Implement Akima1DInterpolator

closes #7588

Author: Gábor Lipták <[email protected]>

Closes #12833 from gliptak/akima and squashes the following commits:

a63dc31 [Gábor Lipták] Implement Akima1DInterpolator

Author: gliptak

ci/requirements-3.5_OSX.run

@@ -4,7 +4,6 @@ openpyxl
 xlsxwriter
 xlrd
 xlwt
-scipy
 numexpr
 pytables
 html5lib

doc/source/conf.py

@@ -292,6 +292,7 @@
     'matplotlib': ('http://matplotlib.org/', None),
     'python': ('http://docs.python.org/3', None),
     'numpy': ('http://docs.scipy.org/doc/numpy', None),
+    'scipy': ('http://docs.scipy.org/doc/scipy', None),
     'py': ('http://pylib.readthedocs.org/en/latest/', None)
 }
 import glob

doc/source/missing_data.rst

@@ -392,9 +392,12 @@ The ``method`` argument gives access to fancier interpolation methods.
 If you have scipy_ installed, you can set pass the name of a 1-d interpolation routine to ``method``.
 You'll want to consult the full scipy interpolation documentation_ and reference guide_ for details.
 The appropriate interpolation method will depend on the type of data you are working with.
-For example, if you are dealing with a time series that is growing at an increasing rate,
-``method='quadratic'`` may be appropriate.  If you have values approximating a cumulative
-distribution function, then ``method='pchip'`` should work well.
+
+* If you are dealing with a time series that is growing at an increasing rate,
+  ``method='quadratic'`` may be appropriate.
+* If you have values approximating a cumulative distribution function,
+  then ``method='pchip'`` should work well.
+* To fill missing values with goal of smooth plotting, use ``method='akima'``.
 
 .. warning::
 
@@ -406,6 +409,8 @@ distribution function, then ``method='pchip'`` should work well.
 
    df.interpolate(method='pchip')
 
+   df.interpolate(method='akima')
+
 When interpolating via a polynomial or spline approximation, you must also specify
 the degree or order of the approximation:
 

doc/source/whatsnew/v0.18.1.txt

@@ -77,6 +77,7 @@ Other Enhancements
 - ``pd.read_csv()`` now supports opening ZIP files that contains a single CSV, via extension inference or explict ``compression='zip'`` (:issue:`12175`)
 - ``pd.read_csv()`` now supports opening files using xz compression, via extension inference or explicit ``compression='xz'`` is specified; ``xz`` compressions is also supported by ``DataFrame.to_csv`` in the same way (:issue:`11852`)
 - ``pd.read_msgpack()`` now always gives writeable ndarrays even when compression is used (:issue:`12359`).
+- ``interpolate()`` now supports ``method='akima'`` (:issue:`7588`).
 - ``Index.take`` now handles ``allow_fill`` and ``fill_value`` consistently (:issue:`12631`)
 
 .. ipython:: python

pandas/core/generic.py

@@ -3451,7 +3451,8 @@ def interpolate(self, method='linear', axis=0, limit=None, inplace=False,
         ----------
         method : {'linear', 'time', 'index', 'values', 'nearest', 'zero',
                   'slinear', 'quadratic', 'cubic', 'barycentric', 'krogh',
-                  'polynomial', 'spline' 'piecewise_polynomial', 'pchip'}
+                  'polynomial', 'spline' 'piecewise_polynomial', 'pchip',
+                  'akima'}
 
             * 'linear': ignore the index and treat the values as equally
               spaced. This is the only method supported on MultiIndexes.
@@ -3465,13 +3466,16 @@ def interpolate(self, method='linear', axis=0, limit=None, inplace=False,
               require that you also specify an `order` (int),
               e.g. df.interpolate(method='polynomial', order=4).
               These use the actual numerical values of the index.
-            * 'krogh', 'piecewise_polynomial', 'spline', and 'pchip' are all
+            * 'krogh', 'piecewise_polynomial', 'spline', 'pchip' and 'akima' are all
               wrappers around the scipy interpolation methods of similar
               names. These use the actual numerical values of the index. See
               the scipy documentation for more on their behavior
               `here <http://docs.scipy.org/doc/scipy/reference/interpolate.html#univariate-interpolation>`__  # noqa
               `and here <http://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html>`__  # noqa
 
+            .. versionadded:: 0.18.1
+               Added support for the 'akima' method
+
         axis : {0, 1}, default 0
             * 0: fill column-by-column
             * 1: fill row-by-row

pandas/core/missing.py

@@ -82,7 +82,7 @@ def clean_interp_method(method, **kwargs):
     order = kwargs.get('order')
     valid = ['linear', 'time', 'index', 'values', 'nearest', 'zero', 'slinear',
              'quadratic', 'cubic', 'barycentric', 'polynomial', 'krogh',
-             'piecewise_polynomial', 'pchip', 'spline']
+             'piecewise_polynomial', 'pchip', 'akima', 'spline']
     if method in ('spline', 'polynomial') and order is None:
         raise ValueError("You must specify the order of the spline or "
                          "polynomial.")
@@ -188,7 +188,7 @@ def _interp_limit(invalid, fw_limit, bw_limit):
 
     sp_methods = ['nearest', 'zero', 'slinear', 'quadratic', 'cubic',
                   'barycentric', 'krogh', 'spline', 'polynomial',
-                  'piecewise_polynomial', 'pchip']
+                  'piecewise_polynomial', 'pchip', 'akima']
     if method in sp_methods:
         inds = np.asarray(xvalues)
         # hack for DatetimeIndex, #1646
@@ -232,12 +232,19 @@ def _interpolate_scipy_wrapper(x, y, new_x, method, fill_value=None,
         # GH 5975, scipy.interp1d can't hande datetime64s
         x, new_x = x._values.astype('i8'), new_x.astype('i8')
 
-    try:
-        alt_methods['pchip'] = interpolate.pchip_interpolate
-    except AttributeError:
-        if method == 'pchip':
-            raise ImportError("Your version of scipy does not support "
+    if method == 'pchip':
+        try:
+            alt_methods['pchip'] = interpolate.pchip_interpolate
+        except AttributeError:
+            raise ImportError("Your version of Scipy does not support "
                               "PCHIP interpolation.")
+    elif method == 'akima':
+        try:
+            from scipy.interpolate import Akima1DInterpolator  # noqa
+            alt_methods['akima'] = _akima_interpolate
+        except ImportError:
+            raise ImportError("Your version of Scipy does not support "
+                              "Akima interpolation.")
 
     interp1d_methods = ['nearest', 'zero', 'slinear', 'quadratic', 'cubic',
                         'polynomial']
@@ -267,6 +274,56 @@ def _interpolate_scipy_wrapper(x, y, new_x, method, fill_value=None,
     return new_y
 
 
+def _akima_interpolate(xi, yi, x, der=0, axis=0):
+    """
+    Convenience function for akima interpolation.
+    xi and yi are arrays of values used to approximate some function f,
+    with ``yi = f(xi)``.
+
+    See `Akima1DInterpolator` for details.
+
+    Parameters
+    ----------
+    xi : array_like
+        A sorted list of x-coordinates, of length N.
+    yi :  array_like
+        A 1-D array of real values.  `yi`'s length along the interpolation
+        axis must be equal to the length of `xi`. If N-D array, use axis
+        parameter to select correct axis.
+    x : scalar or array_like
+        Of length M.
+    der : int or list, optional
+        How many derivatives to extract; None for all potentially
+        nonzero derivatives (that is a number equal to the number
+        of points), or a list of derivatives to extract. This number
+        includes the function value as 0th derivative.
+    axis : int, optional
+        Axis in the yi array corresponding to the x-coordinate values.
+
+    See Also
+    --------
+    scipy.interpolate.Akima1DInterpolator
+
+    Returns
+    -------
+    y : scalar or array_like
+        The result, of length R or length M or M by R,
+
+    """
+    from scipy import interpolate
+    try:
+        P = interpolate.Akima1DInterpolator(xi, yi, axis=axis)
+    except TypeError:
+        # Scipy earlier than 0.17.0 missing axis
+        P = interpolate.Akima1DInterpolator(xi, yi)
+    if der == 0:
+        return P(x)
+    elif interpolate._isscalar(der):
+        return P(x, der=der)
+    else:
+        return [P(x, nu) for nu in der]
+
+
 def interpolate_2d(values, method='pad', axis=0, limit=None, fill_value=None,
                    dtype=None):
     """ perform an actual interpolation of values, values will be make 2-d if

pandas/tests/test_generic.py

@@ -34,6 +34,13 @@ def _skip_if_no_pchip():
     except ImportError:
         raise nose.SkipTest('scipy.interpolate.pchip missing')
 
+
+def _skip_if_no_akima():
+    try:
+        from scipy.interpolate import Akima1DInterpolator  # noqa
+    except ImportError:
+        raise nose.SkipTest('scipy.interpolate.Akima1DInterpolator missing')
+
 # ----------------------------------------------------------------------
 # Generic types test cases
 
@@ -734,7 +741,7 @@ def test_interpolate(self):
         non_ts[0] = np.NaN
         self.assertRaises(ValueError, non_ts.interpolate, method='time')
 
-    def test_interp_regression(self):
+    def test_interpolate_pchip(self):
         tm._skip_if_no_scipy()
         _skip_if_no_pchip()
 
@@ -747,6 +754,21 @@ def test_interp_regression(self):
         # does not blow up, GH5977
         interp_s[49:51]
 
+    def test_interpolate_akima(self):
+        tm._skip_if_no_scipy()
+        _skip_if_no_akima()
+
+        ser = Series([10, 11, 12, 13])
+
+        expected = Series([11.00, 11.25, 11.50, 11.75,
+                           12.00, 12.25, 12.50, 12.75, 13.00],
+                          index=Index([1.0, 1.25, 1.5, 1.75,
+                                       2.0, 2.25, 2.5, 2.75, 3.0]))
+        # interpolate at new_index
+        new_index = ser.index.union(Index([1.25, 1.5, 1.75, 2.25, 2.5, 2.75]))
+        interp_s = ser.reindex(new_index).interpolate(method='akima')
+        assert_series_equal(interp_s[1:3], expected)
+
     def test_interpolate_corners(self):
         s = Series([np.nan, np.nan])
         assert_series_equal(s.interpolate(), s)