f08wtc is usually the third step in the solution of the complex generalized eigenvalue problem
The (optional) first step balances the two matrices using
f08wvc. In the second step, matrix
is reduced to upper triangular form using the
factorization function
f08asc and this unitary transformation
is applied to matrix
by calling
f08auc. The driver,
f08wqc, solves the complex generalized eigenvalue problem by combining all the required steps including those just listed.
f08wtc reduces a pair of complex matrices
, where
is triangular, to the generalized upper Hessenberg form using unitary transformations. This two-sided transformation is of the form
where
is an upper Hessenberg matrix,
is an upper triangular matrix and
and
are unitary matrices determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices
and
, so that
Moler C B and Stewart G W (1973) An algorithm for generalized matrix eigenproblems SIAM J. Numer. Anal. 10 241–256
- 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_2
-
On entry, , and .
Constraint: if or , ;
if , .
On entry, , and .
Constraint: if or , ;
if , .
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INT_2
-
On entry, and .
Constraint: .
On entry, and .
Constraint: .
- NE_INT_3
-
On entry, , and .
Constraint: if , ;
if , and .
- 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 reduction to the generalized Hessenberg form is implemented using unitary transformations which are backward stable.
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.
This function is usually followed by
f08xsc which implements the
algorithm for computing generalized eigenvalues of a reduced pair of matrices.
The real analogue of this function is
f08wfc.