习题2.7代码

import numpy as np
import pandas as pd
import sympy as sp
sp.init_printing(use_unicode=True)
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif']=['Times New Roman + SimSun + WFM Sans SC']
plt.rcParams['mathtext.fontset']='cm'

Times New Roman + SimSun + WFM Sans SC

simsum宋体, times new roman -*, simhei黑体, kaiti楷体,

dengxian等线, fangsong仿宋, Microsoft Yahei微软雅黑

plt.rcParams['axes.unicode_minus']=False
plt.rcParams['figure.dpi'] = 200

plt.rcParams['figure.figsize'] = [4, 3]

plt.rcParams['font.size'] = 12

plt.rcParams['xtick.direction'] = 'in'
plt.rcParams['ytick.direction'] = 'in'
from scipy.optimize import root
fx = lambda x: [
4x[0] + 2x[1] - x[2] - 2,
3x[0] - x[1] + 2x[2] - 10,
11x[0] + 3x[1] - 8
]
root(fx, [0, 0, 0])
A = np.array([[4, 2, -1], [3, -1, 2], [11, 3, 0]])
b = np.array([[2], [10], [8]])
Ab = np.hstack([A, b])
r1 = np.linalg.matrix_rank(A)
r2 = np.linalg.matrix_rank(Ab)
print(f'{r1 = }, {r2 = }')
x = np.linalg.pinv(A)@b
np.round(x, 4)
from scipy.optimize import least_squares
f = lambda x: [
2x[0] + 3x[1] + 1x[2],
1x[0] - 2x[1] + 4x[2],
3x[0] + 8x[1] - 2x[2],
4x[0] - 1x[1] + 9x[2]
]
least_squares(f, [1, 2, 3])