sorgql(3)

NAME

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

columns,

SYNOPSIS

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

PURPOSE

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

columns, which is defined as the last N columns of a product of K

elementary reflectors of order M

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

as returned by SGEQLF.

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. M >= N >=

0.

K (input) INTEGER

The number of elementary reflectors whose product

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

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

On entry, the (n-k+i)-th column must contain the

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

1,2,...,k, as returned by SGEQLF in the last k columns of its ar

ray 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 SGEQLF.

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,N). For optimum performance LWORK >= N*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

SORGQL(3)