1CGERQ2(1)                LAPACK routine (version 3.1)                CGERQ2(1)
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NAME

6       CGERQ2 - an RQ factorization of a complex m by n matrix A
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SYNOPSIS

9       SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
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11           INTEGER        INFO, LDA, M, N
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13           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       CGERQ2 computes an RQ factorization of a complex 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) COMPLEX 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 unitary matrix Q as a product of elementary reflectors (see
34               Further Details).
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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       TAU     (output) COMPLEX array, dimension (min(M,N))
40               The scalar factors of the elementary  reflectors  (see  Further
41               Details).
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43       WORK    (workspace) COMPLEX array, dimension (M)
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45       INFO    (output) INTEGER
46               = 0: successful exit
47               < 0: if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

50       The matrix Q is represented as a product of elementary reflectors
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52          Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
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54       Each H(i) has the form
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56          H(i) = I - tau * v * v'
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58       where  tau  is  a  complex  scalar, and v is a complex vector with v(n-
59       k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
60       A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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65 LAPACK routine (version 3.1)    November 2006                       CGERQ2(1)