EVASF
Computes the largest or smallest eigenvalues of a real symmetric matrix.
Required Arguments
NEVAL — Number of eigenvalues to be computed. (Input)
A — Real symmetric matrix of order N. (Input)
SMALL — Logical variable. (Input)
If .TRUE., the smallest NEVAL eigenvalues are computed. If .FALSE., the largest NEVAL eigenvalues are computed.
EVAL — Real vector of length NEVAL containing the eigenvalues of A in decreasing order of magnitude. (Output)
Optional Arguments
N — Order of the matrix A. (Input)
Default: N = SIZE (A,2).
LDA — Leading dimension of A exactly as specified in the dimension statement in the calling program. (Input)
Default: LDA = SIZE (A,1).
FORTRAN 90 Interface
Generic: CALL EVASF (NEVAL, A, SMALL, EVAL [,…])
Specific: The specific interface names are S_EVASF and D_EVASF.
FORTRAN 77 Interface
Single: CALL EVASF (N, NEVAL, A, LDA, SMALL, EVAL)
Double: The double precision name is DEVASF.
Description
Routine EVASF computes the largest or smallest eigenvalues of a real symmetric matrix. Orthogonal similarity transformations are used to reduce the matrix to an equivalent symmetric tridiagonal matrix. Then, an implicit rational QR algorithm is used to compute the eigenvalues of this tridiagonal matrix.
The reduction routine is based on the EISPACK routine TRED2. See Smith et al. (1976). The rational QR algorithm is called the PWK algorithm. It is given in Parlett (1980, page 169).
Comments
1. Workspace may be explicitly provided, if desired, by use of E4ASF/DE4ASF. The reference is:
CALL E4ASF (N, NEVAL, A, LDA, SMALL, EVAL, WORK, IWK)
Additional arguments are as follows:
WORK — Work array of length 4N.
IWK — Integer work array of length N.
2. Informational error
Type | Code | Description |
|---|
3 | 1 | The iteration for an eigenvalue failed to converge. The best estimate will be returned. |
Example
In this example, the three largest eigenvalues of the computed Hilbert matrix aij = 1/(i + j –1) of order N = 10 are computed and printed.
USE EVASF_INT
USE WRRRN_INT
IMPLICIT NONE
! Declare variables
INTEGER LDA, N, NEVAL
PARAMETER (N=10, NEVAL=3, LDA=N)
!
INTEGER I, J
REAL A(LDA,N), EVAL(NEVAL), REAL
LOGICAL SMALL
INTRINSIC REAL
! Set up Hilbert matrix
DO 20 J=1, N
DO 10 I=1, N
A(I,J) = 1.0/REAL(I+J-1)
10 CONTINUE
20 CONTINUE
! Find the 3 largest eigenvalues
SMALL = .FALSE.
CALL EVASF (NEVAL, A, SMALL, EVAL)
! Print results
CALL WRRRN ('EVAL', EVAL, 1, NEVAL, 1)
END
Output
EVAL
1 2 3
1.752 0.343 0.036
