1SLAQPS(1)           LAPACK auxiliary routine (version 3.1)           SLAQPS(1)
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NAME

6       SLAQPS  -  a step of QR factorization with column pivoting of a real M-
7       by-N matrix A by using Blas-3
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SYNOPSIS

10       SUBROUTINE SLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU,  VN1,  VN2,
11                          AUXV, F, LDF )
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13           INTEGER        KB, LDA, LDF, M, N, NB, OFFSET
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15           INTEGER        JPVT( * )
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17           REAL           A(  LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), VN1(
18                          * ), VN2( * )
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PURPOSE

21       SLAQPS computes a step of QR factorization with column  pivoting  of  a
22       real M-by-N matrix A by using Blas-3.  It tries to factorize NB columns
23       from A starting from the row OFFSET+1, and updates all  of  the  matrix
24       with Blas-3 xGEMM.
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26       In  some  cases, due to catastrophic cancellations, it cannot factorize
27       NB columns.  Hence, the actual number of factorized columns is returned
28       in KB.
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30       Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
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ARGUMENTS

34       M       (input) INTEGER
35               The number of rows of the matrix A. M >= 0.
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37       N       (input) INTEGER
38               The number of columns of the matrix A. N >= 0
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40       OFFSET  (input) INTEGER
41               The  number  of rows of A that have been factorized in previous
42               steps.
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44       NB      (input) INTEGER
45               The number of columns to factorize.
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47       KB      (output) INTEGER
48               The number of columns actually factorized.
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50       A       (input/output) REAL array, dimension (LDA,N)
51               On  entry,  the  M-by-N  matrix  A.   On  exit,  block   A(OFF‐
52               SET+1:M,1:KB) is the triangular
53               factor  obtained and block A(1:OFFSET,1:N) has been accordingly
54               pivoted, but no factorized.  The  rest  of  the  matrix,  block
55               A(OFFSET+1:M,KB+1:N) has been updated.
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57       LDA     (input) INTEGER
58               The leading dimension of the array A. LDA >= max(1,M).
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60       JPVT    (input/output) INTEGER array, dimension (N)
61               JPVT(I)  =  K  <==> Column K of the full matrix A has been per‐
62               muted into position I in AP.
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64       TAU     (output) REAL array, dimension (KB)
65               The scalar factors of the elementary reflectors.
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67       VN1     (input/output) REAL array, dimension (N)
68               The vector with the partial column norms.
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70       VN2     (input/output) REAL array, dimension (N)
71               The vector with the exact column norms.
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73       AUXV    (input/output) REAL array, dimension (NB)
74               Auxiliar vector.
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76       F       (input/output) REAL array, dimension (LDF,NB)
77               Matrix F' = L*Y'*A.
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79       LDF     (input) INTEGER
80               The leading dimension of the array F. LDF >= max(1,N).
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FURTHER DETAILS

83       Based on contributions by
84         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
85         X. Sun, Computer Science Dept., Duke University, USA
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87       Partial column norm updating strategy modified by
88         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
89         University of Zagreb, Croatia.
90         June 2006.
91       For more details see LAPACK Working Note 176.
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95 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLAQPS(1)