*DECK RT
SUBROUTINE RT (NM, N, A, W, MATZ, Z, FV1, IERR)
C***BEGIN PROLOGUE RT
C***PURPOSE Compute the eigenvalues and eigenvectors of a special real
C tridiagonal matrix.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4A5
C***TYPE SINGLE PRECISION (RT-S)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
C
C This subroutine calls the recommended sequence of subroutines
C from the eigensystem subroutine package (EISPACK) to find the
C eigenvalues and eigenvectors (if desired) of a special REAL
C TRIDIAGONAL matrix. The property of the matrix required for use
C of this subroutine is that the products of pairs of corresponding
C off-diagonal elements be all non-negative. If eigenvectors are
C desired, no product can be zero unless both factors are zero.
C
C On Input
C
C NM must be set to the row dimension of the two-dimensional
C array parameter, 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 special real tridiagonal matrix in its first
C three columns. The subdiagonal elements are stored in the
C last N-1 positions of the first column, the diagonal elements
C in the second column, and the superdiagonal elements in the
C first N-1 positions of the third column. Elements A(1,1) and
C A(N,3) are arbitrary. A is a two-dimensional REAL array,
C dimensioned A(NM,3).
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. The eigen-
C vectors are not normalized. Z is a two-dimensional REAL
C 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 N+J if A(J,1)*A(J-1,3) is negative,
C 2*N+J if the product is zero with one factor non-zero,
C and MATZ is non-zero;
C J if the J-th eigenvalue has not been
C determined after 30 iterations.
C The eigenvalues and eigenvectors in the W and Z
C arrays should be correct for indices
C 1, 2, ..., IERR-1.
C
C FV1 is a one-dimensional REAL array used for temporary storage,
C dimensioned FV1(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 FIGI, FIGI2, IMTQL1, IMTQL2
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 RT
C
INTEGER N,NM,IERR,MATZ
REAL A(NM,3),W(*),Z(NM,*),FV1(*)
C
C***FIRST EXECUTABLE STATEMENT RT
IF (N .LE. NM) GO TO 10
IERR = 10 * N
GO TO 50
C
10 IF (MATZ .NE. 0) GO TO 20
C .......... FIND EIGENVALUES ONLY ..........
CALL FIGI(NM,N,A,W,FV1,FV1,IERR)
IF (IERR .GT. 0) GO TO 50
CALL IMTQL1(N,W,FV1,IERR)
GO TO 50
C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS ..........
20 CALL FIGI2(NM,N,A,W,FV1,Z,IERR)
IF (IERR .NE. 0) GO TO 50
CALL IMTQL2(NM,N,W,FV1,Z,IERR)
50 RETURN
END