derivkit.utils module¶
Provides assorted utility functions.
- derivkit.utils.central_difference_error_estimate(step_size, order=1)¶
Provides a rough truncation error estimate for central differences.
- Parameters:
step_size (float) – Finite difference step size.
order (int) – Order of the derivative (1 to 4).
- Returns:
Estimated error magnitude.
- Return type:
float
- derivkit.utils.generate_test_function(name='sin')¶
Returns a known test function and its first/second derivatives.
- Parameters:
name (str) – One of ‘sin’, ‘exp’, ‘polynomial’, ‘gaussian’.
- Returns:
(f(x), df/dx, d2f/dx2)
- Return type:
tuple
- derivkit.utils.is_finite_and_differentiable(function, x, delta=1e-05, tol=0.01)¶
Checks if a function is finite and numerically differentiable at a point.
- Parameters:
function (callable) – The function to test.
x (float or np.ndarray) – The input value(s).
delta (float) – Step size for finite difference.
tol (float) – Tolerance for differentiability check.
- Returns:
- True if function is finite and differentiable at x, False
otherwise.
- Return type:
bool
- derivkit.utils.is_symmetric_grid(x_vals)¶
Checks if evaluation grid is symmetric around 0.
- Parameters:
x_vals (
np.ndarray) – Evaluation points (1D).- Returns:
True if grid is symmetric, False otherwise.
- Return type:
bool
- derivkit.utils.log_debug_message(message, debug=False, log_file=None, log_to_file=None)¶
Logs a debug message to stdout and optionally to a file.
- Parameters:
message (str) – The debug message to print/log.
debug (bool) – Whether to print the message.
log_file (str or None) – Path to the log file.
log_to_file (bool or None) – Whether to write the message to the file.
- derivkit.utils.normalize_derivative(derivative, reference)¶
Computes the relative error between estimated and reference derivative.
- Parameters:
derivative (float or np.ndarray) – Estimated derivative.
reference (float or np.ndarray) – True/reference derivative.
- Returns:
Normalized relative error.
- Return type:
float or np.ndarray