Output Files

A variety of output files are created in the directory specified by the  file_autopath  keyword in the input file (see Optional Input Entries). All files have ASCII format. The stem of the output file names is defined by the  file_outputname  input entry. Assuming  file_outputname = filter,  the following files are created:

filter.log:
contains information on the parameters used in the filter-diagonalization as well as a detailed list of the results
filter.eig:
contains exclusively those results of the filter-diagonalization procedure that have not been labeled spurious
filter.inp:
contains a compilation of all input or default parameters

If  file_fourier = yes,  the file

filter.ft:
contains the Fourier transform of the autocorrelation function

is also created.

The Log File

The information given in the log file can be grouped into two parts. In the first part the calculation that has been made is characterized. The amount of memory required is given and all relevant definitions from the input file are recapitulated. In the second part the results are displayed. Some statistical quantities such as the number of accurate states found and the mean and extremal errors are given. The energies, intensities, and errors are then presented in a table. The energies are given in the same unit as the energies in the input file. If specified, the differences between the computed results and the values from The Comparison File are also shown. Here an example log file can be found.

The output of the complex symmetric version, fdc, is mainly the same as of the real symmetric version, filter, except that also the widths are output. We write the eigenvalues of the complex symmetric Hamiltonian in the form E - i W/2. The results displayed are then E and W, in the unit system defined in the input file.

The Eigenenergy File

In the eigenenergy file those results of the filter-diagonalization procedure that are considered accurate are compiled. The file has two columns. The first one contains the computed energy (given in the same unit as the energies in the input file) and the second one the corresponding intensity:

-0.6157956320071E+001  0.1490531840265E-001
-0.6156696223016E+001  0.6947238058296E-002
-0.6152255257511E+001  0.1894580215085E-002
-0.6150741128375E+001  0.6643072672641E-002
-0.6146348651616E+001  0.2202109986605E-002
-0.6143928233993E+001  0.6573779754760E-003
-0.6139563921858E+001  0.3257708374273E-002
-0.6137741436952E+001  0.9664705874401E-003
-0.6135453802428E+001  0.1772057222989E-003
This file can be used for instance by Plot Routines to plot the spectrum. It can also be specified as Comparison File in the input file.

For analysing the eigenvalues, and in particular for comparing the results of different calculations, a couple of programs exist, which are detailed in Auxiliary Programs.

In the case of a complex symmetric Hamiltonian, the file has an additional column in the middle, containing the widths W (as defined above):

-6.1579563200E+000   8.8434010961E-002   1.4905318402E-002
-6.1566962230E+000   9.7385842510E-002   6.9472380582E-003
-6.1522552575E+000   3.4969316220E-002   1.8945802150E-003
-6.1507411283E+000   5.0983233635E-002   6.6430726726E-003
-6.1463486516E+000   2.5467053413E-002   2.2021099866E-003
-6.1439282339E+000   6.4363025276E-002   6.5737797547E-004
-6.1395639218E+000   6.6497841620E-002   3.2577083742E-003
-6.1377414369E+000   4.4885779929E-003   9.6647058744E-004
-6.1354538024E+000   9.3516450317E-002   1.7720572229E-004
The energies and widths are given in the same unit as the energies in the input file. The eigenenergy file may again be specified as Comparison File in the input file.

The Input File

This file contains a complete list of the input or default parameters. Below an example is given.

# Keyword                   Parameter        Status
  prop_outputinterval     = 0.200000E-02  #  computed
  prop_timeconversion     = 1.0d0         #  input
  prop_energyshift        = 0.0d0         #  input
  prop_sodintegrator      = no            #  input
  prop_skipauto           = 1             #  input
  prop_wavepackets        = 000004        #  computed
  prop_usepackets         = 4             #  cmdline
  file_autopath           = .             #  default
  file_autoformat         = mctdh         #  input
  file_psilength          = 0             #  default/ignored
  file_exactname          =               #  default
  file_outputname         = filter_c0_p4  #  cmdline
  file_fourier            = no            #  input
  file_fourierresolution  = 512           #  input/ignored
  window_minimumenergy    = 50.0d0        #  compulsory
  window_energywidth      = 40.0d0        #  compulsory
  window_energypoints     = 25            #  compulsory
  window_energyconversion = 1.0d0         #  input
  filter_timeinterval     = 2.0d0         #  cmdline
  filter_function         = cos           #  input
  filter_gausswidth       = 0.3d0         #  input/ignored
  filter_autoorder        = zero          #  cmdline
  filter_cutoff           = 1.0d-10       #  input
  vp_principle            = H             #  input
  vp_energyshift          = 0.700000E+02  #  default/ignored
  vp_iterative            = no            #  input/ignored
  vp_accuracy             = 1.0d-9        #  input/ignored
  error_estimate          = variation     #  input
  error_spurious          = 0.1d0         #  input/ignored
  error_principle         = 1/H           #  input
  error_energyshift       = 0.700000E+02  #  default
  error_iterative         = no            #  input/ignored
Displayed are the keywords and the corresponding parameters. The status information in the last column has the following meaning:
compulsory:
the corresponding input entry is compulsory
computed:
the corresponding parameter was computed, e.g. from the data in the autocorrelation files
default:
the default parameter was used
input:
the parameter was taken from the input file
cmdline:
the parameter was taken from the command line
default/ignored:
the given parameter is a default value but was ignored, i.e. never used in the calculation
input/ignored:
the entry was present in the input file but ignored
cmdline/ignored:
the entry was present in the command line but ignored

An input entry is ignored if it is relevant only in conjunction with another parameter which has not been chosen in the input file. (E.g.  filter_gausswidth  will be ignored unless  filter_function = gauss.) Note that the file strictly obeys the input syntax (see Input Structure) and hence can be used as input file for the filter program.

The Fourier File

The fourier file contains the Fourier transform of the (zero-order) autocorrelation function, folded with the selected damping function, in the specified energy range. The two columns represent the energy and intensity:

-6.160000000000000  260.6785668291813
-6.159863013698630  277.5184621569997
-6.159726027397260  294.4093306381895
-6.159589041095891  311.2240400316336
-6.159452054794521  327.8298286201650
-6.159315068493151  344.0899576666821
-6.159178082191780  359.8655338013862
-6.159041095890410  375.0174696607140
-6.158904109589042  389.4085459223212
-6.158767123287672  402.9055335833113
...
The energies are given in the same unit as the energies in the input file. With the aid of Plot Routines the Fourier transform can be plotted.

When the program fdc is used, the Fourier transform of the autocorrelation function is a complex function of the complex argument E - i W/2. The fourier file hence contains the coordinates E and W, as well as the real part, imaginary part, and absolute value of the Fourier transform, e.g.

1.29032E-01 -7.74194E-01 2.47395E-03 -1.44438E-03 2.86473E-03
1.29032E-01 -8.38710E-01 2.39061E-03 -1.37435E-03 2.75750E-03
1.29032E-01 -9.03226E-01 2.31519E-03 -1.30643E-03 2.65836E-03
1.29032E-01 -9.67742E-01 2.24602E-03 -1.24107E-03 2.56610E-03
1.29032E-01 -1.03226E+00 2.18188E-03 -1.17853E-03 2.47983E-03
1.29032E-01 -1.09677E+00 2.12189E-03 -1.11894E-03 2.39884E-03
1.29032E-01 -1.16129E+00 2.06537E-03 -1.06236E-03 2.32258E-03
1.29032E-01 -1.22581E+00 2.01184E-03 -1.00876E-03 2.25058E-03
1.29032E-01 -1.29032E+00 1.96092E-03 -9.58098E-04 2.18247E-03
The range of both E and W is the energy window defined in the input file.

Plot Routines

The computed results (so far of the real symmetric program only) can be visualized by shell-scripts that make use of the Gnuplot program. The existing scripts are tabulated below.

Script Required Files Description
plfdspec file_outputname.eig Plots the line spectrum obtained from the filter-diagonalization procedure.
plfdfour file_outputname.ft Displays the Fourier transform of the autocorrelation function.

The shell-scripts recognize a number of arguments. Type

plfdspec -h

or

plfdfour -h

to get an overview.

Auxiliary Programs

An auxiliary program exists which is designed for comparing the results of different calculations obtained with the real filter program. (It does not work for the complex one since it assumes that the results are lists of energies and intensities, and not energies, widths, and intensities.) It is called as

fdmatchver   k   file_1   ...   file_k   |   sort -n   |   less

where  ver is the version number,  k specifies the number of files to be compared, and  file_1 ...  file_k are the names of the files. The files are typically the *.eig files generated by the filter program.

For instance, if file_1 contains the five energies and intensities

1285.3673185311E+000  1.0740277960000000E-001
1371.0602365654E+000  4.3956966964161830E-004
1388.2371505938E+000  3.4935267560000000E-002
2349.1285061750E+000  3.1545981720000000E-002
2548.3232400815E+000  1.0620001100000000E-001
and file_2 contains the six pairs of values
1285.3668549833E+000  1.074020343487891E-001
1388.2368347075E+000  3.491722659565360E-002
2349.1269376485E+000  3.153875507967670E-002
2383.3355167369E+000  1.263746447807894E-005
2498.4605910470E+000  5.299441725000872E-005
2548.3225966500E+000  1.061952361250140E-001
then type
fdmatch 2 file_1 file_2 | sort -n | less
to get the combined list
1285.367318531   1.074027796E-01   1285.366854983   1.074020343E-01
1371.060236565   4.395696696E-04
1388.237150594   3.493526756E-02   1388.236834708   3.491722660E-02
2349.128506175   3.154598172E-02   2349.126937649   3.153875508E-02
                                   2383.335516737   1.263746448E-05
                                   2498.460591047   5.299441725E-05
2548.323240081   1.062000110E-01   2548.322596650   1.061952361E-01
Where no matches between energies have been found, the corresponding entry is left blank.

A second auxiliary program named fdcheck analysis the output of fdmatch, i.e. it checks whether a state has been found in all comparison calculations and computes the internal errors. It is called as

fdcheckver   k   j

where  ver is the version number,  k denotes the number of data sets (a set consists of two numbers, energy and intensity), and  j is a flag which specifies whether (j = 1) or not (j = 0) the first data set is an "exact" one. Such an "exact" data set is ignored in the decision whether a state has been found and in the computation of the internal error. The "exact" data set must be the first one.

For example, with file_1 and file_2 as above, the command line

fdmatch 2 file_1 file_2 | sort -n | fdcheck 2 0
yields the output
1285.367087   0.000232   1.07402E-01   3.72650E-07
1388.236993   0.000158   3.49262E-02   9.02048E-06
2349.127722   0.000784   3.15424E-02   3.61332E-06
2548.322918   0.000322   1.06198E-01   2.38745E-06
Only those energies being present in all data sets are put out. The first column gives the (mean) energy, the second one the internal error (i.e. the standard deviation), the third one the (mean) intensity, and the last one again the corresponding internal error.

If there was also an exact data set

1285.0000000000E+000   1.1000000000000000E-001
1388.0000000000E+000   3.5000000000000000E-002
2548.0000000000E+000   1.1000000000000000E-001
3000.0000000000E+000   1.0000000000000000E-003
stored in file_0, then type
fdmatch 3 file_0 file_1 file_2 | sort -n | fdcheck 3 1 | less
to obtain the result
1285.000   1285.367   0.000   0.367   1.10E-01   1.07E-01   3.73E-07   2.60E-03
1388.000   1388.237   0.000   0.237   3.50E-02   3.49E-02   9.02E-06   7.38E-05
           2349.128   0.001                      3.15E-02   3.61E-06
2548.000   2548.323   0.000   0.323   1.10E-01   1.06E-01   2.39E-06   3.80E-03
3000.000                              1.00E-03
The first column contains the "exact" energy (of file_0), the second the mean energy (of file_1 and file_2 only), the third the standard deviation or internal error (of file_1 and file_2 only), and the fourth the absolute difference between the first two columns, i.e. the "exact" error. The next four columns contain the corresponding values for the intensities. In the example, the value in line three is spurious and that in the last line is missing.