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NAME

        ZGELQ2 - compute an LQ factorization of a complex m by n matrix A
 

SYNOPSIS

        SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO )
 
            INTEGER        INFO, LDA, M, N
 
            COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
 

PURPOSE

        ZGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L
        * Q.
 

ARGUMENTS

        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.
 
        N       (input) INTEGER
                The number of columns of the matrix A.  N >= 0.
 
        A       (input/output) COMPLEX*16 array, dimension (LDA,N)
                On entry, the m by n matrix A.  On exit, the  elements  on  and
                below the diagonal of the array contain the m by min(m,n) lower
                trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
                elements  above the diagonal, with the array TAU, represent the
                unitary matrix Q as a product  of  elementary  reflectors  (see
                Further  Details).   LDA     (input) INTEGER The leading dimen‐
                sion of the array A.  LDA >= max(1,M).
 
        TAU     (output) COMPLEX*16 array, dimension (min(M,N))
                The scalar factors of the elementary  reflectors  (see  Further
                Details).
 
        WORK    (workspace) COMPLEX*16 array, dimension (M)
 
        INFO    (output) INTEGER
                = 0: successful exit
                < 0: if INFO = -i, the i-th argument had an illegal value
        The matrix Q is represented as a product of elementary reflectors
 
H(1)’, where k = min(m,n).
 
        Each H(i) has the form
 
           H(i) = I - tau * v * v’
 
        where  tau is a complex scalar, and v is a complex vector with v(1:i-1)
        = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n),  and
        tau in TAU(i).
 

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