dtzrzf()

subroutine dtzrzf	(	integer	m,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	tau,
		double precision, dimension( * )	work,
		integer	lwork,
		integer	info )

DTZRZF

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Purpose:

!>
!> DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
!> to upper triangular form by means of orthogonal transformations.
!>
!> The upper trapezoidal matrix A is factored as
!>
!>    A = ( R  0 ) * Z,
!>
!> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
!> triangular matrix.
!> 

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 >= M. !>
[in,out]	A	!> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the leading M-by-N upper trapezoidal part of the !> array A must contain the matrix to be factorized. !> On exit, the leading M-by-M upper triangular part of A !> contains the upper triangular matrix R, and elements M+1 to !> N of the first M rows of A, with the array TAU, represent the !> orthogonal matrix Z as a product of M elementary reflectors. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	TAU	!> TAU is DOUBLE PRECISION array, dimension (M) !> The scalar factors of the elementary reflectors. !>
[out]	WORK	!> WORK is DOUBLE PRECISION 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. LWORK >= max(1,M). !> For optimum performance LWORK >= M*NB, where NB is !> the optimal blocksize. !> !> 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:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

!>
!>  The N-by-N matrix Z can be computed by
!>
!>     Z =  Z(1)*Z(2)* ... *Z(M)
!>
!>  where each N-by-N Z(k) is given by
!>
!>     Z(k) = I - tau(k)*v(k)*v(k)**T
!>
!>  with v(k) is the kth row vector of the M-by-N matrix
!>
!>     V = ( I   A(:,M+1:N) )
!>
!>  I is the M-by-M identity matrix, A(:,M+1:N)
!>  is the output stored in A on exit from DTZRZF,
!>  and tau(k) is the kth element of the array TAU.
!>
!>