To solve a real, symmetric eigenvalue problem you need
the following three EISPACK subroutines: 

tred2.f  --  tridiagonalizes matrix
tql2.f   --  diagonalizes matrix obtained by tred2
pythag.f --  called by tql2    


The call sequence is 

     call tred2(N,N,A,d,e,A)
     call tql2(N,N,d,e,A,ierr)

A   -  real*8 (double prec.) symmetric matrix of dimension NxN
N   -  its dimension, integer
d,e -  real*8 vectors of length N (workspace)
ierr-  error flag, integer


on output d contains the eigenvalues in ascending order, and
the columns of A contain the corresponding normalized eigenvectors.


For more info see source code!