ImageFile.scipy__interpolate__ndgriddata__griddata¶
- ImageFile.scipy__interpolate__ndgriddata__griddata(values, xi, method='linear', fill_value=nan, rescale=False)¶
Interpolate unstructured D-D data.
- points2-D ndarray of floats with shape (n, D), or length D tuple of 1-D ndarrays with shape (n,).
Data point coordinates.
- valuesndarray of float or complex, shape (n,)
Data values.
- xi2-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_valuefloat, 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.- rescalebool, 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.
New in version 0.14.0.
- ndarray
Array of interpolated values.
New in version 0.9.
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:
>>> 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()
- LinearNDInterpolator :
Piecewise linear interpolant in N dimensions.
- NearestNDInterpolator :
Nearest-neighbor interpolation in N dimensions.
- CloughTocher2DInterpolator :
Piecewise cubic, C1 smooth, curvature-minimizing interpolant in 2D.