Python中实现插值法的示例详解

import numpy as np
from scipy.interpolate import interp1d
 
# 已知数据点
x = np.array([1, 2, 3, 4])
y = np.array([10, 20, 30, 40])
 
# 创建线性插值函数
f_linear = interp1d(x, y)
 
# 在新的数据点上进行插值
x_new = np.array([1.5, 2.5, 3.5])
y_new_linear = f_linear(x_new)
 
print("线性插值结果：", y_new_linear)

import numpy as np
 
# 已知数据点
x = np.array([1, 2, 3, 4])
y = np.array([10, 20, 30, 40])
 
# 进行多项式插值
coefficients = np.polyfit(x, y, deg=len(x)-1)
f_poly = np.poly1d(coefficients)
 
# 在新的数据点上进行插值
x_new = np.array([1.5, 2.5, 3.5])
y_new_poly = f_poly(x_new)
 
print("多项式插值结果：", y_new_poly)

from scipy.interpolate import CubicSpline
 
# 已知数据点
x = np.array([1, 2, 3, 4])
y = np.array([10, 20, 30, 40])
 
# 创建样条插值函数
f_spline = CubicSpline(x, y)
 
# 在新的数据点上进行插值
x_new = np.array([1.5, 2.5, 3.5])
y_new_spline = f_spline(x_new)
 
print("样条插值结果：", y_new_spline)

# 在地理空间上进行插值
elevation_interpolated = f_spline(latitude, longitude)

# 图像放大
image_resized = cv2.resize(image, (new_width, new_height), interpolation=cv2.INTER_LINEAR)

# 对离散信号进行插值
signal_interpolated = f_linear(time)

# 数值逼近
approximated_value = f_spline(x)

# 构建利率曲线
interest_rate_curve = f_linear(t)

# 数据预处理
preprocessed_data = interpolate_missing_values(data)