LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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slaqps.f File Reference

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Functions/Subroutines

subroutine slaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
 SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Function/Subroutine Documentation

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)
          Auxiliar 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.
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 [PDF]

Definition at line 178 of file slaqps.f.

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