jacobi 0.1.4

Compute numerical derivatives.

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.