*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