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## man page of LAPACK-3

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

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## NAME

LAPACK-3 - computes 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 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 (M) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal valueFURTHER 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(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). LAPACK routine (version 3.2.2) March 2011 LAPACK-3(3)

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