evaluate

Metrics and evaluations?

pynumdiff.utils.evaluate.error_correlation(dxdt_hat, dxdt_truth, padding=None)

Calculate the error correlation (pearsons correlation coefficient) between the estimated dxdt and true dxdt

Parameters

• dxdt_hat (np.array) – estimated xdot

• dxdt_truth (np.array like x or None) – true value of dxdt, if known, optional

• padding (int, None, or auto) – number of snapshots on either side of the array to ignore when calculating the metric. If autor or None, defaults to 2.5% of the size of x

Returns

r-squared correlation coefficient

Return type

float

pynumdiff.utils.evaluate.metrics(x, dt, x_hat, dxdt_hat, x_truth=None, dxdt_truth=None, padding=None)

Evaluate x_hat based on various metrics, depending on whether dxdt_truth and x_truth are known or not.

Parameters

• x (np.array) – time series that was differentiated

• dt (float) – time step in seconds

• x_hat (np.array) – estimated (smoothed) x

• dxdt_hat (np.array) – estimated xdot

• x_truth (np.array like x or None) – true value of x, if known, optional

• dxdt_truth (np.array like x or None) – true value of dxdt, if known, optional

• padding (int, None, or auto) – number of snapshots on either side of the array to ignore when calculating the metric. If autor or None, defaults to 2.5% of the size of x

Returns

a tuple containing the following: - rms_rec_x: RMS error between the integral of dxdt_hat and x - rms_x: RMS error between x_hat and x_truth, returns None if x_truth is None - rms_dxdt: RMS error between dxdt_hat and dxdt_truth, returns None if dxdt_hat is None

Return type

tuple -> (float, float, float)

pynumdiff.utils.evaluate.plot(x, dt, x_hat, dxdt_hat, x_truth, dxdt_truth, xlim=None, ax_x=None, ax_dxdt=None, show_error=True, markersize=5)

Make comparison plots of ‘x (blue) vs x_truth (black) vs x_hat (red)’ and ‘dxdt_truth (black) vs dxdt_hat (red)’

Parameters

• x (np.array (float)) – array of noisy time series

• dt (float) – a float number representing the time step size

• x_hat (np.array (float)) – array of smoothed estimation of x

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

• x_truth (np.array (float)) – array of noise-free time series

• dxdt_truth (np.array (float)) – array of true derivative

• xlim (list (2 integers), optional) – a list specifying range of x

• ax_x (matplotlib.axes, optional) – axis of the first plot

• ax_dxdt (matplotlib.axes, optional) – axis of the second plot

• show_error (boolean, optional) – whether to show the rmse

• markersize (int, optional) – marker size of noisy observations

Returns

Display two plots

Return type

None

pynumdiff.utils.evaluate.rmse(dxdt_hat, dxdt_truth, padding=None)

Calculate the Root Mean Squared Error between the estimated dxdt and true dxdt

Parameters

• dxdt_hat (np.array) – estimated xdot

• dxdt_truth (np.array like x or None) – true value of dxdt, if known, optional

• padding (int, None, or auto) – number of snapshots on either side of the array to ignore when calculating the metric. If autor or None, defaults to 2.5% of the size of x

Returns

Root Mean Squared Error

Return type

float