.TH DGEQL2 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DGEQL2 - a QL factorization of a real m by n matrix A .SH SYNOPSIS .TP 19 SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO ) .TP 19 .ti +4 INTEGER INFO, LDA, M, N .TP 19 .ti +4 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) .SH PURPOSE DGEQL2 computes a QL factorization of a real m by n matrix A: A = Q * L. .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) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (N) .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) . . . H(2) H(1), 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 real scalar, and v is a real vector with .br 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). .br