zgeqp3()

subroutine zgeqp3	(	integer	m,
		integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	jpvt,
		complex*16, dimension( * )	tau,
		complex*16, dimension( * )	work,
		integer	lwork,
		double precision, dimension( * )	rwork,
		integer	info )

ZGEQP3

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Purpose:

!>
!> ZGEQP3 computes a QR factorization with column pivoting of a
!> matrix A:  A*P = Q*R  using Level 3 BLAS.
!> 

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 upper triangle of the array contains the !> min(M,N)-by-N upper trapezoidal matrix R; the elements below !> the diagonal, together with the array TAU, represent the !> unitary matrix Q as a product of min(M,N) elementary !> reflectors. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[in,out]	JPVT	!> JPVT is INTEGER array, dimension (N) !> On entry, if JPVT(J).ne.0, the J-th column of A is permuted !> to the front of A*P (a leading column); if JPVT(J)=0, !> the J-th column of A is a free column. !> On exit, if JPVT(J)=K, then the J-th column of A*P was the !> the K-th column of A. !>
[out]	TAU	!> TAU is COMPLEX*16 array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors. !>
[out]	WORK	!> WORK is 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. LWORK >= N+1. !> For optimal performance LWORK >= ( N+1 )*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]	RWORK	!> RWORK is DOUBLE PRECISION array, dimension (2*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 real/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).
!> 

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA