*DECK RG SUBROUTINE RG (NM, N, A, WR, WI, MATZ, Z, IV1, FV1, IERR) C***BEGIN PROLOGUE RG C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors C of a real general matrix. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4A2 C***TYPE SINGLE PRECISION (RG-S, CG-C) 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 of a REAL GENERAL matrix. C C On Input C C NM must be set to the row dimension of the two-dimensional C array parameters, A and Z, as declared in the calling C program dimension statement. NM is an INTEGER variable. C C N is the order of the matrix A. N is an INTEGER variable. C N must be less than or equal to NM. C C A contains the real general matrix. A is a two-dimensional C REAL array, dimensioned A(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 has been destroyed. C C WR and WI contain the real and imaginary parts, respectively, C of the eigenvalues. The eigenvalues are unordered except C that complex conjugate pairs of eigenvalues appear consecu- C tively with the eigenvalue having the positive imaginary part C first. If an error exit is made, the eigenvalues should be C correct for indices IERR+1, IERR+2, ..., N. WR and WI are C one-dimensional REAL arrays, dimensioned WR(N) and WI(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 iterations. C The eigenvalues should be correct for indices C IERR+1, IERR+2, ..., N, but no eigenvectors are C computed. C C IV1 and FV1 are one-dimensional temporary storage arrays of C dimension N. IV1 is of type INTEGER and FV1 of type REAL. 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 BALANC, BALBAK, ELMHES, ELTRAN, HQR, HQR2 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 921103 Corrected description of IV1. (DWL, FNF and WRB) C***END PROLOGUE RG C INTEGER N,NM,IS1,IS2,IERR,MATZ REAL A(NM,*),WR(*),WI(*),Z(NM,*),FV1(*) INTEGER IV1(*) C C***FIRST EXECUTABLE STATEMENT RG IF (N .LE. NM) GO TO 10 IERR = 10 * N GO TO 50 C 10 CALL BALANC(NM,N,A,IS1,IS2,FV1) CALL ELMHES(NM,N,IS1,IS2,A,IV1) IF (MATZ .NE. 0) GO TO 20 C .......... FIND EIGENVALUES ONLY .......... CALL HQR(NM,N,IS1,IS2,A,WR,WI,IERR) GO TO 50 C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS .......... 20 CALL ELTRAN(NM,N,IS1,IS2,A,IV1,Z) CALL HQR2(NM,N,IS1,IS2,A,WR,WI,Z,IERR) IF (IERR .NE. 0) GO TO 50 CALL BALBAK(NM,N,IS1,IS2,FV1,N,Z) 50 RETURN END