Automatic-interpolations.md

 **VERSION>=22.02.2021**
 # Introduction
-The number of self-consistent iterations till convergence strongly depends on the quality of starting point: the closer the initial state to the solution - the fewer iterations to converge. W-SLDA Toolkit implements a mechanism supporting the derivation of good quality initial states. Namely, one can use lattice of lower resolution to generate an approximation of the solution and next interpolate to larger/target lattice and use it as starting point. The idea is presented on the figure below. The same mechanism can be used for testing the stability of results with respect to the lattice resolution. 
+The number of self-consistent iterations till convergence strongly depends on the quality of the starting point: the closer the initial state to the solution, the fewer iterations there are to converge. W-SLDA Toolkit implements a mechanism supporting the derivation of good-quality initial states. Namely, one can use a lattice of lower resolution to generate an approximation of the solution and next interpolate to a larger/target lattice and use it as a starting point. The idea is presented in the figure below. The same mechanism can be used for testing the stability of results with respect to the lattice resolution. 
 
 ![automatic-interpolation](uploads/d24e5124cfc0bd36df87937f9ac3d3c8/automatic-interpolation.png)
 
@@ -47,7 +47,7 @@ inprefix                l-32    # start with solution from smaller lattice
 checkpoint              1       # do checkpoints after each iteration
 ```
 
-Once running the code you should see  this type of message on `stdout`:
+Once running the code, you should see  this type of message on `stdout`:
 ```
 # INSPECTING CHECKPOINT FILE `l-32/checkpoint.dat`
 # CHECKPOINT FOR 3D LATTICE: [NX,NY,NZ]=[32,32,32], [DX,DY,DZ]=[1.000,1.000,1.000], [LX,LY,LZ]=[32.000,32.000,32.000]
@@ -60,7 +60,7 @@ Once running the code you should see  this type of message on `stdout`:
 ```
 
 # Changing the volume
-Automatic interpolations were designed to work correctly if the spatial extent has not changed. It means that `[LX,LY,LZ]` is the same for input lattice and target lattice. However, if this criterion is not satisfied, the code will make attempt to load the checkpoint data, squeeze/stretch it accordingly, and then interpolate to the new lattice. Note that result of this operation may be unpredictable. The code will provide the following warning:  
+Automatic interpolations were designed to work correctly if the spatial extent has not changed. It means that `[LX,LY,LZ]` is the same for the input lattice and target lattice. However, if this criterion is not satisfied, the code will make an attempt to load the checkpoint data, squeeze/stretch it accordingly, and then interpolate to the new lattice. Note that the result of this operation may be unpredictable. The code will provide the following warning:  
 ```
 # !!! --- WARNING --- WARNING --- WARNING --- WARNING --- WARNING --- WARNING --- !!!
 #        Checkpoint files is incompatible with code settings!
@@ -69,4 +69,4 @@ Automatic interpolations were designed to work correctly if the spatial extent h
 # !!! --- ------- --- ------- --- ------- --- ------- --- ------- --- ------- --- !!!
 ```
 # Disable mixing in the first iteration
-For advanced functionals that have dependence on quantities that are cut-off dependent it is recommended to [disable mixing in the first iteration](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/wikis/Convergence-control#disabling-mixing-in-the-first-iteration). 
+For advanced functionals that have a dependence on quantities that are cut-off dependent, it is recommended to [disable mixing in the first iteration](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/wikis/Convergence-control#disabling-mixing-in-the-first-iteration).