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

6       DGERQF - an RQ factorization of a real M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       DGERQF  computes an RQ factorization of a real M-by-N matrix A: A = R *
17       Q.
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ARGUMENTS

21       M       (input) INTEGER
22               The number of rows of the matrix A.  M >= 0.
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24       N       (input) INTEGER
25               The number of columns of the matrix A.  N >= 0.
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27       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
28               On entry, the M-by-N matrix A.  On exit, if m <= n,  the  upper
29               triangle  of  the  subarray  A(1:m,n-m+1:n) contains the M-by-M
30               upper triangular matrix R; if m >= n, the elements on and above
31               the  (m-n)-th  subdiagonal contain the M-by-N upper trapezoidal
32               matrix R; the remaining elements, with the array TAU, represent
33               the  orthogonal  matrix  Q  as a product of min(m,n) elementary
34               reflectors (see Further Details).  LDA     (input) INTEGER  The
35               leading dimension of the array A.  LDA >= max(1,M).
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37       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
38               The  scalar  factors  of the elementary reflectors (see Further
39               Details).
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41       WORK      (workspace/output)   DOUBLE   PRECISION   array,    dimension
42       (MAX(1,LWORK))
43               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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45       LWORK   (input) INTEGER
46               The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
47               mum performance LWORK >= M*NB, where NB is the  optimal  block‐
48               size.
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50               If  LWORK  = -1, then a workspace query is assumed; the routine
51               only calculates the optimal size of  the  WORK  array,  returns
52               this  value  as the first entry of the WORK array, and no error
53               message related to LWORK is issued by XERBLA.
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55       INFO    (output) INTEGER
56               = 0:  successful exit
57               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

60       The matrix Q is represented as a product of elementary reflectors
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62          Q = H(1) H(2) . . . H(k), where k = min(m,n).
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64       Each H(i) has the form
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66          H(i) = I - tau * v * v'
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68       where tau is a real scalar, and v is a real vector with
69       v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored  on  exit  in
70       A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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75 LAPACK routine (version 3.1)    November 2006                       DGERQF(1)