fdm.fdm module¶
-
class
fdm.fdm.FDM(grid, deriv=1, bound_estimator=None, condition=10.0, factor=1.0)[source]¶ Bases:
objectA finite difference method.
Call the finite difference method with a function f, an input location x (optional: defaults to 0), and a step size (optional: defaults to an estimate) to estimate the derivative of f at x. For example, if m is an instance of
fdm.FDM, then m(f, 1) estimates the derivative of f at 1.- Parameters
grid (list[int] or
np.ndarray) – Relative spacing of samples of the function used by the method.deriv (int, optional) – Order of the derivative to estimate. Defaults to 1.
bound_estimator (
fdm.FDM, optional) – A finite difference method that is tuned to perform adaptation for this method.condition (float, optional) – Amplification of the infinity norm when passed to the function’s derivatives. Defaults to 10.0.
factor (float, optional) – Amplification of the round-off error on the function’s evaluations. Defaults to 1.0.
-
grid¶ Relative spacing of samples of the function used by the method.
- Type
np.ndarray
-
order¶ Order of the estimator.
- Type
int
-
deriv¶ Order of the derivative to estimate.
- Type
int
-
bound_estimator¶ Estimator that taken in a function f and a location x and gives back an estimate of an upper bound on the len(grid)`th order derivative of `f at x.
- Type
function or None
-
condition¶ Amplification of the infinity norm when passed to the function’s derivatives.
- Type
float
-
factor¶ Amplification of the round-off error on the function’s evaluations.
- Type
float
-
step¶ Estimate of the step size.
- Type
float or None
-
acc¶ Estimate of the accuracy of the method.
- Type
float or None
-
coefs¶ Weighting of the samples used to estimate the derivative.
- Type
np.ndarray
-
df_magnitude_mult¶ Multiplier associated with the truncation error.
- Type
float
-
f_error_mult¶ Multiplier associated with the round-off error.
- Type
float
-
estimate(f=None, x=0, max_range=None)[source]¶ Estimate step size and accuracy of the method.
- Parameters
f (function, optional) – Function to estimate step size and accuracy for. Defaults to the constant function 1.
x (tensor, optional) – Location to estimate derivative at. Defaults to 0.
max_range (float, optional) – Maximum amount to deviate from x.
- Returns
Returns itself.
- Return type
-
fdm.fdm.backward_fdm(order, deriv, adapt=1, **kw_args)[source]¶ Construct a backward finite difference method.
Further takes in keyword arguments of the constructor of
fdm.FDM.- Parameters
order (int) – Order of the method.
deriv (int) – Order of the derivative to estimate.
adapt (int, optional) – Number of recursive calls to higher-order derivatives to dynamically determine the step size. Defaults to 1.
- Returns
The desired finite difference method.
- Return type
-
fdm.fdm.central_fdm(order, deriv, adapt=1, **kw_args)[source]¶ Construct a central finite difference method.
Further takes in keyword arguments of the constructor of
fdm.FDM.- Parameters
order (int) – Order of the method.
deriv (int) – Order of the derivative to estimate.
adapt (int, optional) – Number of recursive calls to higher-order derivatives to dynamically determine the step size. Defaults to 1.
- Returns
The desired finite difference method.
- Return type
-
fdm.fdm.forward_fdm(order, deriv, adapt=1, **kw_args)[source]¶ Construct a forward finite difference method.
Further takes in keyword arguments of the constructor of
fdm.FDM.- Parameters
order (int) – Order of the method.
deriv (int) – Order of the derivative to estimate.
adapt (int, optional) – Number of recursive calls to higher-order derivatives to dynamically determine the step size. Defaults to 1.
- Returns
The desired finite difference method.
- Return type