333 lines
12 KiB
Python
333 lines
12 KiB
Python
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"""
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Convenience interface to N-D interpolation
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.. versionadded:: 0.9
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"""
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import numpy as np
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from .interpnd import LinearNDInterpolator, NDInterpolatorBase, \
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CloughTocher2DInterpolator, _ndim_coords_from_arrays
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from scipy.spatial import cKDTree
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__all__ = ['griddata', 'NearestNDInterpolator', 'LinearNDInterpolator',
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'CloughTocher2DInterpolator']
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#------------------------------------------------------------------------------
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# Nearest-neighbor interpolation
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#------------------------------------------------------------------------------
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class NearestNDInterpolator(NDInterpolatorBase):
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"""NearestNDInterpolator(x, y).
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Nearest-neighbor interpolator in N > 1 dimensions.
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.. versionadded:: 0.9
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Methods
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-------
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__call__
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Parameters
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----------
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x : (npoints, ndims) 2-D ndarray of floats
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Data point coordinates.
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y : (npoints, ) 1-D ndarray of float or complex
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Data values.
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rescale : boolean, optional
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Rescale points to unit cube before performing interpolation.
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This is useful if some of the input dimensions have
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incommensurable units and differ by many orders of magnitude.
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.. versionadded:: 0.14.0
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tree_options : dict, optional
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Options passed to the underlying ``cKDTree``.
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.. versionadded:: 0.17.0
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See Also
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--------
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griddata :
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Interpolate unstructured D-D data.
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LinearNDInterpolator :
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Piecewise linear interpolator in N dimensions.
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CloughTocher2DInterpolator :
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Piecewise cubic, C1 smooth, curvature-minimizing interpolator in 2D.
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interpn : Interpolation on a regular grid or rectilinear grid.
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RegularGridInterpolator : Interpolator on a regular or rectilinear grid
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in arbitrary dimensions (`interpn` wraps this
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class).
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Notes
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-----
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Uses ``scipy.spatial.cKDTree``
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.. note:: For data on a regular grid use `interpn` instead.
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Examples
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--------
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We can interpolate values on a 2D plane:
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>>> from scipy.interpolate import NearestNDInterpolator
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>>> import numpy as np
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>>> import matplotlib.pyplot as plt
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>>> rng = np.random.default_rng()
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>>> x = rng.random(10) - 0.5
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>>> y = rng.random(10) - 0.5
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>>> z = np.hypot(x, y)
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>>> X = np.linspace(min(x), max(x))
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>>> Y = np.linspace(min(y), max(y))
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>>> X, Y = np.meshgrid(X, Y) # 2D grid for interpolation
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>>> interp = NearestNDInterpolator(list(zip(x, y)), z)
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>>> Z = interp(X, Y)
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>>> plt.pcolormesh(X, Y, Z, shading='auto')
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>>> plt.plot(x, y, "ok", label="input point")
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>>> plt.legend()
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>>> plt.colorbar()
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>>> plt.axis("equal")
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>>> plt.show()
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"""
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def __init__(self, x, y, rescale=False, tree_options=None):
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NDInterpolatorBase.__init__(self, x, y, rescale=rescale,
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need_contiguous=False,
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need_values=False)
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if tree_options is None:
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tree_options = dict()
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self.tree = cKDTree(self.points, **tree_options)
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self.values = np.asarray(y)
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def __call__(self, *args, **query_options):
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"""
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Evaluate interpolator at given points.
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Parameters
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----------
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x1, x2, ... xn : array-like of float
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Points where to interpolate data at.
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x1, x2, ... xn can be array-like of float with broadcastable shape.
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or x1 can be array-like of float with shape ``(..., ndim)``
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**query_options
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This allows ``eps``, ``p``, ``distance_upper_bound``, and ``workers``
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being passed to the cKDTree's query function to be explicitly set.
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See `scipy.spatial.cKDTree.query` for an overview of the different options.
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.. versionadded:: 1.12.0
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"""
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# For the sake of enabling subclassing, NDInterpolatorBase._set_xi performs
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# some operations which are not required by NearestNDInterpolator.__call__,
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# hence here we operate on xi directly, without calling a parent class function.
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xi = _ndim_coords_from_arrays(args, ndim=self.points.shape[1])
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xi = self._check_call_shape(xi)
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xi = self._scale_x(xi)
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# We need to handle two important cases:
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# (1) the case where xi has trailing dimensions (..., ndim), and
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# (2) the case where y has trailing dimensions
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# We will first flatten xi to deal with case (1),
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# do the computation in flattened array while retaining y's dimensionality,
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# and then reshape the interpolated values back to match xi's shape.
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# Flatten xi for the query
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xi_flat = xi.reshape(-1, xi.shape[-1])
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original_shape = xi.shape
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flattened_shape = xi_flat.shape
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# if distance_upper_bound is set to not be infinite,
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# then we need to consider the case where cKDtree
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# does not find any points within distance_upper_bound to return.
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# It marks those points as having infinte distance, which is what will be used
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# below to mask the array and return only the points that were deemed
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# to have a close enough neighbor to return something useful.
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dist, i = self.tree.query(xi_flat, **query_options)
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valid_mask = np.isfinite(dist)
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# create a holder interp_values array and fill with nans.
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if self.values.ndim > 1:
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interp_shape = flattened_shape[:-1] + self.values.shape[1:]
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else:
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interp_shape = flattened_shape[:-1]
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if np.issubdtype(self.values.dtype, np.complexfloating):
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interp_values = np.full(interp_shape, np.nan, dtype=self.values.dtype)
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else:
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interp_values = np.full(interp_shape, np.nan)
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interp_values[valid_mask] = self.values[i[valid_mask], ...]
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if self.values.ndim > 1:
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new_shape = original_shape[:-1] + self.values.shape[1:]
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else:
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new_shape = original_shape[:-1]
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interp_values = interp_values.reshape(new_shape)
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return interp_values
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#------------------------------------------------------------------------------
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# Convenience interface function
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#------------------------------------------------------------------------------
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def griddata(points, values, xi, method='linear', fill_value=np.nan,
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rescale=False):
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"""
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Interpolate unstructured D-D data.
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Parameters
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----------
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points : 2-D ndarray of floats with shape (n, D), or length D tuple of 1-D ndarrays with shape (n,).
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Data point coordinates.
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values : ndarray of float or complex, shape (n,)
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Data values.
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xi : 2-D ndarray of floats with shape (m, D), or length D tuple of ndarrays broadcastable to the same shape.
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Points at which to interpolate data.
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method : {'linear', 'nearest', 'cubic'}, optional
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Method of interpolation. One of
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``nearest``
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return the value at the data point closest to
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the point of interpolation. See `NearestNDInterpolator` for
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more details.
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``linear``
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tessellate the input point set to N-D
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simplices, and interpolate linearly on each simplex. See
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`LinearNDInterpolator` for more details.
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``cubic`` (1-D)
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return the value determined from a cubic
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spline.
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``cubic`` (2-D)
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return the value determined from a
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piecewise cubic, continuously differentiable (C1), and
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approximately curvature-minimizing polynomial surface. See
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`CloughTocher2DInterpolator` for more details.
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fill_value : float, optional
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Value used to fill in for requested points outside of the
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convex hull of the input points. If not provided, then the
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default is ``nan``. This option has no effect for the
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'nearest' method.
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rescale : bool, optional
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Rescale points to unit cube before performing interpolation.
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This is useful if some of the input dimensions have
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incommensurable units and differ by many orders of magnitude.
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.. versionadded:: 0.14.0
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Returns
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-------
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ndarray
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Array of interpolated values.
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See Also
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--------
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LinearNDInterpolator :
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Piecewise linear interpolator in N dimensions.
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NearestNDInterpolator :
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Nearest-neighbor interpolator in N dimensions.
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CloughTocher2DInterpolator :
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Piecewise cubic, C1 smooth, curvature-minimizing interpolator in 2D.
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interpn : Interpolation on a regular grid or rectilinear grid.
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RegularGridInterpolator : Interpolator on a regular or rectilinear grid
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in arbitrary dimensions (`interpn` wraps this
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class).
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Notes
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-----
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.. versionadded:: 0.9
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.. note:: For data on a regular grid use `interpn` instead.
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Examples
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--------
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Suppose we want to interpolate the 2-D function
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>>> import numpy as np
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>>> def func(x, y):
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... return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2
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on a grid in [0, 1]x[0, 1]
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>>> grid_x, grid_y = np.mgrid[0:1:100j, 0:1:200j]
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but we only know its values at 1000 data points:
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>>> rng = np.random.default_rng()
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>>> points = rng.random((1000, 2))
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>>> values = func(points[:,0], points[:,1])
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This can be done with `griddata` -- below we try out all of the
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interpolation methods:
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>>> from scipy.interpolate import griddata
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>>> grid_z0 = griddata(points, values, (grid_x, grid_y), method='nearest')
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>>> grid_z1 = griddata(points, values, (grid_x, grid_y), method='linear')
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>>> grid_z2 = griddata(points, values, (grid_x, grid_y), method='cubic')
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One can see that the exact result is reproduced by all of the
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methods to some degree, but for this smooth function the piecewise
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cubic interpolant gives the best results:
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>>> import matplotlib.pyplot as plt
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>>> plt.subplot(221)
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>>> plt.imshow(func(grid_x, grid_y).T, extent=(0,1,0,1), origin='lower')
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>>> plt.plot(points[:,0], points[:,1], 'k.', ms=1)
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>>> plt.title('Original')
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>>> plt.subplot(222)
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>>> plt.imshow(grid_z0.T, extent=(0,1,0,1), origin='lower')
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>>> plt.title('Nearest')
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>>> plt.subplot(223)
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>>> plt.imshow(grid_z1.T, extent=(0,1,0,1), origin='lower')
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>>> plt.title('Linear')
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>>> plt.subplot(224)
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>>> plt.imshow(grid_z2.T, extent=(0,1,0,1), origin='lower')
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>>> plt.title('Cubic')
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>>> plt.gcf().set_size_inches(6, 6)
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>>> plt.show()
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""" # numpy/numpydoc#87 # noqa: E501
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points = _ndim_coords_from_arrays(points)
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if points.ndim < 2:
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ndim = points.ndim
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else:
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ndim = points.shape[-1]
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if ndim == 1 and method in ('nearest', 'linear', 'cubic'):
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from ._interpolate import interp1d
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points = points.ravel()
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if isinstance(xi, tuple):
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if len(xi) != 1:
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raise ValueError("invalid number of dimensions in xi")
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xi, = xi
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# Sort points/values together, necessary as input for interp1d
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idx = np.argsort(points)
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points = points[idx]
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values = values[idx]
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if method == 'nearest':
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fill_value = 'extrapolate'
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ip = interp1d(points, values, kind=method, axis=0, bounds_error=False,
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fill_value=fill_value)
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return ip(xi)
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elif method == 'nearest':
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ip = NearestNDInterpolator(points, values, rescale=rescale)
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return ip(xi)
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elif method == 'linear':
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ip = LinearNDInterpolator(points, values, fill_value=fill_value,
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rescale=rescale)
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return ip(xi)
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elif method == 'cubic' and ndim == 2:
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ip = CloughTocher2DInterpolator(points, values, fill_value=fill_value,
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rescale=rescale)
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return ip(xi)
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else:
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raise ValueError("Unknown interpolation method %r for "
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"%d dimensional data" % (method, ndim))
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