potri

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

Description

potri supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

The routine computes the inverse \(A^{-1}\) of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix \(A\). Before calling this routine, call potrf to factorize \(A\).

potri (Buffer Version)

Syntax

namespace oneapi::mkl::lapack {
  void potri(cl::sycl::queue &queue, oneapi::mkl::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 how the input matrix \(A\) has been factored:

If upper_lower = oneapi::mkl::uplo::upper, the upper triangle of \(A\) is stored.

If upper_lower = oneapi::mkl::uplo::lower, the lower triangle of \(A\) is stored.

n

Specifies the order of the matrix \(A\) (\(0 \le n\)).

a

Contains 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.

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 potri_scratchpad_size function.

Output Parameters

a

Overwritten by the upper or lower triangle of the inverse of \(A\). Specified by upper_lower.

scratchpad

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

potri (USM Version)

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event potri(cl::sycl::queue &queue, oneapi::mkl::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 how the input matrix \(A\) has been factored:

If upper_lower = oneapi::mkl::uplo::upper, the upper triangle of \(A\) is stored.

If upper_lower = oneapi::mkl::uplo::lower, the lower triangle of \(A\) is stored.

n

Specifies the order of the matrix \(A\) (\(0 \le n\)).

a

Contains 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.

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 potri_scratchpad_size function.

events

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

Output Parameters

a

Overwritten by the upper or lower triangle of the inverse of \(A\). Specified by upper_lower.

scratchpad

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

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines