Examples for the use of diagonalize:

1. Download and install diagonalize.
2. Download the Hermitean 1377x1377 sample matrix sample-matrix.gz.
   Note: This is on purpose a rather ill-conditioned problem, with extremal eigenvalues 18J and 26.202624952J.
3. To get all eigenvalues, no eigenvectors, try

        ./diagonalize -z -all -iJ:=1 sample-matrix eigenvals
   

   The option `-z should be omitted if you have already unpacked the sample-matrix. The option -all requests all eigenvalues (no eigenvectors). `-iJ:=1' specifies that J=1 should be substituted in the input matrix. `eigenvals' is the name of the file in which the result for the 1377 eigenvalues are stored.
   Note: You may find that in order to obtain stable results you have to use a version which binds to LaPack.
4. If you want `just' the 100 lowest eigenvalues (and -vectors), you can proceed as follows:

        ./diagonalize -z -le=800 -n150 -b -t -iJ:=1 sample-matrix eigenvals
        ./diagonalize -z -a1e-16 -n100+50 -f -s23.4 -iJ:=1 sample-matrix eigenvals
   

   The first command performs a Lanczos' diagonalization in a Krylov subspace of dimension 800 (option -le=800), without reorthogonalization (option -b) and writes the resulting estimates for the lowest 150 eigenvectors in a file `vi_vecs.dmp' (option -t).
   These 150 vectors are not fully converged. Therefore we need the second command, which also eliminates so-called `ghosts'. This command reads the vectors from the file `vi_vecs.dmp' (option -f) and produces 100 converged eigenvectors (option -n=100+50 - 50 auxiliary vectors included). The other options perform a spectral shift by 23.4 for stabilization purposes (option -s23.4) and request an accuracy for the square of 10<sup>-16</sup>, i.e. at least 8 converged digits (option -a1e-16).
   Of course, one really wishes to apply this strategy only to (much) bigger problems, i.e. dimensions (much) beyond 10 000.
   Note: You have stored an intermediate estimate for the vectors in the file `vi_vecs.dmp' (binary format). You may wish to remove this file once you have finished your computation.