?orgr2/?ungr2

Generates all or part of the orthogonal/unitary matrix Q from an RQ factorization determined by ?gerqf (unblocked algorithm).

Syntax

call sorgr2( m, n, k, a, lda, tau, work, info )

call dorgr2( m, n, k, a, lda, tau, work, info )

call cungr2( m, n, k, a, lda, tau, work, info )

call zungr2( m, n, k, a, lda, tau, work, info )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

The routine ?orgr2/?ungr2 generates an m-by-n real matrix Q with orthonormal 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) for real flavors, or Q = (H(1))^H*(H(2))^H*...*(H(k))^H for complex flavors as returned by ?gerqf.

Input Parameters

m

INTEGER. The number of rows of the matrix Q. m ≥ 0.

n

INTEGER. The number of columns of the matrix Q. n ≥ m

k

INTEGER.

The number of elementary reflectors whose product defines the matrix Q. m ≥ k ≥ 0.

a

REAL for sorgr2

DOUBLE PRECISION for dorgr2

COMPLEX for cungr2

DOUBLE COMPLEX for zungr2.

Array, DIMENSION (lda, n).

On entry, the ( m- k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,..., k, as returned by ?gerqf in the last k rows of its array argument a.

lda

INTEGER. The leading dimension of the array a. lda ≥ max(1,m).

tau

REAL for sorgr2

DOUBLE PRECISION for dorgr2

COMPLEX for cungr2

DOUBLE COMPLEX for zungr2.

Array, DIMENSION (k).tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by ?gerqf.

work

REAL for sorgr2

DOUBLE PRECISION for dorgr2

COMPLEX for cungr2

DOUBLE COMPLEX for zungr2.

Workspace array, DIMENSION (m).

Output Parameters

a

On exit, the m-by-n matrix Q.

info

INTEGER.

= 0: successful exit

< 0: if info = -i, the i-th argument has an illegal value