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101 lines
3.5 KiB
Fortran
101 lines
3.5 KiB
Fortran
*DECK TRBAK1
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SUBROUTINE TRBAK1 (NM, N, A, E, M, Z)
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C***BEGIN PROLOGUE TRBAK1
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C***PURPOSE Form the eigenvectors of real symmetric matrix from
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C the eigenvectors of a symmetric tridiagonal matrix formed
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C by TRED1.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4C4
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C***TYPE SINGLE PRECISION (TRBAK1-S)
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C***KEYWORDS EIGENVECTORS OF A REAL SYMMETRIC MATRIX, 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 TRBAK1,
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C NUM. MATH. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson.
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C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971).
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C
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C This subroutine forms the eigenvectors of a REAL SYMMETRIC
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C matrix by back transforming those of the corresponding
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C symmetric tridiagonal matrix determined by TRED1.
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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, A 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. 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 A contains information about the orthogonal transformations
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C used in the reduction by TRED1 in its strict lower
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C triangle. A is a two-dimensional REAL array, dimensioned
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C A(NM,N).
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C
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C E contains the subdiagonal elements of the tridiagonal matrix
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C in its last N-1 positions. E(1) is arbitrary. These
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C elements provide the remaining information about the
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C orthogonal transformations. E is a one-dimensional REAL
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C array, dimensioned E(N).
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C
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C M is the number of columns of Z 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 M columns.
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C
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C Note that TRBAK1 preserves vector Euclidean norms.
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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 TRBAK1
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C
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INTEGER I,J,K,L,M,N,NM
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REAL A(NM,*),E(*),Z(NM,*)
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REAL S
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C
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C***FIRST EXECUTABLE STATEMENT TRBAK1
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IF (M .EQ. 0) GO TO 200
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IF (N .EQ. 1) GO TO 200
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C
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DO 140 I = 2, N
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L = I - 1
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IF (E(I) .EQ. 0.0E0) GO TO 140
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C
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DO 130 J = 1, M
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S = 0.0E0
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C
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DO 110 K = 1, L
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110 S = S + A(I,K) * Z(K,J)
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C .......... DIVISOR BELOW IS NEGATIVE OF H FORMED IN TRED1.
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C DOUBLE DIVISION AVOIDS POSSIBLE UNDERFLOW ..........
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S = (S / A(I,L)) / E(I)
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C
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DO 120 K = 1, L
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120 Z(K,J) = Z(K,J) + S * A(I,K)
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C
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130 CONTINUE
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C
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140 CONTINUE
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C
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200 RETURN
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END
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