F08NGF (DORMHR) multiplies an arbitrary real matrix
by the real orthogonal matrix
which was determined by
F08NEF (DGEHRD) when reducing a real general matrix to Hessenberg form.
SUBROUTINE F08NGF ( |
SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
INTEGER |
M, N, ILO, IHI, LDA, LDC, LWORK, INFO |
REAL (KIND=nag_wp) |
A(LDA,*), TAU(*), C(LDC,*), WORK(max(1,LWORK)) |
CHARACTER(1) |
SIDE, TRANS |
|
F08NGF (DORMHR) is intended to be used following a call to
F08NEF (DGEHRD), which reduces a real general matrix
to upper Hessenberg form
by an orthogonal similarity transformation:
.
F08NEF (DGEHRD) represents the matrix
as a product of
elementary reflectors. Here
and
are values determined by
F08NHF (DGEBAL) when balancing the matrix; if the matrix has not been balanced,
and
.
This routine may be used to form one of the matrix products
overwriting the result on
(which may be any real rectangular matrix).
The computed result differs from the exact result by a matrix
such that
where
is the
machine precision.
The complex analogue of this routine is
F08NUF (ZUNMHR).
This example computes all the eigenvalues of the matrix
, where
and those eigenvectors which correspond to eigenvalues
such that
. Here
is general and must first be reduced to upper Hessenberg form
by
F08NEF (DGEHRD). The program then calls
F08PEF (DHSEQR) to compute the eigenvalues, and
F08PKF (DHSEIN) to compute the required eigenvectors of
by inverse iteration. Finally F08NGF (DORMHR) is called to transform the eigenvectors of
back to eigenvectors of the original matrix
.