pytorch中histc（）函数与numpy中histogram（）及
histogram。。。
引⾔
  直⽅图是⼀种对数据分布的描述，在图像处理中，直⽅图概念⾮常重要，应⽤⼴泛，如图像对⽐度增强（直⽅图均衡化），图像信息量度量（信息熵），图像配准（利⽤两张图像的互信息度量相似度）等。
1、numpy中histogram()函数⽤于统计⼀个数据的分布
numpy.histogram(a, bins=10, range=None, normed=None, weights=None, density=None)
Compute the histogram of a set of data.
Parameters:  a : array_like
Input data. The histogram is computed over the flattened array.
bins : int or sequence of scalars or str, optional
If bins is an int, it defines the number of equal-width bins in the given range (10, by default). If bins is a sequence, it
defines a monotonically increasing array of bin edges, including the rightmost edge, allowing for non-uniform bin
widths.
New in version 1.11.0.
If bins is a string, it defines the method used to calculate the optimal bin width, as defined by .
range : (float, float), optional
The lower and upper range of the bins. If not provided, range is simply (a.min(), a.max()). Values outside the range are
ignored. The first element of the range must be less than or equal to the second. range affects the automatic bin
computation as well. While bin width is computed to be optimal based on the actual data within range, the bin count
will fill the entire range including portions containing no data.
normed : bool, optional
Deprecated since version 1.6.0.
This is equivalent to the density argument, but produces incorrect results for unequal bin widths. It should not be used.
Changed in version 1.15.0: DeprecationWarnings are actually emitted.
weights : array_like, optional
An array of weights, of the same shape as a. Each value in a only contributes its associated weight towards the bin
count (instead of 1). If density is True, the weights are normalized, so that the integral of the density over the range
remains 1.
density : bool, optional
If False, the result will contain the number of samples in each bin. If True, the result is the value of the
probability density function at the bin, normalized such that the integral over the range is 1. Note that the sum of the
histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability mass function.
Overrides the normed keyword if given.
Returns:hist : array
The values of the histogram. See density and weights for a description of the possible semantics.
bin_edges : array of dtype float
Return the bin edges (length(hist)+1).
Notes
All but the last (righthand-most) bin is half-open. In other words, if bins is:
[1, 2, 3, 4]
then the first bin is [1, 2) (including 1, but excluding 2) and the second [2, 3). The last bin, however, is [3, 4], which includes 4.（是左闭右开的）
注意：函数将输⼊数据视为⼀个整体进⾏直⽅图计算，输⼊是⼀个flattened aray（输⼊是个多维的也可以），返回直⽅图（array形式）及bin（array）
2、numpy中histogram2d()函数⽤于统计两个数据的联合分布（可⽤于计算互信息）numpy.histogram2d(x, y, bins=10, range=None, normed=None, weights=None, density=None)
Compute the bi-dimensional histogram of two data samples.
Parameters:x : array_like, shape (N,)
An array containing the x coordinates of the points to be histogrammed.
y : array_like, shape (N,)
An array containing the y coordinates of the points to be histogrammed.numpy库统计函数
bins : int or array_like or [int, int] or [array, array], optional
The bin specification:
If int, the number of bins for the two dimensions (nx=ny=bins).
If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins).
If [int, int], the number of bins in each dimension (nx, ny = bins).
If [array, array], the bin edges in each dimension (x_edges, y_edges = bins).
A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges.
range : array_like, shape(2,2), optional
The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in
the bins parameters): [[xmin, xmax], [ymin, ymax]]. All values outside of this range will be considered outliers and not
tallied in the histogram.
density : bool, optional
If False, the default, returns the number of samples in each bin. If True, returns the probability density function at the
bin, bin_count / sample_count / bin_area.
normed : bool, optional
An alias for the density argument that behaves identically. To avoid confusion with the broken normed argument
to , density should be preferred.
weights : array_like, shape(N,), optional
An array of values w_i weighing each sample (x_i, y_i). Weights are normalized to 1 if normed is True. If normed is
False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into
each bin.
Returns:H : ndarray, shape(nx, ny)
The bi-dimensional histogram of samples x and y. Values in x are histogrammed along the first dimension and values
in y are histogrammed along the second dimension.
xedges : ndarray, shape(nx+1,)
The bin edges along the first dimension.
yedges : ndarray, shape(ny+1,)
The bin edges along the second dimension.
3、pytorch中计算张量直⽅图的函数：torch.histc()
注意：返回的直⽅图是基于整个输⼊的Tensor来说的，min和max如果默认都为0，则为Tensor的最⼩值和最⼤值。返回的直⽅图没有归⼀化，每个bin的值统计的是个数。
4、局限性
  numpy.histgoram()和torch.histc()都⽆法针对某⼀维度进⾏直⽅图计算。
5、可视化直⽅图：利⽤matplotlib.pyplot中的hist（）函数1import numpy as np
2import matplotlib.pyplot as plt
3
4 test = np.random.randn(1000000)
5 plt.hist(test, bins='auto', density=True)
6 plt.show()
结果：

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