zgeqr2p()

subroutine zgeqr2p	(	integer	m,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( * )	tau,
		complex*16, dimension( * )	work,
		integer	info )

ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Download ZGEQR2P + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a m-by-m orthogonal matrix;
!>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
!>    entries;
!>    0 is a (m-n)-by-n zero matrix, if m > n.
!>
!> 

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 COMPLEX*16 array, dimension (LDA,N) !> On entry, the m by n matrix A. !> On exit, the elements on and above the diagonal of the array !> contain the min(m,n) by n upper trapezoidal matrix R (R is !> upper triangular if m >= n). The diagonal entries of R !> are real and nonnegative; the elements below the diagonal, !> with the array TAU, represent the unitary matrix Q as a !> product of elementary reflectors (see Further Details). !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	TAU	!> TAU is COMPLEX*16 array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details). !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (N) !>
[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.

Further Details:

!>
!>  The matrix Q is represented as a product of elementary reflectors
!>
!>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
!>  and tau in TAU(i).
!>
!> See Lapack Working Note 203 for details
!>