The routine may be called by the names f06trf or nagf_blas_zuhqr.
3Description
f06trf transforms an complex upper Hessenberg matrix to upper triangular form by applying a unitary matrix from the left or the right. is assumed to have real nonzero subdiagonal elements , for , only;
has real diagonal elements. is formed as a sequence of plane rotations in planes to .
If , the rotations are applied from the left:
where and with .
If , the rotations are applied from the right:
where and with .
In either case, is a rotation in the plane, chosen to annihilate .
The plane rotation part of has the form
with real.
4References
None.
5Arguments
1: – Character(1)Input
On entry: specifies whether is operated on from the left or the right.
is pre-multiplied from the left.
is post-multiplied from the right.
Constraint:
or .
2: – IntegerInput
On entry: , the order of the matrix .
Constraint:
.
3: – IntegerInput
4: – IntegerInput
On entry: the dimension of the array c as declared in the (sub)program from which f06trf is called.
The values and .
If or or , an immediate return is effected.
5: – Complex (Kind=nag_wp) arrayOutput
On exit: holds , the cosine of the rotation , for ; holds , the th diagonal element of , if , or , the th diagonal element of , if .
6: – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array s
must be at least
.
On entry: the nonzero subdiagonal elements of :
must hold , for .
On exit: holds , the sine of the rotation , for .
7: – Complex (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
.
On entry: the upper triangular part of the upper Hessenberg matrix .
On exit: the upper triangular matrix . The imaginary parts of the diagonal elements are set to zero.
8: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06trf is called.
Constraint:
.
6Error Indicators and Warnings
None.
7Accuracy
Not applicable.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f06trf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.