Scipy练习题

scipy包含致力于科学计算中常见问题的各个工具箱。它的不同子模块相应于不同的应用。像插值，积分，优化，图像处理，统计，特殊函数等等。

scipy可以与其它标准科学计算程序库进行比较，比如GSL(GNU C或C++科学计算库)，或者Matlab工具箱。scipy是Python中科学计算程序的核心包; 它用于有效地计算numpy矩阵，来让numpy和scipy协同工作。

在实现一个程序之前，值得检查下所需的数据处理方式是否已经在scipy中存在了。作为非专业程序员，科学家总是喜欢重新发明造轮子，导致了充满漏洞的，未经优化的，很难分享和维护的代码。相反，Scipy程序经过优化和测试，因此应该尽可能使用。

作者：Aieru
链接：https://www.jianshu.com/p/1a3db06e786d
來源：简书
著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。

# 10.1 Least squares  
from scipy.optimize import least_squares  
import numpy as np  
  
n = 5  
m = 8  
  
A = []  
for i in range(n):  
    temp = []  
    for j in range(m):  
        temp += [np.random.randint(1, 100)]  
    A += [temp]  
  
print("A:")  
for i in A:  
    print(i)  
  
b = []  
for j in range(n):  
    b += [np.random.randint(1, 100)]  
  
print("b:")  
print(b)  
  
x = [0, 0, 0, 0, 0, 0, 0, 0]  
  
  
def func(x):  
    return np.linalg.norm(np.matmul(A, x)-np.array(b))  
  
  
solutions = least_squares(func, x)  
print("solution:")  
print(solutions.x)  
print("residual:")  
print(func(solutions.x))

输出：

A:  
[3, 78, 35, 57, 43, 48, 97, 66]  
[14, 54, 3, 67, 22, 73, 20, 10]  
[45, 95, 68, 46, 38, 79, 28, 12]  
[17, 17, 75, 78, 60, 76, 15, 62]  
[10, 60, 42, 36, 87, 78, 17, 64]  
b:  
[1, 28, 40, 54, 97]  
solution:  
[-0.04053965  0.14680695 -0.13608394 -0.27262632  0.75309927  0.44620533  
 -0.60086573  0.21903286]  
residual:  
1.9376753415496063e-05

import math  
from scipy.optimize import fmin  
  
  
def func(x):  
    return 1/((math.sin(x-2))**2*math.e**(-x**2))  
  
  
fmin(func, 0)

输出：

Optimization terminated successfully.  
         Current function value: 1.096870  
         Iterations: 20  
         Function evaluations: 40

import numpy as np  
from scipy.linalg import norm  
  
n = 5  
m = 8  
  
A = []  
for i in range(n):  
    temp = []  
    for j in range(m):  
        temp += [np.random.randint(1, 100)]  
    A += [temp]  
  
print("A:")  
for i in A:  
    print(i)  
  
distances = []  
  
for i in range(n):  
    temp = []  
    for j in range(n):  
        temp += [norm(np.subtract(A[i], A[j]))]  
    distances += [temp]  
  
print("distances:")  
for i in distances:  
    print(i)

输出：

A:  
[57, 44, 32, 40, 50, 69, 58, 77]  
[61, 78, 3, 32, 84, 66, 75, 76]  
[4, 91, 41, 74, 17, 52, 7, 7]  
[91, 4, 28, 49, 59, 14, 9, 41]  
[1, 57, 5, 97, 99, 95, 57, 27]  
distances:  
[0.0, 59.430631832414505, 123.02032352420473, 98.26494797230598, 113.4063490286148]  
[59.430631832414505, 0.0, 143.86104406683555, 127.27922061357856, 109.82258419833327]  
[123.02032352420473, 143.86104406683555, 0.0, 142.47806848775008, 120.26221351696466]  
[98.26494797230598, 127.27922061357856, 142.47806848775008, 0.0, 156.2145959889792]  
[113.4063490286148, 109.82258419833327, 120.26221351696466, 156.2145959889792, 0.0]

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