[function document] torch Histc and paddle Histogram and numpy.histogram

1. torch.histc

Excerpt from ：
https://pytorch.org/docs/stable/generated/torch.histc.html

torch.histc(input, bins=100, min=0, max=0, *, out=None) → Tensor

be used for Calculate the histogram of tensor
Elements are classified as min and max Between cells of equal width . If min and max all zero , Then use the minimum and maximum values of the data .

Less than min Value and greater than max The element of will be Ignore

---

Parameters

input（Tensor）—— Input tensor .
bins（int）—— Number of histogram boxes 
min（Scalar）—— The lower limit of the range （ Include ）
max（Scalar）—— The upper limit of the range （ Include ）
out（Tensor , Optional ）– Output tensor .

Return value

The histogram is represented by tensor

Return type

Tensor

Example

import torch

input_tensor = torch.tensor([1., 2, 1, 2.5])
res = torch.histc(input_tensor, bins=4, min=0, max=3)
print(res)

tensor([0., 2., 1., 1.])

Example illustration

2. paddle.histogram

and

Excerpt from ：
https://www.paddlepaddle.org.cn/documentation/docs/zh/api/paddle/histogram_cn.html#histogram

paddle.histogram(input, bins=100, min=0, max=0)

Calculate the histogram of the input tensor .
With min and max by range The border , Divide them into bins A straight bar , Then the sorted data is divided into straight bars (bins) in .
If min and max All for 0, The maximum and minimum values in the data are used as the boundary .

Parameters

input (Tensor) -  Input Tensor. Dimension is multidimensional , The data type is int32、int64、float32 or float64.
bins (int) -  Histogram  bins( Straight bar ) The number of , The default is 100.
min (int) - range The lower boundary of ( contain ), The default is 0.
max (int) - range The upper boundary of ( contain ), The default is 0.

return

Tensor, The data is int64 type , Dimension for (nbins,).

Code example

import paddle

inputs = paddle.to_tensor([1, 2, 1])
result = paddle.histogram(inputs, bins=4, min=0, max=3)
print(result) # [0, 2, 1, 0]

3. numpy.histogram

hist, bin_edges = numpy.histogram(a, bins=10, 
                                     range=None, 
                                     normed=None, 
                                     weights=None, 
                                     density=None)

a Is an array of statistics to be

bins Specify the number of statistical intervals perhaps Directly enter the interval

range Is a length of 2 tuples , Represents the minimum and maximum values of the statistical range , The default value is None, The range of representation is determined by the range of data (a.min(), a.max())

weights Each element of the array is assigned a weight ,histogram() It will sum the weights corresponding to the array in the interval
density by True when , Returns the probability density of each interval ; by False Returns the number of elements in each interval
normed Has been abandoned , Should not be used

Just a few examples ：

import numpy as np
hist, bin_edges = np.histogram([1., 2, 1, 2.5], 4, (0, 3))

hist
# Out: array([0, 2, 1, 1], dtype=int64)

bin_edges
# Out: array([0. , 0.75, 1.5 , 2.25, 3. ])

bin_edges yes (0,3) The division of 4 Intervals ,hist Is the number of each interval , And the one above torch.histc and paddle.histogram In the same way

import numpy as np

input_ = np.arange(5)
bins = np.array([0., 0.4, 0.8, 1.9])
hist, bin_edges = np.histogram(input_, bins=bins)

bin_edges
# Out: array([0. , 0.4, 0.8, 1.9])

hist
# Out: array([1, 0, 1], dtype=int64)

Direct will bins This interval is passed into , It can be seen that bin_edges == bins,hist Is the number of corresponding intervals , Elements that exceed the maximum and minimum values are ignored

import numpy as np

input_ = np.random.random(5,) * 5
# Out: array([2.27585698, 0.32795885, 3.16672458, 4.55222666, 3.71125298])

hist, bin_edges = np.histogram(input_, bins=5, range=(0, 6), density=True)
hist
# Out: array([0.16666667 0.16666667 0.16666667 0.33333333 0. ])

hist, bin_edges = np.histogram(input_, bins=5, range=(0, 6), density=False)
hist
# Out: array([1, 1, 1, 2, 0], dtype=int64)

bin_edges
# Out: array([0. , 1.2, 2.4, 3.6, 4.8, 6. ])

It can be seen that density=False when ,hist It's still quantity ,density=True when ,hist Becomes density , After the integral is 1

Finally, take a look at weights How to use parameters ：

import numpy as np

input_ = np.array([2.27585698, 0.32795885, 3.16672458, 4.55222666, 3.71125298])
weight = np.array([1, 1, 2, 2, 3])
hist, bin_edges = np.histogram(input_, bins=5, range=(0, 6), weights=weight)

bin_edges
# Out: array([0. , 1.2, 2.4, 3.6, 4.8, 6. ])

hist
# Out: array([1, 1, 2, 5, 0])

weights The parameter directly cancels that each weight is 1 The situation of , therefore weights Of shape It should be related to the input vector shape identical

There is another example in the official documents ：

>>> a = np.arange(5)
>>> hist, bin_edges = np.histogram(a, density=True)
>>> hist
array([0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])
>>> hist.sum()
2.4999999999999996
>>> np.sum(hist * np.diff(bin_edges))
1.0

To illustrate ,density=True After the integral is 1