Overall procedure
=================

This program performs simulation as follows (See Fig. :num:`calcflow` ):

#. Read a input file for the numerical condition.
#. (Optional) Read input files for the Hamiltonian and the right hand side vector.
#. (Optional) Read a file for the restart (:math:`\alpha`, :math:`\beta`, residual vectors)
#. (Bi)CG iteration with :math:`K\omega` library
#. Output results (Green's function, residual vectors, :math:`\alpha`, :math:`\beta`)

.. _calcflow:
     
.. figure:: ../figs/flow_en.png
	    :width: 8cm

            Schematic flow of the calculation of this program.


We introduce the detailed procedure as follows.
The format of each file is written in :ref:`fileformat`.

Calculation from scratch
------------------------

Prepare input file
~~~~~~~~~~~~~~~~~~

In this input file, we specify the frequency grid,
the maximum number of iteration, etc.

A example of this input file is shown as follow.

::

    &filename
      inham = ""
      invec = ""
    /
    &ham
    nsite = 4
    Jx = 1d0
    Jy = 1d0
    Jz = 1d0
    Dz = 0d0
    /
    &cg
      maxloops = 100
      convfactor = 6
    /
    &dyn
      calctype = "normal"
      nomega = 100
      omegamin = (-2d0, 0.1d0)
      omegamax = ( 1d0, 0.1d0)
      outrestart = .TRUE.
    /

where ``InHam`` is the file-name for the Hamiltonian in the MatrixMarket format,
``InVec`` is the file-name of the right hand side vector,
``NOmega`` is the number of frequencies where the dynamical Green's function
is computed.
``OmegaMin`` is the lower limit of the frequency :math:`z`,
``OmegaMax`` is the upper limit of the frequency :math:`z`.
These complex frequencies must be written as "``({Real part}, {Imaginaly part})``".
The frequency grid is defined as

.. math::

   \begin{align}
   \omega_n =  {\tt OmegaMin}
   + \frac{n-1}{{\tt NOmega}-1}({\tt OmegaMax} - {\tt OmegaMin}).
   \end{align}

``MaxLoops`` is the maximum number of iterations.
For the details of this input file, see :ref:`modpara`.
The string variable must be specified with two ``'`` or ``"``.

(Optional) Prepare input file for the Hamiltonian and RHS vector
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Prepare input files for the Hamiltonian (MatrixMarket format)
and right hand side vector.

An example of the file of the right hand side vector
is shown as follows:

::

    256
    0.01    0.0
    0.05    0.0
    0.1     0.0
    (continue ...)

Details of the file format is written in
:ref:`ham` and :ref:`vec`.

Launch
~~~~~~

Execute a program ``ShiftK.out`` with a namelist file ``namelist.def``
as follows:

.. code-block:: bash

   $ ShiftK.out namelist.def

Output
~~~~~~

The following files are generated in ``output/`` directory (this directory is
also generated by this program).

::

    TriDiagComp.dat, ResVec.dat, dynamicalG.dat

where
``TriDiagComp.dat`` contains the parameters for the restart,
``ResVec.dat`` contains the residual vector,
``dynamicalG.dat`` contains the dynamical Green's function.
The format of these file is written in
:ref:`revec` - :ref:`dynamicalg`.

Catch up
--------

Compute the Green's function at the different frequency by using the information
of ``output/TriDiagComp.dat`` that are generated in the previous run.
This calculation does not require the matrix-vector product.

Modify the namelist file
~~~~~~~~~~~~~~~~~~~~~~~~

Change ``calctype`` parameter in the file ``namelist.def``
from ``"normal"`` to ``"recalc"``.
``OmegaMin``, ``OmegaMax``, etc. can be modified.

Launch
~~~~~~

Execute a program ``ShiftK.out`` with a namelist file ``namelist.def``
as follows:

.. code-block:: bash

   $ ShiftK.out namelist.def

The ``output/dynamicalG.dat`` will be overwritten.

Output
~~~~~~

The same output files as the previous section are generated.

Restart
-------

Compute the Green's function at the different frequency by using the information
of ``output/TriDiagComp.dat`` and ``output/ResVec.dat``
that are generated in the previous run.

Modify the namelist file
~~~~~~~~~~~~~~~~~~~~~~~~

Change ``calctype`` parameter in the file ``namelist.def``
from ``"normal"`` to ``"restart"``.
``OmegaMin``, ``OmegaMax``, etc. can be modified.
Parameters ``InHam`` ,  ``InVec``, and the files of the Hamiltonian
and RHS vector can not be modified.

Launch
~~~~~~

Execute a program ``ShiftK.out`` with a namelist file ``namelist.def``
as follows:

.. code-block:: bash

   $ ShiftK.out namelist.def

The ``output/dynamicalG.dat`` will be overwritten.

Output
~~~~~~

The following files are generated (or are overwritten) in ``output/`` directory.

::

    TriDiagComp.dat, ResVec.dat, dynamicalG.dat

where
``TriDiagComp.dat`` contains the parameters for the restart,
``ResVec.dat`` contains the residual vector,
``dynamicalG.dat`` contains the dynamical Green's function.
The format of these file is written in
:ref:`revec` - :ref:`dynamicalg`.