slaqp2 (3)

Functions/Subroutines

subroutine slaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)

SLAQP2 computes a QR factorization with column pivoting of the matrix block.

subroutine slaqp2 (integerM, integerN, integerOFFSET, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )VN1, real, dimension( * )VN2, real, dimension( * )WORK)

SLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

 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.

Parameters:

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)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

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.

References:

LAPACK Working Note 176

Definition at line 149 of file slaqp2.f.

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