# 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.

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.

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

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

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

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

If $$\text{info}=i$$, the $$i$$-th diagonal element of the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.

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

## 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 std::vector<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.

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.

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

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

oneapi::mkl::lapack::computation_error

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

If $$\text{info}=-i$$, the $$i$$-th parameter had an illegal value.

If $$\text{info}=i$$, the $$i$$-th diagonal element of the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.

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

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines