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## slaqps()

subroutine slaqps | ( | integer | m,
|  | integer | n,
|  | integer | offset,
|  | integer | nb,
|  | integer | kb,
|  | real, dimension( lda, * ) | a,
|  | integer | lda,
|  | integer, dimension( * ) | jpvt,
|  | real, dimension( * ) | tau,
|  | real, dimension( * ) | vn1,
|  | real, dimension( * ) | vn2,
|  | real, dimension( * ) | auxv,
|  | real, dimension( ldf, * ) | f,
|  | integer | ldf )

SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

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

Purpose:

      !>
      !> SLAQPS computes a step of QR factorization with column pivoting
      !> of a real M-by-N matrix A by using Blas-3.  It tries to factorize
      !> NB columns from A starting from the row OFFSET+1, and updates all
      !> of the matrix with Blas-3 xGEMM.
      !>
      !> In some cases, due to catastrophic cancellations, it cannot
      !> factorize NB columns.  Hence, the actual number of factorized
      !> columns is returned in KB.
      !>
      !> 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 A that have been factorized in
      !>          previous steps.
      !>

  [in]

  NB

      !>          NB is INTEGER
      !>          The number of columns to factorize.
      !>

  [out]

  KB

      !>          KB is INTEGER
      !>          The number of columns actually factorized.
      !>

  [in,out]

  A

      !>          A is REAL array, dimension (LDA,N)
      !>          On entry, the M-by-N matrix A.
      !>          On exit, block A(OFFSET+1:M,1:KB) is the triangular
      !>          factor obtained and block A(1:OFFSET,1:N) has been
      !>          accordingly pivoted, but no factorized.
      !>          The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
      !>          been updated.
      !>

  [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)
      !>          JPVT(I) = K <==> Column K of the full matrix A has been
      !>          permuted into position I in AP.
      !>

  [out]

  TAU

      !>          TAU is REAL array, dimension (KB)
      !>          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.
      !>

  [in,out]

  AUXV

      !>          AUXV is REAL array, dimension (NB)
      !>          Auxiliary vector.
      !>

  [in,out]

  F

      !>          F is REAL array, dimension (LDF,NB)
      !>          Matrix F**T = L*Y**T*A.
      !>

  [in]

  LDF

      !>          LDF is INTEGER
      !>          The leading dimension of the array F. LDF >= max(1,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]