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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3

```NAME
LAPACK-3  - computes a step of QR factorization with column pivoting of
a complex M-by-N matrix A by using Blas-3

SYNOPSIS
SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU,  VN1,  VN2,
AUXV, F, LDF )

INTEGER        KB, LDA, LDF, M, N, NB, OFFSET

INTEGER        JPVT( * )

DOUBLE         PRECISION VN1( * ), VN2( * )

COMPLEX*16     A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )

PURPOSE
ZLAQPS  computes  a  step of QR factorization with column pivoting of a
complex M-by-N matrix A by using Blas-3.  It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns.  Hence, the actual number of factorized
columns is returned in KB.
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

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

OFFSET  (input) INTEGER
The number of rows of A that have been factorized in
previous steps.

NB      (input) INTEGER
The number of columns to factorize.

KB      (output) INTEGER
The number of columns actually factorized.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.

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

JPVT    (input/output) INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.

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

VN1     (input/output) DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.

VN2     (input/output) DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.

AUXV    (input/output) COMPLEX*16 array, dimension (NB)
Auxiliar vector.

F       (input/output) COMPLEX*16 array, dimension (LDF,NB)
Matrix F' = L*Y'*A.

LDF     (input) INTEGER
The leading dimension of the array F. LDF >= max(1,N).

FURTHER DETAILS
Based on contributions by
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
X. Sun, Computer Science Dept., Duke University, USA

LAPACK auxiliary routine (versionMarch22011                       LAPACK-3(3)
```