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101 lines
3.4 KiB
Fortran
101 lines
3.4 KiB
Fortran
*DECK BALBAK
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SUBROUTINE BALBAK (NM, N, LOW, IGH, SCALE, M, Z)
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C***BEGIN PROLOGUE BALBAK
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C***PURPOSE Form the eigenvectors of a real general matrix from the
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C eigenvectors of matrix output from BALANC.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4C4
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C***TYPE SINGLE PRECISION (BALBAK-S, CBABK2-C)
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C***KEYWORDS 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 BALBAK,
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C NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch.
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C HANDBOOK FOR AUTO. COMP., Vol.II-LINEAR ALGEBRA, 315-326(1971).
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C
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C This subroutine forms the eigenvectors of a REAL GENERAL
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C matrix by back transforming those of the corresponding
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C balanced matrix determined by BALANC.
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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, Z, 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 number of components of the vectors in matrix Z.
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C N is an INTEGER variable. N must be less than or equal
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C to NM.
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C
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C LOW and IGH are INTEGER variables determined by BALANC.
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C
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C SCALE contains information determining the permutations and
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C scaling factors used by BALANC. SCALE is a one-dimensional
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C REAL array, dimensioned SCALE(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 real and imaginary parts of the eigen-
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C vectors to be back transformed in its first M columns.
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C Z is a two-dimensional REAL array, 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 real and imaginary parts of the
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C transformed eigenvectors in its first 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 BALBAK
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C
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INTEGER I,J,K,M,N,II,NM,IGH,LOW
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REAL SCALE(*),Z(NM,*)
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REAL S
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C
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C***FIRST EXECUTABLE STATEMENT BALBAK
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IF (M .EQ. 0) GO TO 200
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IF (IGH .EQ. LOW) GO TO 120
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C
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DO 110 I = LOW, IGH
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S = SCALE(I)
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C .......... LEFT HAND EIGENVECTORS ARE BACK TRANSFORMED
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C IF THE FOREGOING STATEMENT IS REPLACED BY
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C S=1.0E0/SCALE(I). ..........
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DO 100 J = 1, M
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100 Z(I,J) = Z(I,J) * S
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C
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110 CONTINUE
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C ......... FOR I=LOW-1 STEP -1 UNTIL 1,
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C IGH+1 STEP 1 UNTIL N DO -- ..........
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120 DO 140 II = 1, N
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I = II
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IF (I .GE. LOW .AND. I .LE. IGH) GO TO 140
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IF (I .LT. LOW) I = LOW - II
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K = SCALE(I)
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IF (K .EQ. I) GO TO 140
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C
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DO 130 J = 1, M
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S = Z(I,J)
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Z(I,J) = Z(K,J)
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Z(K,J) = S
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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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