对于2d数组，要确定最近元素的i, j位置:

import numpy as np
def find_nearest(a, a0):
    idx = (np.abs(a - a0)).argmin()
    w = a.shape[1]
    i = idx // w
    j = idx - i * w
    return a[i,j], i, j

这是unutbu答案的矢量化版本:

def find_nearest(array, values):
    array = np.asarray(array)

    # the last dim must be 1 to broadcast in (array - values) below.
    values = np.expand_dims(values, axis=-1) 

    indices = np.abs(array - values).argmin(axis=-1)

    return array[indices]


image = plt.imread('example_3_band_image.jpg')

print(image.shape) # should be (nrows, ncols, 3)

quantiles = np.linspace(0, 255, num=2 ** 2, dtype=np.uint8)

quantiled_image = find_nearest(quantiles, image)

print(quantiled_image.shape) # should be (nrows, ncols, 3)

如果你的数组已经排序并且非常大，这是一个更快的解决方案:

def find_nearest(array,value):
    idx = np.searchsorted(array, value, side="left")
    if idx > 0 and (idx == len(array) or math.fabs(value - array[idx-1]) < math.fabs(value - array[idx])):
        return array[idx-1]
    else:
        return array[idx]

这可以扩展到非常大的阵列。如果不能假定数组已经排序，可以很容易地修改上面的内容以在方法中排序。对于小型数组来说，这是多余的，但一旦它们变大，这就快得多了。

下面是一个使用2D数组的版本，如果用户拥有scipy的cdist函数，则使用它，如果用户没有，则使用更简单的距离计算。

默认情况下，输出是最接近输入值的索引，但您可以使用output关键字将其更改为'index'， 'value'或'both'之一，其中'value'输出数组[index]， 'both'输出索引，数组[index]。

对于非常大的数组，您可能需要使用kind='euclidean'，因为默认的scipy cdist函数可能会耗尽内存。

这可能不是绝对最快的解决方案，但已经很接近了。

def find_nearest_2d(array, value, kind='cdist', output='index'):
    # 'array' must be a 2D array
    # 'value' must be a 1D array with 2 elements
    # 'kind' defines what method to use to calculate the distances. Can choose one
    #    of 'cdist' (default) or 'euclidean'. Choose 'euclidean' for very large
    #    arrays. Otherwise, cdist is much faster.
    # 'output' defines what the output should be. Can be 'index' (default) to return
    #    the index of the array that is closest to the value, 'value' to return the
    #    value that is closest, or 'both' to return index,value
    import numpy as np
    if kind == 'cdist':
        try: from scipy.spatial.distance import cdist
        except ImportError:
            print("Warning (find_nearest_2d): Could not import cdist. Reverting to simpler distance calculation")
            kind = 'euclidean'
    index = np.where(array == value)[0] # Make sure the value isn't in the array
    if index.size == 0:
        if kind == 'cdist': index = np.argmin(cdist([value],array)[0])
        elif kind == 'euclidean': index = np.argmin(np.sum((np.array(array)-np.array(value))**2.,axis=1))
        else: raise ValueError("Keyword 'kind' must be one of 'cdist' or 'euclidean'")
    if output == 'index': return index
    elif output == 'value': return array[index]
    elif output == 'both': return index,array[index]
    else: raise ValueError("Keyword 'output' must be one of 'index', 'value', or 'both'")

稍微修改一下，上面的答案适用于任意维度的数组(1d, 2d, 3d，…):

def find_nearest(a, a0):
    "Element in nd array `a` closest to the scalar value `a0`"
    idx = np.abs(a - a0).argmin()
    return a.flat[idx]

或者，写成一行:

a.flat[np.abs(a - a0).argmin()]

这个函数使用numpy searchsorted处理任意数量的查询，因此在对输入数组进行排序之后，它的速度也一样快。 它可以在2d, 3d的规则网格上工作…:

#!/usr/bin/env python3
# keywords: nearest-neighbor regular-grid python numpy searchsorted Voronoi

import numpy as np

#...............................................................................
class Near_rgrid( object ):
    """ nearest neighbors on a Manhattan aka regular grid
    1d:
    near = Near_rgrid( x: sorted 1d array )
    nearix = near.query( q: 1d ) -> indices of the points x_i nearest each q_i
        x[nearix[0]] is the nearest to q[0]
        x[nearix[1]] is the nearest to q[1] ...
        nearpoints = x[nearix] is near q
    If A is an array of e.g. colors at x[0] x[1] ...,
    A[nearix] are the values near q[0] q[1] ...
    Query points < x[0] snap to x[0], similarly > x[-1].

    2d: on a Manhattan aka regular grid,
        streets running east-west at y_i, avenues north-south at x_j,
    near = Near_rgrid( y, x: sorted 1d arrays, e.g. latitide longitude )
    I, J = near.query( q: nq × 2 array, columns qy qx )
    -> nq × 2 indices of the gridpoints y_i x_j nearest each query point
        gridpoints = np.column_stack(( y[I], x[J] ))  # e.g. street corners
        diff = gridpoints - querypoints
        distances = norm( diff, axis=1, ord= )
    Values at an array A definded at the gridpoints y_i x_j nearest q: A[I,J]

    3d: Near_rgrid( z, y, x: 1d axis arrays ) .query( q: nq × 3 array )

    See Howitworks below, and the plot Voronoi-random-regular-grid.
    """

    def __init__( self, *axes: "1d arrays" ):
        axarrays = []
        for ax in axes:
            axarray = np.asarray( ax ).squeeze()
            assert axarray.ndim == 1, "each axis should be 1d, not %s " % (
                    str( axarray.shape ))
            axarrays += [axarray]
        self.midpoints = [_midpoints( ax ) for ax in axarrays]
        self.axes = axarrays
        self.ndim = len(axes)

    def query( self, queries: "nq × dim points" ) -> "nq × dim indices":
        """ -> the indices of the nearest points in the grid """
        queries = np.asarray( queries ).squeeze()  # or list x y z ?
        if self.ndim == 1:
            assert queries.ndim <= 1, queries.shape
            return np.searchsorted( self.midpoints[0], queries )  # scalar, 0d ?
        queries = np.atleast_2d( queries )
        assert queries.shape[1] == self.ndim, [
                queries.shape, self.ndim]
        return [np.searchsorted( mid, q )  # parallel: k axes, k processors
                for mid, q in zip( self.midpoints, queries.T )]

    def snaptogrid( self, queries: "nq × dim points" ):
        """ -> the nearest points in the grid, 2d [[y_j x_i] ...] """
        ix = self.query( queries )
        if self.ndim == 1:
            return self.axes[0][ix]
        else:
            axix = [ax[j] for ax, j in zip( self.axes, ix )]
            return np.array( axix )


def _midpoints( points: "array-like 1d, *must be sorted*" ) -> "1d":
    points = np.asarray( points ).squeeze()
    assert points.ndim == 1, points.shape
    diffs = np.diff( points )
    assert np.nanmin( diffs ) > 0, "the input array must be sorted, not %s " % (
            points.round( 2 ))
    return (points[:-1] + points[1:]) / 2  # floats

#...............................................................................
Howitworks = \
"""
How Near_rgrid works in 1d:
Consider the midpoints halfway between fenceposts | | |
The interval [left midpoint .. | .. right midpoint] is what's nearest each post --

    |   |       |                     |   points
    | . |   .   |          .          |   midpoints
      ^^^^^^               .            nearest points[1]
            ^^^^^^^^^^^^^^^             nearest points[2]  etc.

2d:
    I, J = Near_rgrid( y, x ).query( q )
    I = nearest in `x`
    J = nearest in `y` independently / in parallel.
    The points nearest [yi xj] in a regular grid (its Voronoi cell)
    form a rectangle [left mid x .. right mid x] × [left mid y .. right mid y]
    (in any norm ?)
    See the plot Voronoi-random-regular-grid.

Notes
-----
If a query point is exactly halfway between two data points,
e.g. on a grid of ints, the lines (x + 1/2) U (y + 1/2),
which "nearest" you get is implementation-dependent, unpredictable.

"""

Murky = \
""" NaNs in points, in queries ?
"""

__version__ = "2021-10-25 oct  denis-bz-py"