f08ngc multiplies an arbitrary real matrix
by the real orthogonal matrix
which was determined by
f08nec when reducing a real general matrix to Hessenberg form.
f08ngc is intended to be used following a call to
f08nec, which reduces a real general matrix
to upper Hessenberg form
by an orthogonal similarity transformation:
.
f08nec represents the matrix
as a product of
elementary reflectors. Here
and
are values determined by
f08nhc when balancing the matrix; if the matrix has not been balanced,
and
.
This function may be used to form one of the matrix products
overwriting the result on
(which may be any real rectangular matrix).
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_ENUM_INT_3
-
On entry, , , and .
Constraint: if , ;
if , .
On entry, , , and .
Constraint: if ,
;
if ,
.
- NE_ENUM_INT_4
-
On entry, , , , and .
Constraint: if and , ;
if and , and ;
if and , ;
if and , and .
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INT_2
-
On entry, and .
Constraint: .
On entry, and .
Constraint: .
- NE_INTERNAL_ERROR
-
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
The computed result differs from the exact result by a matrix
such that
where
is the
machine precision.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The complex analogue of this function is
f08nuc.
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
f08nec. The program then calls
f08pec to compute the eigenvalues, and
f08pkc to compute the required eigenvectors of
by inverse iteration. Finally
f08ngc is called to transform the eigenvectors of
back to eigenvectors of the original matrix
.