# potrf¶

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.This routine belongs to the `oneapi::mkl::lapack`namespace.

Syntax

void `potrf`(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

`potrf` supports the following precisions and devices:

T

Devices supported

`float`

Host, CPU, and GPU

`double`

Host, CPU, and GPU

`std::complex<float>`

Host, CPU, and GPU

`std::complex<double>`

Host, CPU, and GPU

Description

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

`A` = `U`T*`U` for real data, `A` = `U`H*`U` for complex data

if uplo=`mkl::uplo::upper`

`A` = `L`*`L`T for real data, `A` = `L`*`L`H for complex data

if uplo=`mkl::uplo::lower`

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

Input Parameters

queue

Device queue where calculations will be performed.

uplo

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

If uplo=`mkl::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 uplo=`mkl::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 array holding input matrix a contains either the upper or the lower triangular part of the matrix `A` (see uplo). The second dimension of a must be at least `max(1, n)`.

lda

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

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

Output Parameters

a

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

Exceptions

 mkl::lapack::exception This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If `info = -i`, the `i`-th parameter had an illegal value. If `info = i`, and detail() returns 0, 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` is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.

Known Limitations

GPU support is for only real precisions.

GPU support for this function does not include error reportingthrough the info parameter.