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Calling Sequence
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lu(X, output=L)
lu(X, output=LU)
lu(X, output=LUP)
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Parameters
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X
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MapleMatrix or MatlabMatrix
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output
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specify the form of the output (optional)
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L
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return combined upper and lower decomposed matrices
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LU
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return lower L and upper U decomposed matrices
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LUP
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return L, U, and permutation matrix P
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Description
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The lu command computes the LU decomposition of a MapleMatrix or MatlabMatrix in MATLAB®, where , when output=LUP, and , when output=LU.
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Matrix X is expressed as the product of two triangular matrices: L, a permutation of a lower triangular matrix, and U, a permutation of an upper triangular matrix.
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The LU decomposition for a MatlabMatrix is executed as a string. The matrix must be defined in the MATLAB® session.
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The output parameter L returns a combined lower and upper triangular matrix such that the diagonal and above are the entries of U, and the entries below the diagonal are the entries of L (with all diagonal entries for L implicitly having the value 1). As a matrix equation, this can be described as .
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Note that for MATLAB® version 5.2, the entries of L are stored with the opposite sign, so as a matrix equation this can be described as .
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The output parameter LU returns the lower and upper triangular matrices. This is the default if no output parameter is specified.
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The output parameter LUP returns matrices L and U with a permutation matrix P.
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Examples
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Define the Maple matrix
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The LU decomposition of this MapleMatrix returning L and U is computed as
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L, U :=
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[0.500000000000000000 , -0.517241379310344750 , 0.115789473684210484 , 1. ]
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[0.166666666666666657 , 1. , 0. , 0. ]
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[ 1. , 0. , 0. , 0. ]
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[0.500000000000000000 , -0.103448275862068950 , 1. , 0. ],
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[ 6. , 7. , 8. , 1. ]
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[ ]
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[ 0. , 4.83333333333333392 , 2.66666666666666695 , 1.83333333333333326]
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[ ]
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[ 0. , 0. , 3.27586206896551735 , 2.68965517241379314]
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[ ]
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[ 0. , 0. , 0. , 5.13684210526315788]
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The LU decomposition of this MapleMatrix returning both L and U combined is computed as follows. Since the variable L is defined, the L must have quotation marks around it in the procedure call.
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[ 6. , 7. , 8. , 1. ]
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[0.166666666666666657 , 4.83333333333333392 , 2.66666666666666695 , 1.83333333333333326]
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[0.500000000000000000 , -0.103448275862068950 , 3.27586206896551735 , 2.68965517241379314]
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[0.500000000000000000 , -0.517241379310344750 , 0.115789473684210484 , 5.13684210526315788]
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The same decomposition including the permutation matrix P is
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Verify correctness using MATLAB®.
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>
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>
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