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# scipy.interpolate.interpn

scipy.interpolate.interpn(points, values, xi, method='linear', bounds_error=True, fill_value=nan)

  Multidimensional interpolation on regular or rectilinear grids.

  Strictly speaking, not all regular grids are supported - this function works on rectilinear grids, that is, a rectangular grid with even or uneven spacing.

  Parameters:
    points tuple of ndarray of float, with shapes (m1, ), …, (mn, )

      The points defining the regular grid in n dimensions. The points in each dimension (i.e. every elements of the points tuple) must be strictly ascending or descending.

    values array_like, shape (m1, …, mn, …)

      The data on the regular grid in n dimensions. Complex data is accepted.

      Deprecated since version 1.13.0: Complex data is deprecated with `method="pchip"` and will raise an error in SciPy 1.15.0. This is because `PchipInterpolator` only works with real values. If you are trying to use the real components of the passed array, use `np.real` on `values`.

    xi ndarray of shape (…, ndim)

      The coordinates to sample the gridded data at

    method str, optional

      The method of interpolation to perform. Supported are “linear”, “nearest”, “slinear”, “cubic”, “quintic”, “pchip”, and “splinef2d”. “splinef2d” is only supported for 2-dimensional data.

    bounds_error bool, optional

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

    fill_value number, optional

      If provided, the value to use for points outside of the interpolation domain. If None, values outside the domain are extrapolated. Extrapolation is not supported by method “splinef2d”.

  Returns:
    values_x ndarray, shape xi.shape[:-1] + values.shape[ndim:]

      Interpolated values at xi. See notes for behaviour when `xi.ndim == 1`.

  See also

  `NearestNDInterpolator`

    Nearest neighbor interpolation on unstructured data in N dimensions

  `LinearNDInterpolator`

    Piecewise linear interpolant on unstructured data in N dimensions

  `RegularGridInterpolator`

    interpolation on a regular or rectilinear grid in arbitrary dimensions (`interpn` wraps this class).

  `RectBivariateSpline`

    Bivariate spline approximation over a rectangular mesh

  `scipy.ndimage.map_coordinates`

    interpolation on grids with equal spacing (suitable for e.g., N-D image resampling)

  Notes

  New in version 0.14.

  In the case that `xi.ndim == 1` a new axis is inserted into the 0 position of the returned array, values_x, so its shape is instead `(1,) + values.shape[ndim:]`.

  If the input data is such that input dimensions have incommensurate units and differ by many orders of magnitude, the interpolant may have numerical artifacts. Consider rescaling the data before interpolation.

  Examples

  Evaluate a simple example function on the points of a regular 3-D grid:

      >>> import numpy as np
      >>> from scipy.interpolate import interpn
      >>> def value_func_3d(x, y, z):
      ...     return 2 * x + 3 * y - z
      >>> x = np.linspace(0, 4, 5)
      >>> y = np.linspace(0, 5, 6)
      >>> z = np.linspace(0, 6, 7)
      >>> points = (x, y, z)
      >>> values = value_func_3d(*np.meshgrid(*points, indexing='ij'))

  Evaluate the interpolating function at a point

      >>> point = np.array([2.21, 3.12, 1.15])
      >>> print(interpn(points, values, point))
      [12.63]