Interpolate unstructured D-dimensional 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-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, 1x0, 1
>>> grid_x, grid_y = np.mgrid0:1:100j, 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()