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90 lines
3.1 KiB
Fortran
90 lines
3.1 KiB
Fortran
*DECK REBAKB
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SUBROUTINE REBAKB (NM, N, B, DL, M, Z)
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C***BEGIN PROLOGUE REBAKB
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C***PURPOSE Form the eigenvectors of a generalized symmetric
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C eigensystem from the eigenvectors of derived matrix output
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C from REDUC2.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4C4
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C***TYPE SINGLE PRECISION (REBAKB-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 This subroutine is a translation of the ALGOL procedure REBAKB,
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C NUM. MATH. 11, 99-110(1968) by Martin and Wilkinson.
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C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 303-314(1971).
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C
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C This subroutine forms the eigenvectors of a generalized
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C SYMMETRIC eigensystem by back transforming those of the
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C derived symmetric matrix determined by REDUC2.
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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, B 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 system. N is an INTEGER
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C variable. N must be less than or equal to NM.
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C
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C B contains information about the similarity transformation
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C (Cholesky decomposition) used in the reduction by REDUC2
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C in its strict lower triangle. B is a two-dimensional
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C REAL array, dimensioned B(NM,N).
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C
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C DL contains further information about the transformation.
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C DL is a one-dimensional REAL array, dimensioned DL(N).
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C
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C M is the number of eigenvectors to be back transformed.
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C M is an INTEGER variable.
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C
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C Z contains the eigenvectors to be back transformed in its
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C first M columns. Z is a two-dimensional REAL array
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C dimensioned Z(NM,M).
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C
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C On Output
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C
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C Z contains the transformed eigenvectors in its first
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C M columns.
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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 REBAKB
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C
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INTEGER I,J,K,M,N,I1,II,NM
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REAL B(NM,*),DL(*),Z(NM,*)
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REAL X
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C
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C***FIRST EXECUTABLE STATEMENT REBAKB
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IF (M .EQ. 0) GO TO 200
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C
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DO 100 J = 1, M
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C .......... FOR I=N STEP -1 UNTIL 1 DO -- ..........
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DO 100 II = 1, N
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I1 = N - II
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I = I1 + 1
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X = DL(I) * Z(I,J)
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IF (I .EQ. 1) GO TO 80
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C
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DO 60 K = 1, I1
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60 X = X + B(I,K) * Z(K,J)
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C
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80 Z(I,J) = X
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100 CONTINUE
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C
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200 RETURN
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END
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