# hetrf (USM Version)¶

Computes the Bunch-Kaufman factorization of a complex Hermitian matrix. This routine belongs to the `oneapi::mkl::lapack`namespace.

Syntax

cl::sycl::event `hetrf`(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, T *a, std::int64_t lda, std::int64_t *ipiv, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<cl::sycl::event> &events = {})

`hetrf` (USM version) supports the following precisions and devices:

T

Devices supported

`std::complex<float>`

Host and CPU

`std::complex<double>`

Host and CPU

Description

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

• if `uplo=uplo::upper`, `A = U*D*UH`

• if `uplo=uplo::lower`, `A = L*D*LH,`

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 Hermitian 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

The 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 arraya stores the upper triangular part of `A` and `A` is factored as `U`*`D`*`U`H.

If `uplo = uplo::lower`, the arraya stores the lower triangular part of `A` and `A` is factored as `L`*`D`*`L`H.

n

The order of the matrix `A``(0≤n)`.

a

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

lda

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

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 hetrf_scratchpad_size function.

events

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

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

Pointer to memory 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`, `d`:sub:``i``i`` 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.

Return Values

Output event to wait on to ensure computation is complete.