lu

Perform LU decomposition. More...

Functions
AFAPI void	lu (array &out, array &pivot, const array &in, const bool is_lapack_piv=true)
	C++ Interface for LU decomposition in packed format. More...
AFAPI void	lu (array &lower, array &upper, array &pivot, const array &in)
	C++ Interface for LU decomposition. More...
AFAPI void	luInPlace (array &pivot, array &in, const bool is_lapack_piv=true)
	C++ Interface for in place LU decomposition. More...
AFAPI af_err	af_lu (af_array *lower, af_array *upper, af_array *pivot, const af_array in)
	C Interface for LU decomposition. More...
AFAPI af_err	af_lu_inplace (af_array *pivot, af_array in, const bool is_lapack_piv)
	C Interface for in place LU decomposition. More...

Detailed Description

Perform LU decomposition.

This function decomposes input matrix A into a lower triangle L, an upper triangle U such that

\(A = L * U\)

For stability, a permutation array P is also used to modify the formula in the following manner.

\(A(P, span) = L * U\)

This operation can be performed in ArrayFire using the following code snippet.

    af::array l, u, pivot;
    af::lu(l, u, pivot, a_orig);

The permuted version of the original matrix can be reconstructed using the following snippet.

    af::array a_recon = af::matmul(l, u);
    af::array a_perm = a_orig(pivot, af::span);

The sample output for these operations can be seen below.

a_orig [3 3 1 1]
    0.0000     3.0000     6.0000
    1.0000     4.0000     7.0000
    2.0000     5.0000     8.0000

l [3 3 1 1]
    1.0000     0.0000     0.0000
    0.0000     1.0000     0.0000
    0.5000     0.5000     1.0000

u [3 3 1 1]
    2.0000     5.0000     8.0000
    0.0000     3.0000     6.0000
    0.0000     0.0000     0.0000

pivot [3 1 1 1]
         2
         0
         1

a_recon [3 3 1 1]
    2.0000     5.0000     8.0000
    0.0000     3.0000     6.0000
    1.0000     4.0000     7.0000

a_perm [3 3 1 1]
    2.0000     5.0000     8.0000
    0.0000     3.0000     6.0000
    1.0000     4.0000     7.0000

When memory is a concern, users can perform the LU decomposition in place as shown below.

    af::array out = a_orig.copy();
    af::array pivot2;
    af::luInPlace(pivot2, out, false);

The lower and upper triangle matrices can be obtained if necessary in the following manner.

    af::array l2 = lower(out,  true);
    af::array u2 = upper(out, false);

LU decompositions has many applications including solving a system of linear equations. Check af::solveLU fore more information.

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Function Documentation

AFAPI af_err af_lu	(	af_array *	lower,
		af_array *	upper,
		af_array *	pivot,
		const af_array	in
	)

C Interface for LU decomposition.

Parameters

[out]	lower	will contain the lower triangular matrix of the LU decomposition
[out]	upper	will contain the upper triangular matrix of the LU decomposition
[out]	pivot	will contain the permutation indices to map the input to the decomposition
[in]	in	is the input matrix

AFAPI af_err af_lu_inplace	(	af_array *	pivot,
		af_array	in,
		const bool	is_lapack_piv
	)

C Interface for in place LU decomposition.

Parameters

[out]	pivot	will contain the permutation indices to map the input to the decomposition
[in,out]	in	contains the input on entry, the packed LU decomposition on exit
[in]	is_lapack_piv	specifies if the pivot is returned in original LAPACK compliant format

AFAPI void af::lu	(	array &	out,
		array &	pivot,
		const array &	in,
		const bool	is_lapack_piv = true
	)

C++ Interface for LU decomposition in packed format.

Parameters

[out]	out	is the output array containing the packed LU decomposition
[out]	pivot	will contain the permutation indices to map the input to the decomposition
[in]	in	is the input matrix
[in]	is_lapack_piv	specifies if the pivot is returned in original LAPACK compliant format

Note

This function is not supported in GFOR

Examples:

lin_algebra/lu.cpp.

AFAPI void af::lu	(	array &	lower,
		array &	upper,
		array &	pivot,
		const array &	in
	)

C++ Interface for LU decomposition.

Parameters

[out]	lower	will contain the lower triangular matrix of the LU decomposition
[out]	upper	will contain the upper triangular matrix of the LU decomposition
[out]	pivot	will contain the permutation indices to map the input to the decomposition
[in]	in	is the input matrix

Note

This function is not supported in GFOR

AFAPI void af::luInPlace	(	array &	pivot,
		array &	in,
		const bool	is_lapack_piv = true
	)

C++ Interface for in place LU decomposition.

Parameters

[out]	pivot	will contain the permutation indices to map the input to the decomposition
[in,out]	in	contains the input on entry, the packed LU decomposition on exit
[in]	is_lapack_piv	specifies if the pivot is returned in original LAPACK compliant format

Note

This function is not supported in GFOR

Examples:

lin_algebra/lu.cpp.