.TH CGERQ2 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CGERQ2 - an RQ factorization of a complex m by n matrix A .SH SYNOPSIS .TP 19 SUBROUTINE CGERQ2( 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 CGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * 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, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). .TP 8 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(1)\(aq H(2)\(aq . . . H(k)\(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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). .br