# Density profile

As a second example of the dwa QMC code, we will study the density profile of an optical lattice in an harmonic trap which resembles the experiment

## Column integrated density

### Preparing and running the simulation from the command line

The parameter file parm2a sets up Monte Carlo simulation of a 1003 optical lattice trap that mimicks the Bloch experiment:

```LATTICE="inhomogeneous simple cubic lattice"
L=120

MODEL='boson Hubbard"
Nmax=20

t=1.
U=8.11
mu="4.05 - (0.0073752*(x-(L-1)/2.)*(x-(L-1)/2.) + 0.0036849*(y-(L-1)/2.)*(y-(L-1)/2.) + 0.0039068155*(z-(L-1)/2.)*(z-(L-1)/2.))"

THERMALIZATION=1500
SWEEPS=7000
SKIP=50

MEASURE[Local Density]=1

{ T=1. }
```

Using the standard sequence of commands you can run the simulation using the quantum dwa code

```parameter2xml parm2a
dwa parm2a.in.xml
```

### Preparing and running the simulation from Python

To set up and run the simulation in Python we use the script tutorial2a.py. The first parts of this script imports the required modules and then prepares the input files as a list of Python dictionaries:

```import pyalps

parms = [
{
'LATTICE' : 'inhomogeneous simple cubic lattice' ,
'L'       : 120 ,

'MODEL'   : 'boson Hubbard' ,
'Nmax'    : 20 ,

't'  : 1. ,
'U'  : 8.11 ,
'mu' : '4.05 - (0.0073752*(x-(L-1)/2.)*(x-(L-1)/2.) + 0.0036849*(y-(L-1)/2.)*(y-(L-1)/2.) + 0.0039068155*(z-(L-1)/2.)*(z-(L-1)/2.))' ,

'T'  : 1. ,

'THERMALIZATION' : 1500 ,
'SWEEPS'         : 7000 ,
'SKIP'           : 50 ,

'MEASURE[Local Density]': 1
}
]
```

We next convert this into a job file in XML format and run the worm simulation:

```input_file = pyalps.writeInputFiles('parm2a', parms)
res = pyalps.runApplication('dwa', input_file)
```

We now have the same output files as in the command line version.

### Evaluating the simulation and preparing plots using Python

To load the results and prepare plots we load the results from the output files and collect the magntization density as a function of magnetic field from all output files starting with parm2a. The script is again in tutorial2a.py

```import numpy
import pyalps
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D;