import numpy as np h0 = np.array([1 / math.sqrt(2), 1 / math.sqrt(2)]) print(h0.shape)
时间: 2024-04-11 15:31:38 浏览: 8
根据给出的代码,首先需要导入`numpy`库。然后,创建一个名为`h0`的Numpy数组,其中包含两个元素,每个元素的值都是1除以√2的结果。
接下来,执行`print(h0.shape)`将输出`h0`的形状信息。根据之前的代码解析,`h0`是一个包含两个元素的一维数组。因此,执行`print(h0.shape)`将输出`(2,)`,表示`h0`的形状为`(2,)`。其中,`(2,)`表示数组有2个元素,没有其他维度。
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import pandas as pd import numpy as np import matplotlib.pyplot as plt import math data = np.load('dataset_em.npy') mu0 = np.array([np.mean(data) - 1, np.mean(data) + 1]) sg0 = np.array([1.0, 1.0]) w0 = [0.5, 0.5] ary_mu = [mu0] ary_sg = [sg0] ary_w = [w0] x = np.arange(-10, 15, 0.1) def pdf_gauss(x, mu, sg): c = 1 / np.sqrt(2 * np.pi) p = c / sg * np.exp(-0.5 * ((x - mu) / sg) ** 2) return p def gauss_mix_pdf(w, x, mu, sg): p = w[0] * pdf_gauss(x, mu[0], sg[0]) + w[1] * pdf_gauss(x, mu[1], sg[1]) return p for j in range(0, 100): mu = ary_mu[j] sg = ary_sg[j] w = ary_w[j] gama = [] for i in (0, 1): b = w[i] * pdf_gauss(data, mu[i], sg[i]) c = gauss_mix_pdf(w, data, mu, sg) gama.append(b / c) gama_sum0 = np.sum(gama[0]) gama_sum1 = np.sum(gama[1]) new_mu = [np.sum(data * gama[0]) / gama_sum0, np.sum(data * gama[1]) / gama_sum1] new_sg = [np.sqrt(np.sum(gama[0] * np.power(data - new_mu[0], 2)) / gama_sum0), np.sqrt(np.sum(gama[1] * np.power(data - new_mu[1], 2)) / gama_sum1)] # 第二个数太大了 new_w = [gama_sum0 / data.shape[0], gama_sum1 / data.shape[0]] ary_mu.extend([new_mu]) ary_sg.extend([new_sg]) ary_w.extend([new_w]) del gama y = gauss_mix_pdf(ary_w[100], x, ary_mu[100], ary_sg[100]) plt.figure() plt.hist(data, bins=100, facecolor="blue", edgecolor="black", alpha=0.7, density=True) plt.plot(x, y) plt.show() 请逐句详细解释这段代码
这段代码实现了一个高斯混合模型(Gaussian Mixture Model, GMM)的 EM 算法,用来对给定的数据进行聚类。下面是每一行代码的详细解释:
```python
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math
```
导入所需要的库。
```python
data = np.load('dataset_em.npy')
```
从文件中加载数据。
```python
mu0 = np.array([np.mean(data) - 1, np.mean(data) + 1])
sg0 = np.array([1.0, 1.0])
w0 = [0.5, 0.5]
```
初始化高斯混合模型的均值(mu)、标准差(sg)和权重(w)。
```python
ary_mu = [mu0]
ary_sg = [sg0]
ary_w = [w0]
```
将初始值存储在数组中,以便后续的 EM 算法迭代更新。
```python
x = np.arange(-10, 15, 0.1)
```
生成 X 轴的数据,用于画图。
```python
def pdf_gauss(x, mu, sg):
c = 1 / np.sqrt(2 * np.pi)
p = c / sg * np.exp(-0.5 * ((x - mu) / sg) ** 2)
return p
```
定义高斯分布的概率密度函数。
```python
def gauss_mix_pdf(w, x, mu, sg):
p = w[0] * pdf_gauss(x, mu[0], sg[0]) + w[1] * pdf_gauss(x, mu[1], sg[1])
return p
```
定义高斯混合分布的概率密度函数,其中 w 为权重,x、mu、sg 分别为 X 轴、均值和标准差。
```python
for j in range(0, 100):
mu = ary_mu[j]
sg = ary_sg[j]
w = ary_w[j]
gama = []
for i in (0, 1):
b = w[i] * pdf_gauss(data, mu[i], sg[i])
c = gauss_mix_pdf(w, data, mu, sg)
gama.append(b / c)
gama_sum0 = np.sum(gama[0])
gama_sum1 = np.sum(gama[1])
new_mu = [np.sum(data * gama[0]) / gama_sum0, np.sum(data * gama[1]) / gama_sum1]
new_sg = [np.sqrt(np.sum(gama[0] * np.power(data - new_mu[0], 2)) / gama_sum0),
np.sqrt(np.sum(gama[1] * np.power(data - new_mu[1], 2)) / gama_sum1)]
new_w = [gama_sum0 / data.shape[0], gama_sum1 / data.shape[0]]
ary_mu.extend([new_mu])
ary_sg.extend([new_sg])
ary_w.extend([new_w])
del gama
```
进行 EM 算法的迭代更新,其中 j 为迭代次数,data 为输入数据,mu、sg、w 分别为均值、标准差和权重。gama 为 E 步中计算的后验概率,new_mu、new_sg、new_w 分别为 M 步中更新后的均值、标准差和权重。最后将更新后的均值、标准差和权重存储在数组中。
```python
y = gauss_mix_pdf(ary_w[100], x, ary_mu[100], ary_sg[100])
plt.figure()
plt.hist(data, bins=100, facecolor="blue", edgecolor="black", alpha=0.7, density=True)
plt.plot(x, y)
plt.show()
```
画出最终的 GMM 模型和数据的分布直方图。其中 y 为高斯混合分布的概率密度函数,ary_w[100]、ary_mu[100]、ary_sg[100] 分别为最终的权重、均值和标准差。plt.hist() 画出数据的分布直方图,plt.plot() 画出 GMM 模型的曲线。
请以import matplotlib.pyplot as plt import numpy as np import pandas as pd import seaborn as sns import copy import math import random import time from multiprocessing import Pool as ThreadPool #读取数据 path1='att48.tsp' path2='eil76.tsp' path3='pcb442.tsp' path4='rd100.tsp' path5='tsp225.tsp' def readcity(path): df = pd.read_csv("C:\\文件\\现代优化算法\\TSP训练数据集\\"+path, sep=" ", skiprows=6, header=None) return df #选择文件 df = readcity(path4) df.head() city = np.array(range(1,len(df[0][0:len(df)-1])+1)) city_x = np.array(df[1][0:len(df)-1]) city_y = np.array(df[2][0:len(df)-1])为开头补充完成一个模拟退火求解tsp问题的代码,我发给你的代码是用于获取输入数据并将其转化成坐标的
下面是一个简单的模拟退火求解TSP问题的代码,它使用了上面提到的数据读取和坐标转化代码:
```python
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
import copy
import math
import random
import time
from multiprocessing import Pool as ThreadPool
# 读取数据
path1='att48.tsp'
path2='eil76.tsp'
path3='pcb442.tsp'
path4='rd100.tsp'
path5='tsp225.tsp'
def readcity(path):
df = pd.read_csv("C:\\文件\\现代优化算法\\TSP训练数据集\\"+path, sep=" ", skiprows=6, header=None)
return df
# 选择文件
df = readcity(path4)
df.head()
# 获取城市坐标
city = np.array(range(1,len(df[0][0:len(df)-1])+1))
city_x = np.array(df[1][0:len(df)-1])
city_y = np.array(df[2][0:len(df)-1])
city_pos = np.stack((city_x, city_y), axis=1)
# 计算两点之间的距离
def distance(city1, city2):
return math.sqrt((city1[0]-city2[0])**2 + (city1[1]-city2[1])**2)
# 计算路径长度
def path_length(path):
length = 0
for i in range(len(path)-1):
length += distance(city_pos[path[i]-1], city_pos[path[i+1]-1])
length += distance(city_pos[path[-1]-1], city_pos[path[0]-1])
return length
# 生成随机解
def generate_random_solution():
return np.random.permutation(city)
# 退火算法求解TSP问题
def simulated_annealing():
# 设置参数
initial_temperature = 100
cooling_rate = 0.99
temperature = initial_temperature
current_path = generate_random_solution()
current_length = path_length(current_path)
best_path = current_path
best_length = current_length
# 迭代求解
while temperature > 1:
# 生成新解
new_path = copy.deepcopy(current_path)
i = random.randint(0, len(city)-1)
j = random.randint(0, len(city)-1)
new_path[i], new_path[j] = new_path[j], new_path[i]
new_length = path_length(new_path)
# 计算接受概率
delta = new_length - current_length
if delta < 0 or random.random() < math.exp(-delta/temperature):
current_path = new_path
current_length = new_length
# 更新最优解
if current_length < best_length:
best_path = current_path
best_length = current_length
# 降温
temperature *= cooling_rate
return best_path, best_length
# 运行算法
start_time = time.time()
best_path, best_length = simulated_annealing()
end_time = time.time()
# 打印结果
print("最优路径:", best_path)
print("最优路径长度:", best_length)
print("运行时间:", end_time - start_time)
# 绘制路径
plt.figure(figsize=(8, 8))
plt.plot(city_pos[best_path-1, 0], city_pos[best_path-1, 1], 'o-')
plt.title("Simulated Annealing TSP Solution (length={})".format(round(best_length)))
plt.show()
```
这段代码实现了一个简单的模拟退火算法求解TSP问题。它首先读取数据,然后计算出每个城市的坐标,并且定义了计算两个城市之间距离和计算路径长度的函数。接着,它使用随机解作为初始解,并且迭代地生成新解并计算接受概率,直到降温至最低温度。最后,它输出最优路径和路径长度,并且绘制路径。