*DECK FIGI SUBROUTINE FIGI (NM, N, T, D, E, E2, IERR) C***BEGIN PROLOGUE FIGI C***PURPOSE Transforms certain real non-symmetric tridiagonal matrix C to symmetric tridiagonal matrix. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4C1C C***TYPE SINGLE PRECISION (FIGI-S) C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK C***AUTHOR Smith, B. T., et al. C***DESCRIPTION C C Given a NONSYMMETRIC TRIDIAGONAL matrix such that the products C of corresponding pairs of off-diagonal elements are all C non-negative, this subroutine reduces it to a symmetric C tridiagonal matrix with the same eigenvalues. If, further, C a zero product only occurs when both factors are zero, C the reduced matrix is similar to the original matrix. C C On INPUT C C NM must be set to the row dimension of the two-dimensional C array parameter, T, as declared in the calling program C dimension statement. NM is an INTEGER variable. C C N is the order of the matrix T. N is an INTEGER variable. C N must be less than or equal to NM. C C T contains the nonsymmetric matrix. Its subdiagonal is C stored in the last N-1 positions of the first column, C its diagonal in the N positions of the second column, C and its superdiagonal in the first N-1 positions of C the third column. T(1,1) and T(N,3) are arbitrary. C T is a two-dimensional REAL array, dimensioned T(NM,3). C C On OUTPUT C C T is unaltered. C C D contains the diagonal elements of the tridiagonal symmetric C matrix. D is a one-dimensional REAL array, dimensioned D(N). C C E contains the subdiagonal elements of the tridiagonal C symmetric matrix in its last N-1 positions. E(1) is not set. C E is a one-dimensional REAL array, dimensioned E(N). C C E2 contains the squares of the corresponding elements of E. C E2 may coincide with E if the squares are not needed. C E2 is a one-dimensional REAL array, dimensioned E2(N). C C IERR is an INTEGER flag set to C Zero for normal return, C N+I if T(I,1)*T(I-1,3) is negative and a symmetric C matrix cannot be produced with FIGI, C -(3*N+I) if T(I,1)*T(I-1,3) is zero with one factor C non-zero. In this case, the eigenvectors of C the symmetric matrix are not simply related C to those of T and should not be sought. 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 (NONE) 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 FIGI C INTEGER I,N,NM,IERR REAL T(NM,3),D(*),E(*),E2(*) C C***FIRST EXECUTABLE STATEMENT FIGI IERR = 0 C DO 100 I = 1, N IF (I .EQ. 1) GO TO 90 E2(I) = T(I,1) * T(I-1,3) IF (E2(I)) 1000, 60, 80 60 IF (T(I,1) .EQ. 0.0E0 .AND. T(I-1,3) .EQ. 0.0E0) GO TO 80 C .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL C ELEMENTS IS ZERO WITH ONE MEMBER NON-ZERO .......... IERR = -(3 * N + I) 80 E(I) = SQRT(E2(I)) 90 D(I) = T(I,2) 100 CONTINUE C GO TO 1001 C .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL C ELEMENTS IS NEGATIVE .......... 1000 IERR = N + I 1001 RETURN END