[Scipy-svn] r6657 - in trunk/scipy/interpolate: . tests

scipy-svn@scip... scipy-svn@scip...
Tue Aug 31 16:58:55 CDT 2010


Author: ptvirtan
Date: 2010-08-31 16:58:55 -0500 (Tue, 31 Aug 2010)
New Revision: 6657

Added:
   trunk/scipy/interpolate/griddatand.py
   trunk/scipy/interpolate/tests/test_griddatand.py
Modified:
   trunk/scipy/interpolate/__init__.py
Log:
interpolate: add griddata, convenience function for N-d interpolation

Add a convenience function for easy N-d interpolation.

Modified: trunk/scipy/interpolate/__init__.py
===================================================================
--- trunk/scipy/interpolate/__init__.py	2010-08-31 21:58:25 UTC (rev 6656)
+++ trunk/scipy/interpolate/__init__.py	2010-08-31 21:58:55 UTC (rev 6657)
@@ -14,6 +14,8 @@
 
 from polyint import *
 
+from griddatand import *
+
 __all__ = filter(lambda s:not s.startswith('_'),dir())
 from numpy.testing import Tester
 test = Tester().test

Added: trunk/scipy/interpolate/griddatand.py
===================================================================
--- trunk/scipy/interpolate/griddatand.py	                        (rev 0)
+++ trunk/scipy/interpolate/griddatand.py	2010-08-31 21:58:55 UTC (rev 6657)
@@ -0,0 +1,172 @@
+"""
+Convenience interface to N-D interpolation
+
+.. versionadded:: 0.9
+
+"""
+
+import numpy as np
+from interpnd import LinearNDInterpolator, NDInterpolatorBase, \
+     CloughTocher2DInterpolator, _ndim_coords_from_arrays
+from scipy.spatial import cKDTree
+
+__all__ = ['griddata', 'NearestNDInterpolator', 'LinearNDInterpolator',
+           'CloughTocher2DInterpolator']
+
+#------------------------------------------------------------------------------
+# Nearest-neighbour interpolation
+#------------------------------------------------------------------------------
+
+class NearestNDInterpolator(NDInterpolatorBase):
+    """
+    NearestNDInterpolator(points, values)
+
+    Nearest-neighbour interpolation in N dimensions.
+
+    .. versionadded:: 0.9
+
+    Parameters
+    ----------
+    points : ndarray of floats, shape (npoints, ndims)
+        Data point coordinates.
+    values : ndarray of float or complex, shape (npoints, ...)
+        Data values.
+
+    Notes
+    -----
+    Uses ``scipy.spatial.cKDTree``
+
+    """
+
+    def __init__(self, x, y):
+        x = _ndim_coords_from_arrays(x)
+        self._check_init_shape(x, y)
+        self.tree = cKDTree(x)
+        self.points = x
+        self.values = y
+
+    def __call__(self, xi):
+        """
+        Evaluate interpolator at given points.
+
+        Parameters
+        ----------
+        xi : ndarray of float, shape (..., ndim)
+            Points where to interpolate data at.
+
+        """
+        xi = self._check_call_shape(xi)
+        dist, i = self.tree.query(xi)
+        return self.values[i]
+
+
+#------------------------------------------------------------------------------
+# Convenience interface function
+#------------------------------------------------------------------------------
+
+def griddata(points, values, xi, method='linear'):
+    """
+    griddata(points, values, xi, method='linear')
+
+    Interpolate unstructured N-dimensional data.
+
+    .. versionadded:: 0.9
+
+    Parameters
+    ----------
+    points : ndarray of floats, shape (npoints, ndims)
+        Data point coordinates. Can either be a ndarray of
+        size (npoints, ndim), or a tuple of `ndim` arrays.
+    values : ndarray of float or complex, shape (npoints, ...)
+        Data values.
+    xi : ndarray of float, shape (..., ndim)
+        Points where to interpolate data at.
+
+    method : {'linear', 'nearest', 'cubic'}
+        Method of interpolation. One of
+
+        - ``nearest``: return the value at the data point closest to
+          the point of interpolation.  See `NearestNDInterpolator` for
+          more details.
+
+        - ``linear``: tesselate the input point set to n-dimensional
+          simplices, and interpolate linearly on each simplex.  See
+          `LinearNDInterpolator` for more details.
+
+        - ``cubic`` (1-D): return the value detemined from a cubic
+          spline.
+
+        - ``cubic`` (2-D): return the value determined from a
+          piecewise cubic, continuously differentiable (C1), and
+          approximately curvature-minimizing polynomial surface. See
+          `CloughTocher2DInterpolator` for more details.
+
+
+    Examples
+    --------
+
+    Suppose we want to interpolate the 2-D function
+
+    >>> def func(x, y):
+    >>>     return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2
+
+    on a grid in [0, 1]x[0, 1]
+
+    >>> grid_x, grid_y = np.mgrid[0:1:100j, 0:1:200j]
+
+    but we only know its values at 1000 data points:
+
+    >>> points = np.random.rand(1000, 2)
+    >>> values = func(points[:,0], points[:,1])
+
+    This can be done with `griddata` -- below we try out all of the
+    interpolation methods:
+
+    >>> from scipy.interpolate import griddata
+    >>> grid_z0 = griddata(points, values, (grid_x, grid_y), method='nearest')
+    >>> grid_z1 = griddata(points, values, (grid_x, grid_y), method='linear')
+    >>> grid_z2 = griddata(points, values, (grid_x, grid_y), method='cubic')
+
+    One can see that the exact result is reproduced by all of the
+    methods to some degree, but for this smooth function the piecewise
+    cubic interpolant gives the best results:
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.subplot(221)
+    >>> plt.imshow(func(grid_x, grid_y).T, extent=(0,1,0,1), origin='lower')
+    >>> plt.plot(points[:,0], points[:,1], 'k.', ms=1)
+    >>> plt.title('Original')
+    >>> plt.subplot(222)
+    >>> plt.imshow(grid_z0.T, extent=(0,1,0,1), origin='lower')
+    >>> plt.title('Nearest')
+    >>> plt.subplot(223)
+    >>> plt.imshow(grid_z1.T, extent=(0,1,0,1), origin='lower')
+    >>> plt.title('Linear')
+    >>> plt.subplot(224)
+    >>> plt.imshow(grid_z2.T, extent=(0,1,0,1), origin='lower')
+    >>> plt.title('Cubic')
+    >>> plt.gcf().set_size_inches(6, 6)
+    >>> plt.show()
+
+    """
+
+    points = _ndim_coords_from_arrays(points)
+    xi = _ndim_coords_from_arrays(xi)
+
+    ndim = points.shape[-1]
+
+    if ndim == 1 and method in ('nearest', 'linear', 'cubic'):
+        ip = interp1d(points, values, kind=method, axis=0, bounds_error=False)
+        return ip(xi)
+    elif method == 'nearest':
+        ip = NearestNDInterpolator(points, values)
+        return ip(xi)
+    elif method == 'linear':
+        ip = LinearNDInterpolator(points, values)
+        return ip(xi)
+    elif method == 'cubic' and ndim == 2:
+        ip = CloughTocher2DInterpolator(points, values)
+        return ip(xi)
+    else:
+        raise ValueError("Unknown interpolation method %r for "
+                         "%d dimensional data" % (method, ndim))

Added: trunk/scipy/interpolate/tests/test_griddatand.py
===================================================================
--- trunk/scipy/interpolate/tests/test_griddatand.py	                        (rev 0)
+++ trunk/scipy/interpolate/tests/test_griddatand.py	2010-08-31 21:58:55 UTC (rev 6657)
@@ -0,0 +1,57 @@
+import numpy as np
+from numpy.testing import *
+
+from scipy.interpolate.griddatand import griddata
+
+
+class TestGriddata(object):
+
+    def test_alternative_call(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = (np.arange(x.shape[0], dtype=np.double)[:,None]
+             + np.array([0,1])[None,:])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            yi = griddata((x[:,0], x[:,1]), y, (x[:,0], x[:,1]), method=method)
+            assert_almost_equal(y, yi, err_msg=method)
+
+    def test_multivalue_2d(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = (np.arange(x.shape[0], dtype=np.double)[:,None]
+             + np.array([0,1])[None,:])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            yi = griddata(x, y, x, method=method)
+            assert_almost_equal(y, yi, err_msg=method)
+
+    def test_multipoint_2d(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+
+        xi = x[:,None,:] + np.array([0,0,0])[None,:,None]
+
+        for method in ('nearest', 'linear', 'cubic'):
+            yi = griddata(x, y, xi, method=method)
+
+            assert_equal(yi.shape, (5, 3), err_msg=method)
+            assert_almost_equal(yi, np.tile(y[:,None], (1, 3)), err_msg=method)
+
+    def test_complex_2d(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 2j*y[::-1]
+
+        xi = x[:,None,:] + np.array([0,0,0])[None,:,None]
+
+        for method in ('nearest', 'linear', 'cubic'):
+            yi = griddata(x, y, xi, method=method)
+
+            assert_equal(yi.shape, (5, 3), err_msg=method)
+            assert_almost_equal(yi, np.tile(y[:,None], (1, 3)), err_msg=method)
+
+if __name__ == "__main__":
+    run_module_suite()



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