Expanded derivatives

examples/1_feature_overview.ipynb

@@ -716,7 +716,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Pass in pre-computed derivatives"
+    "### Pass in pre-computed derivatives\n",
+    "Rather than using one of PySINDy's built-in differentiators, you can compute numerical derivatives using a method of your choice then pass them directly to the `fit` method. This option also enables you to use derivative data obtained directly from experiments."
    ]
   },
   {
@@ -751,7 +752,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Drop end points from finite difference computation"
+    "### Drop end points from finite difference computation\n",
+    "Many methods of numerical differentiation exhibit poor performance near the endpoints of the data. The `FiniteDifference` and `SmoothedFiniteDifference` methods allow one to easily drop the endpoints for improved accuracy."
    ]
   },
   {
@@ -786,7 +788,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Smoothed finite difference"
+    "### Smoothed finite difference\n",
+    "This method, designed for noisy data, applies a smoother (the default is `scipy.signal.savgol_filter`) before performing differentiation."
    ]
   },
   {
@@ -817,6 +820,14 @@
     "model.print()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### More differentiation options\n",
+    "PySINDy provides many other differentiation methods (powered by the [derivative](https://pypi.org/project/derivative/) package). They are explored in detail in [this notebook](https://github.com/dynamicslab/pysindy/blob/master/examples/5_differentiation.ipynb)."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1485,7 +1496,7 @@
     "width": "296.475px"
    },
    "toc_section_display": true,
-   "toc_window_display": true
+   "toc_window_display": false
   },
   "varInspector": {
    "cols": {

examples/4_scikit_learn_compatibility.ipynb

@@ -20,8 +20,8 @@
    "execution_count": 1,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:35.177225Z",
-     "start_time": "2020-07-14T21:07:33.573951Z"
+     "end_time": "2020-08-22T22:47:55.509529Z",
+     "start_time": "2020-08-22T22:47:54.323781Z"
     }
    },
    "outputs": [],
@@ -44,8 +44,8 @@
    "execution_count": 2,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:35.285747Z",
-     "start_time": "2020-07-14T21:07:35.184412Z"
+     "end_time": "2020-08-22T22:47:56.708081Z",
+     "start_time": "2020-08-22T22:47:56.618948Z"
     }
    },
    "outputs": [],
@@ -95,8 +95,8 @@
    "execution_count": 3,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:44.101945Z",
-     "start_time": "2020-07-14T21:07:35.293352Z"
+     "end_time": "2020-08-22T22:50:47.967603Z",
+     "start_time": "2020-08-22T22:50:40.520544Z"
     }
    },
    "outputs": [
@@ -135,6 +135,62 @@
     "search.best_estimator_.print()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Some extra care must be taken when working with differentiation methods from the `derivative` package (i.e. those accessed via the `SINDyDerivative` class). See the example below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-08-22T22:59:18.558877Z",
+     "start_time": "2020-08-22T22:58:57.908732Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Best parameters: {'differentiation_method__kwargs': {'kind': 'spline', 's': 0.01}, 'optimizer__threshold': 0.1}\n",
+      "x0' = -10.000 x0 + 10.000 x1\n",
+      "x1' = 28.003 x0 + -1.001 x1 + -1.000 x0 x2\n",
+      "x2' = -2.667 x2 + 1.000 x0 x1\n"
+     ]
+    }
+   ],
+   "source": [
+    "model = ps.SINDy(\n",
+    "    t_default=dt,\n",
+    "    differentiation_method=ps.SINDyDerivative(kind='spline', s=1e-2)\n",
+    ")\n",
+    "\n",
+    "param_grid = {\n",
+    "    \"optimizer__threshold\": [0.001, 0.01, 0.1],\n",
+    "    \"differentiation_method__kwargs\": [\n",
+    "        {'kind': 'spline', 's': 1e-2},\n",
+    "        {'kind': 'spline', 's': 1e-1},\n",
+    "        {'kind': 'finite_difference', 'k': 1},\n",
+    "        {'kind': 'finite_difference', 'k': 2},\n",
+    "    ]\n",
+    "}\n",
+    "\n",
+    "# This part is identical to what we did before\n",
+    "search = GridSearchCV(\n",
+    "    model,\n",
+    "    param_grid,\n",
+    "    cv=TimeSeriesSplit(n_splits=5)\n",
+    ")\n",
+    "search.fit(x_train)\n",
+    "\n",
+    "print(\"Best parameters:\", search.best_params_)\n",
+    "search.best_estimator_.print()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -145,11 +201,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:44.133790Z",
-     "start_time": "2020-07-14T21:07:44.116536Z"
+     "end_time": "2020-08-22T22:59:50.283609Z",
+     "start_time": "2020-08-22T22:59:50.261397Z"
     }
    },
    "outputs": [],
@@ -203,11 +259,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:50.098150Z",
-     "start_time": "2020-07-14T21:07:44.137586Z"
+     "end_time": "2020-08-22T22:59:56.316952Z",
+     "start_time": "2020-08-22T22:59:52.131651Z"
     }
    },
    "outputs": [
@@ -256,11 +312,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:50.552501Z",
-     "start_time": "2020-07-14T21:07:50.107361Z"
+     "end_time": "2020-08-22T22:59:59.313750Z",
+     "start_time": "2020-08-22T22:59:58.992166Z"
     }
    },
    "outputs": [
@@ -284,11 +340,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2020-07-14T21:07:50.660764Z",
-     "start_time": "2020-07-14T21:07:50.577603Z"
+     "end_time": "2020-08-22T23:00:00.375038Z",
+     "start_time": "2020-08-22T23:00:00.333557Z"
     }
    },
    "outputs": [

pysindy/differentiation/__init__.py

@@ -1,3 +1,12 @@
 from .base import BaseDifferentiation
+from .derivative import SINDyDerivative
 from .finite_difference import FiniteDifference
 from .smoothed_finite_difference import SmoothedFiniteDifference
+
+
+__all__ = [
+    "BaseDifferentiation",
+    "SINDyDerivative",
+    "FiniteDifference",
+    "SmoothedFiniteDifference",
+]

pysindy/differentiation/derivative.py

@@ -0,0 +1,72 @@
+"""
+Wrapper classes for differentiation methods from the `derivative` package.
+
+Some default values used here may differ from those used in `derivative`.
+"""
+from derivative import dxdt
+from numpy import arange
+from sklearn.base import BaseEstimator
+
+from pysindy.utils.base import validate_input
+
+
+class SINDyDerivative(BaseEstimator):
+    """
+    Wrapper class for differentiation classes from the ``derivative`` package.
+
+    Imbues the class with ``_differentiate`` and ``__call__`` methods which are
+    used by PySINDy.
+
+    Parameters
+    ----------
+    derivative_kws: dictionary, optional
+        Keyword arguments to be passed to the ``derivative.dxdt`` method.
+
+    Notes
+    -----
+    See the `derivative documentation <https://derivative.readthedocs.io/en/latest/>`_
+    for acceptable keywords.
+    """
+
+    def __init__(self, **kwargs):
+        self.kwargs = kwargs
+
+    def set_params(self, **params):
+        """
+        Set the parameters of this estimator.
+        Modification of the pysindy method to allow unknown kwargs. This allows using
+        the full range of derivative parameters that are not defined as member variables
+        in sklearn grid search.
+
+        Returns
+        -------
+        self
+        """
+        if not params:
+            # Simple optimization to gain speed (inspect is slow)
+            return self
+        else:
+            self.kwargs.update(params)
+
+        return self
+
+    def get_params(self, deep=True):
+        """Get parameters."""
+        params = super().get_params(deep)
+
+        if isinstance(self.kwargs, dict):
+            params.update(self.kwargs)
+
+        return params
+
+    def _differentiate(self, x, t=1):
+        if isinstance(t, (int, float)):
+            if t < 0:
+                raise ValueError("t must be a positive constant or an array")
+            t = arange(x.shape[0]) * t
+
+        return dxdt(x, t, axis=0, **self.kwargs)
+
+    def __call__(self, x, t=1):
+        x = validate_input(x, t=t)
+        return self._differentiate(x, t)

pysindy/pysindy.py

@@ -1,6 +1,7 @@
 import warnings
 from typing import Sequence
 
+from derivative.differentiation import Derivative
 from numpy import concatenate
 from numpy import isscalar
 from numpy import ndim
@@ -15,14 +16,15 @@
 from sklearn.pipeline import Pipeline
 from sklearn.utils.validation import check_is_fitted
 
-from pysindy.differentiation import FiniteDifference
-from pysindy.feature_library import PolynomialLibrary
-from pysindy.optimizers import SINDyOptimizer
-from pysindy.optimizers import STLSQ
-from pysindy.utils.base import drop_nan_rows
-from pysindy.utils.base import equations
-from pysindy.utils.base import validate_control_variables
-from pysindy.utils.base import validate_input
+from .differentiation import FiniteDifference
+from .differentiation import SINDyDerivative
+from .feature_library import PolynomialLibrary
+from .optimizers import SINDyOptimizer
+from .optimizers import STLSQ
+from .utils.base import drop_nan_rows
+from .utils.base import equations
+from .utils.base import validate_control_variables
+from .utils.base import validate_input
 
 
 class SINDy(BaseEstimator):
@@ -156,6 +158,8 @@ def __init__(
         self.feature_library = feature_library
         if differentiation_method is None:
             differentiation_method = FiniteDifference()
+        elif isinstance(differentiation_method, Derivative):
+            differentiation_method = SINDyDerivative(differentiation_method)
         self.differentiation_method = differentiation_method
         if not isinstance(t_default, float) and not isinstance(t_default, int):
             raise ValueError("t_default must be a positive number")

requirements.txt

@@ -1,3 +1,4 @@
 scikit-learn[alldeps]>=0.23
 numpy
 scipy
+derivative