Compute numerical derivatives

PyAstronomy.pyaC.diffCFD(x, y, derivative, errOrd=2)

Calculate the numerical derivative using central finite distances.

Parameters

xarray

The abscissa values.

yarray

The ordinate values.

derivativeint

The derivative to calculate. Use, e.g., 1 to obtain the first derivative.

errOrdint

The order of the error term. The default is 2. Other possibilities are 4, 6, and 8. Note the finite differences may not be available for all combinations.

Returns

indicesarray of int

The indices with respect to the input abscissa to which the derivative applies.

derarray

The derivative.

Example

from PyAstronomy import pyaC
import matplotlib.pylab as plt
import numpy as np

x = np.linspace(-10, 10, 1000)

# Computer polynomial and its derivatives
# (quasi analytically)
y = [np.poly1d((0.03, -0.31, 0.4, 0.35, 1.4))]
for i in range(4):
    y.append(y[-1].deriv())

# Compute derivates numerically and compare to
# analytic solution
erro = 2
for i in range(1, 5):
    indi, der = pyaC.diffCFD(x, np.polyval(y[0], x), i, erro)
    plt.plot(x[indi], np.polyval(y[i], x[indi]), 'b.')
    plt.plot(x[indi], der, 'r--')
    plt.show()