1SLAQPS(1)           LAPACK auxiliary routine (version 3.2)           SLAQPS(1)
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NAME

6       SLAQPS  - computes a step of QR factorization with column pivoting of a
7       real M-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.
25       In  some  cases, due to catastrophic cancellations, it cannot factorize
26       NB columns.  Hence, the actual number of factorized columns is returned
27       in KB.
28       Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
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ARGUMENTS

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

80       Based on contributions by
81         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
82         X. Sun, Computer Science Dept., Duke University, USA
83       Partial column norm updating strategy modified by
84         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
85         University of Zagreb, Croatia.
86         June 2006.
87       For more details see LAPACK Working Note 176.
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91 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLAQPS(1)
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