*DECK RST SUBROUTINE RST (NM, N, W, E, MATZ, Z, IERR) C***BEGIN PROLOGUE RST C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors C of a real symmetric tridiagonal matrix. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4A5 C***TYPE SINGLE PRECISION (RST-S) 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 REAL SYMMETRIC TRIDIAGONAL matrix. C C On Input C C NM must be set to the row dimension of the two-dimensional C array parameter, Z, as declared in the calling program C dimension statement. NM is an INTEGER variable. C C N is the order of the matrix. N is an INTEGER variable. C N must be less than or equal to NM. C C W contains the diagonal elements of the real symmetric C tridiagonal matrix. W is a one-dimensional REAL array, C dimensioned W(N). C C E contains the subdiagonal elements of the matrix in its last C N-1 positions. E(1) is arbitrary. E is a one-dimensional C REAL array, dimensioned E(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 C Z contains the eigenvectors if MATZ is not zero. The eigen- C vectors are orthonormal. Z is a two-dimensional REAL array, C 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 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 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 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 RST C INTEGER I,J,N,NM,IERR,MATZ REAL W(*),E(*),Z(NM,*) C C***FIRST EXECUTABLE STATEMENT RST 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 IMTQL1(N,W,E,IERR) GO TO 50 C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS .......... 20 DO 40 I = 1, N C DO 30 J = 1, N Z(J,I) = 0.0E0 30 CONTINUE C Z(I,I) = 1.0E0 40 CONTINUE C CALL IMTQL2(NM,N,W,E,Z,IERR) 50 RETURN END