Type:
Class

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a m-by-m permutation matrix P so that L*U = P*A. If m < n, then L is m-by-m and U is m-by-n.

The LUP decomposition with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if singular? returns true.

det

det() Instance Public methods Returns the determinant of A, calculated

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singular?

singular?() Instance Public methods Returns true if U

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l

l() Instance Public methods

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u

u() Instance Public methods Returns the upper triangular factor U

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determinant

determinant() Instance Public methods Alias for:

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new

new(a) Class Public methods

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to_ary

to_ary() Instance Public methods Returns L, U, P

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solve

solve(b) Instance Public methods Returns m so that A*m =

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to_a

to_a() Instance Public methods Alias for:

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p

p() Instance Public methods Returns the permutation matrix P

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