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100 lines
3.9 KiB
Fortran
100 lines
3.9 KiB
Fortran
*DECK FIGI
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SUBROUTINE FIGI (NM, N, T, D, E, E2, IERR)
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C***BEGIN PROLOGUE FIGI
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C***PURPOSE Transforms certain real non-symmetric tridiagonal matrix
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C to symmetric tridiagonal matrix.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4C1C
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C***TYPE SINGLE PRECISION (FIGI-S)
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C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
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C***AUTHOR Smith, B. T., et al.
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C***DESCRIPTION
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C
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C Given a NONSYMMETRIC TRIDIAGONAL matrix such that the products
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C of corresponding pairs of off-diagonal elements are all
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C non-negative, this subroutine reduces it to a symmetric
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C tridiagonal matrix with the same eigenvalues. If, further,
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C a zero product only occurs when both factors are zero,
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C the reduced matrix is similar to the original matrix.
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C
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C On INPUT
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C
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C NM must be set to the row dimension of the two-dimensional
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C array parameter, T, as declared in the calling program
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C dimension statement. NM is an INTEGER variable.
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C
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C N is the order of the matrix T. N is an INTEGER variable.
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C N must be less than or equal to NM.
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C
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C T contains the nonsymmetric matrix. Its subdiagonal is
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C stored in the last N-1 positions of the first column,
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C its diagonal in the N positions of the second column,
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C and its superdiagonal in the first N-1 positions of
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C the third column. T(1,1) and T(N,3) are arbitrary.
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C T is a two-dimensional REAL array, dimensioned T(NM,3).
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C
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C On OUTPUT
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C
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C T is unaltered.
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C
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C D contains the diagonal elements of the tridiagonal symmetric
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C matrix. D is a one-dimensional REAL array, dimensioned D(N).
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C
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C E contains the subdiagonal elements of the tridiagonal
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C symmetric matrix in its last N-1 positions. E(1) is not set.
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C E is a one-dimensional REAL array, dimensioned E(N).
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C
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C E2 contains the squares of the corresponding elements of E.
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C E2 may coincide with E if the squares are not needed.
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C E2 is a one-dimensional REAL array, dimensioned E2(N).
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C
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C IERR is an INTEGER flag set to
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C Zero for normal return,
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C N+I if T(I,1)*T(I-1,3) is negative and a symmetric
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C matrix cannot be produced with FIGI,
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C -(3*N+I) if T(I,1)*T(I-1,3) is zero with one factor
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C non-zero. In this case, the eigenvectors of
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C the symmetric matrix are not simply related
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C to those of T and should not be sought.
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C
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C Questions and comments should be directed to B. S. Garbow,
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C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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C ------------------------------------------------------------------
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C
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C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
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C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
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C system Routines - EISPACK Guide, Springer-Verlag,
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C 1976.
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C***ROUTINES CALLED (NONE)
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C***REVISION HISTORY (YYMMDD)
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C 760101 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE FIGI
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C
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INTEGER I,N,NM,IERR
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REAL T(NM,3),D(*),E(*),E2(*)
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C
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C***FIRST EXECUTABLE STATEMENT FIGI
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IERR = 0
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C
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DO 100 I = 1, N
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IF (I .EQ. 1) GO TO 90
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E2(I) = T(I,1) * T(I-1,3)
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IF (E2(I)) 1000, 60, 80
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60 IF (T(I,1) .EQ. 0.0E0 .AND. T(I-1,3) .EQ. 0.0E0) GO TO 80
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C .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL
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C ELEMENTS IS ZERO WITH ONE MEMBER NON-ZERO ..........
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IERR = -(3 * N + I)
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80 E(I) = SQRT(E2(I))
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90 D(I) = T(I,2)
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100 CONTINUE
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C
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GO TO 1001
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C .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL
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C ELEMENTS IS NEGATIVE ..........
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1000 IERR = N + I
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1001 RETURN
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END
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