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 """ 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, *args): """ Evaluate interpolator at given points. Parameters ---------- xi : ndarray of float, shape (..., ndim) Points where to interpolate data at. """ xi = _ndim_coords_from_arrays(args) 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', fill_value=np.nan): """ 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. 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. 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 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) return ip(xi) elif method == 'linear': ip = LinearNDInterpolator(points, values, fill_value=fill_value) return ip(xi) elif method == 'cubic' and ndim == 2: ip = CloughTocher2DInterpolator(points, values, fill_value=fill_value) return ip(xi) else: raise ValueError("Unknown interpolation method %r for " "%d dimensional data" % (method, ndim))
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