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

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

10       SUBROUTINE CLAQPS( 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           VN1( * ), VN2( * )
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19           COMPLEX        A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
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PURPOSE

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

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

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