rocsolver_sormtr Interface Reference

rocsolver_sormtr Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sormtr Interface Reference

The ORMTR functions multiply an orthogonal matrix Q by a general m -by-n matrix C. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sormtr_ (handle, side, uplo, trans, m, n, a, lda, ipiv, c, ldc)

integer(kind(rocblas_status_success)) function	rocsolver_sormtr_rank_0 (handle, side, uplo, trans, m, n, a, lda, ipiv, c, ldc)

integer(kind(rocblas_status_success)) function	rocsolver_sormtr_rank_1 (handle, side, uplo, trans, m, n, a, lda, ipiv, c, ldc)

integer(kind(rocblas_status_success)) function	rocsolver_sormtr_full_rank (handle, side, uplo, trans, m, n, a, lda, ipiv, c, ldc)

Detailed Description

The ORMTR functions multiply an orthogonal matrix Q by a general m -by-n matrix C.

The matrix Q is applied in one of the following forms, depending on the values of side and trans:

\[ \begin{array}{cl} QC & \: \text{No transpose from the left,}\\% Q^TC & \: \text{Transpose from the left,}\\% CQ & \: \text{No transpose from the right, and}\\% CQ^T & \: \text{Transpose from the right.} \end{array} \]

The order q of the orthogonal matrix Q is q = m if applying from the left, or q = n if applying from the right.

Q is defined as a product of q-1 Householder reflectors. If uplo indicates upper, then Q has the form

\[ Q = H(q-1)H(q-2)\cdots H(1). \]

However, if uplo indicates lower, then Q has the form

\[ Q = H(1)H(2)\cdots H(q-1) \]

The Householder matrices \(H(i)\) are never stored. They are computed from their corresponding Householder vectors and scalars as returned by SYTRD in its arguments A and tau.

Parameters

[in]	handle	- rocblas_handle.
[in]	side	- rocblas_side. Specifies from which side to apply Q.
[in]	uplo	- rocblas_fill. Specifies whether the SYTRD factorization was upper or lower triangular. If uplo indicates lower (or upper), then the upper (or lower) part of A is not used.
[in]	trans	- rocblas_operation. Specifies whether the matrix Q or its transpose is to be applied.
[in]	m	- rocblas_int. m >= 0. Number of rows of matrix C.
[in]	n	- rocblas_int. n >= 0. Number of columns of matrix C.
[in]	A	- pointer to type. Array on the GPU of size lda*q. On entry, the Householder vectors as returned by SYTRD.
[in]	lda	- rocblas_int. lda >= q. Leading dimension of A.
[in]	ipiv	- pointer to type. Array on the GPU of dimension at least q-1. The Householder scalars as returned by SYTRD.
[in,out]	C	- pointer to type. Array on the GPU of size ldc*n. On entry, the matrix C. On exit, it is overwritten with \(QC\), \(CQ\), \(Q^TC\), or \(CQ^T\).
[in]	ldc	- rocblas_int. ldc >= m. Leading dimension of C.

Member Function/Subroutine Documentation