学号后四位:3018
2.1:
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import math
import pylab as plt
import numpy as np
plt.rc('text', usetex=True) # 调用字库
x = np.linspace(-10, 10, 100)
y1 = np.cosh(x)
y2 = np.sinh(x)
y3 = math.e**x/2
plt.plot(x, y1, label='$\\mathrm{cosh}(x)$')
plt.plot(x, y2, label='$\\mathrm{sinh}(x)$')
plt.plot(x, y3, label='$\\frac{1}{2} \cdot e^x$')
plt.legend()
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.show()
print("xuehao3018")
2.2:
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import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import quad
def fun(t, x):
return np.exp(-t) * (t ** (x - 1))
x = np.linspace(0, 10, 100) # x 的范围
y = [quad(fun, 0, np.inf, args=i)[0] for i in x] # 计算积分
plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('$ y = \int_0^{\infty} e^{-t} \cdot t^{x-1} dt $')
plt.grid(True)
plt.show()
print("xuehao3018")
2.3:
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import numpy as np
import matplotlib.pyplot as plt
k_values = [1, 2, 3, 4, 5, 6] # k的取值
x = np.linspace(-10, 10, 100) # x的范围
for k in k_values:
y = k * x ** 2 + 2 * k # 计算y值
label = f'k={k}' # 设置标注
plt.plot(x, y, label=label) # 绘制曲线
plt.xlabel('x') # 添加x轴标签
plt.ylabel('y') # 添加y轴标签
plt.legend() # 添加图例
plt.grid(True) # 添加网格线
plt.show() # 显示图形
print("xuehao43018")
2.4:
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import numpy as np
import matplotlib.pyplot as plt
plt.rc('font', family='SimHei') # 用来正常显示中文标签
plt.rc('axes', unicode_minus=False) # 用来正常显示负号
k_values = [1, 2, 3, 4, 5, 6] # k的取值
x = np.linspace(-10, 10, 100) # x的范围
fig, axs = plt.subplots(2, 3, figsize=(10, 6)) # 创建2行3列的子窗口
for i, k in enumerate(k_values):
y = k * x ** 2 + 2 * k # 计算y值
row = i // 3 # 计算子窗口所在的行数
col = i % 3 # 计算子窗口所在的列数
ax = axs[row, col] # 获取当前子窗口
label = f'k={k}' # 设置标注
ax.plot(x, y, label=label) # 绘制曲线
ax.set_xlabel('x') # 添加x轴标签
ax.set_ylabel('y') # 添加y轴标签
ax.set_title(f'图 {i+1}') # 添加子窗口标题
ax.legend() # 添加图例
ax.grid(True) # 添加网格线
plt.tight_layout() # 自动调整子窗口布局
plt.show() # 显示图形
print("xuehao3018")
2.5(1):
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import numpy as np
import matplotlib.pyplot as plt
a = 2
b = np.sqrt(10)
c = np.sqrt(8)
phi = np.arange(0, 2*np.pi+0.1, 0.1)
theta = np.arange(-1, 1.1, 0.1)[:, np.newaxis]
x = a * np.cosh(theta) * np.cos(phi)
y = b * np.cosh(theta) * np.sin(phi)
z = c * np.sinh(theta)
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.plot_surface(x, y, z, cmap='viridis')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_box_aspect([1, 1, 1])
ax.set_title('$\\frac{x^2}{4}+\\frac{y^2}{10}-\\frac{z^2}{8}=1$')
plt.show()
print("xuehao3018")
2.5(2):
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import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# 创建一个三维坐标系
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# 生成x，y的网格
x = np.linspace(-50, 50, 1000)
y = np.linspace(-50, 50, 1000)
X, Y = np.meshgrid(x, y)
# 计算z的值
Z = (X**2)/4+(Y**2)/6
# 绘制二次曲面
ax.plot_surface(X, Y, Z, cmap='viridis')
# 添加坐标轴标签
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
# 添加标题
ax.set_title('$(\\frac{x^2}{4}+\\frac{y^2}{6})=z$')
# 设置z轴的范围
ax.set_zlim(0, 1000)
# 显示图形
plt.show()
print("xuehao3018")
2.6:
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import pandas as pd
import numpy as np
# 生成x、y和z数据
x = np.arange(0, 101, 1)
y = np.arange(0, 101, 1)
z = np.random.randint(0, 1001, size=(101, 101))
# 创建DataFrame对象
df = pd.DataFrame(data=z, index=x, columns=y)
# 写入Excel文件
df.to_excel('data.xlsx')
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import RectBivariateSpline
df = pd.read_excel('data.xlsx', header=None)
x = df.iloc[1:, 0].values
y = df.iloc[0, 1:].values
z = df.iloc[1:, 1:].values
# 绘制等高线图
plt.contour(x, y, z)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Contour Plot')
plt.colorbar() # 添加颜色条
# 在已知点处添加标注
point1 = (30, 0)
point2 = (43, 30)
plt.annotate('(30,0)', point1, textcoords="offset points", xytext=(0,10), ha='center')
plt.annotate('(43,30)', point2, textcoords="offset points", xytext=(0,10), ha='center')
# 创建插值函数
interp_func = RectBivariateSpline(x, y, z)
# 定义积分区间
x_min, x_max = min(x), max(x)
y_min, y_max = min(y), max(y)
# 计算积分区间的网格点数
grid_size = 100 # 可根据需要调整
# 生成网格点
x_grid = np.linspace(x_min, x_max, grid_size)
y_grid = np.linspace(y_min, y_max, grid_size)
# 计算网格点上的插值值
z_grid = interp_func(x_grid, y_grid)
# 计算曲面面积
area = np.trapz(np.trapz(z_grid, x_grid), y_grid)
print('区域面积:', area)
plt.show()
print("xuehao3018")
点击查看代码
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
df = pd.read_excel('data2.xlsx', header=None)
x = df.iloc[1:, 0].values
y = df.iloc[0, 1:].values
z = df.iloc[1:, 1:].values
# 创建网格
X, Y = np.meshgrid(y, x)
# 创建画布和3D坐标轴
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# 绘制三维网格图
ax.plot_surface(X, Y, z)
# 设置坐标轴标签
ax.set_xlabel('Y')
ax.set_ylabel('X')
ax.set_zlabel('Z')
# 显示三维网格图
plt.show()
print("xuehao3018")
2.7:
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import numpy as np
# 定义系数矩阵 A 和常数向量 b
A = np.array([[4, 2, -1], [3, -1, 2], [11, 3, 0]])
b = np.array([2, 10, 8])
# 解线性方程组 Ax = b
x = np.linalg.solve(A, b)
# 判断解的情况
if np.linalg.matrix_rank(A) == np.linalg.matrix_rank(np.column_stack((A, b))):
if np.linalg.matrix_rank(A) == A.shape[1]:
print("线性方程组有唯一解")
x_unique = np.linalg.solve(A, b)
print("唯一解 x =", x_unique)
else:
print("线性方程组有无穷多解")
x_least_squares = np.linalg.lstsq(A, b, rcond=None)[0]
print("最小二乘解 x =", x_least_squares)
else:
print("线性方程组无解")
x_least_squares = np.linalg.lstsq(A, b, rcond=None)[0]
print("最小二乘解 x =", x_least_squares)
x_min_norm = np.linalg.pinv(A).dot(b)
print("最小范数解 x =", x_min_norm)
print("xuehao3018")
