[nm,n,low,igh,scalemlv,m,zr,zi]=cbabk2(nm,n,low,igh,scalemlv,m,zr,zi);

function [nm,n,low,igh,scalemlv,m,zr,zi]=cbabk2(nm,n,low,igh,scalemlv,m,zr,zi);
%***BEGIN PROLOGUE  CBABK2
%***PURPOSE  Form the eigenvectors of a complex general matrix from the
%            eigenvectors of matrix output from CBAL.
%***LIBRARY   SLATEC (EISPACK)
%***CATEGORY  D4C4
%***TYPE      COMPLEX (BALBAK-S, CBABK2-C)
%***KEYWORDS  EIGENVECTORS, EISPACK
%***AUTHOR  Smith, B. T., et al.
%***DESCRIPTION
%
%     This subroutine is a translation of the ALGOL procedure
%     CBABK2, which is a complex version of BALBAK,
%     NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch.
%     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 315-326(1971).
%
%     This subroutine forms the eigenvectors of a COMPLEX GENERAL
%     matrix by back transforming those of the corresponding
%     balanced matrix determined by  CBAL.
%
%     On INPUT
%
%        NM must be set to the row dimension of the two-dimensional
%          array parameters, ZR and ZI, as declared in the calling
%          program dimension statement.  NM is an INTEGER variable.
%
%        N is the order of the matrix Z=(ZR,ZI).  N is an INTEGER
%          variable.  N must be less than or equal to NM.
%
%        LOW and IGH are INTEGER variables determined by  CBAL.
%
%        SCALE contains information determining the permutations and
%          scaling factors used by  CBAL.  SCALE is a one-dimensional
%          REAL array, dimensioned SCALE(N).
%
%        M is the number of eigenvectors to be back transformed.
%          M is an INTEGER variable.
%
%        ZR and ZI contain the real and imaginary parts, respectively,
%          of the eigenvectors to be back transformed in their first
%          M columns.  ZR and ZI are two-dimensional REAL arrays,
%          dimensioned ZR(NM,M) and ZI(NM,M).
%
%     On OUTPUT
%
%        ZR and ZI contain the real and imaginary parts,
%          respectively, of the transformed eigenvectors
%          in their first M columns.
%
%     Questions and comments should be directed to B. S. Garbow,
%     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
%     ------------------------------------------------------------------
%
%***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
%                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
%                 system Routines - EISPACK Guide, Springer-Verlag,
%                 1976.
%***ROUTINES CALLED  (NONE)
%***REVISION HISTORY  (YYMMDD)
%   760101  DATE WRITTEN
%   890831  Modified array declarations.  (WRB)
%   890831  REVISION DATE from Version 3.2
%   891214  Prologue converted to Version 4.0 format.  (BAB)
%   920501  Reformatted the REFERENCES section.  (WRB)
%***end PROLOGUE  CBABK2
%
persistent i ii j k s ; 

if isempty(i), i=0; end;
if isempty(j), j=0; end;
if isempty(k), k=0; end;
if isempty(ii), ii=0; end;
scale_shape=size(scalemlv);scalemlv=reshape(scalemlv,1,[]);
zr_shape=size(zr);zr=reshape([zr(:).',zeros(1,ceil(numel(zr)./prod([nm])).*prod([nm])-numel(zr))],nm,[]);
zi_shape=size(zi);zi=reshape([zi(:).',zeros(1,ceil(numel(zi)./prod([nm])).*prod([nm])-numel(zi))],nm,[]);
if isempty(s), s=0; end;
%
%***FIRST EXECUTABLE STATEMENT  CBABK2
if( m~=0 )
if( igh~=low )
%
for i = low : igh;
s = scalemlv(i);
%     .......... LEFT HAND EIGENVECTORS ARE BACK TRANSFORMED
%                IF THE FOREGOING STATEMENT IS REPLACED BY
%                S=1.0E0/SCALE(I). ..........
for j = 1 : m;
zr(i,j) = zr(i,j).*s;
zi(i,j) = zi(i,j).*s;
end; j = fix(m+1);
%
end; i = fix(igh+1);
end;
%     .......... FOR I=LOW-1 STEP -1 UNTIL 1,
%                IGH+1 STEP 1 UNTIL N DO -- ..........
for ii = 1 : n;
i = fix(ii);
if( i<low || i>igh )
if( i<low )
i = fix(low - ii);
end;
k = fix(scalemlv(i));
if( k~=i )
%
for j = 1 : m;
s = zr(i,j);
zr(i,j) = zr(k,j);
zr(k,j) = s;
s = zi(i,j);
zi(i,j) = zi(k,j);
zi(k,j) = s;
end; j = fix(m+1);
end;
end;
%
end; ii = fix(n+1);
end;
%
scale_shape=zeros(scale_shape);scale_shape(:)=scalemlv(1:numel(scale_shape));scalemlv=scale_shape;
zr_shape=zeros(zr_shape);zr_shape(:)=zr(1:numel(zr_shape));zr=zr_shape;
zi_shape=zeros(zi_shape);zi_shape(:)=zi(1:numel(zi_shape));zi=zi_shape;
end
%DECK CBAL