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- *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
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