1ZGEQP3(1)                LAPACK routine (version 3.2)                ZGEQP3(1)
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NAME

6       ZGEQP3 - computes a QR factorization with column pivoting of a matrix A
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SYNOPSIS

9       SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           INTEGER        JPVT( * )
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15           DOUBLE         PRECISION RWORK( * )
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17           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

20       ZGEQP3  computes a QR factorization with column pivoting of a matrix A:
21       A*P = Q*R  using Level 3 BLAS.
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ARGUMENTS

24       M       (input) INTEGER
25               The number of rows of the matrix A. M >= 0.
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27       N       (input) INTEGER
28               The number of columns of the matrix A.  N >= 0.
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30       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
31               On entry, the M-by-N matrix A.  On exit, the upper triangle  of
32               the  array  contains the min(M,N)-by-N upper trapezoidal matrix
33               R; the elements below the diagonal,  together  with  the  array
34               TAU,  represent  the  unitary matrix Q as a product of min(M,N)
35               elementary reflectors.
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37       LDA     (input) INTEGER
38               The leading dimension of the array A. LDA >= max(1,M).
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40       JPVT    (input/output) INTEGER array, dimension (N)
41               On entry, if JPVT(J).ne.0, the J-th column of A is permuted  to
42               the  front  of  A*P  (a leading column); if JPVT(J)=0, the J-th
43               column of A is a free column.  On exit, if JPVT(J)=K, then  the
44               J-th column of A*P was the the K-th column of A.
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46       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
47               The scalar factors of the elementary reflectors.
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49       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
50               On exit, if INFO=0, WORK(1) returns the optimal LWORK.
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52       LWORK   (input) INTEGER
53               The  dimension  of  the  array WORK. LWORK >= N+1.  For optimal
54               performance LWORK >= ( N+1 )*NB, where NB is the optimal block‐
55               size.   If  LWORK  = -1, then a workspace query is assumed; the
56               routine only calculates the optimal size  of  the  WORK  array,
57               returns this value as the first entry of the WORK array, and no
58               error message related to LWORK is issued by XERBLA.
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60       RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)
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62       INFO    (output) INTEGER
63               = 0: successful exit.
64               < 0: if INFO = -i, the i-th argument had an illegal value.
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FURTHER DETAILS

67       The matrix Q is represented as a product of elementary reflectors
68          Q = H(1) H(2) . . . H(k), where k = min(m,n).
69       Each H(i) has the form
70          H(i) = I - tau * v * v'
71       where tau is a real/complex scalar, and v is a real/complex vector with
72       v(1:i-1)  =  0  and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
73       and tau in TAU(i).
74       Based on contributions by
75         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
76         X. Sun, Computer Science Dept., Duke University, USA
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80 LAPACK routine (version 3.2)    November 2008                       ZGEQP3(1)