It searches for zero or negligible off-diagonal elements of
to see if the matrix splits into block diagonal form:
It performs bisection on each of the blocks
and returns the block index of each computed eigenvalue, so that a subsequent call to
f08jkf to compute eigenvectors can also take advantage of the block structure.
-
1:
– Character(1)
Input
-
On entry: indicates which eigenvalues are required.
- All the eigenvalues are required.
- All the eigenvalues in the half-open interval (vl,vu] are required.
- Eigenvalues with indices il to iu are required.
Constraint:
, or .
-
2:
– Character(1)
Input
-
On entry: indicates the order in which the eigenvalues and their block numbers are to be stored.
- The eigenvalues are to be grouped by split-off block and ordered from smallest to largest within each block.
- The eigenvalues for the entire matrix are to be ordered from smallest to largest.
Constraint:
or .
-
3:
– Integer
Input
-
On entry: , the order of the matrix .
Constraint:
.
-
4:
– Real (Kind=nag_wp)
Input
-
5:
– Real (Kind=nag_wp)
Input
-
On entry: if
, the lower and upper bounds, respectively, of the half-open interval
within which the required eigenvalues lie.
If
or
,
vl is not referenced.
Constraint:
if , .
-
6:
– Integer
Input
-
7:
– Integer
Input
-
On entry: if
, the indices of the first and last eigenvalues, respectively, to be computed (assuming that the eigenvalues are in ascending order).
If
or
,
il is not referenced.
Constraint:
if , .
-
8:
– Real (Kind=nag_wp)
Input
-
On entry: the absolute tolerance to which each eigenvalue is required. An eigenvalue (or cluster) is considered to have converged if it lies in an interval of width . If , the tolerance is taken as .
-
9:
– Real (Kind=nag_wp) array
Input
-
Note: the dimension of the array
d
must be at least
.
On entry: the diagonal elements of the tridiagonal matrix .
-
10:
– Real (Kind=nag_wp) array
Input
-
Note: the dimension of the array
e
must be at least
.
On entry: the off-diagonal elements of the tridiagonal matrix .
-
11:
– Integer
Output
-
On exit: , the actual number of eigenvalues found.
-
12:
– Integer
Output
-
On exit: the number of diagonal blocks which constitute the tridiagonal matrix .
-
13:
– Real (Kind=nag_wp) array
Output
-
On exit: the required eigenvalues of the tridiagonal matrix stored in to .
-
14:
– Integer array
Output
-
On exit: at each row/column
where
is zero or negligible,
is considered to split into a block diagonal matrix and
contains the block number of the eigenvalue stored in
, for
. Note that
for some
whenever
or
(see
Section 6) and
or
.
-
15:
– Integer array
Output
-
On exit: the leading
nsplit elements contain the points at which
splits up into sub-matrices as follows. The first sub-matrix consists of rows/columns
to
, the second sub-matrix consists of rows/columns
to
,
, and the
nsplit(th) sub-matrix consists of rows/columns
to
(
).
-
16:
– Real (Kind=nag_wp) array
Workspace
-
-
17:
– Integer array
Workspace
-
-
18:
– Integer
Output
-
On exit:
unless the routine detects an error (see
Section 6).
If failures with
are causing persistent trouble and you have checked that the routine is being called correctly, please contact
NAG.
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 routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
There is no complex analogue of this routine.