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## man page of LAPACK-3

### LAPACK-3: computes a QL factorization of a complex m by n matrix A

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## NAME

LAPACK-3 - computes a QL factorization of a complex m by n matrix A## SYNOPSIS

SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO ) INTEGER INFO, LDA, M, N COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )PURPOSE

ZGEQL2 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*16 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*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace) COMPLEX*16 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-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). LAPACK routine (version 3.2.2) March 2011 LAPACK-3(3)

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