Cholesky and LDLT decompositions

Functions
arm_status	arm_mat_cholesky_f16 (const arm_matrix_instance_f16 *pSrc, arm_matrix_instance_f16 *pDst)
	Floating-point Cholesky decomposition of positive-definite matrix.
arm_status	arm_mat_cholesky_f32 (const arm_matrix_instance_f32 *pSrc, arm_matrix_instance_f32 *pDst)
	Floating-point Cholesky decomposition of positive-definite matrix.
arm_status	arm_mat_cholesky_f64 (const arm_matrix_instance_f64 *pSrc, arm_matrix_instance_f64 *pDst)
	Floating-point Cholesky decomposition of positive-definite matrix.
arm_status	arm_mat_ldlt_f32 (const arm_matrix_instance_f32 *pSrc, arm_matrix_instance_f32 *pl, arm_matrix_instance_f32 *pd, uint16_t *pp)
	Floating-point LDL^t decomposition of positive semi-definite matrix.
arm_status	arm_mat_ldlt_f64 (const arm_matrix_instance_f64 *pSrc, arm_matrix_instance_f64 *pl, arm_matrix_instance_f64 *pd, uint16_t *pp)
	Floating-point LDL^t decomposition of positive semi-definite matrix.

Description

Computes the Cholesky or LL^t decomposition of a matrix.

If the input matrix does not have a decomposition, then the algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE.

Function Documentation

arm_mat_cholesky_f16()

arm_status arm_mat_cholesky_f16	(	const arm_matrix_instance_f16 *	pSrc,
		arm_matrix_instance_f16 *	pDst
	)

Floating-point Cholesky decomposition of positive-definite matrix.

Floating-point Cholesky decomposition of Symmetric Positive Definite Matrix.

Parameters

[in]	pSrc	points to the instance of the input floating-point matrix structure.
[out]	pDst	points to the instance of the output floating-point matrix structure.

Returns

The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.

execution status

• ARM_MATH_SUCCESS : Operation successful
• ARM_MATH_SIZE_MISMATCH : Matrix size check failed
• ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed

If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition. The decomposition of A is returning a lower triangular matrix U such that A = L L^t

The destination matrix should be set to 0 before calling the functions because the function may not overwrite all output elements.

arm_mat_cholesky_f32()

arm_status arm_mat_cholesky_f32	(	const arm_matrix_instance_f32 *	pSrc,
		arm_matrix_instance_f32 *	pDst
	)

Floating-point Cholesky decomposition of positive-definite matrix.

Floating-point Cholesky decomposition of Symmetric Positive Definite Matrix.

Parameters

[in]	pSrc	points to the instance of the input floating-point matrix structure.
[out]	pDst	points to the instance of the output floating-point matrix structure.

Returns

The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.

execution status

• ARM_MATH_SUCCESS : Operation successful
• ARM_MATH_SIZE_MISMATCH : Matrix size check failed
• ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed

If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition. The decomposition of A is returning a lower triangular matrix L such that A = L L^t

The destination matrix should be set to 0 before calling the functions because the function may not overwrite all output elements.

arm_mat_cholesky_f64()

arm_status arm_mat_cholesky_f64	(	const arm_matrix_instance_f64 *	pSrc,
		arm_matrix_instance_f64 *	pDst
	)

Floating-point Cholesky decomposition of positive-definite matrix.

Floating-point Cholesky decomposition of Symmetric Positive Definite Matrix.

Parameters

[in]	pSrc	points to the instance of the input floating-point matrix structure.
[out]	pDst	points to the instance of the output floating-point matrix structure.

Returns

The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.

execution status

• ARM_MATH_SUCCESS : Operation successful
• ARM_MATH_SIZE_MISMATCH : Matrix size check failed
• ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed

If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition. The decomposition of A is returning a lower triangular matrix L such that A = L L^t

The destination matrix should be set to 0 before calling the functions because the function may not overwrite all output elements.

arm_mat_ldlt_f32()

arm_status arm_mat_ldlt_f32	(	const arm_matrix_instance_f32 *	pSrc,
		arm_matrix_instance_f32 *	pl,
		arm_matrix_instance_f32 *	pd,
		uint16_t *	pp
	)

Floating-point LDL^t decomposition of positive semi-definite matrix.

Floating-point LDL decomposition of Symmetric Positive Semi-Definite Matrix.

Parameters

[in]	pSrc	points to the instance of the input floating-point matrix structure.
[out]	pl	points to the instance of the output floating-point triangular matrix structure.
[out]	pd	points to the instance of the output floating-point diagonal matrix structure.
[out]	pp	points to the instance of the output floating-point permutation vector.

Returns

The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.

execution status

• ARM_MATH_SUCCESS : Operation successful
• ARM_MATH_SIZE_MISMATCH : Matrix size check failed
• ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed

Computes the LDL^t decomposition of a matrix A such that P A P^t = L D L^t.

arm_mat_ldlt_f64()

arm_status arm_mat_ldlt_f64	(	const arm_matrix_instance_f64 *	pSrc,
		arm_matrix_instance_f64 *	pl,
		arm_matrix_instance_f64 *	pd,
		uint16_t *	pp
	)

Floating-point LDL^t decomposition of positive semi-definite matrix.

Floating-point LDL decomposition of Symmetric Positive Semi-Definite Matrix.

Parameters

[in]	pSrc	points to the instance of the input floating-point matrix structure.
[out]	pl	points to the instance of the output floating-point triangular matrix structure.
[out]	pd	points to the instance of the output floating-point diagonal matrix structure.
[out]	pp	points to the instance of the output floating-point permutation vector.

Returns

The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.

execution status

• ARM_MATH_SUCCESS : Operation successful
• ARM_MATH_SIZE_MISMATCH : Matrix size check failed
• ARM_MATH_DECOMPOSITION_FAILURE : Input matrix cannot be decomposed

Computes the LDL^t decomposition of a matrix A such that P A P^t = L D L^t.