问题：

假设我有一个2D阵列,我想从中随机采样(使用蒙特卡洛)较小的2D子阵列,如下图中的黑色小块所示.我正在寻找一种有效的方法.

预期(但部分)的解决方案：

我遇到了一个function,在经过几个小时的搜索后,它部分实现了我要尝试的功能,但是它缺乏在随机位置采样补丁的功能.至少我不认为它可以基于其参数从随机位置进行采样,尽管它确实具有一个我不理解的random_state参数.

sklearn.feature_extraction.image.extract_patches_2d(image, patch_size, max_patches=None, random_state=None)

题：

选择随机面片坐标(2D子阵列),然后使用它们从较大的阵列中切出面片,如上图所示.允许随机采样的色块重叠.

解决方法:

这是一个采样器,可以从任何尺寸的数组中创建一个样本.它使用功能来控制从何处开始切割以及沿任何轴的切割宽度.

这是参数的说明：

> arr-输入numpy数组.
> loc_sampler_fn-这是您要用来设置框角的函数.如果要从轴上的任何位置均匀采样框的角,请使用np.random.uniform.如果您希望拐角更靠近数组的中心,请使用np.random.normal.但是,我们需要告诉函数要采样的范围.这将我们带入下一个参数.
> loc_dim_param-这会将每个轴的大小传递给loc_sampler_fn.如果我们将np.random.uniform用于位置采样器,则希望从轴的整个范围进行采样. np.random.uniform具有两个参数：低和高,因此,通过将轴的长度传递到高,可以在整个轴上均匀采样.换句话说,如果轴的长度为120,我们需要np.random.uniform(low = 0,high = 120),因此我们将loc_dim_param =’high’设置为1.
> loc_params-这会将任何其他参数传递给loc_sampler_fn.与该示例保持一致,我们需要将low = 0传递给np.random.uniform,因此需要传递字典loc_params = {‘low’：0}.

从这里开始,盒子的形状基本上是相同的.如果要从3到10均匀采样框的高度和宽度,请传入shape_sampler_fn = np.random.uniform,其中shape_dim_param = None,因为我们没有将轴的大小用于任何东西,并且shape_params = {‘low ‘：3,’high’：11}.

def box_sampler(arr, 
                loc_sampler_fn, 
                loc_dim_param, 
                loc_params, 
                shape_sampler_fn, 
                shape_dim_param,
                shape_params):
    '''
    Extracts a sample cut from `arr`.

    Parameters:
    -----------
    loc_sampler_fn : function
        The function to determine the where the minimum coordinate
        for each axis should be placed.
    loc_dim_param : string or None
        The parameter in `loc_sampler_fn` that should use the axes
        dimension size
    loc_params : dict
        Parameters to pass to `loc_sampler_fn`.
    shape_sampler_fn : function
        The function to determine the width of the sample cut 
        along each axis.
    shape_dim_param : string or None
        The parameter in `shape_sampler_fn` that should use the
        axes dimension size.
    shape_params : dict
        Parameters to pass to `shape_sampler_fn`.

    Returns:
    --------
    (slices, x) : A tuple of the slices used to cut the sample as well as
    the sampled subsection with the same dimensionality of arr.
        slice :: list of slice objects
        x :: array object with the same ndims as arr
    '''
    slices = []
    for dim in arr.shape:
        if loc_dim_param:
            loc_params.update({loc_dim_param: dim})
        if shape_dim_param:
            shape_params.update({shape_dim_param: dim})
        start = int(loc_sampler_fn(**loc_params))
        stop = start + int(shape_sampler_fn(**shape_params))
        slices.append(slice(start, stop))
    return slices, arr[slices]

在宽度在3到9之间的2D阵列上均匀切割的示例：

a = np.random.randint(0, 1+1, size=(100,150))
box_sampler(a, 
            np.random.uniform, 'high', {'low':0}, 
            np.random.uniform, None, {'low':3, 'high':10})
# returns:
([slice(49, 55, None), slice(86, 89, None)], 
 array([[0, 0, 1],
        [0, 1, 1],
        [0, 0, 0],
        [0, 0, 1],
        [1, 1, 1],
        [1, 1, 0]]))

从10x20x30 3D数组中提取2x2x2块的示例：

a = np.random.randint(0,2,size=(10,20,30))
box_sampler(a, np.random.uniform, 'high', {'low':0}, 
               np.random.uniform, None, {'low':2, 'high':2})
# returns:
([slice(7, 9, None), slice(9, 11, None), slice(19, 21, None)], 
 array([[[0, 1],
         [1, 0]],
        [[0, 1],
         [1, 1]]]))

根据评论进行更新.

对于您的特定目的,您似乎想要一个矩形样本,该样本的起始角是从数组中的任何位置均匀采样的,并且沿每个轴的样本宽度是均匀采样的,但是可以限制.

这是一个生成这些样本的函数. min_width和max_width可以接受整数(例如元组)或单个整数的可迭代值.

def uniform_box_sampler(arr, min_width, max_width):
    '''
    Extracts a sample cut from `arr`.

    Parameters:
    -----------
    arr : array
        The numpy array to sample a box from
    min_width : int or tuple
        The minimum width of the box along a given axis.
        If a tuple of integers is supplied, it my have the
        same length as the number of dimensions of `arr`
    max_width : int or tuple
        The maximum width of the box along a given axis.
        If a tuple of integers is supplied, it my have the
        same length as the number of dimensions of `arr`

    Returns:
    --------
    (slices, x) : A tuple of the slices used to cut the sample as well as
    the sampled subsection with the same dimensionality of arr.
        slice :: list of slice objects
        x :: array object with the same ndims as arr
    '''
    if isinstance(min_width, (tuple, list)):
        assert len(min_width)==arr.ndim, 'Dimensions of `min_width` and `arr` must match'
    else:
        min_width = (min_width,)*arr.ndim
    if isinstance(max_width, (tuple, list)):
        assert len(max_width)==arr.ndim, 'Dimensions of `max_width` and `arr` must match'
    else:
        max_width = (max_width,)*arr.ndim

    slices = []
    for dim, mn, mx in zip(arr.shape, min_width, max_width):
        fn = np.random.uniform
        start = int(np.random.uniform(0,dim))
        stop = start + int(np.random.uniform(mn, mx+1))
        slices.append(slice(start, stop))
    return slices, arr[slices]

生成从数组中的任意位置均匀开始的箱形切割的示例,高度为1到4的随机均匀绘制,宽度为2到6的随机均匀绘制(仅显示).在这种情况下,框的大小从第66行和第19列开始为3×4.

x = np.random.randint(0,2,size=(100,100))
uniform_box_sampler(x, (1,2), (4,6))
# returns:
([slice(65, 68, None), slice(18, 22, None)], 
 array([[1, 0, 0, 0],
        [0, 0, 1, 1],
        [0, 1, 1, 0]]))