U @f#@sbdZddlZddlmZmZmZmZddlm Z dddd gZ Gd ddeZ d ej d fd dZ dS)zD Convenience interface to N-D interpolation .. versionadded:: 0.9 N)LinearNDInterpolatorNDInterpolatorBaseCloughTocher2DInterpolator_ndim_coords_from_arrays)cKDTreegriddataNearestNDInterpolatorrrc@s"eZdZdZdddZddZdS) r aNearestNDInterpolator(x, y). Nearest-neighbor interpolation in N > 1 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`` Examples -------- We can interpolate values on a 2D plane: >>> from scipy.interpolate import NearestNDInterpolator >>> import numpy as np >>> import matplotlib.pyplot as plt >>> rng = np.random.default_rng() >>> x = rng.random(10) - 0.5 >>> y = rng.random(10) - 0.5 >>> z = np.hypot(x, y) >>> X = np.linspace(min(x), max(x)) >>> Y = np.linspace(min(y), max(y)) >>> X, Y = np.meshgrid(X, Y) # 2D grid for interpolation >>> interp = NearestNDInterpolator(list(zip(x, y)), z) >>> Z = interp(X, Y) >>> plt.pcolormesh(X, Y, Z, shading='auto') >>> plt.plot(x, y, "ok", label="input point") >>> plt.legend() >>> plt.colorbar() >>> plt.axis("equal") >>> plt.show() See also -------- griddata : Interpolate unstructured D-D data. LinearNDInterpolator : Piecewise linear interpolant in N dimensions. CloughTocher2DInterpolator : Piecewise cubic, C1 smooth, curvature-minimizing interpolant in 2D. FNcCsDtj||||ddd|dkr$t}t|jf||_t||_dS)NF)rescaleZneed_contiguousZ need_values) r__init__dictrpointstreenpZasarrayvalues)selfxyr Z tree_optionsrA/tmp/pip-unpacked-wheel-w7avvj8p/scipy/interpolate/_ndgriddata.pyr Ws zNearestNDInterpolator.__init__cGsBt||jjdd}||}||}|j|\}}|j|S)aV Evaluate interpolator at given points. Parameters ---------- x1, x2, ... xn : array-like of float Points where to interpolate data at. x1, x2, ... xn can be array-like of float with broadcastable shape. or x1 can be array-like of float with shape ``(..., ndim)`` r)ndim)rr shapeZ_check_call_shapeZ_scale_xrqueryr)rargsxidistirrr__call__`s   zNearestNDInterpolator.__call__)FN)__name__ __module__ __qualname____doc__r rrrrrr sB linearFc Cs,t|}|jdkr|j}n |jd}|dkr|dkrddlm}|}t|trlt|dkrft d|\}t |}||}||}|dkrd}||||d d |d } | |S|dkrt |||d } | |S|d krt ||||d} | |S|dkr|dkrt||||d} | |St d||fdS)aL Interpolate unstructured D-D data. Parameters ---------- points : 2-D ndarray of floats with shape (n, D), or length D tuple of 1-D ndarrays with shape (n,). Data point coordinates. values : ndarray of float or complex, shape (n,) Data values. xi : 2-D ndarray of floats with shape (m, D), or length D tuple of ndarrays broadcastable to the same shape. 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-D 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 For data on a regular grid use `interpn` instead. Examples -------- Suppose we want to interpolate the 2-D function >>> import numpy as np >>> 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: >>> rng = np.random.default_rng() >>> points = rng.random((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() See Also -------- LinearNDInterpolator : Piecewise linear interpolant in N dimensions. NearestNDInterpolator : Nearest-neighbor interpolation in N dimensions. CloughTocher2DInterpolator : Piecewise cubic, C1 smooth, curvature-minimizing interpolant in 2D. r)nearestr"cubic)interp1dz"invalid number of dimensions in xir%Z extrapolaterF)kindZaxisZ bounds_error fill_value)r r")r)r r&z7Unknown interpolation method %r for %d dimensional dataN)rrrZ _interpolater'Zravel isinstancetuplelen ValueErrorrZargsortr rr) r rrmethodr)r rr'idxiprrrrwsHv       )r!ZnumpyrZinterpndrrrrZ scipy.spatialr__all__r nanrrrrrs c