_ndgriddata.py

"""
Convenience interface to N-D interpolation

.. versionadded:: 0.9

"""
import numpy as np
from .interpnd import LinearNDInterpolator, NDInterpolatorBase, \
     CloughTocher2DInterpolator, _ndim_coords_from_arrays
from scipy.spatial import cKDTree

__all__ = ['griddata', 'NearestNDInterpolator', 'LinearNDInterpolator',
           'CloughTocher2DInterpolator']

#------------------------------------------------------------------------------
# Nearest-neighbor interpolation
#------------------------------------------------------------------------------


class NearestNDInterpolator(NDInterpolatorBase):
    """NearestNDInterpolator(x, y).

    Nearest-neighbor interpolation in N > 1 dimensions.

    .. versionadded:: 0.9

    Methods
    -------
    __call__

    Parameters
    ----------
    x : (npoints, ndims) 2-D ndarray of floats
        Data point coordinates.
    y : (npoints, ) 1-D ndarray of float or complex
        Data values.
    rescale : boolean, 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.

        .. versionadded:: 0.14.0
    tree_options : dict, optional
        Options passed to the underlying ``cKDTree``.

        .. versionadded:: 0.17.0

    See Also
    --------
    griddata :
        Interpolate unstructured D-D data.
    LinearNDInterpolator :
        Piecewise linear interpolant in N dimensions.
    CloughTocher2DInterpolator :
        Piecewise cubic, C1 smooth, curvature-minimizing interpolant in 2D.
    interpn : Interpolation on a regular grid or rectilinear grid.
    RegularGridInterpolator : Interpolation on a regular or rectilinear grid
                              in arbitrary dimensions (`interpn` wraps this
                              class).

    Notes
    -----
    Uses ``scipy.spatial.cKDTree``

    .. note:: For data on a regular grid use `interpn` instead.

    Examples
    --------
    We can interpolate values on a 2D plane:

    >>> from scipy.interpolate import NearestNDInterpolator
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> rng = np.random.default_rng()
    >>> x = rng.random(10) - 0.5
    >>> y = rng.random(10) - 0.5
    >>> z = np.hypot(x, y)
    >>> X = np.linspace(min(x), max(x))
    >>> Y = np.linspace(min(y), max(y))
    >>> X, Y = np.meshgrid(X, Y)  # 2D grid for interpolation
    >>> interp = NearestNDInterpolator(list(zip(x, y)), z)
    >>> Z = interp(X, Y)
    >>> plt.pcolormesh(X, Y, Z, shading='auto')
    >>> plt.plot(x, y, "ok", label="input point")
    >>> plt.legend()
    >>> plt.colorbar()
    >>> plt.axis("equal")
    >>> plt.show()

    """

    def __init__(self, x, y, rescale=False, tree_options=None):
        NDInterpolatorBase.__init__(self, x, y, rescale=rescale,
                                    need_contiguous=False,
                                    need_values=False)
        if tree_options is None:
            tree_options = dict()
        self.tree = cKDTree(self.points, **tree_options)
        self.values = np.asarray(y)

    def __call__(self, *args):
        """
        Evaluate interpolator at given points.

        Parameters
        ----------
        x1, x2, ... xn : array-like of float
            Points where to interpolate data at.
            x1, x2, ... xn can be array-like of float with broadcastable shape.
            or x1 can be array-like of float with shape ``(..., ndim)``

        """
        xi = _ndim_coords_from_arrays(args, ndim=self.points.shape[1])
        xi = self._check_call_shape(xi)
        xi = self._scale_x(xi)
        dist, i = self.tree.query(xi)
        return self.values[i]


#------------------------------------------------------------------------------
# Convenience interface function
#------------------------------------------------------------------------------

def griddata(points, values, xi, method='linear', fill_value=np.nan,
             rescale=False):
    """
    Interpolate unstructured D-D data.

    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.

        .. versionadded:: 0.14.0

    Returns
    -------
    ndarray
        Array of interpolated values.

    See Also
    --------
    LinearNDInterpolator :
        Piecewise linear interpolant in N dimensions.
    NearestNDInterpolator :
        Nearest-neighbor interpolation in N dimensions.
    CloughTocher2DInterpolator :
        Piecewise cubic, C1 smooth, curvature-minimizing interpolant in 2D.
    interpn : Interpolation on a regular grid or rectilinear grid.
    RegularGridInterpolator : Interpolation on a regular or rectilinear grid
                              in arbitrary dimensions (`interpn` wraps this
                              class).

    Notes
    -----

    .. versionadded:: 0.9

    .. note:: For data on a regular grid use `interpn` instead.

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

    """

    points = _ndim_coords_from_arrays(points)

    if points.ndim < 2:
        ndim = points.ndim
    else:
        ndim = points.shape[-1]

    if ndim == 1 and method in ('nearest', 'linear', 'cubic'):
        from ._interpolate import interp1d
        points = points.ravel()
        if isinstance(xi, tuple):
            if len(xi) != 1:
                raise ValueError("invalid number of dimensions in xi")
            xi, = xi
        # Sort points/values together, necessary as input for interp1d
        idx = np.argsort(points)
        points = points[idx]
        values = values[idx]
        if method == 'nearest':
            fill_value = 'extrapolate'
        ip = interp1d(points, values, kind=method, axis=0, bounds_error=False,
                      fill_value=fill_value)
        return ip(xi)
    elif method == 'nearest':
        ip = NearestNDInterpolator(points, values, rescale=rescale)
        return ip(xi)
    elif method == 'linear':
        ip = LinearNDInterpolator(points, values, fill_value=fill_value,
                                  rescale=rescale)
        return ip(xi)
    elif method == 'cubic' and ndim == 2:
        ip = CloughTocher2DInterpolator(points, values, fill_value=fill_value,
                                        rescale=rescale)
        return ip(xi)
    else:
        raise ValueError("Unknown interpolation method %r for "
                         "%d dimensional data" % (method, ndim))