Previous: zgerq2 Up: ../lapack-z.html Next: zgesv
NAME ZGERQF - compute an RQ factorization of a complex M-by-N matrix A SYNOPSIS SUBROUTINE ZGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) INTEGER INFO, LDA, LWORK, M, N COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK ) PURPOSE ZGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R * 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, 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 subdi- agonal 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 min(m,n) 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 (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. 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(1)' H(2)' . . . H(k)', 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(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).