*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