cholesky

Perform Cholesky decomposition. More...

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

Detailed Description

Perform Cholesky decomposition.

This function decomposes a positive definite matrix \(A\) into two triangular matrices such that, \(A = L * U\) and \(L = U^T\).

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.

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

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

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

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Function Documentation

af_cholesky()

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

C Interface to perform Cholesky decomposition.

Multiplying out with its conjugate transpose reproduces the input in.

The input must be positive definite.

Parameters

[out]	out	triangular matrix;
[out]	info	0 if cholesky decomposition passes; if not, it returns the rank at which the decomposition fails
[in]	in	input matrix
[in]	is_upper	boolean determining if out is upper or lower triangular

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

af_cholesky_inplace()

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

C Interface to perform in-place Cholesky decomposition.

The input must be positive definite.

Parameters

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

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

cholesky()

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

C++ Interface to perform Cholesky decomposition.

Multiplying out with its conjugate transpose reproduces the input in.

The input must be positive definite.

This function is not supported in GFOR.

Parameters

[out]	out	triangular matrix;
[in]	in	input matrix
[in]	is_upper	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 fails

choleskyInPlace()

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

C++ Interface to perform in-place Cholesky decomposition.

The input must be positive definite.

This function is not supported in GFOR.

Parameters

[in,out]	in	input matrix on entry; triangular matrix on exit
[in]	is_upper	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 fails