The function may be called by the names: f08jac, nag_lapackeig_dstev or nag_dstev.
f08jac 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: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
2: – Nag_JobTypeInput
On entry: indicates whether eigenvectors are computed.
Only eigenvalues are computed.
Eigenvalues and eigenvectors are computed.
3: – IntegerInput
On entry: , the order of the matrix.
4: – doubleInput/Output
Note: the dimension, dim, of the array d
must be at least
On entry: the diagonal elements of the tridiagonal matrix .
On exit: if NE_NOERROR, the eigenvalues in ascending order.
5: – doubleInput/Output
Note: the dimension, dim, of the array e
must be at least
On entry: the subdiagonal elements of the tridiagonal matrix .
On entry: the stride separating row or column elements (depending on the value of order) in the array z.
if , ;
8: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
The algorithm failed to converge; off-diagonal elements of e did not converge to zero.
On entry, , and .
Constraint: if , ;
On entry, .
On entry, . Constraint: .
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.
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.
The computed eigenvalues and eigenvectors are exact for a nearby matrix , where
Background information to multithreading can be found in the Multithreading documentation.
f08jac is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08jac 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 function. 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.