Integration

xr-scipy wraps some of scipy.integrate functions. Let’s create a simple example DataArray:

In [1]: arr = xr.DataArray(np.sin(np.linspace(0, 6.28, 30)) ** 2,
   ...:                    dims=('x'), coords={'x': np.linspace(0, 5, 30)})
   ...: 

In [2]: arr
Out[2]: 
<xarray.DataArray (x: 30)>
array([0.00000000e+00, 4.61661813e-02, 1.76139460e-01, 3.65918356e-01,
       5.80457402e-01, 7.80138804e-01, 9.28088451e-01, 9.96985262e-01,
       9.74106426e-01, 8.63676857e-01, 6.86089001e-01, 4.74137072e-01,
       2.66961112e-01, 1.02819215e-01, 1.20225984e-02, 1.13381944e-02,
       1.00892388e-01, 2.64147680e-01, 4.70956575e-01, 6.83128766e-01,
       8.61483534e-01, 9.73085045e-01, 9.97324436e-01, 9.29725546e-01,
       7.82771507e-01, 5.83599545e-01, 3.68989697e-01, 1.78572829e-01,
       4.75122222e-02, 1.01461475e-05])
Coordinates:
  * x        (x) float64 0.0 0.1724 0.3448 0.5172 ... 4.483 4.655 4.828 5.0

Our integration function takes an xarray object and coordinate name along which the array to be integrated. The return type is also a DataArray,

# trapz computes definite integration
In [3]: xrscipy.integrate.trapezoid(arr, coord='x')
Out[3]: 
<xarray.DataArray ()>
array(2.50124814)

# cumurative integration returns a same shaped array
In [4]: integ = xrscipy.integrate.cumulative_trapezoid(arr, 'x')

In [5]: integ
Out[5]: 
<xarray.DataArray (x: 30)>
array([0.        , 0.00397984, 0.02314412, 0.06987324, 0.15145736,
       0.26875014, 0.41601111, 0.58196574, 0.75188744, 0.91031703,
       1.04391753, 1.14393702, 1.2078248 , 1.23970241, 1.24960257,
       1.25161643, 1.26129148, 1.29276045, 1.35613151, 1.45562162,
       1.58877786, 1.74693032, 1.91679321, 2.08291821, 2.23054726,
       2.34833787, 2.43045763, 2.4776613 , 2.49715139, 2.50124814])
Coordinates:
  * x        (x) float64 0.0 0.1724 0.3448 0.5172 ... 4.483 4.655 4.828 5.0

In [6]: arr.plot(label='arr')
Out[6]: [<matplotlib.lines.Line2D at 0x7f47ccf36f60>]

In [7]: integ.plot(label='integration')
Out[7]: [<matplotlib.lines.Line2D at 0x7f47cc5f5100>]

In [8]: plt.legend()
Out[8]: <matplotlib.legend.Legend at 0x7f47cd11fb90>

In [9]: plt.show()
_images/cumulative_trapezoid.png

See trapezoid() for other options.

Note

There are slight difference from the original implementations. Our cumulative_trapezoid() always assume initial=0.