cungrq(3)

NAME

CUNGRQ - generate an M-by-N complex matrix Q with or

thonormal rows,

SYNOPSIS

SUBROUTINE CUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO
)
    INTEGER        INFO, K, LDA, LWORK, M, N
    COMPLEX        A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

CUNGRQ generates an M-by-N complex matrix Q with orthonor

mal rows, which is defined as the last M rows of a product of K

elementary reflectors of order N

Q = H(1)' H(2)' . . . H(k)'

as returned by CGERQF.

ARGUMENTS

M (input) INTEGER

The number of rows of the matrix Q. M >= 0.

N (input) INTEGER

The number of columns of the matrix Q. N >= M.

K (input) INTEGER

The number of elementary reflectors whose product

defines the matrix Q. M >= K >= 0.

A (input/output) COMPLEX array, dimension (LDA,N)

On entry, the (m-k+i)-th row must contain the vec

tor which defines the elementary reflector H(i), for i =

1,2,...,k, as returned by CGERQF in the last k rows of its array

argument A. On exit, the M-by-N matrix Q.

LDA (input) INTEGER

The first dimension of the array A. LDA >=

max(1,M).

TAU (input) COMPLEX array, dimension (K)

TAU(i) must contain the scalar factor of the ele

mentary reflector H(i), as returned by CGERQF.

WORK (workspace/output) COMPLEX 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.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument has an ille

gal value

LAPACK version 3.0 15 June 2000

CUNGRQ(3)