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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: routine i deprecated and has been replaced by routine ZGEQP3

```NAME
LAPACK-3 - routine i deprecated and has been replaced by routine ZGEQP3

SYNOPSIS
SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )

INTEGER        INFO, LDA, M, N

INTEGER        JPVT( * )

DOUBLE         PRECISION RWORK( * )

COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
This routine is deprecated and has been replaced by routine ZGEQP3.
ZGEQPF computes a QR factorization with column pivoting of a
complex M-by-N matrix A: A*P = Q*R.

ARGUMENTS
M       (input) INTEGER
The number of rows of the matrix A. M >= 0.

N       (input) INTEGER
The number of columns of the matrix A. N >= 0

A       (input/output) 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 triangular 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.

LDA     (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT    (input/output) INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.

TAU     (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

WORK    (workspace) COMPLEX*16 array, dimension (N)

RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n)
Each H(i) has the form
H = I - tau * v * v'
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).
The matrix P is represented in jpvt as follows: If
jpvt(j) = i
then the jth column of P is the ith canonical unit vector.
Partial column norm updating strategy modified by
Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
University of Zagreb, Croatia.
June 2010
For more details see LAPACK Working Note 176.

LAPACK deprecated computational rMarche2011rsion 3.2.2)           LAPACK-3(3)
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