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108 lines
3.9 KiB
Fortran
108 lines
3.9 KiB
Fortran
*DECK CH
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SUBROUTINE CH (NM, N, AR, AI, W, MATZ, ZR, ZI, FV1, FV2, FM1,
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+ IERR)
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C***BEGIN PROLOGUE CH
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C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors
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C of a complex Hermitian matrix.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4A3
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C***TYPE COMPLEX (RS-S, CH-C)
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C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
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C***AUTHOR Smith, B. T., et al.
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C***DESCRIPTION
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C
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C This subroutine calls the recommended sequence of
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C subroutines from the eigensystem subroutine package (EISPACK)
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C to find the eigenvalues and eigenvectors (if desired)
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C of a COMPLEX HERMITIAN matrix.
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C
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C On INPUT
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C
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C NM must be set to the row dimension of the two-dimensional
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C array parameters, AR, AI, ZR and ZI, as declared in the
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C calling program dimension statement. NM is an INTEGER
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C variable.
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C
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C N is the order of the matrix A=(AR,AI). N is an INTEGER
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C variable. N must be less than or equal to NM.
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C
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C AR and AI contain the real and imaginary parts, respectively,
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C of the complex Hermitian matrix. AR and AI are
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C two-dimensional REAL arrays, dimensioned AR(NM,N)
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C and AI(NM,N).
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C
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C MATZ is an INTEGER variable set equal to zero if only
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C eigenvalues are desired. Otherwise, it is set to any
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C non-zero integer for both eigenvalues and eigenvectors.
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C
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C On OUTPUT
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C
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C W contains the eigenvalues in ascending order.
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C W is a one-dimensional REAL array, dimensioned W(N).
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C
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C ZR and ZI contain the real and imaginary parts, respectively,
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C of the eigenvectors if MATZ is not zero. ZR and ZI are
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C two-dimensional REAL arrays, dimensioned ZR(NM,N) and
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C ZI(NM,N).
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C
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C IERR is an INTEGER flag set to
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C Zero for normal return,
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C 10*N if N is greater than NM,
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C J if the J-th eigenvalue has not been
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C determined after a total of 30 iterations.
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C The eigenvalues should be correct for indices
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C 1, 2, ..., IERR-1, but no eigenvectors are
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C computed.
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C
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C FV1 and FV2 are one-dimensional REAL arrays used for
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C temporary storage, dimensioned FV1(N) and FV2(N).
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C
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C FM1 is a two-dimensional REAL array used for temporary
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C storage, dimensioned FM1(2,N).
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C
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C Questions and comments should be directed to B. S. Garbow,
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C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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C ------------------------------------------------------------------
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C
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C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
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C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
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C system Routines - EISPACK Guide, Springer-Verlag,
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C 1976.
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C***ROUTINES CALLED HTRIBK, HTRIDI, TQL2, TQLRAT
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C***REVISION HISTORY (YYMMDD)
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C 760101 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE CH
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C
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INTEGER I,J,N,NM,IERR,MATZ
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REAL AR(NM,*),AI(NM,*),W(*),ZR(NM,*),ZI(NM,*)
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REAL FV1(*),FV2(*),FM1(2,*)
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C
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C***FIRST EXECUTABLE STATEMENT CH
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IF (N .LE. NM) GO TO 10
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IERR = 10 * N
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GO TO 50
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C
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10 CALL HTRIDI(NM,N,AR,AI,W,FV1,FV2,FM1)
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IF (MATZ .NE. 0) GO TO 20
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C .......... FIND EIGENVALUES ONLY ..........
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CALL TQLRAT(N,W,FV2,IERR)
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GO TO 50
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C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS ..........
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20 DO 40 I = 1, N
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C
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DO 30 J = 1, N
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ZR(J,I) = 0.0E0
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30 CONTINUE
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C
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ZR(I,I) = 1.0E0
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40 CONTINUE
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C
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CALL TQL2(NM,N,W,FV1,ZR,IERR)
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IF (IERR .NE. 0) GO TO 50
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CALL HTRIBK(NM,N,AR,AI,FM1,N,ZR,ZI)
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50 RETURN
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END
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