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----------  BSE code, Absorption  -------------------------------
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  Version 1.1   (June, 2014)

  Version 1.0	(July, 2011) J. Deslippe, M. Jain, D. A. Strubbe, G. Samsonidze
  Version 0.5	J. Deslippe, D. Prendergast, L. Yang, F. Ribeiro, G. Samsonidze (2008)
  Version 0.2	M. L. Tiago, C. Spataru, S. Ismail-Beigi (2004)

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Description:

This code is the second half of the BSE code.  It interpolates the coarse grid
electron-hole kernel onto the fine grid and then diagonalized the BSE equation.
The output is the electron-hole eigenfunctions and eigenvalues as well the
absorption spectra.

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Required Input:

	absorption.inp	Input parameters.  See detailed explanation below.
	WFN_fi		Wavefunctions in unshifted fine grid
			(conduction and valence for momentum operator,
			conduction for velocity operator).
	WFNq_fi		Wavefunctions in shifted fine grid
			(not needed for momentum operator,
			valence for velocity operator).
	WFN_co		Wavefunctions on unshifted coarse grid.
			Must be the same as used for Kernel.
	eps0mat		Must be same as used in Kernel.
	epsmat		Must be same as used in Kernel.
	bsedmat		BSE matrix elements in coarse grid, direct part. This
			should be generated with Kernel code using same WFN_co.
	bsexmat		BSE exchange matrix elements.  This should be generated
			with Kernel code using same WFN_co.

Additional Input:

	eqp.dat		A list of quasiparticle energy corrections for the bands in WFN_fi.
                        Used if eqp_corrections is set in absorption.inp.
	eqp_q.dat	A list of quasiparticle energy corrections for the bands in WFNq_fi.
                        Used if eqp_corrections is set in absorption.inp.
	eqp_co.dat	A list of quasiparticle energy corrections for the bands in WFN_co.
                        Used if eqp_co_corrections is set in absorption.inp.

	kpoints		A list of k-points in unshifted fine grid. EXPERIMENTAL.
			If absent k-points from WFN_fi file are used.
	kpoints_co	A list of k-points in unshifted coarse grid. EXPERIMENTAL.
			If absent k-points from WFN_co file are used.

Auxiliary Files: (output files from previous runs - used as input to speed up calculation)

	dtmat		Transformation matrices, dcc/dvv use for interpolation
			between coarse and fine grid.  This file must be consistent
			with your bsedmat and bsexmat files and corresponding
			coarse and fine wavefunctions.
			NOTE: the file format for dtmat was changed in BerkeleyGW 1.1.0	(r5961)
	vmtxel		Optical matrix elements (velocity or momentum) between
			single particle states.
	epsdiag.dat	Diagonal elements of dielectric matrix on the q-grid.
			Must be consistent with epsmat and eps0mat.
	eigenvalues.dat	Contains electron-hole eigenvalues and transition matrix elements.


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	absorption.inp	Please see example absorption.inp in this directory
			for more complete options.

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Output Files:

	eigenvalues.dat	  	Has eigenvalues/transition matrix elements of e-h states,
			  	eigenvalues in eV, mtxels in atomic units.
	eigenvalues_noeh.dat	As above but for non-interacting e-h transitions, showing
                                k-point, bands, and spin for each.
	eigenvectors	  	Has the excitonic wavefunctions in Bloch space: A_svck 
	absorption_eh.dat	Dielectric function and density of excitonic states.
			  	Four Columns
			  	energy (in eV) | epsilon_2 | epsilon_1 | DOS
			 	DOS is normalized (\int (DOS) d(omega) = 1)
	absorption_noeh.dat	Non-interacting (RPA) dielectric function and joint density
				of states.  Four columns:
				energy (in eV) | epsilon_2 | epsilon_1 | JDOS
				JDOS is normalized (\int (JDOS) d(omega) = 1)
        dvmat_norm.dat		The norms of the dvv overlap matrices between the valence 
                        	band k on the fine grid and the closest k-point on the coarse grid
        dcmat_norm.dat		The norms of the dcc overlap matrices between the conduction
                        	band k on the fine grid and the closest k-point on the coarse grid
	eqp.dat, eqp_q.dat      Quasiparticle corrections for WFN_fi and WFNq_fi interpolated from
                                the coarse grid if eqp_co_corrections is used.
        bandstructure.dat       Same as eqp.dat and eqp_q.dat but in a format suitable for plotting
                                as a bandstructure.

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Tricks and hints:

1. To optimize distribution of work among PEs, choose the number of
PEs so that Nk*Nc*Nv in the fine grid is a multiple of the
number of PEs. The parallelization is first done over over k-points.

2. The Brillouin zone is built using a Wigner-Seitz construction;
this way the head matrix elements are easily calculated.

3. Check if the transformation matrices have norm close to 1! They
are usually normalized (look at the end of intwfn.f90). The norms are in
the files dvmat_norm.dat and dcmat_norm.dat.
 
4. Unfolding of irreducible BZ: if you want to skip the unfolding and
use the set of k-points in WFN_fi as a sampling of the whole BZ, specify
the no_symmetries_* options in absorption.inp.

5. The "number_eigenvalues" keyword: using this keyword tells the code 
to store only the first nn eigenvalues/eigenvectors. So far, this option 
is implemented only with the SCALAPACK diagonalization routines. 

6.  Analyzing eigenvectors.  We have a tool called summarize_eigenvectors to read in
and analyze eigenvectors for a group of exciton states.  For specific states
specified, it sums the total contribution from each k-point.
Please see the example input summarize_eigenvectors.inp.
