Merge pull request #137 from florisvb/make-spline-not-FD

splines already have a derivative implemented, so there isn't necessarily a need to FD on top of them

Author: pavelkomarov

examples/1_basic_tutorial.ipynb

@@ -11,7 +11,7 @@
 # Smoothing finite differences #
 ################################
 def mediandiff(x, dt, params=None, options={}, window_size=5, num_iterations=1):
-    """Perform median smoothing using scipy.signal.medfilt followed by first order finite difference
+    """Perform median smoothing using scipy.signal.medfilt followed by second order finite difference
 
     :param np.array[float] x: data to differentiate
     :param float dt: step size
@@ -44,7 +44,7 @@ def mediandiff(x, dt, params=None, options={}, window_size=5, num_iterations=1):
 
 
 def meandiff(x, dt, params=None, options={}, window_size=5, num_iterations=1):
-    """Perform mean smoothing by convolving mean kernel with x followed by first order finite difference
+    """Perform mean smoothing by convolving mean kernel with x followed by second order finite difference
 
     :param np.ndarray[float] x: data to differentiate
     :param float dt: step size
@@ -74,7 +74,7 @@ def meandiff(x, dt, params=None, options={}, window_size=5, num_iterations=1):
 
 
 def gaussiandiff(x, dt, params=None, options={}, window_size=5, num_iterations=1):
-    """Perform gaussian smoothing by convolving gaussian kernel with x followed by first order finite difference
+    """Perform gaussian smoothing by convolving gaussian kernel with x followed by second order finite difference
 
     :param np.array[float] x: data to differentiate
     :param float dt: step size
@@ -103,7 +103,7 @@ def gaussiandiff(x, dt, params=None, options={}, window_size=5, num_iterations=1
 
 
 def friedrichsdiff(x, dt, params=None, options={}, window_size=5, num_iterations=1):
-    """Perform friedrichs smoothing by convolving friedrichs kernel with x followed by first order finite difference
+    """Perform friedrichs smoothing by convolving friedrichs kernel with x followed by second order finite difference
 
     :param np.array[float] x: data to differentiate
     :param float dt: step size
@@ -132,7 +132,7 @@ def friedrichsdiff(x, dt, params=None, options={}, window_size=5, num_iterations
 
 
 def butterdiff(x, dt, params=None, options={}, filter_order=2, cutoff_freq=0.5, num_iterations=1):
-    """Perform butterworth smoothing on x with scipy.signal.filtfilt followed by first order finite difference
+    """Perform butterworth smoothing on x with scipy.signal.filtfilt followed by second order finite difference
 
     :param np.array[float] x: data to differentiate
     :param float dt: step size
@@ -171,7 +171,8 @@ def butterdiff(x, dt, params=None, options={}, filter_order=2, cutoff_freq=0.5,
 
 
 def splinediff(x, dt, params=None, options={}, order=3, s=None, num_iterations=1):
-    """Perform spline smoothing on x with scipy.interpolate.UnivariateSpline followed by first order finite difference
+    """Find smoothed data and derivative estimates by fitting a smoothing spline to the data with
+    scipy.interpolate.UnivariateSpline.
 
     :param np.array[float] x: data to differentiate
     :param float dt: step size
@@ -200,6 +201,7 @@ def splinediff(x, dt, params=None, options={}, order=3, s=None, num_iterations=1
         spline = scipy.interpolate.UnivariateSpline(t, x_hat, k=order, s=s)
         x_hat = spline(t)
 
-    x_hat, dxdt_hat = finite_difference(x_hat, dt)
+    dspline = spline.derivative()
+    dxdt_hat = dspline(t)
 
     return x_hat, dxdt_hat

examples/2a_optimizing_parameters_with_dxdt_known.ipynb

@@ -137,7 +137,7 @@ def iterated_first_order(*args, **kwargs): return first_order(*args, **kwargs)
                  [(1, 0), (1, 1), (1, 0), (1, 1)],
                  [(2, 2), (3, 2), (2, 2), (3, 2)],
                  [(2, 1), (3, 3), (2, 1), (3, 3)]],
-    splinediff: [[(-14, -15), (-14, -14), (-1, -1), (0, 0)],
+    splinediff: [[(-14, -15), (-14, -15), (-1, -1), (0, 0)],
                  [(-14, -14), (-13, -14), (-1, -1), (0, 0)],
                  [(-14, -14), (-13, -13), (-1, -1), (0, 0)],
                  [(0, 0), (1, 1), (0, 0), (1, 1)],