ENH: Add ext parameter to UnivariateSpline

Pass parameter to fitpack.splev to control how to handle out of range
evaluations. Parameter ext can be passed via __init__ or __call__. Added
test to scipy/interpolate/tests/test_fitpack2.py. Tests if UnivariateSpline
call equals x ** 3 for out of range x and extrapolation modes 0 and 1.

See ticket 3557.

closes scipygh-3557

scipy/interpolate/fitpack2.py

@@ -91,6 +91,15 @@ class UnivariateSpline(object):
         If None (default), s=len(w) which should be a good value if 1/w[i] is
         an estimate of the standard deviation of y[i].  If 0, spline will
         interpolate through all data points.
+    ext : int, optional
+        Controls the extrapolation mode for elements 
+        not in the interval defined by the knot sequence            
+           
+        * if ext=0, return the extrapolated value.
+        * if ext=1, return 0
+        * if ext=2, raise a ValueError
+
+        The default value is 0.
 
     See Also
     --------
@@ -124,7 +133,7 @@ class UnivariateSpline(object):
 
     """
 
-    def __init__(self, x, y, w=None, bbox=[None]*2, k=3, s=None):
+    def __init__(self, x, y, w=None, bbox=[None]*2, k=3, s=None, ext=0):
         """
         Input:
           x,y   - 1-d sequences of data points (x must be
@@ -142,8 +151,19 @@ def __init__(self, x, y, w=None, bbox=[None]*2, k=3, s=None):
                        Default s=len(w) which should be a good value
                        if 1/w[i] is an estimate of the standard
                        deviation of y[i].
+          ext        - Controls the extrapolation mode for elements 
+                       not in the interval defined by the knot sequence            
+                       
+                       * if ext=0, return the extrapolated value.
+                       * if ext=1, return 0
+                       * if ext=2, raise a ValueError
+
+                       The default value is 0.
         """
         # _data == x,y,w,xb,xe,k,s,n,t,c,fp,fpint,nrdata,ier
+        self.ext = ext
+        if ext not in (0, 1, 2):
+            raise ValueError("unknown extrapolation mode")
         data = dfitpack.fpcurf0(x,y,k,w=w,
                                 xb=bbox[0],xe=bbox[1],s=s)
         if data[-1] == 1:
@@ -228,7 +248,7 @@ def set_smoothing_factor(self, s):
         self._data = data
         self._reset_class()
 
-    def __call__(self, x, nu=0, ext=0):
+    def __call__(self, x, nu=0, ext=None):
         """ 
         Evaluate spline (or its nu-th derivative) at positions x.
 
@@ -248,8 +268,8 @@ def __call__(self, x, nu=0, ext=0):
             * if ext=1, return 0
             * if ext=2, raise a ValueError
 
-            The default value is 0.
-
+            The default value is 0, passed from the initialization of 
+            UnivariateSpline.
         """
         x = np.asarray(x)
         # empty input yields empty output
@@ -258,6 +278,8 @@ def __call__(self, x, nu=0, ext=0):
 #        if nu is None:
 #            return dfitpack.splev(*(self._eval_args+(x,)))
 #        return dfitpack.splder(nu=nu,*(self._eval_args+(x,)))
+        if ext is None:
+            ext = self.ext
         return fitpack.splev(x, self._eval_args, der=nu, ext=ext)
 
     def get_knots(self):

scipy/interpolate/tests/test_fitpack2.py

@@ -79,19 +79,15 @@ def test_resize_regression(self):
         assert_allclose(spl([0.1, 0.5, 0.9, 0.99]), desired, atol=5e-4)
 
     def test_out_of_range_regression(self):
-        """Regression test for #3557."""
-        x_in_range = [-3., -2.33333333, -1.66666667, -1., -0.33333333,
-                      0.33333333, 1., 1.66666667, 2.33333333, 3.]
-        x_out_of_range = [-3.66666667, -3., -2.33333333, -1.66666667, -1.,
-                          -0.33333333, 0.33333333, 1., 1.66666667, 2.33333333,
-                          3., 3.66666667]
-        y = [-0.03443365, 0.02969204, 0.16251805, 0.33279394, 1.07995049, 
-             0.88203547,  0.31274008, -0.10215527, -0.0274716, -0.06661292]
-        desired = array([0., -0.21332128, 0.16590419, 0.41822373, 0.55728419,
-                         0.59673238, 0.55021514, 0.43137928, 0.25387164, 
-                         0.03133904, -0.22257169, 0.])
-        spl = UnivariateSpline(x=x_in_range, y=y)
-        assert_allclose(spl(x_out_of_range, ext=1), desired, atol=5e-4)
+        # Test different extrapolation modes. See ticket 3557
+        x = np.arange(5, dtype=np.float)
+        y = x ** 3
+        spl = UnivariateSpline(x=x, y=y)
+        xp = linspace(-8, 13, 100)
+        xp_zeros = xp.copy()
+        xp_zeros[np.logical_or(xp_zeros < 0., xp_zeros > 4.)] = 0
+        assert_allclose(spl(xp, ext=0), xp**3, atol=1e-16)
+        assert_allclose(spl(xp, ext=1), xp_zeros**3, atol=1e-16)
 
     def test_derivative_and_antiderivative(self):
         # Thin wrappers to splder/splantider, so light smoke test only.