Python求逆矩阵_矩阵乘法_导数_偏导数_定积分_不定积分

numpy矩阵运算：

import numpy as np

A = np.array([1, 2, 3])
T = np.transpose(A)  # 矩阵转置
print(A.dot(T))  # 矩阵乘法
B = np.array([[1, 2, 3], [2, 2, 1], [3, 4, 3]])
print(np.linalg.inv(B))  # 矩阵求逆

 sympy求导数：

import numpy as np
from sympy import *

x = symbols("x")
e = np.e
f = log(1 + e ** x) / (1 + e ** (-x))
# 一阶导数
f1 = diff(f, x, 1)
# 二阶导数
f2 = diff(f, x, 2)
#  三阶导数
f3 = diff(f, x, 3)
print(f1, f2, f3, sep='\n')

sympy求偏导数：

from sympy import *

x1, x2 = symbols("x1, x2")
f = (x1 - 1) ** 2 + 100 * (x2 - x1 ** 2) ** 2
fx1 = diff(f, x1)  # 偏导数
fx2 = diff(f, x2)
print(diff(fx1, x1))  # 二阶偏导数
print(diff(fx1, x2))
print(diff(fx2, x1))
print(diff(fx2, x2))

 sympy求不定积分：

from sympy import *

x = symbols("x")
f = log(x)
str = integrate(f, x)  # 不定积分
print(str)

scipy求定积分：

from scipy import integrate
import numpy as np


def f(x, y):
    return 6 - x - y


# 二重积分，参数为先x的下限和上限，后y的下限和上限，err为误差
ans, err = integrate.dblquad(f, 0, 2, lambda x: 0, lambda x: 4 - x)
print(ans / 24)
# 一重积分
ans, err = integrate.quad(lambda x: x ** 2 - 12 * x + 32, 0, 2)
print(ans / 48)


def w(x):
    return 1 / np.sqrt(abs(x))


# w函数在x=0处存在断点 用quad()函数中的points可跳过求解
ans, err = integrate.quad(w, -1, 1, points=[0])
print(ans)