The routine may be called by the names f06skf, nagf_blas_ztbsv or its BLAS name ztbsv.
3Description
f06skf performs one of the matrix-vector operations
where is an complex triangular band matrix with subdiagonals or superdiagonals, and is an -element complex vector. denotes or equivalently ; denotes or equivalently .
No test for singularity or near-singularity of is included in this routine. Such tests must be performed before calling this routine.
4References
None.
5Arguments
1: – Character(1)Input
On entry: specifies whether is upper or lower triangular.
is upper triangular.
is lower triangular.
Constraint:
or .
2: – Character(1)Input
On entry: specifies the operation to be performed.
.
.
.
Constraint:
, or .
3: – Character(1)Input
On entry: specifies whether has nonunit or unit diagonal elements.
The diagonal elements are stored explicitly.
The diagonal elements are assumed to be , and are not referenced.
Constraint:
or .
4: – IntegerInput
On entry: , the order of the matrix .
Constraint:
.
5: – IntegerInput
On entry: , the number of subdiagonals or superdiagonals of the matrix .
Constraint:
.
6: – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array a
must be at least
.
On entry: the triangular band matrix
The matrix is stored in rows to , more precisely,
if , the elements of the upper triangle of within the band must be stored with element in ;
if , the elements of the lower triangle of within the band must be stored with element in
If , the diagonal elements of are assumed to be , and are not referenced.
7: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06skf is called.
Constraint:
.
8: – Complex (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array x
must be at least
.
On entry: the vector .
If ,
must be stored in , for .
If ,
must be stored in , for .
On exit: the updated vector stored in the array elements used to supply the original vector .
9: – IntegerInput
On entry: the increment in the subscripts of x between successive elements of .
Constraint:
.
6Error Indicators and Warnings
None.
7Accuracy
Not applicable.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.