.TH CGELQ2 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CGELQ2 - an LQ factorization of a complex m by n matrix A .SH SYNOPSIS .TP 19 SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO ) .TP 19 .ti +4 INTEGER INFO, LDA, M, N .TP 19 .ti +4 COMPLEX A( LDA, * ), TAU( * ), WORK( * ) .SH PURPOSE CGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q. .br .SH ARGUMENTS .TP 8 M (input) INTEGER The number of rows of the matrix A. M >= 0. .TP 8 N (input) INTEGER The number of columns of the matrix A. N >= 0. .TP 8 A (input/output) COMPLEX 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). .TP 8 TAU (output) COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). .TP 8 WORK (workspace) COMPLEX array, dimension (M) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .SH FURTHER DETAILS The matrix Q is represented as a product of elementary reflectors Q = H(k)\(aq . . . H(2)\(aq H(1)\(aq, where k = min(m,n). .br Each H(i) has the form .br H(i) = I - tau * v * v\(aq .br 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). .br