added huberM param to optimizer

Author: pavelkomarov

pynumdiff/optimize/_optimize.py

@@ -65,8 +65,10 @@
               {'sigma': (1e-2, 1e3),
                 'lmbd': (1e-3, 0.5)}),
     tvrdiff: ({'gamma': [1e-2, 1e-1, 1, 10, 100, 1000],
-               'order': {1, 2, 3}}, # warning: order 1 hacks the loss function when tvgamma is used, tends to win but is usually suboptimal choice in terms of true RMSE
-              {'gamma': (1e-4, 1e7)}),
+               'order': {1, 2, 3}, # warning: order 1 hacks the loss function when tvgamma is used, tends to win but is usually suboptimal choice in terms of true RMSE
+              'huberM': [0., 1, 2, 3, 6]},
+              {'gamma': (1e-4, 1e7),
+              'huberM': (0, 6)}),
     velocity: ({'gamma': [1e-2, 1e-1, 1, 10, 100, 1000]}, # Deprecated method
                {'gamma': (1e-4, 1e7)}),
     iterative_velocity: ({'scale': 'small', # Rare to optimize this one, because it's longer-running than convex version

pynumdiff/utils/utility.py

@@ -130,10 +130,10 @@ def estimate_integration_constant(x, x_hat, M=6):
 
     :param np.array[float] x: timeseries of measurements
     :param np.array[float] x_hat: smoothed estimate of x
-    :param float M: constant estimation is robustified with the Huber loss. The default is intended to capture the idea
-        of "six sigma": Assuming Gaussian :code:`x - xhat` errors and :code:`M` in units of standard deviation, the
-        portion of inliers beyond the Huber loss' transition is only about 1.97e-9. :code:`M` here is in units of scaled
-        mean absolute deviation, so scatter can be calculated and used to normalize without being thrown off by outliers.
+    :param float M: constant estimation is robustified with the Huber loss. :code:`M` here is in units of scaled
+        mean absolute deviation of residuals, so scatter can be calculated and used to normalize without being
+        thrown off by outliers. The default is intended to capture the idea of "six sigma": Assuming Gaussian
+        :code:`x - xhat` errors, the portion of inliers beyond the Huber loss' transition is only about 1.97e-9.
 
     :return: **integration constant** (float) -- initial condition that best aligns x_hat with x
     """