sytrf¶

Computes the Bunch-Kaufman factorization of a symmetric matrix.

sytrf supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

Description

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

if upper_lower=uplo::upper, A = U*D*U^T
if upper_lower=uplo::lower, A = L*D*L^T

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.

sytrf (BUFFER Version)¶

Syntax

void onemkl::lapack::sytrf(cl::sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, cl::sycl::buffer<T, 1> &a, std::int64_t lda, cl::sycl::buffer<int_64, 1> &ipiv, 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=uplo::upper, the buffer a stores the upper triangular part of the matrix A, and A is factored as U*D*UT.

If upper_lower=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: The buffer a, size max(1,lda*n). 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: 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 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, size at least max(1, n). Contains details of the interchanges and the block structure of D. If ipiv(i)=k>0, then d_ii 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 upper_lower=onemkl::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 upper_lower=onemkl::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.
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

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

If info=-i, the i-th parameter had an illegal value.

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

sytrf (USM Version)¶