SLAQP2 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.

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 the matrix A that must be pivoted


          but no factorized. OFFSET >= 0.

A

          A is REAL array, dimension (LDA,N)


          On entry, the M-by-N matrix 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 no factorized.

LDA

          LDA is INTEGER


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

JPVT

          JPVT is INTEGER array, dimension (N)


          On entry, if JPVT(i) .ne. 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.


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


          was the k-th column of A.

TAU

          TAU is REAL array, dimension (min(M,N))


          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.

WORK

          WORK is REAL array, dimension (N)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

LAPACK Working Note 176