*DECK RSG SUBROUTINE RSG (NM, N, A, B, W, MATZ, Z, FV1, FV2, IERR) C***BEGIN PROLOGUE RSG C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors C of a symmetric generalized eigenproblem. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4B1 C***TYPE SINGLE PRECISION (RSG-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 SYMMETRIC 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 symmetric matrix. A is a two-dimensional C REAL array, dimensioned A(NM,N). C C B contains a positive definite real symmetric matrix. B is a C two-dimensional 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 W contains the eigenvalues in ascending order. W is a C one-dimensional REAL array, dimensioned W(N). C C Z contains the eigenvectors if MATZ is not zero. Z is a C 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 7*N+1 if B is not positive definite, C J if the J-th eigenvalue has not been C determined after 30 iterations. C The eigenvalues should be correct for indices C 1, 2, ..., IERR-1, but no eigenvectors are C computed. C C FV1 and FV2 are one-dimensional REAL arrays used for temporary C storage, dimensioned FV1(N) and FV2(N). 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 REBAK, REDUC, TQL2, TQLRAT, TRED1, TRED2 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 RSG C INTEGER N,NM,IERR,MATZ REAL A(NM,*),B(NM,*),W(*),Z(NM,*),FV1(*),FV2(*) C C***FIRST EXECUTABLE STATEMENT RSG IF (N .LE. NM) GO TO 10 IERR = 10 * N GO TO 50 C 10 CALL REDUC(NM,N,A,B,FV2,IERR) IF (IERR .NE. 0) GO TO 50 IF (MATZ .NE. 0) GO TO 20 C .......... FIND EIGENVALUES ONLY .......... CALL TRED1(NM,N,A,W,FV1,FV2) CALL TQLRAT(N,W,FV2,IERR) GO TO 50 C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS .......... 20 CALL TRED2(NM,N,A,W,FV1,Z) CALL TQL2(NM,N,W,FV1,Z,IERR) IF (IERR .NE. 0) GO TO 50 CALL REBAK(NM,N,B,FV2,N,Z) 50 RETURN END