cholesky

Perform Cholesky decomposition. More...

Functions
AFAPI int	cholesky (array &out, const array &in, const bool is_upper=true)
	C++ Interface for cholesky decomposition. More...
AFAPI int	choleskyInPlace (array &in, const bool is_upper=true)
	C++ Interface for in place cholesky decomposition. More...
AFAPI af_err	af_cholesky (af_array *out, int *info, const af_array in, const bool is_upper)
	C++ Interface for cholesky decomposition. More...
AFAPI af_err	af_cholesky_inplace (int *info, af_array in, const bool is_upper)
	C Interface for in place cholesky decomposition. More...

Detailed Description

Perform Cholesky decomposition.

This function decomposes a positive definite matrix A into two triangular matrices such that

\(A = L * U\)

\(L = U^T\)

Only one of L and U is stored to conserve space when solving linear equations.

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

    af::array out;
    cholesky(out, in, is_upper);

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

    af::array in2 = in.copy();
    choleskyInPlace(in2, is_upper);

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Function Documentation

AFAPI af_err af_cholesky	(	af_array *	out,
		int *	info,
		const af_array	in,
		const bool	is_upper
	)

C++ Interface for cholesky decomposition.

Parameters

[out]	out	contains the triangular matrix. Multiply out with it conjugate transpose reproduces the input in.
[out]	info	is 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.
[in]	in	is the input matrix
[in]	is_upper	a boolean determining if out is upper or lower triangular

Note

The input matrix has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non zero output.

AFAPI af_err af_cholesky_inplace	(	int *	info,
		af_array	in,
		const bool	is_upper
	)

C Interface for in place cholesky decomposition.

Parameters

[out]	info	is 0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.
[in,out]	in	is the input matrix on entry. It contains the triangular matrix on exit.
[in]	is_upper	a boolean determining if in is upper or lower triangular

Note

The input matrix has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non zero output.

AFAPI int af::cholesky	(	array &	out,
		const array &	in,
		const bool	is_upper = true
	)

C++ Interface for cholesky decomposition.

Parameters

[out]	out	contains the triangular matrix. Multiply out with its conjugate transpose reproduces the input in.
[in]	in	is the input matrix
[in]	is_upper	a boolean determining if out is upper or lower triangular

Returns

0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.

Note

The input matrix has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non-zero output.

This function is not supported in GFOR

Examples:

lin_algebra/cholesky.cpp.

AFAPI int af::choleskyInPlace	(	array &	in,
		const bool	is_upper = true
	)

C++ Interface for in place cholesky decomposition.

Parameters

[in,out]	in	is the input matrix on entry. It contains the triangular matrix on exit.
[in]	is_upper	a boolean determining if in is upper or lower triangular

Returns

0 if cholesky decomposition passes, if not it returns the rank at which the decomposition failed.

Note

The input matrix has to be a positive definite matrix, if it is not zero, the cholesky decomposition functions return a non-zero output.

This function is not supported in GFOR