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***LIBRARY SLATEC (EISPACK)
C***TYPE SINGLE PRECISION (ELMBAK-S, COMBAK-C)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
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 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 On INPUT
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 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 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 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 M is the number of columns of Z to be back transformed.
C M is an INTEGER variable.
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 On OUTPUT
C Z contains the real and imaginary parts of the transformed
C eigenvectors in its first M columns.
C Questions and comments should be directed to B. S. Garbow,
C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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***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