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## slaqp2()

subroutine slaqp2 | ( | integer | m,
|  | integer | n,
|  | integer | offset,
|  | real, dimension( lda, * ) | a,
|  | integer | lda,
|  | 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.

Download SLAQP2 + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix A. M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix A. N >= 0.
      !>

  [in]

  OFFSET

      !>          OFFSET is INTEGER
      !>          The number of rows of the matrix A that must be pivoted
      !>          but no factorized. OFFSET >= 0.
      !>

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [in,out]

  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.
      !>

  [out]

  TAU

      !>          TAU is REAL array, dimension (min(M,N))
      !>          The scalar factors of the elementary reflectors.
      !>

  [in,out]

  VN1

      !>          VN1 is REAL array, dimension (N)
      !>          The vector with the partial column norms.
      !>

  [in,out]

  VN2

      !>          VN2 is REAL array, dimension (N)
      !>          The vector with the exact column norms.
      !>

  [out]

  WORK

      !>          WORK is REAL array, dimension (N)
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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 [PDF]