# potrf¶

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

Description

potrf supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

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 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.

## potrf (Buffer Version)¶

Syntax

namespace oneapi::mkl::lapack {
void potrf(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 whether the upper or lower triangular part of $$A$$ is stored and how $$A$$ is factored:

If upper_lower=oneapi::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 upper_lower=oneapi::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 $$A$$ ($$0 \le n$$).

a

Buffer holding input matrix $$A$$. The buffer a contains either the upper or the lower triangular part of the matrix $$A$$ (see upper_lower). The second dimension of a must be at least $$\max(1, n)$$.

lda

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

Output Parameters

a

The buffer a is overwritten by the Cholesky factor $$U$$ or $$L$$, as 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 $$\text{info}=i$$, and detail() returns 0, then 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 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.

## potrf (USM Version)¶

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event potrf(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 whether the upper or lower triangular part of $$A$$ is stored and how $$A$$ is factored:

If upper_lower=oneapi::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 upper_lower=oneapi::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 $$A$$ ($$0 \le n$$).

a

Pointer to input matrix $$A$$. The array a contains either the upper or the lower triangular part of the matrix $$A$$ (see upper_lower). The second dimension of a must be at least $$\max(1, n)$$.

lda

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

events

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

Output Parameters

a

The memory pointer to by pointer a is overwritten by the Cholesky factor $$U$$ or $$L$$, as 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 $$\text{info}=i$$, and detail() returns 0, then 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 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