# rocsolver_ssytf2 Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytf2 Interface Reference
hipfort_rocsolver::rocsolver_ssytf2 Interface Reference

SYTF2 computes the factorization of a symmetric indefinite matrix $$A$$ using Bunch-Kaufman diagonal pivoting. More...

## Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_ssytf2_ (handle, uplo, n, A, lda, ipiv, myInfo)

integer(kind(rocblas_status_success)) function rocsolver_ssytf2_full_rank (handle, uplo, n, A, lda, ipiv, myInfo)

integer(kind(rocblas_status_success)) function rocsolver_ssytf2_rank_0 (handle, uplo, n, A, lda, ipiv, myInfo)

integer(kind(rocblas_status_success)) function rocsolver_ssytf2_rank_1 (handle, uplo, n, A, lda, ipiv, myInfo)

## Detailed Description

SYTF2 computes the factorization of a symmetric indefinite matrix $$A$$ using Bunch-Kaufman diagonal pivoting.

(This is the unblocked version of the algorithm).

The factorization has the form

$\begin{array}{cl} A = U D U^T & \: \text{or}\newline A = L D L^T & \end{array}$

where $$U$$ or $$L$$ is a product of permutation and unit upper/lower triangular matrices (depending on the value of uplo), and $$D$$ is a symmetric block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks $$D(k)$$.

Specifically, $$U$$ and $$L$$ are computed as

$\begin{array}{cl} U = P(n) U(n) \cdots P(k) U(k) \cdots & \: \text{and}\newline L = P(1) L(1) \cdots P(k) L(k) \cdots & \end{array}$

where $$k$$ decreases from $$n$$ to 1 (increases from 1 to $$n$$) in steps of 1 or 2, depending on the order of block $$D(k)$$, and $$P(k)$$ is a permutation matrix defined by $$ipiv[k]$$. If we let $$s$$ denote the order of block $$D(k)$$, then $$U(k)$$ and $$L(k)$$ are unit upper/lower triangular matrices defined as

$U(k) = \left[ \begin{array}{ccc} I_{k-s} & v & 0 \newline 0 & I_s & 0 \newline 0 & 0 & I_{n-k} \end{array} \right]$

and

$L(k) = \left[ \begin{array}{ccc} I_{k-1} & 0 & 0 \newline 0 & I_s & 0 \newline 0 & v & I_{n-k-s+1} \end{array} \right].$

If $$s = 1$$, then $$D(k)$$ is stored in $$A[k,k]$$ and $$v$$ is stored in the upper/lower part of column $$k$$ of $$A$$. If $$s = 2$$ and uplo is upper, then $$D(k)$$ is stored in $$A[k-1,k-1]$$, $$A[k-1,k]$$, and $$A[k,k]$$, and $$v$$ is stored in the upper parts of columns $$k-1$$ and $$k$$ of $$A$$. If $$s = 2$$ and uplo is lower, then $$D(k)$$ is stored in $$A[k,k]$$, $$A[k+1,k]$$, and $$A[k+1,k+1]$$, and $$v$$ is stored in the lower parts of columns $$k$$ and $$k+1$$ of $$A$$.

Parameters
 [in] handle rocblas_handle. [in] uplo rocblas_fill. Specifies whether the upper or lower part of the matrix A is stored. If uplo indicates lower (or upper), then the upper (or lower) part of A is not used. [in] n rocblas_int. n >= 0. The number of rows and columns of the matrix A. [in,out] A pointer to type. Array on the GPU of dimension lda*n. On entry, the symmetric matrix A to be factored. On exit, the block diagonal matrix D and the multipliers needed to compute U or L. [in] lda rocblas_int. lda >= n. Specifies the leading dimension of A. [out] ipiv pointer to rocblas_int. Array on the GPU of dimension n. The vector of pivot indices. Elements of ipiv are 1-based indices. For 1 <= k <= n, if ipiv[k] > 0 then rows and columns k and ipiv[k] were interchanged and D[k,k] is a 1-by-1 diagonal block. If, instead, ipiv[k] = ipiv[k-1] < 0 and uplo is upper (or ipiv[k] = ipiv[k+1] < 0 and uplo is lower), then rows and columns k-1 and -ipiv[k] (or rows and columns k+1 and -ipiv[k]) were interchanged and D[k-1,k-1] to D[k,k] (or D[k,k] to D[k+1,k+1]) is a 2-by-2 diagonal block. [out] info pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info[i] = j > 0, D is singular. D[j,j] is the first diagonal zero.

## ◆ rocsolver_ssytf2_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytf2::rocsolver_ssytf2_ ( type(c_ptr), value handle, integer(kind(rocblas_fill_upper)), value uplo, integer(c_int), value n, type(c_ptr), value A, integer(c_int), value lda, type(c_ptr), value ipiv, integer(c_int) myInfo )

## ◆ rocsolver_ssytf2_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytf2::rocsolver_ssytf2_full_rank ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), dimension(:,:), target A, integer(c_int) lda, integer(c_int), dimension(:), target ipiv, integer(c_int) myInfo )

## ◆ rocsolver_ssytf2_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytf2::rocsolver_ssytf2_rank_0 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), target A, integer(c_int) lda, integer(c_int), target ipiv, integer(c_int) myInfo )

## ◆ rocsolver_ssytf2_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_ssytf2::rocsolver_ssytf2_rank_1 ( type(c_ptr) handle, integer(kind(rocblas_fill_upper)) uplo, integer(c_int) n, real(c_float), dimension(:), target A, integer(c_int) lda, integer(c_int), dimension(:), target ipiv, integer(c_int) myInfo )

The documentation for this interface was generated from the following file: