[nm,n,t,d,e,e2,ierr]=figi(nm,n,t,d,e,e2,ierr);

function [nm,n,t,d,e,e2,ierr]=figi(nm,n,t,d,e,e2,ierr);
%***BEGIN PROLOGUE  FIGI
%***PURPOSE  Transforms certain real non-symmetric tridiagonal matrix
%            to symmetric tridiagonal matrix.
%***LIBRARY   SLATEC (EISPACK)
%***CATEGORY  D4C1C
%***TYPE      SINGLE PRECISION (FIGI-S)
%***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
%***AUTHOR  Smith, B. T., et al.
%***DESCRIPTION
%
%     Given a NONSYMMETRIC TRIDIAGONAL matrix such that the products
%     of corresponding pairs of off-diagonal elements are all
%     non-negative, this subroutine reduces it to a symmetric
%     tridiagonal matrix with the same eigenvalues.  If, further,
%     a zero product only occurs when both factors are zero,
%     the reduced matrix is similar to the original matrix.
%
%     On INPUT
%
%        NM must be set to the row dimension of the two-dimensional
%          array parameter, T, as declared in the calling program
%          dimension statement.  NM is an INTEGER variable.
%
%        N is the order of the matrix T.  N is an INTEGER variable.
%          N must be less than or equal to NM.
%
%        T contains the nonsymmetric matrix.  Its subdiagonal is
%          stored in the last N-1 positions of the first column,
%          its diagonal in the N positions of the second column,
%          and its superdiagonal in the first N-1 positions of
%          the third column.  T(1,1) and T(N,3) are arbitrary.
%          T is a two-dimensional REAL array, dimensioned T(NM,3).
%
%     On OUTPUT
%
%        T is unaltered.
%
%        D contains the diagonal elements of the tridiagonal symmetric
%          matrix.  D is a one-dimensional REAL array, dimensioned D(N).
%
%        E contains the subdiagonal elements of the tridiagonal
%          symmetric matrix in its last N-1 positions.  E(1) is not set.
%          E is a one-dimensional REAL array, dimensioned E(N).
%
%        E2 contains the squares of the corresponding elements of E.
%          E2 may coincide with E if the squares are not needed.
%          E2 is a one-dimensional REAL array, dimensioned E2(N).
%
%        IERR is an INTEGER flag set to
%          Zero       for normal return,
%          N+I        if T(I,1)*T(I-1,3) is negative and a symmetric
%                     matrix cannot be produced with FIGI,
%          -(3*N+I)   if T(I,1)*T(I-1,3) is zero with one factor
%                     non-zero.  In this case, the eigenvectors of
%                     the symmetric matrix are not simply related
%                     to those of  T  and should not be sought.
%
%     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  FIGI
%
persistent i ; 

if isempty(i), i=0; end;
t_orig=t;t_shape=[nm,3];t=reshape([t_orig(1:min(prod(t_shape),numel(t_orig))),zeros(1,max(0,prod(t_shape)-numel(t_orig)))],t_shape);
d_shape=size(d);d=reshape(d,1,[]);
e_shape=size(e);e=reshape(e,1,[]);
e2_shape=size(e2);e2=reshape(e2,1,[]);
%
%***FIRST EXECUTABLE STATEMENT  FIGI
ierr = 0;
%
for i = 1 : n;
if( i~=1 )
e2(i) = t(i,1).*t(i-1,3);
if( e2(i)<0 )
%     .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL
%                ELEMENTS IS NEGATIVE ..........
ierr = fix(n + i);
break;
elseif( e2(i)==0 ) ;
%     .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL
%                ELEMENTS IS ZERO WITH ONE MEMBER NON-ZERO ..........
if( t(i,1)~=0.0e0 || t(i-1,3)~=0.0e0 )
ierr = fix(-(3.*n+i));
end;
end;
e(i) = sqrt(e2(i));
end;
d(i) = t(i,2);
%
end;
t_orig(1:prod(t_shape))=t;t=t_orig;
d_shape=zeros(d_shape);d_shape(:)=d(1:numel(d_shape));d=d_shape;
e_shape=zeros(e_shape);e_shape(:)=e(1:numel(e_shape));e=e_shape;
e2_shape=zeros(e2_shape);e2_shape(:)=e2(1:numel(e2_shape));e2=e2_shape;
end
%DECK FMAT