Numpy 入门（四）Basic reductions
本帖最后由 hj170520 于 2020-6-10 11:31 编辑入门代码（四）
# 6. Basic reductions
## Computing sums
```
>> x = np.array()
>> np.sum(x)
10
>> x.sum()
10
```
### Sum by rows and by columns:
```
>> x = np.array([, ])
>> x
array([,
])
>> x.sum(axis=0) # columns (first dimension)
array()
>> x[:, 0].sum(), x[:, 1].sum()
(3, 3)
>> x.sum(axis=1) # rows (second dimension)
array()
>> x.sum(), x.sum()
(2, 4)
```
###Same idea in higher dimensions:
```
>> x = np.random.rand(2,2,2)
>> x.sum(axis=2)
1.345648389754668
>> x.sum()
1.345648389754668
```
# Other reductions
> — works the same way (and take axis=)
>
## Extrema:
```
>> x = np.array()
>> x.min()
1
>> x.max()
3
>> x.argmin()# index of minimum
0
>> x.argmax()# index of maximum
1
```
## Logical operations:
```
>> np.all()
False
>> np.any()
True
```
### Note Can be used for array comparisons:
```
>> a = np.zeros((100, 100))
>> np.any(a != 0)
>> np.all(a == a)
>> a = np.array()
>> b = np.array()
>> c = np.array()
>> ((a <= b) & (b <= c)).all()
True
```
## Statistics:
```
>> x = np.array()
>> y = np.array([, ])
>> x.mean()
1.75
>> np.median(x)
1.5
>> np.median(y, axis=-1) # last axis
array()
>> x.std() # full population standard dev.
0.82915619758885
```
> Exercise: Reductions
>
> Given there is a sum, what other function might you expect to see?
> What is the difference between sum and cumsum?
### Worked Example: data statistics
> Data in populations.txt describes the populations of hares and lynxes (and carrots) in northern Canada during 20 years.
>
```
>> !cat data/populations.txt
>> data = np.loadtxt('data/populations.txt')
>> year, hares, lynxes, carrots = data.T# trick: columns to variables
>> from matplotlib import pyplot as plt
>> plt.axes()
>> plt.plot(year, hares, year, lynxes, year, carrots)
>> plt.legend(('Hare', 'Lynx', 'Carrot'), loc=(1.05, 0.5))
>> plt.show()
```
```
>> populations = data[:, 1:]
>> populations.mean(axis=0) # <-- The mean populations over time:
array()
>> populations.std(axis=0) # <-- The sample standard deviations:
array()
>> np.argmax(populations, axis=1)# <-- Which species has the highest population each year?:
array()
```
### Worked Example: diffusion using a random walk algorithm
> Let us consider a simple 1D random walk process: at each time step a walker jumps right or left with equal probability.
> We are interested in finding the typical distance from the origin of a random walker after t left or right jumps?
We are going to simulate many “walkers” to find this law, and we are going to do so using array computing tricks: we are going to create a 2D array with the “stories” (each walker has a story) in one direction, and the time in the other:
```
>> n_stories = 1000 # number of walkers
>> t_max = 200 # time during which we follow the walker
>> t = np.arange(t_max)
>> steps = 2 * np.random.randint(0, 1 + 1, (n_stories, t_max)) - 1 # +1 because the high value is exclusive
>> np.unique(steps) # Verification: all steps are 1 or -1
array([-1,1])
>> positions = np.cumsum(steps, axis=1) # axis = 1: dimension of time
>> sq_distance = positions**2
>> mean_sq_distance = np.mean(sq_distance, axis=0)
>> plt.figure(figsize=(4, 3))
>> plt.plot(t, np.sqrt(mean_sq_distance), 'g.', t, np.sqrt(t), 'y-')
>> plt.xlabel(r"$t$")
>> plt.ylabel(r"$\sqrt{\langle (\delta x)^2 \rangle}$")
>> plt.tight_layout() # provide sufficient space for labels
# ply.show()# <-- We find a well-known result in physics: the RMS distance grows as the square root of the time!
```
本帖最后由 hj170520 于 2020-6-9 23:12 编辑
```
populations.txt :
# year hare lynx carrot
1900 30e3 4e3 48300
1901 47.2e3 6.1e3 48200
1902 70.2e3 9.8e3 41500
1903 77.4e3 35.2e3 38200
1904 36.3e3 59.4e3 40600
1905 20.6e3 41.7e3 39800
1906 18.1e3 19e3 38600
1907 21.4e3 13e3 42300
1908 22e3 8.3e3 44500
1909 25.4e3 9.1e3 42100
1910 27.1e3 7.4e3 46000
1911 40.3e3 8e3 46800
1912 57e3 12.3e3 43800
1913 76.6e3 19.5e3 40900
1914 52.3e3 45.7e3 39400
1915 19.5e3 51.1e3 39000
1916 11.2e3 29.7e3 36700
1917 7.6e3 15.8e3 41800
1918 14.6e3 9.7e3 43300
1919 16.2e3 10.1e3 41300
1920 24.7e3 8.6e3 47300
``` 学习中，感谢总结分享 上一篇还没看。。。 看着挺好，能给翻译一下？ ymhld 发表于 2020-6-10 09:53
看着挺好，能给翻译一下？
可以先适应着看，看着看着后面速度就提上来了。
代码结合英文看才是最大的提升，很多代码都是英文简写。{:301_986:}
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