ó ˽÷Xc@`s¡dZddlmZmZmZddlZddlmZm Z m Z m Z ddl m Z ddd d gZde fd „ƒYZd ejed „ZdS(sD Convenience interface to N-D interpolation .. versionadded:: 0.9 i(tdivisiontprint_functiontabsolute_importNi(tLinearNDInterpolatortNDInterpolatorBasetCloughTocher2DInterpolatort_ndim_coords_from_arrays(tcKDTreetgriddatatNearestNDInterpolatorRRcB`s&eZdZedd„Zd„ZRS(s NearestNDInterpolator(points, values) 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`` c C`s_tj|||d|dtdtƒ|dkr=tƒ}nt|j||_||_dS(Ntrescaletneed_contiguoust need_values( Rt__init__tFalsetNonetdictRtpointsttreetvalues(tselftxtyR t tree_options((s;/tmp/pip-build-7oUkmx/scipy/scipy/interpolate/ndgriddata.pyR :s  cG`s]t|d|jjdƒ}|j|ƒ}|j|ƒ}|jj|ƒ\}}|j|S(s Evaluate interpolator at given points. Parameters ---------- xi : ndarray of float, shape (..., ndim) Points where to interpolate data at. tndimi(RRtshapet_check_call_shapet_scale_xRtqueryR(Rtargstxitdistti((s;/tmp/pip-build-7oUkmx/scipy/scipy/interpolate/ndgriddata.pyt__call__Cs N(t__name__t __module__t__doc__RRR R!(((s;/tmp/pip-build-7oUkmx/scipy/scipy/interpolate/ndgriddata.pyR s" tlinearc C`sÀt|ƒ}|jdkr'|j}n |jd}|dkr |dkr ddlm}|jƒ}t|tƒr¤t|ƒdkr˜t dƒ‚n|\}nt j |ƒ}||}||}|dkrÜd }n|||d |d d d t d|ƒ} | |ƒS|dkr8t ||d|ƒ} | |ƒS|dkrit||d|d|ƒ} | |ƒS|dkr¦|dkr¦t||d|d|ƒ} | |ƒSt d||fƒ‚dS(sV 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`` 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 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 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() iiÿÿÿÿitnearestR%tcubic(tinterp1ds"invalid number of dimensions in xit extrapolatetkindtaxisit bounds_errort fill_valueR s7Unknown interpolation method %r for %d dimensional dataN(R&R%R'(RRRt interpolateR(travelt isinstancettupletlent ValueErrortnptargsortRR RR( RRRtmethodR-R RR(tidxtip((s;/tmp/pip-build-7oUkmx/scipy/scipy/interpolate/ndgriddata.pyRXs@e                  (R$t __future__RRRtnumpyR4tinterpndRRRRt scipy.spatialRt__all__R tnanRR(((s;/tmp/pip-build-7oUkmx/scipy/scipy/interpolate/ndgriddata.pyts "  B