sorgrq(3)

NAME

SORGRQ - generate an M-by-N real matrix Q with orthonormal

rows,

SYNOPSIS

SUBROUTINE SORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO
)
    INTEGER        INFO, K, LDA, LWORK, M, N
    REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

SORGRQ generates an M-by-N real matrix Q with orthonormal

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

mentary reflectors of order N

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

as returned by SGERQF.

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) REAL 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 SGERQF 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) REAL array, dimension (K)

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

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

WORK (workspace/output) REAL 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

SORGRQ(3)