potrs#

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix.

Description

potrs supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

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

The routine solves for \(X\) the system of linear equations \(AX = B\) with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix \(A\), given the Cholesky factorization of \(A\):

\(A = U^TU\) for real data, \(A = U^HU\) for complex data	if `upper_lower=oneapi::mkl::uplo::upper`
\(A = LL^T\) for real data, \(A = LL^H\) for complex data	if `upper_lower=oneapi::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 \(A\).

potrs (Buffer Version)#

Syntax

namespace oneapi::mkl::lapack {
  void potrs(sycl::queue &queue, oneapi::mkl::uplo upper_lower, std::int64_t n, std::int64_t nrhs, sycl::buffer<T,1> &a, std::int64_t lda, sycl::buffer<T,1> &b, std::int64_t ldb, sycl::buffer<T,1> &scratchpad, std::int64_t scratchpad_size)
}

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Indicates how the input matrix has been factored:

If upper_lower = oneapi::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 upper_lower = oneapi::mkl::uplo::lower, the lower triangle \(L\) of \(A\) is stored, where \(A\) = \(LL^{T}\) for real data, \(A\) = \(LL^{H}\) for complex data.

n

The order of matrix \(A\) (\(0 \le n\)).

nrhs

The number of right-hand sides (\(0 \le \text{nrhs}\)).

a

Buffer containing the 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

The array b contains the matrix \(B\) whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least \(\max(1,\text{nrhs})\).

ldb

The leading dimension of b.

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 potrs_scratchpad_size function.

Output Parameters

b: Overwritten by the solution matrix \(X\).
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

potrs (USM Version)#