EVLCH
Computes all of the eigenvalues of a complex upper Hessenberg matrix.
Required Arguments
A — Complex upper Hessenberg matrix of order N. (Input)
EVAL — Complex vector of length N containing the eigenvalues of A in decreasing order of magnitude. (Output)
Required 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 EVLCH (A, EVAL [,…])
Specific: The specific interface names are S_EVLCH and D_EVLCH.
FORTRAN 77 Interface
Single: CALL EVLCH (N, A, LDA, EVAL)
Double: The double precision name is DEVLCH.
Description
Routine EVLCH computes the eigenvalues of a complex upper Hessenberg matrix using the QR algorithm. This routine is based on the EISPACK routine COMQR2; see Smith et al. (1976).
Comments
1. Workspace may be explicitly provided, if desired, by use of E3LCH/DE3LCH. The reference is:
CALL E3LCH (N, A, LDA, EVAL, ACOPY, RWK, IWK)
The additional arguments are as follows:
ACOPY — Complex N by N work array. A and ACOPY may be the same, in which case A is destroyed.
RWK — Real work array of length N.
IWK — Integer work array of length N.
2. Informational error
Type | Code | Description |
|---|
4 | 1 | The iteration for the eigenvalues failed to converge. |
Example
In this example, a DATA statement is used to set the matrix A. The program computes and prints the eigenvalues of this matrix.
USE EVLCH_INT
USE WRCRN_INT
IMPLICIT NONE
! Declare variables
INTEGER LDA, N
PARAMETER (N=4, LDA=N)
COMPLEX A(LDA,N), EVAL(N)
! Set values of A
!
! A = (5+9i 5+5i -6-6i -7-7i)
! (3+3i 6+10i -5-5i -6-6i)
! ( 0 3+3i -1+3i -5-5i)
! ( 0 0 -3-3i 4i)
!
DATA A /(5.0,9.0), (3.0,3.0), (0.0,0.0), (0.0,0.0), &
(5.0,5.0), (6.0,10.0), (3.0,3.0), (0.0,0.0), &
(-6.0,-6.0), (-5.0,-5.0), (-1.0,3.0), (-3.0,-3.0), &
(-7.0,-7.0), (-6.0,-6.0), (-5.0,-5.0), (0.0,4.0)/
!
! Find the eigenvalues of A
CALL EVLCH (A, EVAL)
! Print results
CALL WRCRN ('EVAL', EVAL, 1, N, 1)
END
Output
EVAL
1 2 3 4
( 8.22, 12.22) ( 3.40, 7.40) ( 1.60, 5.60) ( -3.22, 0.78)
