[doc] more doc fixes

.gitignore

@@ -13,6 +13,7 @@ POTCAR
 vasp*.tgz
 
 doc/input_output/DMFT_input/advanced.rst
+doc/input_output/DMFT_input/gw.rst
 doc/input_output/DMFT_input/dft.rst
 doc/input_output/DMFT_input/general.rst
 doc/input_output/DMFT_input/input.rst

doc/cRPA_VASP/README.md

@@ -70,9 +70,6 @@ ulimit -s unlimited
 and is written in the OUTCAR as two sets of bare interaction, where for one of them
 it says: low cutoff result for V_ijkl. Here ENCUT was used and for the one above 1.1*ENCUT or VCUTOFF was used.
 * usually a converged ENCUT gives also a reasonably high VCUTOFF, so that explicitly setting VCUTOFF is not necessary. Moreover, the effect of the VCUTOFF convergence is included by subtracting the constant shift between LOW and HIGH VCUTOFF test output in the OUTCAR
-* One can see in the convergence plot "debugging_examples/LaTiO3/VCUTOFF_convergence.png" the effect of ENCUT and VCUTOFF:
-
-![vcutoff_test](VCUTOFF_convergence.png)
 
 ## convergency tests:
 $`E_{corr}^{RPA}`$  converges for NBANDS,ENCUT to $`\infty`$, where the asymptotic
@@ -90,10 +87,10 @@ The procedure is then to first convergence KPOINTS and ENCUT, where KPOINTS depe
 
 ## Parameterization of U and J from cRPA calculations
 `eval_u.py` provides four different methods:
-- Kanamori: `calc_kan_params(...)` for extracting Kanamori parameters for a cubic system 
+- Kanamori: `calc_kan_params(...)` for extracting Kanamori parameters for a cubic system
 - Slater 1: `calc_u_avg_fulld(...)` using averaging and symmetries: $`U_\mathrm{cubic} = \frac1{2l+1} \sum_i (U_{iiii})`$, $`J_\mathrm{cubic} = \frac1{2l(2l+1)} \sum_{i, j\neq i} U_{ijji}`$. Then, the interaction parameters follow from the conversion $`U = U_\mathrm{cubic} - \frac85 J_\mathrm{cubic}, J = \frac75 J_\mathrm{cubic}`$.
 - Slater 2: `calculate_interaction_from_averaging(...)` using direct averaging: $`U = \frac1{(2l+1)^2} \sum_{i, j} U_{iijj}`$ and $`J = U - \frac1{2l(2l+1)} \sum_{i, j} U_{ijij}`$. This is more straight forward that Slater 1, but ignores the basis in which the cRPA Uijkl matrix is written. For a perfect Slater matrix this gives the same results if applied in cubic or spherical harmonics basis.
-- Slater 3: `fit_slater_fulld(...) `using an least-square fit (summed over the matrix elements) of the two-index matrices $`U_{iijj}`$ and $`U_{ijij}`$ to the Slater Hamiltonian. 
+- Slater 3: `fit_slater_fulld(...) `using an least-square fit (summed over the matrix elements) of the two-index matrices $`U_{iijj}`$ and $`U_{ijij}`$ to the Slater Hamiltonian.
 
 These three methods give the same results if the cRPA matrix is of the Slater type already. Be aware of the order of your basis functions and the basis in which the $U$ tensor is written!
 

python/solid_dmft/gw_embedding/bdft_converter.py

@@ -175,16 +175,14 @@ def calc_Sigma_DC_gw(Wloc_dlr, Gloc_dlr, Vloc, verbose=False):
 
 def calc_W_from_Gloc(Gloc_dlr, U):
     r"""
-
     Calculate Wijkl from given constant U tensor and Gf on DLRMesh
+    triqs notation for Uijkl:
 
-
-    triqs notation for Uijkl = phi*_i(r) phi*_j(r') U(r,r') phi_l'(r') phi_k(r)
-                            = Uijkl c^+_i c^+_j' c_l' c_k
+    phi*_i(r) phi*_j(r') U(r,r') phi_l'(r') phi_k(r) = Uijkl c^+_i c^+_j' c_l' c_k
 
     where the ' denotes a spin index different from the other without '
 
-    the according diagram is (left and right have same spin):
+    the according diagram is (left and right have same spin)::
 
        j (phi)         k' (phi)
          \              /
@@ -196,7 +194,7 @@ def calc_W_from_Gloc(Gloc_dlr, U):
        i (phi*)          l'
 
     we now have to move to a product basis form to combine two indices
-    i.e. go from nb,nb,nb,nb to nb**2,nb**2 tensors:
+    i.e. go from nb,nb,nb,nb to nb**2,nb**2 tensors::
 
         Uji,kl = phi*_i(r) phi_j(r) U(r,r') phi*_k(r') phi_l(r')
                = Psi*_ji(r) U(r,r') Psi_kl(r')
@@ -209,11 +207,12 @@ def calc_W_from_Gloc(Gloc_dlr, U):
 
     Pi_ab,kl(tau) = -2 G_bl(tau) G_ka(beta - tau)
 
-    So that
+    So that::
 
-    [ U Pi(iwn) ]_ji,kl = sum_ab U_ji,ab Pi_ab,kl(iwn)
+        [ U Pi(iwn) ]_ji,kl = sum_ab U_ji,ab Pi_ab,kl(iwn)
+
+    i.e.::
 
-    i.e.
        j'              a ___
          \              /   \ k
           <            <     \
@@ -223,18 +222,20 @@ def calc_W_from_Gloc(Gloc_dlr, U):
          /              \___/ l
        i'               b
 
-    then the screened Coulomb interaction in product basis is:
+    then the screened Coulomb interaction in product basis is::
 
-    W_ji,kl(iwn) = [1 - U Pi(iwn) ]^-1_ji,kl Uji,kl - Uji,kl
+        W_ji,kl(iwn) = [1 - U Pi(iwn) ]^-1_ji,kl Uji,kl - Uji,kl
 
     (subtract static shift here), and finally convert back to triqs notation.
 
 
     Parameters
     ----------
     Gloc_dlr : BlockGf or Gf with MeshDLR
+        local Green's function
 
     U : np.ndarray of with shape [Gloc_dlr.target_shape]*4 or dict of np.ndarray
+        constant U tensor
 
     Returns
     -------

python/solid_dmft/gw_embedding/iaft.py

@@ -100,6 +100,7 @@ def __str__(self):
     def wn_mesh(self, stats, ir_notation= True):
         """
         Return Matsubara frequency indices.
+
         :param stats: str
             statistics: 'f' for fermions and 'b' for bosons
         :param ir_notation: bool

python/solid_dmft/postprocessing/eval_U_cRPA_RESPACK.py

@@ -191,12 +191,14 @@ def construct_Uijkl(Uijij, Uiijj):
     construct full 4 index Uijkl tensor from respack data
     assuming Uijji = Uiijj
 
-    ----------
+    Parameters:
+    -----------
     Uijij: np.ndarray
         Uijij matrix
     Uiijj: np.ndarray
         Uiijj matrix
 
+    Returns:
     -------
     uijkl : numpy array
         uijkl Coulomb tensor
@@ -236,6 +238,7 @@ def fit_slater(u_ijij_crpa, u_ijji_crpa, U_init, J_init, fixed_F4_F2=True):
         inital value of J for optimization
     fixed_F4_F2: bool, optional default=True
         fix F4/F2 ratio to 0.625
+
     Returns:
     --------
     U_int: float