?laqp2

Computes a QR factorization with column pivoting of the matrix block.

Syntax

call slaqp2( m, n, offset, a, lda, jpvt, tau, vn1, vn2, work )

call dlaqp2( m, n, offset, a, lda, jpvt, tau, vn1, vn2, work )

call claqp2( m, n, offset, a, lda, jpvt, tau, vn1, vn2, work )

call zlaqp2( m, n, offset, a, lda, jpvt, tau, vn1, vn2, work )

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 QR factorization with column pivoting of the block A(offset+1:m,1:n). The 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 the matrix A that must be pivoted but no factorized. offset ≥ 0.

a

REAL for slaqp2

DOUBLE PRECISION for dlaqp2

COMPLEX for claqp2

COMPLEX*16 for zlaqp2

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).

On entry, if jpvt(i) ≠ 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.

vn1, vn2

REAL for slaqp2/claqp2

DOUBLE PRECISION for dlaqp2/zlaqp2

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

work

REAL for slaqp2

DOUBLE PRECISION for dlaqp2

COMPLEX for claqp2

COMPLEX*16 for zlaqp2 Workspace array, DIMENSION (n).

Output Parameters

a

On exit, the upper triangle of block A(offset+1:m,1:n) is the triangular factor obtained; the elements in block A(offset+1:m,1:n) below the diagonal, together with the array tau, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:offset,1:n) has been accordingly pivoted, but not factorized.

jpvt

On exit, if jpvt(i) = k, then the i-th column of A*P was the k-th column of A.

tau

REAL for slaqp2

DOUBLE PRECISION for dlaqp2

COMPLEX for claqp2

COMPLEX*16 for zlaqp2

Array, DIMENSION (min(m,n)).

The scalar factors of the elementary reflectors.

vn1, vn2

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