dlaorhr_col_getrfnp()

subroutine dlaorhr_col_getrfnp	(	integer	m,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	d,
		integer	info )

DLAORHR_COL_GETRFNP

Download DLAORHR_COL_GETRFNP + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> DLAORHR_COL_GETRFNP computes the modified LU factorization without
!> pivoting of a real general M-by-N matrix A. The factorization has
!> the form:
!>
!>     A - S = L * U,
!>
!> where:
!>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
!>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
!>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
!>    i-1 steps of Gaussian elimination. This means that the diagonal
!>    element at each step of  Gaussian elimination is
!>    at least one in absolute value (so that division-by-zero not
!>    not possible during the division by the diagonal element);
!>
!>    L is a M-by-N lower triangular matrix with unit diagonal elements
!>    (lower trapezoidal if M > N);
!>
!>    and U is a M-by-N upper triangular matrix
!>    (upper trapezoidal if M < N).
!>
!> This routine is an auxiliary routine used in the Householder
!> reconstruction routine DORHR_COL. In DORHR_COL, this routine is
!> applied to an M-by-N matrix A with orthonormal columns, where each
!> element is bounded by one in absolute value. With the choice of
!> the matrix S above, one can show that the diagonal element at each
!> step of Gaussian elimination is the largest (in absolute value) in
!> the column on or below the diagonal, so that no pivoting is required
!> for numerical stability [1].
!>
!> For more details on the Householder reconstruction algorithm,
!> including the modified LU factorization, see [1].
!>
!> This is the blocked right-looking version of the algorithm,
!> calling Level 3 BLAS to update the submatrix. To factorize a block,
!> this routine calls the recursive routine DLAORHR_COL_GETRFNP2.
!>
!> [1] ,
!>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
!>     E. Solomonik, J. Parallel Distrib. Comput.,
!>     vol. 85, pp. 3-31, 2015.
!> 

Parameters

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix A. N >= 0. !>
[in,out]	A	!> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the M-by-N matrix to be factored. !> On exit, the factors L and U from the factorization !> A-S=L*U; the unit diagonal elements of L are not stored. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	D	!> D is DOUBLE PRECISION array, dimension min(M,N) !> The diagonal elements of the diagonal M-by-N sign matrix S, !> D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can !> be only plus or minus one. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

!>
!> November 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>