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- *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
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