# potrs¶

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix. This routine belongs to the `oneapi::mkl::lapack`namespace.

Syntax

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

potrs 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 solves for `X` the system of linear equations `A*X = B` with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix `A`, given the Cholesky factorization of `A`:

`A = UT*U` for real data, `A = UH*U` for complex data

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

`A = L*LT` for real data, `A = L*LH` for complex data

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

where `L` is a lower triangular matrix and `U` is upper triangular. The system is solved with multiple right-hand sides stored in the columns of the matrix `B`.

Before calling this routine, you must call potrf to compute the Cholesky factorization of `A`.

Input Parameters

queue

Device queue where calculations will be performed.

uplo

Indicates how the input matrix has been factored:

If uplo=`mkl::uplo::upper`, the upper triangle `U` of `A` is stored, where `A` = `U`T*`U` for real data, `A` = `U`H*`U` for complex data.

If uplo=`mkl::uplo::lower`, the upper triangle `L` of `A` is stored, where `A` = `L`*`L`T for real data, `A` = `L`*`L`H for complex data.

n

The order of matrix `A` (0≤n).

nrhs

The number of right-hand sides (0≤nrhs).

a

Buffer holding factorization of the matrix `A`, as returned by potrf. The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

b

Buffer holding the data of matrix `B` whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least max(1,nrhs).

ldb

The leading dimension of b.

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 potrs_scratchpad_size function.

Output Parameters

b

Buffer b is overwritten by the solution matrix `X`.

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`, the `i`-th diagonal element of the Cholesky factor is zero, and the solve could not be completed. 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.