?laqps

Computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Syntax

call slaqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )

call dlaqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )

call claqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )

call zlaqps( m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

The routine computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. The routine tries to factorize NB columns from A starting from the row offset+1, and updates all of the matrix with BLAS level 3 routine ?gemm.

In some cases, due to catastrophic cancellations, ?laqps 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.

Input Parameters

m

INTEGER. The number of rows of the matrix A. m ≥ 0.

n

INTEGER. The number of columns of the matrix A. n ≥ 0.

offset

INTEGER. The number of rows of A that have been factorized in previous steps.

nb

INTEGER. The number of columns to factorize.

a

REAL for slaqps

DOUBLE PRECISION for dlaqps

COMPLEX for claqps

COMPLEX*16 for zlaqps

Array, DIMENSION (lda,n).

On entry, the m-by-n matrix A.

lda

INTEGER. The leading dimension of the array a.

lda ≥ max(1,m).

jpvt

INTEGER. Array, DIMENSION (n).

If jpvt(I) = k then column k of the full matrix A has been permuted into position i in AP.

vn1, vn2

REAL for slaqps/claqps

DOUBLE PRECISION for dlaqps/zlaqps

Arrays, DIMENSION (n) each. Contain the vectors with the partial and exact column norms, respectively.

auxv

REAL for slaqps

DOUBLE PRECISION for dlaqps

COMPLEX for claqps

COMPLEX*16 for zlaqps

Array, DIMENSION (nb). Auxiliary vector.

f

REAL for slaqps

DOUBLE PRECISION for dlaqps

COMPLEX for claqps

COMPLEX*16 for zlaqps

Array, DIMENSION (ldf,nb). Matrix F' = L*Y'*A.

ldf

INTEGER. The leading dimension of the array f.

ldf ≥ max(1,n).

Output Parameters

kb

INTEGER. The number of columns actually factorized.

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.

jpvt

INTEGER array, DIMENSION (n). If jpvt(I) = k then column k of the full matrix A has been permuted into position i in AP.

tau

REAL for slaqps

DOUBLE PRECISION for dlaqps

COMPLEX for claqps

COMPLEX*16 for zlaqps

Array, DIMENSION (kb). The scalar factors of the elementary reflectors.

vn1, vn2

The vectors with the partial and exact column norms, respectively.

auxv

Auxiliary vector.

f

Matrix F' = L*Y'*A.