?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

mkl.fi

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

DOUBLE COMPLEX 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

DOUBLE COMPLEX 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

DOUBLE COMPLEX 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.