1SGEQP3(1)                LAPACK routine (version 3.2)                SGEQP3(1)
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NAME

6       SGEQP3 - computes a QR factorization with column pivoting of a matrix A
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SYNOPSIS

9       SUBROUTINE SGEQP3( 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           REAL           A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

18       SGEQP3  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) REAL 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) REAL array, dimension (min(M,N))
45               The scalar factors of the elementary reflectors.
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47       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
48               On exit, if INFO=0, WORK(1) returns the optimal LWORK.
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50       LWORK   (input) INTEGER
51               The  dimension  of the array WORK. LWORK >= 3*N+1.  For optimal
52               performance LWORK >= 2*N+( N+1 )*NB, where NB  is  the  optimal
53               blocksize.   If  LWORK = -1, then a workspace query is assumed;
54               the routine only calculates the optimal size of the WORK array,
55               returns this value as the first entry of the WORK array, and no
56               error message related to LWORK is issued by XERBLA.
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58       INFO    (output) INTEGER
59               = 0: successful exit.
60               < 0: if INFO = -i, the i-th argument had an illegal value.
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FURTHER DETAILS

63       The matrix Q is represented as a product of elementary reflectors
64          Q = H(1) H(2) . . . H(k), where k = min(m,n).
65       Each H(i) has the form
66          H(i) = I - tau * v * v'
67       where tau is a real/complex scalar, and v is a real/complex vector with
68       v(1:i-1)  =  0  and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
69       and tau in TAU(i).
70       Based on contributions by
71         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
72         X. Sun, Computer Science Dept., Duke University, USA
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76 LAPACK routine (version 3.2)    November 2008                       SGEQP3(1)