*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