Faster eigensolver for the benchmark

[certik]

TODO:

• [ ] Expose this cleanly, similarly to the Schroedinger expert lapack interface
• [ ] change (lower) the number of requested eigenvectors based on kappa

[certik]

With the latest commit, the fastest I am able to get is:

$ time build/gfortran_565E65E7876A06C6/test/test_dft_dirac_fast
 SCF iteration:           1
 SCF iteration:           2
 SCF iteration:           3
 SCF iteration:           4
 SCF iteration:           5
 SCF iteration:           6
 SCF iteration:           7
 SCF convergence error:   2.4220418857676123     
 SCF iteration:           8
 SCF convergence error:   5.9357534701121040E-003
 SCF iteration:           9
 SCF convergence error:   1.8806871048582252E-003
 SCF iteration:          10
 SCF convergence error:   1.0455984192958567E-004
 SCF iteration:          11
 SCF convergence error:   3.2101015676744282E-005
 SCF iteration:          12
 SCF convergence error:   1.1781998182414100E-005
 SCF iteration:          13
 SCF convergence error:   1.2883829185739160E-006
 SCF iteration:          14
 SCF convergence error:   8.7908847490325570E-007
 SCF iteration:          15
 SCF convergence error:   1.6529884305782616E-007
 Comparison of calculated and reference energies

 Total energy:
               E           E_ref     error
 -28001.13232635 -28001.13232549  8.65E-07

 Eigenvalues:
   n               E           E_ref     error
   1  -4223.41902075  -4223.41902046  2.94E-07
   2   -789.48978246   -789.48978233  1.35E-07
   3   -761.37447601   -761.37447597  3.29E-08
   4   -622.84809461   -622.84809456  4.34E-08
   5   -199.42980567   -199.42980564  2.36E-08
   6   -186.66371312   -186.66371312  6.40E-09
   7   -154.70102667   -154.70102667  2.26E-09
   8   -134.54118029   -134.54118029  2.11E-09
   9   -128.01665738   -128.01665738  8.76E-10
  10    -50.78894805    -50.78894806  1.06E-08
  11    -45.03717127    -45.03717129  1.59E-08
  12    -36.68861047    -36.68861049  1.22E-08
  13    -27.52930623    -27.52930624  1.41E-08
  14    -25.98542889    -25.98542891  1.51E-08
  15    -13.88951422    -13.88951423  1.64E-08
  16    -13.48546968    -13.48546969  1.61E-08
  17    -11.29558710    -11.29558710  4.23E-10
  18     -9.05796425     -9.05796425  7.23E-10
  19     -7.06929564     -7.06929563  4.66E-09
  20     -3.79741624     -3.79741623  8.66E-09
  21     -3.50121719     -3.50121718  7.14E-09
  22     -0.14678840     -0.14678838  1.89E-08
  23     -0.11604718     -0.11604717  1.83E-08
  24     -1.74803998     -1.74803995  2.22E-08
  25     -1.10111902     -1.10111900  2.19E-08
  26     -0.77578420     -0.77578418  2.18E-08
  27     -0.10304083     -0.10304082  1.50E-08
  28     -0.08480204     -0.08480202  1.37E-08
  29     -0.16094729     -0.16094728  9.98E-09
build/gfortran_565E65E7876A06C6/test/test_dft_dirac_fast  0.40s user 0.00s system 99% cpu 0.407 total