zgetsqrhrt()

subroutine zgetsqrhrt	(	integer	m,
		integer	n,
		integer	mb1,
		integer	nb1,
		integer	nb2,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldt, * )	t,
		integer	ldt,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info )

ZGETSQRHRT

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

Purpose:

!>
!> ZGETSQRHRT computes a NB2-sized column blocked QR-factorization
!> of a complex M-by-N matrix A with M >= N,
!>
!>    A = Q * R.
!>
!> The routine uses internally a NB1-sized column blocked and MB1-sized
!> row blocked TSQR-factorization and perfors the reconstruction
!> of the Householder vectors from the TSQR output. The routine also
!> converts the R_tsqr factor from the TSQR-factorization output into
!> the R factor that corresponds to the Householder QR-factorization,
!>
!>    A = Q_tsqr * R_tsqr = Q * R.
!>
!> The output Q and R factors are stored in the same format as in ZGEQRT
!> (Q is in blocked compact WY-representation). See the documentation
!> of ZGEQRT for more details on the format.
!> 

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. M >= N >= 0. !>
[in]	MB1	!> MB1 is INTEGER !> The row block size to be used in the blocked TSQR. !> MB1 > N. !>
[in]	NB1	!> NB1 is INTEGER !> The column block size to be used in the blocked TSQR. !> N >= NB1 >= 1. !>
[in]	NB2	!> NB2 is INTEGER !> The block size to be used in the blocked QR that is !> output. NB2 >= 1. !>
[in,out]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> !> On entry: an M-by-N matrix A. !> !> On exit: !> a) the elements on and above the diagonal !> of the array contain the N-by-N upper-triangular !> matrix R corresponding to the Householder QR; !> b) the elements below the diagonal represent Q by !> the columns of blocked V (compact WY-representation). !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	T	!> T is COMPLEX*16 array, dimension (LDT,N)) !> The upper triangular block reflectors stored in compact form !> as a sequence of upper triangular blocks. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. LDT >= NB2. !>
[out]	WORK	!> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. !> If MIN(M,N) = 0, LWORK >= 1, else !> LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), !> where !> NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), !> NB1LOCAL = MIN(NB1,N). !> LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, !> LW1 = NB1LOCAL * N, !> LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ). !> !> If LWORK = -1, then a workspace query is assumed. !> The routine only calculates the optimal size of the WORK !> array, returns this value as the first entry of the WORK !> array, and no error message related to LWORK is issued !> by XERBLA. !>
[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 2020, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>