112 lines
2.9 KiB
FortranFixed
112 lines
2.9 KiB
FortranFixed
SUBROUTINE EIGEN(NM,N,A,WR,WI,Z)
|
|
COMMON/CSTAK/DSTAK(500)
|
|
C
|
|
REAL A(NM,N),WR(N),WI(N),Z(NM,N)
|
|
REAL RSTAK(1000)
|
|
C
|
|
EQUIVALENCE (DSTAK(1),RSTAK(1))
|
|
C
|
|
C EIGEN FINDS THE EIGENVALUES AND EIGENVECTORS
|
|
C OF A REAL MATRIX (NOT IMAGINARY) BY
|
|
C CALLING THE SEQUENCE OF SUBROUTINES
|
|
C ORTHE,ORTRA, AND HQR2, WHICH, IN TURN, ARE
|
|
C THE EISPACK ROUTINES ORTHES, ORTRAN, AND HQR2,
|
|
C ADJUSTED FOR USE IN THE PORT LIBRARY.
|
|
C
|
|
C ON INPUT -
|
|
C
|
|
C NM - AN INTEGER INPUT VARIABLE SET EQUAL TO
|
|
C THE ROW DIMENSION OF THE TWO-DIMENSIONAL ARRAYS
|
|
C A AND Z AS SPECIFIED IN THE DIMENSION STATEMENTS
|
|
C FOR A AND Z IN THE CALLING PROGRAM.
|
|
C
|
|
C N - AN INTEGER INPUT VARIABLE SET EQUAL TO THE
|
|
C ORDER OF THE MATRIX A.
|
|
C
|
|
C N MUST NOT BE GREATER THAN NM.
|
|
C
|
|
C A - THE MATRIX, A REAL TWO-DIMENSIONAL
|
|
C ARRAY WITH ROW DIMENSION NM AND COLUMN
|
|
C DIMENSION AT LEAST N.
|
|
C
|
|
C A IS OVERWRITTEN.
|
|
C
|
|
C
|
|
C
|
|
C ON OUTPUT -
|
|
C
|
|
C WR - A REAL ARRAY OF DIMENSION
|
|
C AT LEAST N CONTAINING THE REAL PARTS OF THE EIGENVALUES
|
|
C
|
|
C WI - A REAL ARRAY OF DIMENSION
|
|
C AT LEAST N CONTAINING THE IMAGINARY PARTS OF THE EIGENVALUES.
|
|
C
|
|
C THE EIGENVALUES ARE UNORDERED EXCEPT THAT
|
|
C COMPLEX CONJUGATE PAIRS OF EIGENVALUES
|
|
C APPEAR CONSECUTIVELY WITH THE EIGENVALUE HAVING
|
|
C THE POSITIVE IMAGINARY PART FIRST.
|
|
C
|
|
C Z - A REAL TWO-DIMENSIONAL ARRAY
|
|
C WITH ROW DIMENSION NM AND COLUMN DIMENSION
|
|
C AT LEAST N CONTAINING THE REAL AND IMAGINARY PARTS
|
|
C OF THE EIGENVECTORS.
|
|
C
|
|
C IF THE J-TH EIGENVALUE IS REAL, THE J-TH
|
|
C COLUMN OF Z CONTAINS ITS EIGENVECTOR.
|
|
C
|
|
C IF THE J-TH EIGENVALUE IS COMPLEX WITH
|
|
C POSITIVE REAL PART, THE J-TH AND (J+1)-TH
|
|
C COLUMNS OF Z CONTAIN THE REAL AND IMAGINARY
|
|
C PARTS OF ITS EIGENVECTOR.
|
|
C
|
|
C THE CONJUGATE OF THIS VECTOR IS THE
|
|
C EIGENVECTOR FOR THE CONJUGATE EIGENVALUE.
|
|
C THE EIGENVECTORS ARE NOT NORMALIZED.
|
|
C
|
|
C
|
|
C ERROR STATES -
|
|
C
|
|
C 1 - N IS GREATER THAN NM
|
|
C
|
|
C K - THE K-TH EIGENVALUE COULD NOT BE COMPUTED
|
|
C WITHIN 30 ITERATIONS.
|
|
C
|
|
C THE EIGENVALUES IN THE WR AND WRI ARRAYS
|
|
C SHOULD BE CORRECT FOR INDICES
|
|
C K+1, K+2,...,N, BUT NO EIGENVECTORS ARE COMPUTED.
|
|
C
|
|
C
|
|
C
|
|
C
|
|
C CHECK FOR INPUT ERROR IN N
|
|
C
|
|
C/6S
|
|
C IF (N .GT. NM) CALL SETERR(
|
|
C 1 29H EIGEN - N IS GREATER THAN NM,29,1,2)
|
|
C/7S
|
|
IF (N .GT. NM) CALL SETERR(
|
|
1 ' EIGEN - N IS GREATER THAN NM',29,1,2)
|
|
C/
|
|
C
|
|
C ALLOCATE A SCRATCH VECTOR
|
|
IORT = ISTKGT(N,3)
|
|
C
|
|
CALL ORTHE (NM,N,1,N,A,RSTAK(IORT))
|
|
CALL ORTRA (NM,N,1,N,A,RSTAK(IORT),Z)
|
|
CALL HQR2 (NM,N,1,N,A,WR,WI,Z,IERR)
|
|
C
|
|
IF (IERR .NE. 0) GO TO 10
|
|
CALL ISTKRL(1)
|
|
RETURN
|
|
C/6S
|
|
C 10 CALL SETERR(
|
|
C 1 34H EIGEN - FAILED ON THAT EIGENVALUE,34,IERR,1)
|
|
C/7S
|
|
10 CALL SETERR(
|
|
1 ' EIGEN - FAILED ON THAT EIGENVALUE',34,IERR,1)
|
|
C/
|
|
C
|
|
CALL ISTKRL(1)
|
|
RETURN
|
|
END
|