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""" Convenience interface to N-D interpolation
.. versionadded:: 0.9
"""
CloughTocher2DInterpolator, _ndim_coords_from_arrays
'CloughTocher2DInterpolator']
#------------------------------------------------------------------------------ # Nearest-neighbour interpolation #------------------------------------------------------------------------------
""" NearestNDInterpolator(x, y)
Nearest-neighbour interpolation in N dimensions.
.. versionadded:: 0.9
Methods ------- __call__
Parameters ---------- x : (Npoints, Ndims) ndarray of floats Data point coordinates. y : (Npoints,) ndarray of float or complex Data values. rescale : boolean, optional Rescale points to unit cube before performing interpolation. This is useful if some of the input dimensions have incommensurable units and differ by many orders of magnitude.
.. versionadded:: 0.14.0 tree_options : dict, optional Options passed to the underlying ``cKDTree``.
.. versionadded:: 0.17.0
Notes ----- Uses ``scipy.spatial.cKDTree``
"""
NDInterpolatorBase.__init__(self, x, y, rescale=rescale, need_contiguous=False, need_values=False) if tree_options is None: tree_options = dict() self.tree = cKDTree(self.points, **tree_options) self.values = y
""" Evaluate interpolator at given points.
Parameters ---------- xi : ndarray of float, shape (..., ndim) Points where to interpolate data at.
""" xi = _ndim_coords_from_arrays(args, ndim=self.points.shape[1]) xi = self._check_call_shape(xi) xi = self._scale_x(xi) dist, i = self.tree.query(xi) return self.values[i]
#------------------------------------------------------------------------------ # Convenience interface function #------------------------------------------------------------------------------
rescale=False): """ Interpolate unstructured D-dimensional data.
Parameters ---------- points : ndarray of floats, shape (n, D) Data point coordinates. Can either be an array of shape (n, D), or a tuple of `ndim` arrays. values : ndarray of float or complex, shape (n,) Data values. xi : 2-D ndarray of float or tuple of 1-D array, shape (M, D) Points at which to interpolate data. method : {'linear', 'nearest', 'cubic'}, optional 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`` tessellate 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 determined 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. fill_value : float, optional Value used to fill in for requested points outside of the convex hull of the input points. If not provided, then the default is ``nan``. This option has no effect for the 'nearest' method. rescale : bool, optional Rescale points to unit cube before performing interpolation. This is useful if some of the input dimensions have incommensurable units and differ by many orders of magnitude.
.. versionadded:: 0.14.0
Returns ------- ndarray Array of interpolated values.
Notes -----
.. versionadded:: 0.9
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)
if points.ndim < 2: ndim = points.ndim else: ndim = points.shape[-1]
if ndim == 1 and method in ('nearest', 'linear', 'cubic'): from .interpolate import interp1d points = points.ravel() if isinstance(xi, tuple): if len(xi) != 1: raise ValueError("invalid number of dimensions in xi") xi, = xi # Sort points/values together, necessary as input for interp1d idx = np.argsort(points) points = points[idx] values = values[idx] if method == 'nearest': fill_value = 'extrapolate' ip = interp1d(points, values, kind=method, axis=0, bounds_error=False, fill_value=fill_value) return ip(xi) elif method == 'nearest': ip = NearestNDInterpolator(points, values, rescale=rescale) return ip(xi) elif method == 'linear': ip = LinearNDInterpolator(points, values, fill_value=fill_value, rescale=rescale) return ip(xi) elif method == 'cubic' and ndim == 2: ip = CloughTocher2DInterpolator(points, values, fill_value=fill_value, rescale=rescale) return ip(xi) else: raise ValueError("Unknown interpolation method %r for " "%d dimensional data" % (method, ndim)) |