changed name of rts_const_deriv to rtsdiff to match all the other pithy little names, and added the analysis notebook I've been using to make plots these last days

Author: pavelkomarov

docs/source/kalman_smooth.rst

@@ -4,7 +4,7 @@ kalman_smooth
 .. automodule:: pynumdiff.kalman_smooth
     :no-members:
 
-.. autofunction:: pynumdiff.kalman_smooth.rts_const_deriv
+.. autofunction:: pynumdiff.kalman_smooth.rtsdiff
 .. autofunction:: pynumdiff.kalman_smooth.constant_velocity
 .. autofunction:: pynumdiff.kalman_smooth.constant_acceleration
 .. autofunction:: pynumdiff.kalman_smooth.constant_jerk

examples/1_basic_tutorial.ipynb

@@ -843,7 +843,7 @@
    "source": [
     "## 5. Kalman smoothing\n",
     "\n",
-    "Here we use the general `rts_const_deriv` function. There are also module functions `constant_velocity`, `constant_acceleration`, and `constant_jerk`, which call the general function, with `order=1`, `2`, or `3`, respectively, and have separate `q` and `r` parameters rather than a `qr_ratio`."
+    "Here we use the general `rtsdiff` function. There are also module functions `constant_velocity`, `constant_acceleration`, and `constant_jerk`, which call the general function, with `order=1`, `2`, or `3`, respectively, and have separate `q` and `r` parameters rather than a `qr_ratio`."
    ]
   },
   {
@@ -871,7 +871,7 @@
     }
    ],
    "source": [
-    "x_hat, dxdt_hat = pynumdiff.kalman_smooth.rts_const_deriv(x, dt, order=2, qr_ratio=1.2e5, forwardbackward=True)\n",
+    "x_hat, dxdt_hat = pynumdiff.kalman_smooth.rtsdiff(x, dt, order=2, qr_ratio=1.2e5, forwardbackward=True)\n",
     "evaluate.plot(x, dt, x_hat, dxdt_hat, x_truth, dxdt_truth)"
    ]
   },

examples/2a_optimizing_parameters_with_dxdt_known.ipynb

@@ -38,7 +38,7 @@
     "    friedrichsdiff, butterdiff\n",
     "from pynumdiff.polynomial_fit import splinediff, polydiff, savgoldiff\n",
     "from pynumdiff.total_variation_regularization import tvrdiff, smooth_acceleration\n",
-    "from pynumdiff.kalman_smooth import rts_const_deriv\n",
+    "from pynumdiff.kalman_smooth import rtsdiff\n",
     "from pynumdiff.linear_model import spectraldiff, lineardiff"
    ]
   },
@@ -595,9 +595,9 @@
     }
    ],
    "source": [
-    "params, val = optimize(rts_const_deriv, x, dt, dxdt_truth=dxdt_truth)\n",
+    "params, val = optimize(rtsdiff, x, dt, dxdt_truth=dxdt_truth)\n",
     "print('Optimal parameters: ', params)\n",
-    "x_hat, dxdt_hat = rts_const_deriv(x, dt, **params)\n",
+    "x_hat, dxdt_hat = rtsdiff(x, dt, **params)\n",
     "evaluate.plot(x, dt, x_hat, dxdt_hat, x_truth, dxdt_truth)"
    ]
   },

examples/2b_optimizing_parameters_with_dxdt_unknown.ipynb

@@ -39,7 +39,7 @@
     "    friedrichsdiff, butterdiff\n",
     "from pynumdiff.polynomial_fit import splinediff, polydiff, savgoldiff\n",
     "from pynumdiff.total_variation_regularization import tvrdiff, smooth_acceleration\n",
-    "from pynumdiff.kalman_smooth import rts_const_deriv\n",
+    "from pynumdiff.kalman_smooth import rtsdiff\n",
     "from pynumdiff.linear_model import spectraldiff, lineardiff"
    ]
   },
@@ -626,9 +626,9 @@
     }
    ],
    "source": [
-    "params, val = optimize(rts_const_deriv, x, dt, tvgamma=tvgamma)\n",
+    "params, val = optimize(rtsdiff, x, dt, tvgamma=tvgamma)\n",
     "print('Optimal parameters: ', params)\n",
-    "x_hat, dxdt_hat = rts_const_deriv(x, dt, **params)\n",
+    "x_hat, dxdt_hat = rtsdiff(x, dt, **params)\n",
     "evaluate.plot(x, dt, x_hat, dxdt_hat, x_truth, dxdt_truth)"
    ]
   },

examples/3_automatic_method_suggestion.ipynb

@@ -165,7 +165,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Best method: rts_const_deriv with params: {'qr_ratio': np.float64(212.5), 'forwardbackward': True, 'order': 1}\n",
+      "Best method: rtsdiff with params: {'qr_ratio': np.float64(212.5), 'forwardbackward': True, 'order': 1}\n",
       "RMS error in velocity:  0.732788003100273\n",
       "Error correlation:  0.0087737054466213\n"
      ]

examples/4_performance_analysis.ipynb

@@ -2,7 +2,7 @@
 - `kalman_smooth` contains classic linear Kalman filter and RTS smoothing code, as well as a constant-derivative naive-model smoothing method for 1st (velocity), 2nd (acceleration), or 3rd (jerk) order.
 - `linear_model` contains `lineardiff`, which tries to fit a linear model on a sliding window, and `spectraldiff`, based on Fourier transforms.
 - `optimize` contains code to find best parameter settings for methods, tuned using Nelder-Mead according to the paper "Numerical differentiation of noisy data: A unifying multi-objective optimization framework", as well as a method suggestion metamethod.
-- `polynomial_fit` contains `splinediff`, `polydiff`, and `savgoldiff`, which all explicitly or implicitly fit polynomials over pieces of the data.
+- `polynomial_fit` contains methods which explicitly or implicitly fit polynomials over pieces of the data.
 - `smooth_finite_difference` contains methods which do a smoothing step followed by simple finite difference.
 - `tests` contains `pytest` unit tests of
 	1. all the differentiation methods, checking their results against a suite of known analytic functions (including an ability to plot if the `--plot` command is passed to `pytest`, see `conftest.py`)

pynumdiff/README.md

@@ -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 rts_const_deriv, constant_velocity, constant_acceleration, constant_jerk, known_dynamics
+from .kalman_smooth import rtsdiff, constant_velocity, constant_acceleration, constant_jerk, known_dynamics
 from .linear_model import spectraldiff, lineardiff

pynumdiff/__init__.py

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

pynumdiff/kalman_smooth/__init__.py

@@ -80,8 +80,8 @@ def _RTS_smooth(xhat0, P0, y, A, C, Q, R, u=None, B=None):
 #########################################
 # Constant 1st, 2nd, and 3rd derivative #
 #########################################
-def rts_const_deriv(x, dt, order, qr_ratio, forwardbackward):
-    """Perform Rauch-Tung-Striebel smoothing with a constant derivative model. Other constant derivative
+def rtsdiff(x, dt, order, qr_ratio, forwardbackward):
+    """Perform Rauch-Tung-Striebel smoothing with a naive constant derivative model. Other constant derivative
     methods in this module call this function.
 
     :param np.array[float] x: data series to differentiate
@@ -176,7 +176,7 @@ def constant_velocity(x, dt, params=None, options=None, r=None, q=None, forwardb
     elif r == None or q == None:
         raise ValueError("`q` and `r` must be given.")
 
-    return rts_const_deriv(x, dt, 1, q/r, forwardbackward)
+    return rtsdiff(x, dt, 1, q/r, forwardbackward)
 
 
 def constant_acceleration(x, dt, params=None, options=None, r=None, q=None, forwardbackward=True):
@@ -205,7 +205,7 @@ def constant_acceleration(x, dt, params=None, options=None, r=None, q=None, forw
     elif r == None or q == None:
         raise ValueError("`q` and `r` must be given.")
 
-    return rts_const_deriv(x, dt, 2, q/r, forwardbackward)
+    return rtsdiff(x, dt, 2, q/r, forwardbackward)
 
 
 def constant_jerk(x, dt, params=None, options=None, r=None, q=None, forwardbackward=True):
@@ -234,7 +234,7 @@ def constant_jerk(x, dt, params=None, options=None, r=None, q=None, forwardbackw
     elif r == None or q == None:
         raise ValueError("`q` and `r` must be given.")
 
-    return rts_const_deriv(x, dt, 3, q/r, forwardbackward)
+    return rtsdiff(x, dt, 3, q/r, forwardbackward)
 
 
 def known_dynamics(x, params, u=None, options=None, xhat0=None, P0=None, A=None,