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
f08jkc to compute eigenvectors can also take advantage of the block structure.
-
1:
– Nag_RangeType
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:
– Nag_EigValRankType
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:
– double
Input
-
5:
– double
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:
– double
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:
– const double
Input
-
Note: the dimension,
dim, of the array
d
must be at least
.
On entry: the diagonal elements of the tridiagonal matrix .
-
10:
– const double
Input
-
Note: the dimension,
dim, 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:
– double
Output
-
On exit: the required eigenvalues of the tridiagonal matrix stored in to .
-
14:
– Integer
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
NE_CONVERGENCE (see
Section 6) and
or
.
-
15:
– Integer
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:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_CONVERGENCE
-
If or , the algorithm failed to compute some (or all) of the required eigenvalues to the required accuracy. More precisely, indicates that eigenvalue (stored in ) failed to converge.
If , the algorithm failed to compute some (or all) of the required eigenvalues. Try calling the function again with .
No eigenvalues have been computed. The floating-point arithmetic on the computer is not behaving as expected.
- NE_ENUM_INT_3
-
On entry, , , and .
Constraint: if , .
- NE_ENUM_REAL_2
-
On entry, , and .
Constraint: if , .
- NE_INT
-
On entry, .
Constraint: .
- NE_INTERNAL_ERROR
-
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
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 function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
There is no complex analogue of this function.