1DGEQP3(1)                LAPACK routine (version 3.2)                DGEQP3(1)
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NAME

6       DGEQP3 - computes 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

22       M       (input) INTEGER
23               The number of rows of the matrix A. M >= 0.
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25       N       (input) INTEGER
26               The number of columns of the matrix A.  N >= 0.
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28       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
29               On entry, the M-by-N matrix A.  On exit, the upper triangle  of
30               the  array  contains the min(M,N)-by-N upper trapezoidal matrix
31               R; the elements below the diagonal,  together  with  the  array
32               TAU, represent the orthogonal matrix Q as a product of min(M,N)
33               elementary reflectors.
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35       LDA     (input) INTEGER
36               The leading dimension of the array A. LDA >= max(1,M).
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38       JPVT    (input/output) INTEGER array, dimension (N)
39               On entry, if JPVT(J).ne.0, the J-th column of A is permuted  to
40               the  front  of  A*P  (a leading column); if JPVT(J)=0, the J-th
41               column of A is a free column.  On exit, if JPVT(J)=K, then  the
42               J-th column of A*P was the the K-th column of A.
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44       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
45               The scalar factors of the elementary reflectors.
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47       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
48       (MAX(1,LWORK))
49               On exit, if INFO=0, WORK(1) returns the optimal LWORK.
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51       LWORK   (input) INTEGER
52               The dimension of the array WORK. LWORK >= 3*N+1.   For  optimal
53               performance  LWORK  >=  2*N+( N+1 )*NB, where NB is the optimal
54               blocksize.  If LWORK = -1, then a workspace query  is  assumed;
55               the routine only calculates the optimal size of the WORK array,
56               returns this value as the first entry of the WORK array, and no
57               error message related to LWORK is issued by XERBLA.
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59       INFO    (output) INTEGER
60               = 0: successful exit.
61               < 0: if INFO = -i, the i-th argument had an illegal value.
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FURTHER DETAILS

64       The matrix Q is represented as a product of elementary reflectors
65          Q = H(1) H(2) . . . H(k), where k = min(m,n).
66       Each H(i) has the form
67          H(i) = I - tau * v * v'
68       where tau is a real/complex scalar, and v is a real/complex vector with
69       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on  exit  in  A(i+1:m,i),
70       and tau in TAU(i).
71       Based on contributions by
72         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
73         X. Sun, Computer Science Dept., Duke University, USA
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77 LAPACK routine (version 3.2)    November 2008                       DGEQP3(1)