*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