The routine may be called by the names f06qvf or nagf_blas_dutsrh.
3Description
f06qvf transforms an real upper triangular matrix to an upper Hessenberg matrix , by applying a given sequence of plane rotations from either the left or the right, in planes to ; has 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
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: – Real (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: – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
.
On entry: the upper triangular matrix .
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 f06qvf 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.