The routine may be called by the names f06tvf or nagf_blas_zutsrh.
3Description
f06tvf transforms an complex upper triangular matrix with real diagonal elements, to an upper Hessenberg matrix , by applying a given sequence of plane rotations from either the left or the right, in planes to ; has real nonzero subdiagonal elements , for only.
If , the rotations are applied from the left:
where .
If , the rotations are applied from the right:
where .
In either case, is a rotation in the plane.
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 matrices and .
Constraint:
.
3: – IntegerInput
4: – IntegerInput
On entry: the values and .
If or or , an immediate return is effected.
5: – Complex (Kind=nag_wp) arrayInput
Note: the dimension of the array c
must be at least
.
On entry: must hold , the cosine of the rotation , for .
6: – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array s
must be at least
.
On entry: must hold , the sine of the rotation , for .
On exit: holds , the subdiagonal element of , 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 matrix . The imaginary parts of the diagonal elements must be zero.
On exit: the upper triangular part of the upper Hessenberg matrix .
8: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06tvf 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.