cgeql2 man page on IRIX

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CGEQL2(3F)							    CGEQL2(3F)

NAME
     CGEQL2 - compute a QL factorization of a complex m by n matrix A

SYNOPSIS
     SUBROUTINE CGEQL2( M, N, A, LDA, TAU, WORK, INFO )

	 INTEGER	INFO, LDA, M, N

	 COMPLEX	A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
     CGEQL2 computes a QL factorization of a complex m by n matrix A:  A = Q *
     L.

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 array, dimension (LDA,N)
	     On entry, the m by n matrix A.  On exit, if m >= n, the lower
	     triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower
	     triangular matrix L; if m <= n, the elements on and below the
	     (n-m)-th superdiagonal contain the m by n lower trapezoidal
	     matrix L; the remaining elements, with the array TAU, represent
	     the unitary matrix Q as a product of elementary reflectors (see
	     Further Details).	LDA	(input) INTEGER The leading dimension
	     of the array A.  LDA >= max(1,M).

     TAU     (output) COMPLEX array, dimension (min(M,N))
	     The scalar factors of the elementary reflectors (see Further
	     Details).

     WORK    (workspace) COMPLEX array, dimension (N)

     INFO    (output) INTEGER
	     = 0: successful exit
	     < 0: if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
     The matrix Q is represented as a product of elementary reflectors

	Q = H(k) . . . H(2) 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(m-

									Page 1

CGEQL2(3F)							    CGEQL2(3F)

     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-
     k+i-1,n-k+i), and tau in TAU(i).

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