finite_difference

This module implements some common finite difference schemes. This is handy for this module https://web.media.mit.edu/~crtaylor/calculator.html

pynumdiff.finite_difference.finitediff(x, dt, num_iterations=1, order=2, axis=0)

Perform iterated finite difference of a given order. This serves as the common backing function for all other methods in this module.

Parameters:

  • x (np.array[float]) – data to differentiate. May be multidimensional; see axis.

  • dt (float) – step size

  • num_iterations (int) – number of iterations. If >1, the derivative is integrated with trapezoidal rule, that result is finite-differenced again, and the cycle is repeated num_iterations-1 times

  • order (int) – 1, 2, or 4, controls which finite differencing scheme to employ

  • axis (int) – data dimension along which differentiation is performed

Returns:

  • x_hat (np.array) – original x if num_iterations=1, else smoothed x that yielded dxdt_hat

  • dxdt_hat (np.array) – estimated derivative of x

pynumdiff.finite_difference.first_order(x, dt, params=None, options={}, num_iterations=1)

First-order difference method

Deprecated, prefer finitediff with order 1 instead.

Parameters:

  • x (np.array[float]) – data to differentiate

  • dt (float) – step size

  • params (list[float] or float) – (deprecated, prefer num_iterations)

  • options (dict) – (deprecated, prefer num_iterations) a dictionary consisting of {‘iterate’: (bool)}

  • num_iterations (int) – number of iterations. If >1, the derivative is integrated with trapezoidal rule, that result is finite-differenced again, and the cycle is repeated num_iterations-1 times

Returns:

  • x_hat (np.array) – original x if num_iterations=1, else smoothed x that yielded dxdt_hat

  • dxdt_hat (np.array) – estimated derivative of x

pynumdiff.finite_difference.second_order(x, dt, num_iterations=1)

Second-order centered difference method, with special endpoint formulas.

Deprecated, prefer finitediff with order 2 instead.

Parameters:

  • x (np.array[float]) – data to differentiate

  • dt (float) – step size

  • num_iterations (int) – number of iterations. If >1, the derivative is integrated with trapezoidal rule, that result is finite-differenced again, and the cycle is repeated num_iterations-1 times

Returns:

  • x_hat (np.array) – original x if num_iterations=1, else smoothed x that yielded dxdt_hat

  • dxdt_hat (np.array) – estimated derivative of x

pynumdiff.finite_difference.fourth_order(x, dt, num_iterations=1)

Fourth-order centered difference method, with special endpoint formulas.

Deprecated, prefer finitediff with order 4 instead.

Parameters:

  • x (np.array[float]) – data to differentiate

  • dt (float) – step size

  • num_iterations (int) – number of iterations. If >1, the derivative is integrated with trapezoidal rule, that result is finite-differenced again, and the cycle is repeated num_iterations-1 times

Returns:

  • x_hat (np.array) – original x if num_iterations=1, else smoothed x that yielded dxdt_hat

  • dxdt_hat (np.array) – estimated derivative of x