1CGEQL2(1)                LAPACK routine (version 3.1)                CGEQL2(1)
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NAME

6       CGEQL2 - a QL factorization of a complex m by n matrix A
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SYNOPSIS

9       SUBROUTINE CGEQL2( 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       CGEQL2  computes a QL factorization of a complex m by n matrix A: A = Q
17       * L.
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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  lower
29               triangle  of  the  subarray  A(m-n+1:m,1:n) contains the n by n
30               lower triangular matrix L; if m <= n, the elements on and below
31               the (n-m)-th superdiagonal contain the m by n lower trapezoidal
32               matrix L; the remaining elements, with the array TAU, represent
33               the unitary matrix Q as a product of elementary reflectors (see
34               Further Details).  LDA     (input) INTEGER The  leading  dimen‐
35               sion of the array A.  LDA >= max(1,M).
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37       TAU     (output) COMPLEX array, dimension (min(M,N))
38               The  scalar  factors  of the elementary reflectors (see Further
39               Details).
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41       WORK    (workspace) COMPLEX array, dimension (N)
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43       INFO    (output) INTEGER
44               = 0: successful exit
45               < 0: if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

48       The matrix Q is represented as a product of elementary reflectors
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50          Q = H(k) . . . H(2) H(1), where k = min(m,n).
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52       Each H(i) has the form
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54          H(i) = I - tau * v * v'
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56       where tau is a complex scalar, and v is  a  complex  vector  with  v(m-
57       k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-
58       k+i-1,n-k+i), and tau in TAU(i).
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63 LAPACK routine (version 3.1)    November 2006                       CGEQL2(1)
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