bundles / scipy 1.18.0 / scipy / interpolate / _ndgriddata / griddata

function

`scipy.interpolate._ndgriddata:griddata`

source: /scipy/interpolate/_ndgriddata.py:170

Signature

def griddata(points, values, xi, method = linear, fill_value = nan, rescale = False, simplex_tolerance = 1.0)

Summary

Convenience function for interpolating unstructured data in multiple dimensions.

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.

simplex_tolerance : float, optional

Multiplier for the default tolerance QHull uses to assign a simplex to the xi. Default is 1.0. Increase if there are difficulties assigning points to simplexes; this is most reproducible with points exatly on the border of a very oblique triangle. Only relevant for linear and 2-D cubic interpolation.

Returns

: ndarray: Array of interpolated values.

Raises

: ValueError: If simplex_tolerance <= 0

Notes

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')

✗

Text(0.5, 1.0, 'Cubic')

plt.gcf().set_size_inches(6, 6)
plt.show()

✓

Aliases

scipy.interpolate.griddata

Signature

Summary

Parameters

Returns

Raises

Notes

Examples

See also

Aliases