1DGEQP3(1)                LAPACK routine (version 3.1)                DGEQP3(1)
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NAME

6       DGEQP3 - a QR factorization with column pivoting of a matrix A
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SYNOPSIS

9       SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, 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 A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

18       DGEQP3  computes a QR factorization with column pivoting of a matrix A:
19       A*P = Q*R  using Level 3 BLAS.
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ARGUMENTS

23       M       (input) INTEGER
24               The number of rows of the matrix A. M >= 0.
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26       N       (input) INTEGER
27               The number of columns of the matrix A.  N >= 0.
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29       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
30               On entry, the M-by-N matrix A.  On exit, the upper triangle  of
31               the  array  contains the min(M,N)-by-N upper trapezoidal matrix
32               R; the elements below the diagonal,  together  with  the  array
33               TAU, represent the orthogonal matrix Q as a product of min(M,N)
34               elementary reflectors.
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36       LDA     (input) INTEGER
37               The leading dimension of the array A. LDA >= max(1,M).
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39       JPVT    (input/output) INTEGER array, dimension (N)
40               On entry, if JPVT(J).ne.0, the J-th column of A is permuted  to
41               the  front  of  A*P  (a leading column); if JPVT(J)=0, the J-th
42               column of A is a free column.  On exit, if JPVT(J)=K, then  the
43               J-th column of A*P was the the K-th column of A.
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45       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
46               The scalar factors of the elementary reflectors.
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48       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
49       (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 >= 3*N+1.   For  optimal
54               performance  LWORK  >=  2*N+( N+1 )*NB, where NB is the optimal
55               blocksize.
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57               If LWORK = -1, then a workspace query is assumed;  the  routine
58               only  calculates  the  optimal  size of the WORK array, returns
59               this value as the first entry of the WORK array, and  no  error
60               message related to LWORK is issued by XERBLA.
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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
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69          Q = H(1) H(2) . . . H(k), where k = min(m,n).
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71       Each H(i) has the form
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73          H(i) = I - tau * v * v'
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75       where tau is a real/complex scalar, and v is a real/complex vector with
76       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on  exit  in  A(i+1:m,i),
77       and tau in TAU(i).
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79       Based on contributions by
80         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
81         X. Sun, Computer Science Dept., Duke University, USA
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86 LAPACK routine (version 3.1)    November 2006                       DGEQP3(1)