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- *DECK COMBAK
- SUBROUTINE COMBAK (NM, LOW, IGH, AR, AI, INT, M, ZR, ZI)
- C***BEGIN PROLOGUE COMBAK
- C***PURPOSE Form the eigenvectors of a complex general matrix from the
- C eigenvectors of a upper Hessenberg matrix output from
- C COMHES.
- C***LIBRARY SLATEC (EISPACK)
- C***CATEGORY D4C4
- C***TYPE COMPLEX (ELMBAK-S, COMBAK-C)
- C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
- C***AUTHOR Smith, B. T., et al.
- C***DESCRIPTION
- C
- C This subroutine is a translation of the ALGOL procedure COMBAK,
- C NUM. MATH. 12, 349-368(1968) by Martin and Wilkinson.
- C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971).
- C
- C This subroutine forms the eigenvectors of a COMPLEX GENERAL
- C matrix by back transforming those of the corresponding
- C upper Hessenberg matrix determined by COMHES.
- C
- C On INPUT
- C
- C NM must be set to the row dimension of the two-dimensional
- C array parameters, AR, AI, ZR and ZI, as declared in the
- C calling program dimension statement. NM is an INTEGER
- C variable.
- C
- C LOW and IGH are two INTEGER variables determined by the
- C balancing subroutine CBAL. If CBAL has not been used,
- C set LOW=1 and IGH equal to the order of the matrix.
- C
- C AR and AI contain the multipliers which were used in the
- C reduction by COMHES in their lower triangles below
- C the subdiagonal. AR and AI are two-dimensional REAL
- C arrays, dimensioned AR(NM,IGH) and AI(NM,IGH).
- C
- C INT contains information on the rows and columns
- C interchanged in the reduction by COMHES. Only
- C elements LOW through IGH are used. INT is a
- C one-dimensional INTEGER array, dimensioned INT(IGH).
- C
- C M is the number of eigenvectors to be back transformed.
- C M is an INTEGER variable.
- C
- C ZR and ZI contain the real and imaginary parts, respectively,
- C of the eigenvectors to be back transformed in their first M
- C columns. ZR and ZI are two-dimensional REAL arrays,
- C dimensioned ZR(NM,M) and ZI(NM,M).
- C
- C On OUTPUT
- C
- C ZR and ZI contain the real and imaginary parts, respectively,
- C of the transformed eigenvectors in their first M columns.
- C
- C Questions and comments should be directed to B. S. Garbow,
- C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
- C ------------------------------------------------------------------
- C
- C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
- C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
- C system Routines - EISPACK Guide, Springer-Verlag,
- C 1976.
- C***ROUTINES CALLED (NONE)
- C***REVISION HISTORY (YYMMDD)
- C 760101 DATE WRITTEN
- C 890831 Modified array declarations. (WRB)
- C 890831 REVISION DATE from Version 3.2
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C 920501 Reformatted the REFERENCES section. (WRB)
- C***END PROLOGUE COMBAK
- C
- INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1
- REAL AR(NM,*),AI(NM,*),ZR(NM,*),ZI(NM,*)
- REAL XR,XI
- INTEGER INT(*)
- C
- C***FIRST EXECUTABLE STATEMENT COMBAK
- IF (M .EQ. 0) GO TO 200
- LA = IGH - 1
- KP1 = LOW + 1
- IF (LA .LT. KP1) GO TO 200
- C .......... FOR MP=IGH-1 STEP -1 UNTIL LOW+1 DO -- ..........
- DO 140 MM = KP1, LA
- MP = LOW + IGH - MM
- MP1 = MP + 1
- C
- DO 110 I = MP1, IGH
- XR = AR(I,MP-1)
- XI = AI(I,MP-1)
- IF (XR .EQ. 0.0E0 .AND. XI .EQ. 0.0E0) GO TO 110
- C
- DO 100 J = 1, M
- ZR(I,J) = ZR(I,J) + XR * ZR(MP,J) - XI * ZI(MP,J)
- ZI(I,J) = ZI(I,J) + XR * ZI(MP,J) + XI * ZR(MP,J)
- 100 CONTINUE
- C
- 110 CONTINUE
- C
- I = INT(MP)
- IF (I .EQ. MP) GO TO 140
- C
- DO 130 J = 1, M
- XR = ZR(I,J)
- ZR(I,J) = ZR(MP,J)
- ZR(MP,J) = XR
- XI = ZI(I,J)
- ZI(I,J) = ZI(MP,J)
- ZI(MP,J) = XI
- 130 CONTINUE
- C
- 140 CONTINUE
- C
- 200 RETURN
- END
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