potrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.

potrf supports the following precisions.

T
float
double
std::complex<float>
std::complex<double>

Description

The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix A:

A = UT*U for real data, A = UH*U for complex data	if upper_lower=onemkl::uplo::upper
A = L*LT for real data, A = L*LH for complex data	if upper_lower=onemkl::uplo::lower

where L is a lower triangular matrix and U is upper triangular.

potrf (BUFFER Version)

Syntax

void onemkl::lapack::potrf(cl::sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, cl::sycl::buffer<T, 1> &a, std::int64_t lda, cl::sycl::buffer<T, 1> &scratchpad, std::int64_t scratchpad_size)

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Indicates whether the upper or lower triangular part of A is stored and how A is factored:

If upper_lower=onemkl::uplo::upper, the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.

If upper_lower=onemkl::uplo::lower, the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.

n

Specifies the order of the matrix A (0≤n).

a

Buffer holding input matrix A. The buffer a contains either the upper or the lower triangular part of the matrix A (see upper_lower). The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by potrf_scratchpad_size function.

Output Parameters

a

The buffer a is overwritten by the Cholesky factor U or L, as specified by upper_lower.

scratchpad

Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info=i, and get_detail() returns 0, then the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A.

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

potrf (USM Version)

Syntax

cl::sycl::event onemkl::lapack::potrf(cl::sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, T *a, std::int64_t lda, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<cl::sycl::event> &events = {})

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Indicates whether the upper or lower triangular part of A is stored and how A is factored:

If upper_lower=onemkl::uplo::upper, the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.

If upper_lower=onemkl::uplo::lower, the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.

n

Specifies the order of the matrix A (0≤n).

a

Pointer to input matrix A. The array a contains either the upper or the lower triangular part of the matrix A (see upper_lower). The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by potrf_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

a

The memory pointer to by pointer a is overwritten by the Cholesky factor U or L, as specified by upper_lower.

scratchpad

Pointer to scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info=i, and get_detail() returns 0, then the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A.

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines