*DECK ELMBAK
SUBROUTINE ELMBAK (NM, LOW, IGH, A, INT, M, Z)
C***BEGIN PROLOGUE ELMBAK
C***PURPOSE Form the eigenvectors of a real general matrix from the
C eigenvectors of the upper Hessenberg matrix output from
C ELMHES.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C4
C***TYPE SINGLE PRECISION (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 ELMBAK,
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 REAL GENERAL
C matrix by back transforming those of the corresponding
C upper Hessenberg matrix determined by ELMHES.
C
C On INPUT
C
C NM must be set to the row dimension of the two-dimensional
C array parameters, A and Z, as declared in the calling
C program dimension statement. NM is an INTEGER variable.
C
C LOW and IGH are two INTEGER variables determined by the
C balancing subroutine BALANC. If BALANC has not been
C used, set LOW=1 and IGH equal to the order of the matrix.
C
C A contains the multipliers which were used in the reduction
C by ELMHES in its lower triangle below the subdiagonal.
C A is a two-dimensional REAL array, dimensioned A(NM,IGH).
C
C INT contains information on the rows and columns interchanged
C in the reduction by ELMHES. Only elements LOW through IGH
C are used. INT is a one-dimensional INTEGER array,
C dimensioned INT(IGH).
C
C M is the number of columns of Z to be back transformed.
C M is an INTEGER variable.
C
C Z contains the real and imaginary parts of the eigenvectors
C to be back transformed in its first M columns. Z is a
C two-dimensional REAL array, dimensioned Z(NM,M).
C
C On OUTPUT
C
C Z contains the real and imaginary parts of the transformed
C eigenvectors in its 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 ELMBAK
C
INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1
REAL A(NM,*),Z(NM,*)
REAL X
INTEGER INT(*)
C
C***FIRST EXECUTABLE STATEMENT ELMBAK
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
X = A(I,MP-1)
IF (X .EQ. 0.0E0) GO TO 110
C
DO 100 J = 1, M
100 Z(I,J) = Z(I,J) + X * Z(MP,J)
C
110 CONTINUE
C
I = INT(MP)
IF (I .EQ. MP) GO TO 140
C
DO 130 J = 1, M
X = Z(I,J)
Z(I,J) = Z(MP,J)
Z(MP,J) = X
130 CONTINUE
C
140 CONTINUE
C
200 RETURN
END