 0, 0, 1/2800])
] */
/* solve for a given right-hand side */
lu_backsub(lup, transpose([1, 1, -1, -1]));
/* matrix([-204], [2100], [-4740], [2940]) */