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SUBROUTINE RGG(NM,N,A,B,ALFR,ALFI,BETA,MATZ,Z,IERR)
C
INTEGER N,NM,IERR,MATZ
REAL A(NM,N),B(NM,N),ALFR(N),ALFI(N),BETA(N),Z(NM,N)
LOGICAL TF
C
C THIS SUBROUTINE CALLS THE RECOMMENDED SEQUENCE OF
C SUBROUTINES FROM THE EIGENSYSTEM SUBROUTINE PACKAGE (EISPACK)
C TO FIND THE EIGENVALUES AND EIGENVECTORS (IF DESIRED)
C FOR THE REAL GENERAL GENERALIZED EIGENPROBLEM AX = (LAMBDA)BX.
C
C ON INPUT
C
C NM MUST BE SET TO THE ROW DIMENSION OF THE TWO-DIMENSIONAL
C ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM
C DIMENSION STATEMENT.
C
C N IS THE ORDER OF THE MATRICES A AND B.
C
C A CONTAINS A REAL GENERAL MATRIX.
C
C B CONTAINS A REAL GENERAL MATRIX.
C
C MATZ IS AN INTEGER VARIABLE SET EQUAL TO ZERO IF
C ONLY EIGENVALUES ARE DESIRED. OTHERWISE IT IS SET TO
C ANY NON-ZERO INTEGER FOR BOTH EIGENVALUES AND EIGENVECTORS.
C
C ON OUTPUT
C
C ALFR AND ALFI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE NUMERATORS OF THE EIGENVALUES.
C
C BETA CONTAINS THE DENOMINATORS OF THE EIGENVALUES,
C WHICH ARE THUS GIVEN BY THE RATIOS (ALFR+I*ALFI)/BETA.
C COMPLEX CONJUGATE PAIRS OF EIGENVALUES APPEAR CONSECUTIVELY
C WITH THE EIGENVALUE HAVING THE POSITIVE IMAGINARY PART FIRST.
C
C Z CONTAINS THE REAL AND IMAGINARY PARTS OF THE EIGENVECTORS
C IF MATZ IS NOT ZERO. IF THE J-TH EIGENVALUE IS REAL, THE
C J-TH COLUMN OF Z CONTAINS ITS EIGENVECTOR. IF THE J-TH
C EIGENVALUE IS COMPLEX WITH POSITIVE IMAGINARY PART, THE
C J-TH AND (J+1)-TH COLUMNS OF Z CONTAIN THE REAL AND
C IMAGINARY PARTS OF ITS EIGENVECTOR. THE CONJUGATE OF THIS
C VECTOR IS THE EIGENVECTOR FOR THE CONJUGATE EIGENVALUE.
C
C IERR IS AN INTEGER OUTPUT VARIABLE SET EQUAL TO AN ERROR
C COMPLETION CODE DESCRIBED IN THE DOCUMENTATION FOR QZIT.
C THE NORMAL COMPLETION CODE IS ZERO.
C
C QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW,
C MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
C
C THIS VERSION DATED AUGUST 1983.
C
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C