sytrf

Computes the Bunch-Kaufman factorization of a symmetric matrix. This routine belongs to the oneapi::mkl::lapacknamespace.

Syntax

void sytrf(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, std::int64_t *ipiv, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

sytrf supports the following precisions and devices:

T

Devices Supported

float

Host and CPU

double

Host and CPU

std::complex<float>

Host and CPU

std::complex<double>

Host and CPU

Description

The routine computes thefactorization of a real/complex symmetric matrix A usingthe Bunch-Kaufman diagonal pivoting method. The form of thefactorization is:

  • if uplo=uplo::upper, A = U*D*UT

  • if uplo=uplo::lower, A = L*D*LT

where A is the input matrix, U and L are products of permutation and triangular matrices with unit diagonal (upper triangular for U and lower triangular for L), and D is a symmetric block-diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks. U and L have 2-by-2 unit diagonal blocks corresponding to the 2-by-2 blocks of D.

Input Parameters

queue

Device queue where calculations will be performed.

uplo

Indicates whether the upper or lower triangular part of A is stored and how A is factored: If uplo=uplo::upper, the buffer a stores the upper triangular part of the matrix A, and A is factored as U*D*UT. If uplo=uplo::lower, the buffer a stores the lower triangular part of the matrix A, and A is factored as L*D*LT.

n

The order of matrix A (0≤n).

a

Buffer holding the coefficients of matrix A, size max(1,lda*n) containing either the upper or lower triangular part of the matrix A (see uplo). The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

scratchpad

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

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 the sytrf_scratchpad_size function.

Output Parameters

a

The upper or lower triangular part of a is overwritten by details of the block-diagonal matrix D and the multipliers used to obtain the factor U (or L).

ipiv

Buffer holding array of size at least max(1, n). Contains details of the interchanges and the block structure of D. If ipiv(i)=k>0, then dii is a 1-by-1 block, and the i-th row and column of A was interchanged with the k-th row and column. If uplo=mkl::uplo::upper and ipiv(i)=ipiv(i-1)=-m<0, then D has a 2-by-2 block in rows/columns i and i-1, and (i-1)-th row and column of A was interchanged with the m-th row and column. If uplo=mkl::uplo::lower and ipiv(i)=ipiv(i+1)=-m<0, then D has a 2-by-2 block in rows/columns i and i+1, and (i+1)-th row and column of A was interchanged with the m-th row and column.

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, dii is 0. The factorization has been completed, but D is exactly singular. Division by 0 will occur if you use D for solving a system of linear equations. 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.