fdm.numerics module

fdm.numerics.approx_equal(x, y, eps_abs=2.220446049250313e-14, eps_rel=1.4901161193847656e-08)

Check whether x and y are approximately equal.

Let eps_z = eps_abs / eps_rel. Call x and y small if abs(x) < eps_z and abs(y) < eps_z, and call x and y large otherwise. If this function returns True, then it is guaranteed that abs(x - y) < 2 eps_rel max(abs(x), abs(y)) if x and y are large, and abs(x - y) < 2 eps_abs if x and y are small.

Parameters

• x (object) – First object to compare.

• y (object) – Second object to compare.

• eps_abs (float, optional) – Absolute tolerance.

• eps_rel (float, optional) – Relative tolerance.

Returns

Approximate equality of x and y.

Return type

bool

fdm.numerics.check_sensitivity(f, s_f, args, kw_args=None, eps_abs=2.220446049250313e-12, eps_rel=1.4901161193847656e-07, method=<fdm.fdm.FDM object>)

Check the sensitivity of a function.

Parameters

• f (function) – Function to check.

• s_f (function) – Sensitivity of f. Should have signature s_f(s_y, y, *args, **kw_args), where s_y is the sensitivity of the output, y = f(*args, **kw_args), and *args and **kw_args the arguments and keyword arguments that f was evaluated at.

• args (tuple) – Arguments to test f at.

• kw_args (dict, optional) – Keyword arguments to test f at. Defaults to {}.

• eps_abs (float, optional) – Absolute tolerance.

• eps_rel (float, optional) – Relative tolerance.

• method (fdm.FDM, optional) – Finite difference method to use. Defaults to multivariate.default_adaptive_method.