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

6       DGERQF - computes 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

20       M       (input) INTEGER
21               The number of rows of the matrix A.  M >= 0.
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23       N       (input) INTEGER
24               The number of columns of the matrix A.  N >= 0.
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26       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
27               On entry, the M-by-N matrix A.  On exit, if m <= n,  the  upper
28               triangle  of  the  subarray  A(1:m,n-m+1:n) contains the M-by-M
29               upper triangular matrix R; if m >= n, the elements on and above
30               the  (m-n)-th  subdiagonal contain the M-by-N upper trapezoidal
31               matrix R; the remaining elements, with the array TAU, represent
32               the  orthogonal  matrix  Q  as a product of min(m,n) elementary
33               reflectors (see Further Details).  LDA     (input) INTEGER  The
34               leading dimension of the array A.  LDA >= max(1,M).
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36       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
37               The  scalar  factors  of the elementary reflectors (see Further
38               Details).
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40       WORK      (workspace/output)   DOUBLE   PRECISION   array,    dimension
41       (MAX(1,LWORK))
42               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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44       LWORK   (input) INTEGER
45               The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
46               mum performance LWORK >= M*NB, where NB is the  optimal  block‐
47               size.   If  LWORK  = -1, then a workspace query is assumed; the
48               routine only calculates the optimal size  of  the  WORK  array,
49               returns this value as the first entry of the WORK array, and no
50               error message related to LWORK is issued by XERBLA.
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52       INFO    (output) INTEGER
53               = 0:  successful exit
54               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

57       The matrix Q is represented as a product of elementary reflectors
58          Q = H(1) H(2) . . . H(k), where k = min(m,n).
59       Each H(i) has the form
60          H(i) = I - tau * v * v'
61       where tau is a real scalar, and v is a real vector with
62       v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored  on  exit  in
63       A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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67 LAPACK routine (version 3.2)    November 2008                       DGERQF(1)