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109 lines
4 KiB
Fortran
109 lines
4 KiB
Fortran
*DECK FIGI2
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SUBROUTINE FIGI2 (NM, N, T, D, E, Z, IERR)
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C***BEGIN PROLOGUE FIGI2
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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 (FIGI2-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, and zero only when both factors are zero, this
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C subroutine reduces it to a SYMMETRIC TRIDIAGONAL matrix
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C using and accumulating diagonal similarity transformations.
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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 parameters, T and Z, as declared in the calling
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C program 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 Z contains the diagonal transformation matrix produced in the
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C symmetrization. Z is a two-dimensional REAL array,
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C dimensioned Z(NM,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,
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C 2*N+I if T(I,1)*T(I-1,3) is zero with one factor
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C non-zero. In these cases, there does not exist
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C a symmetrizing similarity transformation which
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C is essential for the validity of the later
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C eigenvector computation.
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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 FIGI2
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C
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INTEGER I,J,N,NM,IERR
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REAL T(NM,3),D(*),E(*),Z(NM,*)
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REAL H
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C
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C***FIRST EXECUTABLE STATEMENT FIGI2
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IERR = 0
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C
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DO 100 I = 1, N
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C
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DO 50 J = 1, N
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50 Z(I,J) = 0.0E0
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C
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IF (I .EQ. 1) GO TO 70
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H = T(I,1) * T(I-1,3)
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IF (H) 900, 60, 80
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60 IF (T(I,1) .NE. 0.0E0 .OR. T(I-1,3) .NE. 0.0E0) GO TO 1000
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E(I) = 0.0E0
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70 Z(I,I) = 1.0E0
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GO TO 90
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80 E(I) = SQRT(H)
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Z(I,I) = Z(I-1,I-1) * E(I) / T(I-1,3)
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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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900 IERR = N + I
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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 ZERO WITH ONE MEMBER NON-ZERO ..........
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1000 IERR = 2 * N + I
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1001 RETURN
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END
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