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	__all__ = ['RegularGridInterpolator', 'interpn']

	import itertools

	import numpy as np

	import scipy.sparse.linalg as ssl

	from ._interpnd import _ndim_coords_from_arrays
	from ._cubic import PchipInterpolator
	from ._rgi_cython import evaluate_linear_2d, find_indices
	from ._bsplines import make_interp_spline
	from ._fitpack2 import RectBivariateSpline
	from ._ndbspline import make_ndbspl


	def _check_points(points):
	descending_dimensions = []
	grid = []
	for i, p in enumerate(points):
	# early make points float
	# see https://github.com/scipy/scipy/pull/17230
	p = np.asarray(p, dtype=float)
	if not np.all(p[1:] > p[:-1]):
	if np.all(p[1:] < p[:-1]):
	# input is descending, so make it ascending
	descending_dimensions.append(i)
	p = np.flip(p)
	else:
	raise ValueError(
	"The points in dimension %d must be strictly "
	"ascending or descending" % i)
	# see https://github.com/scipy/scipy/issues/17716
	p = np.ascontiguousarray(p)
	grid.append(p)
	return tuple(grid), tuple(descending_dimensions)


	def _check_dimensionality(points, values):
	if len(points) > values.ndim:
	raise ValueError("There are %d point arrays, but values has %d "
	"dimensions" % (len(points), values.ndim))
	for i, p in enumerate(points):
	if not np.asarray(p).ndim == 1:
	raise ValueError("The points in dimension %d must be "
	"1-dimensional" % i)
	if not values.shape[i] == len(p):
	raise ValueError("There are %d points and %d values in "
	"dimension %d" % (len(p), values.shape[i], i))


	class RegularGridInterpolator:
	"""
	Interpolator on a regular or rectilinear grid in arbitrary dimensions.

	The data must be defined on a rectilinear grid; that is, a rectangular
	grid with even or uneven spacing. Linear, nearest-neighbor, spline
	interpolations are supported. After setting up the interpolator object,
	the interpolation method may be chosen at each evaluation.

	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.

	method : str, optional
	The method of interpolation to perform. Supported are "linear",
	"nearest", "slinear", "cubic", "quintic" and "pchip". This
	parameter will become the default for the object's ``__call__``
	method. Default is "linear".

	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.
	Default is True.

	fill_value : float or None, optional
	The value to use for points outside of the interpolation domain.
	If None, values outside the domain are extrapolated.
	Default is ``np.nan``.

	solver : callable, optional
	Only used for methods "slinear", "cubic" and "quintic".
	Sparse linear algebra solver for construction of the NdBSpline instance.
	Default is the iterative solver `scipy.sparse.linalg.gcrotmk`.

	.. versionadded:: 1.13

	solver_args: dict, optional
	Additional arguments to pass to `solver`, if any.

	.. versionadded:: 1.13

	Methods
	-------
	__call__

	Attributes
	----------
	grid : tuple of ndarrays
	The points defining the regular grid in n dimensions.
	This tuple defines the full grid via
	``np.meshgrid(*grid, indexing='ij')``
	values : ndarray
	Data values at the grid.
	method : str
	Interpolation method.
	fill_value : float or ``None``
	Use this value for out-of-bounds arguments to `__call__`.
	bounds_error : bool
	If ``True``, out-of-bounds argument raise a ``ValueError``.

	Notes
	-----
	Contrary to `LinearNDInterpolator` and `NearestNDInterpolator`, this class
	avoids expensive triangulation of the input data by taking advantage of the
	regular grid structure.

	In other words, this class assumes that the data is defined on a
	rectilinear grid.

	.. versionadded:: 0.14

	The 'slinear'(k=1), 'cubic'(k=3), and 'quintic'(k=5) methods are
	tensor-product spline interpolators, where `k` is the spline degree,
	If any dimension has fewer points than `k` + 1, an error will be raised.

	.. versionadded:: 1.9

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

	Choosing a solver for spline methods

	Spline methods, "slinear", "cubic" and "quintic" involve solving a
	large sparse linear system at instantiation time. Depending on data,
	the default solver may or may not be adequate. When it is not, you may
	need to experiment with an optional `solver` argument, where you may
	choose between the direct solver (`scipy.sparse.linalg.spsolve`) or
	iterative solvers from `scipy.sparse.linalg`. You may need to supply
	additional parameters via the optional `solver_args` parameter (for instance,
	you may supply the starting value or target tolerance). See the
	`scipy.sparse.linalg` documentation for the full list of available options.

	Alternatively, you may instead use the legacy methods, "slinear_legacy",
	"cubic_legacy" and "quintic_legacy". These methods allow faster construction
	but evaluations will be much slower.

	Examples
	--------
	Evaluate a function on the points of a 3-D grid

	As a first example, we evaluate a simple example function on the points of
	a 3-D grid:

	>>> from scipy.interpolate import RegularGridInterpolator
	>>> import numpy as np
	>>> def f(x, y, z):
	... return 2 * x*3 + 3 y**2 - z
	>>> x = np.linspace(1, 4, 11)
	>>> y = np.linspace(4, 7, 22)
	>>> z = np.linspace(7, 9, 33)
	>>> xg, yg ,zg = np.meshgrid(x, y, z, indexing='ij', sparse=True)
	>>> data = f(xg, yg, zg)

	``data`` is now a 3-D array with ``data[i, j, k] = f(x[i], y[j], z[k])``.
	Next, define an interpolating function from this data:

	>>> interp = RegularGridInterpolator((x, y, z), data)

	Evaluate the interpolating function at the two points
	``(x,y,z) = (2.1, 6.2, 8.3)`` and ``(3.3, 5.2, 7.1)``:

	>>> pts = np.array([[2.1, 6.2, 8.3],
	... [3.3, 5.2, 7.1]])
	>>> interp(pts)
	array([ 125.80469388, 146.30069388])

	which is indeed a close approximation to

	>>> f(2.1, 6.2, 8.3), f(3.3, 5.2, 7.1)
	(125.54200000000002, 145.894)

	Interpolate and extrapolate a 2D dataset

	As a second example, we interpolate and extrapolate a 2D data set:

	>>> x, y = np.array([-2, 0, 4]), np.array([-2, 0, 2, 5])
	>>> def ff(x, y):
	... return x2 + y2

	>>> xg, yg = np.meshgrid(x, y, indexing='ij')
	>>> data = ff(xg, yg)
	>>> interp = RegularGridInterpolator((x, y), data,
	... bounds_error=False, fill_value=None)

	>>> import matplotlib.pyplot as plt
	>>> fig = plt.figure()
	>>> ax = fig.add_subplot(projection='3d')
	>>> ax.scatter(xg.ravel(), yg.ravel(), data.ravel(),
	... s=60, c='k', label='data')

	Evaluate and plot the interpolator on a finer grid

	>>> xx = np.linspace(-4, 9, 31)
	>>> yy = np.linspace(-4, 9, 31)
	>>> X, Y = np.meshgrid(xx, yy, indexing='ij')

	>>> # interpolator
	>>> ax.plot_wireframe(X, Y, interp((X, Y)), rstride=3, cstride=3,
	... alpha=0.4, color='m', label='linear interp')

	>>> # ground truth
	>>> ax.plot_wireframe(X, Y, ff(X, Y), rstride=3, cstride=3,
	... alpha=0.4, label='ground truth')
	>>> plt.legend()
	>>> plt.show()

	Other examples are given
	:ref:`in the tutorial <tutorial-interpolate_regular_grid_interpolator>`.

	See Also
	--------
	NearestNDInterpolator : Nearest neighbor interpolator on unstructured
	data in N dimensions

	LinearNDInterpolator : Piecewise linear interpolator on unstructured data
	in N dimensions

	interpn : a convenience function which wraps `RegularGridInterpolator`

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

	References
	----------
	.. [1] Python package regulargrid by Johannes Buchner, see
	https://pypi.python.org/pypi/regulargrid/
	.. [2] Wikipedia, "Trilinear interpolation",
	https://en.wikipedia.org/wiki/Trilinear_interpolation
	.. [3] Weiser, Alan, and Sergio E. Zarantonello. "A note on piecewise linear
	and multilinear table interpolation in many dimensions." MATH.
	COMPUT. 50.181 (1988): 189-196.
	https://www.ams.org/journals/mcom/1988-50-181/S0025-5718-1988-0917826-0/S0025-5718-1988-0917826-0.pdf
	:doi:`10.1090/S0025-5718-1988-0917826-0`

	"""
	# this class is based on code originally programmed by Johannes Buchner,
	# see https://github.com/JohannesBuchner/regulargrid

	_SPLINE_DEGREE_MAP = {"slinear": 1, "cubic": 3, "quintic": 5, 'pchip': 3,
	"slinear_legacy": 1, "cubic_legacy": 3, "quintic_legacy": 5,}
	_SPLINE_METHODS_recursive = {"slinear_legacy", "cubic_legacy",
	"quintic_legacy", "pchip"}
	_SPLINE_METHODS_ndbspl = {"slinear", "cubic", "quintic"}
	_SPLINE_METHODS = list(_SPLINE_DEGREE_MAP.keys())
	_ALL_METHODS = ["linear", "nearest"] + _SPLINE_METHODS

	def __init__(self, points, values, method="linear", bounds_error=True,
	fill_value=np.nan, *, solver=None, solver_args=None):
	if method not in self._ALL_METHODS:
	raise ValueError(f"Method '{method}' is not defined")
	elif method in self._SPLINE_METHODS:
	self._validate_grid_dimensions(points, method)
	self.method = method
	self._spline = None
	self.bounds_error = bounds_error
	self.grid, self._descending_dimensions = _check_points(points)
	self.values = self._check_values(values)
	self._check_dimensionality(self.grid, self.values)
	self.fill_value = self._check_fill_value(self.values, fill_value)
	if self._descending_dimensions:
	self.values = np.flip(values, axis=self._descending_dimensions)
	if self.method == "pchip" and np.iscomplexobj(self.values):
	msg = ("`PchipInterpolator` only works with real values. If you are trying "
	"to use the real components of the passed array, use `np.real` on "
	"the array before passing to `RegularGridInterpolator`.")
	raise ValueError(msg)
	if method in self._SPLINE_METHODS_ndbspl:
	if solver_args is None:
	solver_args = {}
	self._spline = self._construct_spline(method, solver, **solver_args)
	else:
	if solver is not None or solver_args:
	raise ValueError(
	f"{method =} does not accept the 'solver' argument. Got "
	f" {solver = } and with arguments {solver_args}."
	)

	def _construct_spline(self, method, solver=None, **solver_args):
	if solver is None:
	solver = ssl.gcrotmk
	spl = make_ndbspl(
	self.grid, self.values, self._SPLINE_DEGREE_MAP[method],
	solver=solver, **solver_args
	)
	return spl

	def _check_dimensionality(self, grid, values):
	_check_dimensionality(grid, values)

	def _check_points(self, points):
	return _check_points(points)

	def _check_values(self, values):
	if not hasattr(values, 'ndim'):
	# allow reasonable duck-typed values
	values = np.asarray(values)

	if hasattr(values, 'dtype') and hasattr(values, 'astype'):
	if not np.issubdtype(values.dtype, np.inexact):
	values = values.astype(float)

	return values

	def _check_fill_value(self, values, fill_value):
	if fill_value is not None:
	fill_value_dtype = np.asarray(fill_value).dtype
	if (hasattr(values, 'dtype') and not
	np.can_cast(fill_value_dtype, values.dtype,
	casting='same_kind')):
	raise ValueError("fill_value must be either 'None' or "
	"of a type compatible with values")
	return fill_value

	def __call__(self, xi, method=None, *, nu=None):
	"""
	Interpolation at coordinates.

	Parameters
	----------
	xi : ndarray of shape (..., ndim)
	The coordinates to evaluate the interpolator at.

	method : str, optional
	The method of interpolation to perform. Supported are "linear",
	"nearest", "slinear", "cubic", "quintic" and "pchip". Default is
	the method chosen when the interpolator was created.

	nu : sequence of ints, length ndim, optional
	If not None, the orders of the derivatives to evaluate.
	Each entry must be non-negative.
	Only allowed for methods "slinear", "cubic" and "quintic".

	.. versionadded:: 1.13

	Returns
	-------
	values_x : ndarray, shape xi.shape[:-1] + values.shape[ndim:]
	Interpolated values at `xi`. See notes for behaviour when
	``xi.ndim == 1``.

	Notes
	-----
	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:]``.

	Examples
	--------
	Here we define a nearest-neighbor interpolator of a simple function

	>>> import numpy as np
	>>> x, y = np.array([0, 1, 2]), np.array([1, 3, 7])
	>>> def f(x, y):
	... return x2 + y2
	>>> data = f(*np.meshgrid(x, y, indexing='ij', sparse=True))
	>>> from scipy.interpolate import RegularGridInterpolator
	>>> interp = RegularGridInterpolator((x, y), data, method='nearest')

	By construction, the interpolator uses the nearest-neighbor
	interpolation

	>>> interp([[1.5, 1.3], [0.3, 4.5]])
	array([2., 9.])

	We can however evaluate the linear interpolant by overriding the
	`method` parameter

	>>> interp([[1.5, 1.3], [0.3, 4.5]], method='linear')
	array([ 4.7, 24.3])
	"""
	_spline = self._spline
	method = self.method if method is None else method
	is_method_changed = self.method != method
	if method not in self._ALL_METHODS:
	raise ValueError(f"Method '{method}' is not defined")
	if is_method_changed and method in self._SPLINE_METHODS_ndbspl:
	_spline = self._construct_spline(method)

	if nu is not None and method not in self._SPLINE_METHODS_ndbspl:
	raise ValueError(
	f"Can only compute derivatives for methods "
	f"{self._SPLINE_METHODS_ndbspl}, got {method =}."
	)

	xi, xi_shape, ndim, nans, out_of_bounds = self._prepare_xi(xi)

	if method == "linear":
	indices, norm_distances = self._find_indices(xi.T)
	if (ndim == 2 and hasattr(self.values, 'dtype') and
	self.values.ndim == 2 and self.values.flags.writeable and
	self.values.dtype in (np.float64, np.complex128) and
	self.values.dtype.byteorder == '='):
	# until cython supports const fused types, the fast path
	# cannot support non-writeable values
	# a fast path
	out = np.empty(indices.shape[1], dtype=self.values.dtype)
	result = evaluate_linear_2d(self.values,
	indices,
	norm_distances,
	self.grid,
	out)
	else:
	result = self._evaluate_linear(indices, norm_distances)
	elif method == "nearest":
	indices, norm_distances = self._find_indices(xi.T)
	result = self._evaluate_nearest(indices, norm_distances)
	elif method in self._SPLINE_METHODS:
	if is_method_changed:
	self._validate_grid_dimensions(self.grid, method)
	if method in self._SPLINE_METHODS_recursive:
	result = self._evaluate_spline(xi, method)
	else:
	result = _spline(xi, nu=nu)

	if not self.bounds_error and self.fill_value is not None:
	result[out_of_bounds] = self.fill_value

	# f(nan) = nan, if any
	if np.any(nans):
	result[nans] = np.nan
	return result.reshape(xi_shape[:-1] + self.values.shape[ndim:])

	def _prepare_xi(self, xi):
	ndim = len(self.grid)
	xi = _ndim_coords_from_arrays(xi, ndim=ndim)
	if xi.shape[-1] != len(self.grid):
	raise ValueError("The requested sample points xi have dimension "
	f"{xi.shape[-1]} but this "
	f"RegularGridInterpolator has dimension {ndim}")

	xi_shape = xi.shape
	xi = xi.reshape(-1, xi_shape[-1])
	xi = np.asarray(xi, dtype=float)

	# find nans in input
	nans = np.any(np.isnan(xi), axis=-1)

	if self.bounds_error:
	for i, p in enumerate(xi.T):
	if not np.logical_and(np.all(self.grid[i][0] <= p),
	np.all(p <= self.grid[i][-1])):
	raise ValueError("One of the requested xi is out of bounds "
	"in dimension %d" % i)
	out_of_bounds = None
	else:
	out_of_bounds = self._find_out_of_bounds(xi.T)

	return xi, xi_shape, ndim, nans, out_of_bounds

	def _evaluate_linear(self, indices, norm_distances):
	# slice for broadcasting over trailing dimensions in self.values
	vslice = (slice(None),) + (None,)*(self.values.ndim - len(indices))

	# Compute shifting up front before zipping everything together
	shift_norm_distances = [1 - yi for yi in norm_distances]
	shift_indices = [i + 1 for i in indices]

	# The formula for linear interpolation in 2d takes the form:
	# values = self.values[(i0, i1)] * (1 - y0) * (1 - y1) + \
	# self.values[(i0, i1 + 1)] * (1 - y0) * y1 + \
	# self.values[(i0 + 1, i1)] * y0 * (1 - y1) + \
	# self.values[(i0 + 1, i1 + 1)] * y0 * y1
	# We pair i with 1 - yi (zipped1) and i + 1 with yi (zipped2)
	zipped1 = zip(indices, shift_norm_distances)
	zipped2 = zip(shift_indices, norm_distances)

	# Take all products of zipped1 and zipped2 and iterate over them
	# to get the terms in the above formula. This corresponds to iterating
	# over the vertices of a hypercube.
	hypercube = itertools.product(*zip(zipped1, zipped2))
	value = np.array([0.])
	for h in hypercube:
	edge_indices, weights = zip(*h)
	weight = np.array([1.])
	for w in weights:
	weight = weight * w
	term = np.asarray(self.values[edge_indices]) * weight[vslice]
	value = value + term # cannot use += because broadcasting
	return value

	def _evaluate_nearest(self, indices, norm_distances):
	idx_res = [np.where(yi <= .5, i, i + 1)
	for i, yi in zip(indices, norm_distances)]
	return self.values[tuple(idx_res)]

	def _validate_grid_dimensions(self, points, method):
	k = self._SPLINE_DEGREE_MAP[method]
	for i, point in enumerate(points):
	ndim = len(np.atleast_1d(point))
	if ndim <= k:
	raise ValueError(f"There are {ndim} points in dimension {i},"
	f" but method {method} requires at least "
	f" {k+1} points per dimension.")

	def _evaluate_spline(self, xi, method):
	# ensure xi is 2D list of points to evaluate (`m` is the number of
	# points and `n` is the number of interpolation dimensions,
	# ``n == len(self.grid)``.)
	if xi.ndim == 1:
	xi = xi.reshape((1, xi.size))
	m, n = xi.shape

	# Reorder the axes: n-dimensional process iterates over the
	# interpolation axes from the last axis downwards: E.g. for a 4D grid
	# the order of axes is 3, 2, 1, 0. Each 1D interpolation works along
	# the 0th axis of its argument array (for 1D routine it's its ``y``
	# array). Thus permute the interpolation axes of `values` *and keep
	# trailing dimensions trailing*.
	axes = tuple(range(self.values.ndim))
	axx = axes[:n][::-1] + axes[n:]
	values = self.values.transpose(axx)

	if method == 'pchip':
	_eval_func = self._do_pchip
	else:
	_eval_func = self._do_spline_fit
	k = self._SPLINE_DEGREE_MAP[method]

	# Non-stationary procedure: difficult to vectorize this part entirely
	# into numpy-level operations. Unfortunately this requires explicit
	# looping over each point in xi.

	# can at least vectorize the first pass across all points in the
	# last variable of xi.
	last_dim = n - 1
	first_values = _eval_func(self.grid[last_dim],
	values,
	xi[:, last_dim],
	k)

	# the rest of the dimensions have to be on a per point-in-xi basis
	shape = (m, *self.values.shape[n:])
	result = np.empty(shape, dtype=self.values.dtype)
	for j in range(m):
	# Main process: Apply 1D interpolate in each dimension
	# sequentially, starting with the last dimension.
	# These are then "folded" into the next dimension in-place.
	folded_values = first_values[j, ...]
	for i in range(last_dim-1, -1, -1):
	# Interpolate for each 1D from the last dimensions.
	# This collapses each 1D sequence into a scalar.
	folded_values = _eval_func(self.grid[i],
	folded_values,
	xi[j, i],
	k)
	result[j, ...] = folded_values

	return result

	@staticmethod
	def _do_spline_fit(x, y, pt, k):
	local_interp = make_interp_spline(x, y, k=k, axis=0)
	values = local_interp(pt)
	return values

	@staticmethod
	def _do_pchip(x, y, pt, k):
	local_interp = PchipInterpolator(x, y, axis=0)
	values = local_interp(pt)
	return values

	def _find_indices(self, xi):
	return find_indices(self.grid, xi)

	def _find_out_of_bounds(self, xi):
	# check for out of bounds xi
	out_of_bounds = np.zeros((xi.shape[1]), dtype=bool)
	# iterate through dimensions
	for x, grid in zip(xi, self.grid):
	out_of_bounds += x < grid[0]
	out_of_bounds += x > grid[-1]
	return out_of_bounds


	def interpn(points, values, xi, method="linear", bounds_error=True,
	fill_value=np.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:: 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
	-----

	.. versionadded:: 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]

	"""
	# sanity check 'method' kwarg
	if method not in ["linear", "nearest", "cubic", "quintic", "pchip",
	"splinef2d", "slinear",
	"slinear_legacy", "cubic_legacy", "quintic_legacy"]:
	raise ValueError("interpn only understands the methods 'linear', "
	"'nearest', 'slinear', 'cubic', 'quintic', 'pchip', "
	f"and 'splinef2d'. You provided {method}.")

	if not hasattr(values, 'ndim'):
	values = np.asarray(values)

	ndim = values.ndim
	if ndim > 2 and method == "splinef2d":
	raise ValueError("The method splinef2d can only be used for "
	"2-dimensional input data")
	if not bounds_error and fill_value is None and method == "splinef2d":
	raise ValueError("The method splinef2d does not support extrapolation.")

	# sanity check consistency of input dimensions
	if len(points) > ndim:
	raise ValueError("There are %d point arrays, but values has %d "
	"dimensions" % (len(points), ndim))
	if len(points) != ndim and method == 'splinef2d':
	raise ValueError("The method splinef2d can only be used for "
	"scalar data with one point per coordinate")

	grid, descending_dimensions = _check_points(points)
	_check_dimensionality(grid, values)

	# sanity check requested xi
	xi = _ndim_coords_from_arrays(xi, ndim=len(grid))
	if xi.shape[-1] != len(grid):
	raise ValueError("The requested sample points xi have dimension "
	"%d, but this RegularGridInterpolator has "
	"dimension %d" % (xi.shape[-1], len(grid)))

	if bounds_error:
	for i, p in enumerate(xi.T):
	if not np.logical_and(np.all(grid[i][0] <= p),
	np.all(p <= grid[i][-1])):
	raise ValueError("One of the requested xi is out of bounds "
	"in dimension %d" % i)

	# perform interpolation
	if method in RegularGridInterpolator._ALL_METHODS:
	interp = RegularGridInterpolator(points, values, method=method,
	bounds_error=bounds_error,
	fill_value=fill_value)
	return interp(xi)
	elif method == "splinef2d":
	xi_shape = xi.shape
	xi = xi.reshape(-1, xi.shape[-1])

	# RectBivariateSpline doesn't support fill_value; we need to wrap here
	idx_valid = np.all((grid[0][0] <= xi[:, 0], xi[:, 0] <= grid[0][-1],
	grid[1][0] <= xi[:, 1], xi[:, 1] <= grid[1][-1]),
	axis=0)
	result = np.empty_like(xi[:, 0])

	# make a copy of values for RectBivariateSpline
	interp = RectBivariateSpline(points[0], points[1], values[:])
	result[idx_valid] = interp.ev(xi[idx_valid, 0], xi[idx_valid, 1])
	result[np.logical_not(idx_valid)] = fill_value

	return result.reshape(xi_shape[:-1])
	else:
	raise ValueError(f"unknown {method = }")