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

6       ZLAQPS  -  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 ZLAQPS( 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           DOUBLE         PRECISION VN1( * ), VN2( * )
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19           COMPLEX*16     A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
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PURPOSE

22       ZLAQPS  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*16 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*16 array, dimension (KB)
66               The scalar factors of the elementary reflectors.
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68       VN1     (input/output) DOUBLE PRECISION array, dimension (N)
69               The vector with the partial column norms.
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71       VN2     (input/output) DOUBLE PRECISION array, dimension (N)
72               The vector with the exact column norms.
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74       AUXV    (input/output) COMPLEX*16 array, dimension (NB)
75               Auxiliar vector.
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77       F       (input/output) COMPLEX*16 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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91 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAQPS(1)