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How to use the NDDataArray class

Introduction

This notebook explains how to use the class gammapy.utils.nddata.NDDataArray

The NDDataArray is basically an numpy array with associated axes and convenience methods for interpolation. For now only the scipy RegularGridInterpolator can be used, i.e. available interpolation methods are “nearest neighbour” and “linear”. A spline interpolator will be added in the future. The interpolation behaviour (“log”, “linear”) can be set for each axis individually.

The NDDataArray is currently used in the following classes

Feedback welcome!

Setup

As usual, we’ll start with some setup …

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
In [2]:
from gammapy.utils.nddata import NDDataArray, DataAxis, BinnedDataAxis
from gammapy.utils.energy import Energy, EnergyBounds
import numpy as np
import astropy.units as u

1D example

Let’s start with a simple example. A one dimensional array storing an exposure in cm-2 s-1 as a function of energy. The energy axis is log spaced and thus also the interpolation shall take place in log.

In [3]:
energies = Energy.equal_log_spacing(10, 100, 10, unit=u.TeV)
x_axis = DataAxis(energies, name='energy', interpolation_mode='log')
data = np.arange(20,0,-2) / u.cm **2 / u.s
nddata = NDDataArray(axes=[x_axis], data=data)
print(nddata)
print(nddata.axis('energy'))
NDDataArray summary info
energy         : size =    10, min = 10.000 TeV, max = 100.000 TeV
Data           : size =    10, min =  2.000 1 / (cm2 s), max = 20.000 1 / (cm2 s)

DataAxis
Name: energy
Unit: TeV
Nodes: 10
Interpolation mode: log
In [4]:
eval_energies = np.linspace(2, 6, 20) *1e4 * u.GeV
eval_exposure = nddata.evaluate(energy=eval_energies, method='linear')

plt.plot(nddata.axis('energy').nodes.value, nddata.data.value, '.', label='Interpolation nodes')
print(nddata.axis('energy').nodes)
plt.plot(eval_energies.to('TeV').value, eval_exposure, '--', label='Interpolated values')
plt.xlabel('{} [{}]'.format(nddata.axes[0].name, nddata.axes[0].unit))
plt.ylabel('{} [{}]'.format('Exposure', nddata.data.unit))
plt.legend()
[  10.           12.91549665   16.68100537   21.5443469    27.82559402
   35.93813664   46.41588834   59.94842503   77.42636827  100.        ] TeV
Out[4]:
<matplotlib.legend.Legend at 0x11273bda0>
../_images/notebooks_nddata_demo_8_2.png

2D example

Another common use case is to store a Quantity as a function of field of view offset and energy. The following shows how to use the NDDataArray to slice the data array at any values of offset and energy

In [5]:
energy_data = EnergyBounds.equal_log_spacing(1, 10, 50, unit=u.TeV)
energy_axis = BinnedDataAxis(lo=energy_data.lower_bounds,
                             hi=energy_data.upper_bounds,
                             name='energy', interpolation_mode='log')
offset_data = np.linspace(0, 2, 4) * u.deg
offset_axis = DataAxis(offset_data, name='offset')

data_temp = 10 * np.exp(- energy_data.log_centers.value / 10)
data = np.outer(data_temp, (offset_data.value + 1))

nddata2d = NDDataArray(axes=[energy_axis, offset_axis], data=data * u.Unit('cm-2 s-1 TeV-1'))

print(nddata2d)
extent_x = nddata2d.axis('energy').bins[[0, -1]].value
extent_y = nddata2d.axis('offset').nodes[[0, -1]].value
extent = extent_x[0], extent_x[1], extent_y[0], extent_y[1]
plt.imshow(nddata2d.data, extent=extent, aspect='auto')
plt.xlabel('Energy')
plt.ylabel('Offset')
plt.colorbar()
NDDataArray summary info
energy         : size =    50, min =  1.023 TeV, max =  9.772 TeV
offset         : size =     4, min =  0.000 deg, max =  2.000 deg
Data           : size =   200, min =  3.763 1 / (cm2 s TeV), max = 27.082 1 / (cm2 s TeV)

Out[5]:
<matplotlib.colorbar.Colorbar at 0x1127cecc0>
../_images/notebooks_nddata_demo_10_2.png
In [6]:
offsets = [0.23, 1.23, 2] * u.deg
eval_energies = Energy.equal_log_spacing(3, 8, 20, u.TeV)

for offset in offsets:
    slice_ = nddata2d.evaluate(offset=offset, energy=eval_energies)
    plt.plot(eval_energies.value, slice_, label='Offset: {}'.format(offset))
plt.xlabel('Energy [TeV]')
plt.legend()
Out[6]:
<matplotlib.legend.Legend at 0x112bb1cf8>
../_images/notebooks_nddata_demo_11_1.png