emg3d.maps.interpolate(grid, values, xi, method='linear', extrapolate=True, log=False, **kwargs)[source]#

Interpolate values from one grid to another grid or to points.


Input grid; a emg3d.meshes.TensorMesh instance.


A model property such as Model.property_x, or a field such as Field.fx (ndim=3; the dimension in each direction must either correspond to the number of nodes or cell centers in the corresponding direction).

xi{TensorMesh, tuple, ndarray}

Output coordinates; possibilities:

  • A grid (emg3d.meshes.TensorMesh): interpolation from one grid to another.

  • A tuple (array_like, array_like, array_like) containing x-, y-, and z-coordinates. The length of each can be either one or the number of coordinates, the size-one elements will be expanded internally to the length of the coordinates. E.g., (x, [y0, y1, y2], z) will be expanded to ([x, x, x], [y0, y1, y2], [z, z, z]).

  • Arbitrary point coordinates as ndarray of shape (..., 3), e.g., array([[x0, y0, z0], ..., [xN, yN, zN])).

method{‘nearest’, ‘linear’, ‘volume’, ‘cubic’}, default: ‘linear’

The method of interpolation to perform.

  • 'nearest', 'linear': Fastest methods; work for model properties and fields living on edges or faces. Carried out with scipy.interpolate.RegularGridInterpolator.

  • 'cubic': Cubic spline interpolation using emg3d.maps.interp_spline_3d.

  • 'volume': Volume average interpolation using emg3d.maps.interp_volume_average.

    Volume average interpolation ensures that the total sum of the interpolated quantity stays constant. The result can be quite different if you provide resistivity, conductivity, or the logarithm of any of the two. The recommended way is to use log=True, in which case the output is the same for conductivities and resistivities.

    This method is only implemented for quantities living on cell centers, not on edges/faces (hence not for fields); and only for grids as input to xi.

extrapolatebool, default: True

This parameter controls the default parameters provided to the interpolation routines.

  • 'nearest', 'linear': If True, values outside of the domain are extrapolated (bounds_error=False, fill_value=None); if False, values outside are set to 0.0 (bounds_error=False, fill_value=0.0)

  • 'cubic': If True, values outside of the domain are extrapolated using nearest interpolation (mode='nearest'); if False, values outside are set to 0.0 (mode='constant', cval=0.0).

  • 'volume': Always uses nearest interpolation for points outside of the provided grid, independent of the choice of extrapolate.

logbool, default: False

If True, the interpolation is carried out on a log10-scale; this corresponds to 10**interpolate(grid, np.log10(values), ...).

kwargsdict, optional

Will be forwarded to the corresponding interpolation algorithm, if they accept additional keywords. This can be used, e.g., to change the behaviour outlined in the parameter extrapolate.


Values corresponding to the new grid.