*DECK CH SUBROUTINE CH (NM, N, AR, AI, W, MATZ, ZR, ZI, FV1, FV2, FM1, + IERR) C***BEGIN PROLOGUE CH C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors C of a complex Hermitian matrix. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4A3 C***TYPE COMPLEX (RS-S, CH-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 COMPLEX HERMITIAN matrix. C C On INPUT C C NM must be set to the row dimension of the two-dimensional C array parameters, AR, AI, ZR and ZI, as declared in the C calling program dimension statement. NM is an INTEGER C variable. C C N is the order of the matrix A=(AR,AI). N is an INTEGER C variable. N must be less than or equal to NM. C C AR and AI contain the real and imaginary parts, respectively, C of the complex Hermitian matrix. AR and AI are C two-dimensional REAL arrays, dimensioned AR(NM,N) C and AI(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. C W is a one-dimensional REAL array, dimensioned W(N). C C ZR and ZI contain the real and imaginary parts, respectively, C of the eigenvectors if MATZ is not zero. ZR and ZI are C two-dimensional REAL arrays, dimensioned ZR(NM,N) and C ZI(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 1, 2, ..., IERR-1, but no eigenvectors are C computed. C C FV1 and FV2 are one-dimensional REAL arrays used for C temporary storage, dimensioned FV1(N) and FV2(N). C C FM1 is a two-dimensional REAL array used for temporary C storage, dimensioned FM1(2,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 HTRIBK, HTRIDI, TQL2, TQLRAT 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 CH C INTEGER I,J,N,NM,IERR,MATZ REAL AR(NM,*),AI(NM,*),W(*),ZR(NM,*),ZI(NM,*) REAL FV1(*),FV2(*),FM1(2,*) C C***FIRST EXECUTABLE STATEMENT CH IF (N .LE. NM) GO TO 10 IERR = 10 * N GO TO 50 C 10 CALL HTRIDI(NM,N,AR,AI,W,FV1,FV2,FM1) IF (MATZ .NE. 0) GO TO 20 C .......... FIND EIGENVALUES ONLY .......... CALL TQLRAT(N,W,FV2,IERR) GO TO 50 C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS .......... 20 DO 40 I = 1, N C DO 30 J = 1, N ZR(J,I) = 0.0E0 30 CONTINUE C ZR(I,I) = 1.0E0 40 CONTINUE C CALL TQL2(NM,N,W,FV1,ZR,IERR) IF (IERR .NE. 0) GO TO 50 CALL HTRIBK(NM,N,AR,AI,FM1,N,ZR,ZI) 50 RETURN END