The routine may be called by the names f08jaf, nagf_lapackeig_dstev or its LAPACK name dstev.
f08jaf computes all the eigenvalues and, optionally, all the eigenvectors of using a combination of the and algorithms, with an implicit shift.
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia https://www.netlib.org/lapack/lug
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
1: – Character(1)Input
On entry: indicates whether eigenvectors are computed.
Only eigenvalues are computed.
Eigenvalues and eigenvectors are computed.
2: – IntegerInput
On entry: , the order of the matrix.
3: – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array d
must be at least
On entry: the diagonal elements of the tridiagonal matrix .
On exit: if , the eigenvalues in ascending order.
4: – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array e
must be at least
On entry: the subdiagonal elements of the tridiagonal matrix .
Background information to multithreading can be found in the Multithreading documentation.
f08jaf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08jaf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
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.
The total number of floating-point operations is proportional to if and is proportional to if .
This example finds all the eigenvalues and eigenvectors of the symmetric tridiagonal matrix
together with approximate error bounds for the computed eigenvalues and eigenvectors.