Merge pull request #151 from florisvb/kalman-variable-dt

Kalman variable dt

Author: pavelkomarov

docs/source/kalman_smooth.rst

@@ -8,4 +8,5 @@ kalman_smooth
 .. autofunction:: pynumdiff.kalman_smooth.constant_velocity
 .. autofunction:: pynumdiff.kalman_smooth.constant_acceleration
 .. autofunction:: pynumdiff.kalman_smooth.constant_jerk
-.. autofunction:: pynumdiff.kalman_smooth.known_dynamics
+.. autofunction:: pynumdiff.kalman_smooth.kalman_filter
+.. autofunction:: pynumdiff.kalman_smooth.rts_smooth

examples/1_basic_tutorial.ipynb

@@ -6,5 +6,5 @@
 from .smooth_finite_difference import meandiff, mediandiff, gaussiandiff, friedrichsdiff, butterdiff
 from .polynomial_fit import splinediff, polydiff, savgoldiff
 from .total_variation_regularization import tvrdiff, velocity, acceleration, jerk, iterative_velocity, smooth_acceleration, jerk_sliding
-from .kalman_smooth import rtsdiff, constant_velocity, constant_acceleration, constant_jerk, known_dynamics
+from .kalman_smooth import kalman_filter, rts_smooth, rtsdiff, constant_velocity, constant_acceleration, constant_jerk
 from .linear_model import spectraldiff, lineardiff, rbfdiff

examples/2a_optimizing_parameters_with_dxdt_known.ipynb

@@ -1,3 +1,3 @@
 """This module implements Kalman filters
 """
-from ._kalman_smooth import rtsdiff, constant_velocity, constant_acceleration, constant_jerk, known_dynamics
+from ._kalman_smooth import kalman_filter, rts_smooth, rtsdiff, constant_velocity, constant_acceleration, constant_jerk

examples/2b_optimizing_parameters_with_dxdt_unknown.ipynb

@@ -238,19 +238,19 @@ def rbfdiff(x, _t, sigma=1, lmbd=0.01):
 
     :param np.array[float] x: data to differentiate
     :param float or array[float] _t: This function supports variable step size. This parameter is either the constant
-        step size if given as a single float, or data locations if given as an array of same length as :code:`x`.
+        :math:`\\Delta t` if given as a single float, or data locations if given as an array of same length as :code:`x`.
     :param float sigma: controls width of radial basis function
     :param float lmbd: controls strength of bias toward data
 
     :return: tuple[np.array, np.array] of\n
              - **x_hat** -- estimated (smoothed) x
              - **dxdt_hat** -- estimated derivative of x
     """
-    if isinstance(_t, (np.ndarray, list)): # support variable step size for this function
+    if np.isscalar(_t):
+        t = np.arange(len(x))*_t
+    else: # support variable step size for this function
         if len(x) != len(_t): raise ValueError("If `_t` is given as array-like, must have same length as `x`.")
         t = _t
-    else:
-        t = np.arange(len(x))*_t
 
     # The below does the approximate equivalent of this code, but sparsely in O(N sigma), since the rbf falls off rapidly
     # t_i, t_j = np.meshgrid(t,t)

examples/3_automatic_method_suggestion.ipynb

@@ -11,7 +11,7 @@ def splinediff(x, _t, params=None, options={}, degree=3, s=None, num_iterations=
 
     :param np.array[float] x: data to differentiate
     :param float or array[float] _t: This function supports variable step size. This parameter is either the constant
-        step size if given as a single float, or data locations if given as an array of same length as :code:`x`.
+        :math:`\\Delta t` if given as a single float, or data locations if given as an array of same length as :code:`x`.
     :param list params: (**deprecated**, prefer :code:`degree`, :code:`cutoff_freq`, and :code:`num_iterations`)
     :param dict options: (**deprecated**, prefer :code:`num_iterations`) an empty dictionary or {'iterate': (bool)}
     :param int degree: polynomial degree of the spline. A kth degree spline can be differentiated k times.
@@ -30,11 +30,11 @@ def splinediff(x, _t, params=None, options={}, degree=3, s=None, num_iterations=
         if 'iterate' in options and options['iterate']:
             num_iterations = params[2]
 
-    if isinstance(_t, (np.ndarray, list)): # support variable step size for this function
+    if np.isscalar(_t):
+        t = np.arange(len(x))*_t
+    else: # support variable step size for this function
         if len(x) != len(_t): raise ValueError("If `_t` is given as array-like, must have same length as `x`.")
         t = _t
-    else:
-        t = np.arange(len(x))*_t
 
     x_hat = x
     for _ in range(num_iterations):