*DECK RGG SUBROUTINE RGG (NM, N, A, B, ALFR, ALFI, BETA, MATZ, Z, IERR) C***BEGIN PROLOGUE RGG C***PURPOSE Compute the eigenvalues and eigenvectors for a real C generalized eigenproblem. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4B2 C***TYPE SINGLE PRECISION (RGG-S) C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK C***AUTHOR Smith, B. T., et al. C***DESCRIPTION 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, A, B, and Z, as declared in the calling C program dimension statement. NM is an INTEGER variable. C C N is the order of the matrices A and B. N is an INTEGER C variable. N must be less than or equal to NM. C C A contains a real general matrix. A is a two-dimensional C REAL array, dimensioned A(NM,N). C C B contains a real general matrix. B is a two-dimensional C REAL array, dimensioned B(NM,N). C C MATZ is an INTEGER variable set equal to zero if only C eigenvalues are desired. Otherwise, it is set to any C non-zero integer for both eigenvalues and eigenvectors. C C On Output C C A and B have been destroyed. C C ALFR and ALFI contain the real and imaginary parts, C respectively, of the numerators of the eigenvalues. C ALFR and ALFI are one-dimensional REAL arrays, C dimensioned ALFR(N) and ALFI(N). 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 BETA is a one-dimensional REAL array, dimensioned BETA(N). 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 Z is a two-dimensional REAL array, dimensioned Z(NM,N). C C IERR is an INTEGER flag set to C Zero for normal return, C 10*N if N is greater than NM, C J if the J-th eigenvalue has not been C determined after a total of 30*N iterations. C The eigenvalues should be correct for indices C IERR+1, IERR+2, ..., N, but no eigenvectors are C computed. C C Questions and comments should be directed to B. S. Garbow, C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY C ------------------------------------------------------------------ C C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- C system Routines - EISPACK Guide, Springer-Verlag, C 1976. C***ROUTINES CALLED QZHES, QZIT, QZVAL, QZVEC C***REVISION HISTORY (YYMMDD) C 760101 DATE WRITTEN C 890831 Modified array declarations. (WRB) C 890831 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE RGG C INTEGER N,NM,IERR,MATZ REAL A(NM,*),B(NM,*),ALFR(*),ALFI(*),BETA(*),Z(NM,*) LOGICAL TF C C***FIRST EXECUTABLE STATEMENT RGG IF (N .LE. NM) GO TO 10 IERR = 10 * N GO TO 50 C 10 IF (MATZ .NE. 0) GO TO 20 C .......... FIND EIGENVALUES ONLY .......... TF = .FALSE. CALL QZHES(NM,N,A,B,TF,Z) CALL QZIT(NM,N,A,B,0.0E0,TF,Z,IERR) CALL QZVAL(NM,N,A,B,ALFR,ALFI,BETA,TF,Z) GO TO 50 C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS .......... 20 TF = .TRUE. CALL QZHES(NM,N,A,B,TF,Z) CALL QZIT(NM,N,A,B,0.0E0,TF,Z,IERR) CALL QZVAL(NM,N,A,B,ALFR,ALFI,BETA,TF,Z) IF (IERR .NE. 0) GO TO 50 CALL QZVEC(NM,N,A,B,ALFR,ALFI,BETA,Z) 50 RETURN END