EVBSB
Computes the eigenvalues in a given interval of a real symmetric matrix stored in band symmetric storage mode.
Required Arguments
MXEVAL — Maximum number of eigenvalues to be computed. (Input)
A — Band symmetric matrix of order N. (Input)
NCODA — Number of codiagonals in A. (Input)
ELOW — Lower limit of the interval in which the eigenvalues are sought. (Input)
EHIGH — Upper limit of the interval in which the eigenvalues are sought. (Input)
NEVAL — Number of eigenvalues found. (Output)
EVAL — Real vector of length MXEVAL containing the eigenvalues of A in the interval (ELOW, EHIGH) in decreasing order of magnitude. (Output)
Only the first NEVAL elements of EVAL are set.
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 EVBSB (MXEVAL, A, NCODA, ELOW, EHIGH, NEVAL, EVAL [,…])
Specific: The specific interface names are S_EVBSB and D_EVBSB.
FORTRAN 77 Interface
Single: CALL EVBSB (N, MXEVAL, A, LDA, NCODA, ELOW, EHIGH, NEVAL, EVAL)
Double: The double precision name is DEVBSB.
Description
Routine EVBSB computes the eigenvalues in a given range of a real band symmetric matrix. Orthogonal similarity transformations are used to reduce the matrix to an equivalent symmetric tridiagonal matrix. A bisection algorithm is used to compute the eigenvalues of the tridiagonal matrix in a given range.
The reduction routine is based on the EISPACK routine BANDR; see Garbow et al. (1977). The bisection routine is based on the EISPACK routine BISECT; see Smith et al. (1976).
Comments
1. Workspace may be explicitly provided, if desired, by use of E3BSB/DE3BSB. The reference is:
CALL E3BSB (N, MXEVAL, A, LDA, NCODA, ELOW, EHIGH, NEVAL, EVAL, ACOPY, WK)
The additional arguments are as follows:
ACOPY — Work matrix of size NCODA + 1 by N. A and ACOPY may be the same, in which case the first N(NCODA + 1) elements of A will be destroyed.
WK — Work array of length 5N.
2. Informational error
Type | Code | Description |
|---|
3 | 1 | The number of eigenvalues in the specified interval exceeds MXEVAL. NEVAL contains the number of eigenvalues in the interval. No eigenvalues will be returned. |
Example
In this example, a DATA statement is used to set A to a matrix given by Gregory and Karney (1969, page 77). The eigenvalues in the range (-2.5, 1.5) are computed and printed. As a test, this example uses MXEVAL = 5. The routine EVBSB computes NEVAL, the number of eigenvalues in the given range, has the value 3.
USE EVBSB_INT
USE UMACH_INT
USE WRRRN_INT
IMPLICIT NONE
! Declare variables
INTEGER LDA, MXEVAL, N, NCODA
PARAMETER (MXEVAL=5, N=5, NCODA=2, LDA=NCODA+1)
!
INTEGER NEVAL, NOUT
REAL A(LDA,N), EHIGH, ELOW, EVAL(MXEVAL)
!
! Define values of A:
! A = ( -1 2 1 )
! ( 2 0 2 1 )
! ( 1 2 0 2 1 )
! ( 1 2 0 2 )
! ( 1 2 -1 )
! Representedin band symmetric
! form this is:
! A = ( 0 0 1 1 1 )
! ( 0 2 2 2 2 )
! ( -1 0 0 0 -1 )
DATA A/0.0, 0.0, -1.0, 0.0, 2.0, 0.0, 1.0, 2.0, 0.0, 1.0, 2.0, &
0.0, 1.0, 2.0, -1.0/
!
ELOW = -2.5
EHIGH = 1.5
CALL EVBSB (MXEVAL, A, NCODA, ELOW, EHIGH, NEVAL, EVAL)
! Print results
CALL UMACH (2, NOUT)
WRITE (NOUT,'(/,A,I1)') ' NEVAL = ', NEVAL
CALL WRRRN ('EVAL', EVAL, 1, NEVAl, 1)
END
Output
NEVAL = 3
EVAL
1 2 3
-2.464 -2.000 1.000
