Python 2d interpolation regular grid

Interpolate over a 2-D grid.

x, y and z are arrays of values used to approximate some function f: z = f[x, y] which returns a scalar value z. This class returns a function whose call method uses spline interpolation to find the value of new points.

If x and y represent a regular grid, consider using RectBivariateSpline.

If z is a vector value, consider using interpn.

Note that calling interp2d with NaNs present in input values results in undefined behaviour.

Arrays defining the data point coordinates.

If the points lie on a regular grid, x can specify the column coordinates and y the row coordinates, for example:

>>> x = [0,1,2];  y = [0,3]; z = [[1,2,3], [4,5,6]]

Otherwise, x and y must specify the full coordinates for each point, for example:

>>> x = [0,1,2,0,1,2];  y = [0,0,0,3,3,3]; z = [1,4,2,5,3,6]

If x and y are multidimensional, they are flattened before use.

The values of the function to interpolate at the data points. If z is a multidimensional array, it is flattened before use assuming Fortran-ordering [order=’F’]. The length of a flattened z array is either len[x]*len[y] if x and y specify the column and row coordinates or len[z] == len[x] == len[y] if x and y specify coordinates for each point.

The kind of spline interpolation to use. Default is ‘linear’.

If True, the class makes internal copies of x, y and z. If False, references may be used. The default is to copy.

If True, when interpolated values are requested outside of the domain of the input data [x,y], a ValueError is raised. If False, then fill_value is used.

If provided, the value to use for points outside of the interpolation domain. If omitted [None], values outside the domain are extrapolated via nearest-neighbor extrapolation.

Notes

The minimum number of data points required along the interpolation axis is [k+1]**2, with k=1 for linear, k=3 for cubic and k=5 for quintic interpolation.

The interpolator is constructed by bisplrep, with a smoothing factor of 0. If more control over smoothing is needed, bisplrep should be used directly.

Examples

Construct a 2-D grid and interpolate on it:

>>> from scipy import interpolate
>>> x = np.arange[-5.01, 5.01, 0.25]
>>> y = np.arange[-5.01, 5.01, 0.25]
>>> xx, yy = np.meshgrid[x, y]
>>> z = np.sin[xx**2+yy**2]
>>> f = interpolate.interp2d[x, y, z, kind='cubic']

Now use the obtained interpolation function and plot the result:

>>> import matplotlib.pyplot as plt
>>> xnew = np.arange[-5.01, 5.01, 1e-2]
>>> ynew = np.arange[-5.01, 5.01, 1e-2]
>>> znew = f[xnew, ynew]
>>> plt.plot[x, z[0, :], 'ro-', xnew, znew[0, :], 'b-']
>>> plt.show[]

Methods