!>
!> CLAQPS 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.
!> 

M

!>          M is INTEGER
!>          The number of rows of the matrix A. M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix A. N >= 0
!> 

OFFSET

!>          OFFSET is INTEGER
!>          The number of rows of A that have been factorized in
!>          previous steps.
!> 

NB

!>          NB is INTEGER
!>          The number of columns to factorize.
!> 

KB

!>          KB is INTEGER
!>          The number of columns actually factorized.
!> 

A

!>          A is COMPLEX 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

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

JPVT

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

TAU

!>          TAU is COMPLEX array, dimension (KB)
!>          The scalar factors of the elementary reflectors.
!> 

VN1

!>          VN1 is REAL array, dimension (N)
!>          The vector with the partial column norms.
!> 

VN2

!>          VN2 is REAL array, dimension (N)
!>          The vector with the exact column norms.
!> 

AUXV

!>          AUXV is COMPLEX array, dimension (NB)
!>          Auxiliary vector.
!> 

F

!>          F is COMPLEX array, dimension (LDF,NB)
!>          Matrix  F**H = L * Y**H * A.
!> 

LDF

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

LAPACK Working Note 176