Compute numerical derivatives.
Project description
Fast numerical derivatives for real analytic functions with arbitrary round-off error.
Features
Robustly compute the generalised Jacobi matrix for an arbitrary real analytic mapping of ℝⁿ → ℝⁱ¹ × … × ℝⁱⁿ
Derivative is computed to specified accuracy or until precision of function is reached
Algorithm based on John D’Errico’s DERIVEST: flawlessly works even with functions that have large round-off error
Up to 1200x faster than numdifftools at equivalent precision
Returns error estimates for derivatives
Supports calculation of derivative up to target precision (speed-up)
Supports arbitrary auxiliary function arguments
Lightweight package, only depends on numpy
Example
from matplotlib import pyplot as plt
import numpy as np
from jacobi import jacobi
# function of one variable with auxiliary argument; returns a vector
def f(p, x):
y = p + x
return np.sin(y) / y
x = np.linspace(-10, 10, 1000)
fx = f(0, x)
fdx, fdex = jacobi(f, 0, x)
plt.plot(x, fx, label="f(x) = sin(x) / x")
plt.plot(x, fdx, ls="--", label="f'(x)")
plt.legend()
Comparison to numdifftools
Speed
Jacobi makes better use of vectorised computation than numdifftools.
Precision
The machine precision is indicated by the dashed line.
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