使用 RBFInterpolator 进行二维样条插值外推-Python教程-PHP中文网

使用 RBFInterpolator 进行二维样条插值外推

霞舞

发布： 2025-09-26 18:25:15

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使用 rbfinterpolator 进行二维样条插值外推

本文介绍了如何使用 scipy.interpolate 库中的 RBFInterpolator 类进行二维样条插值，并实现超出原始数据范围的外推。通过示例代码详细展示了数据准备、模型训练以及外推的具体步骤，并强调了使用 RBFInterpolator 相对于 Rbf 和 griddata 的优势。

scipy.interpolate 模块提供了多种插值方法，其中径向基函数（Radial Basis Function, RBF）插值是一种常用的方法，特别适用于散乱数据的插值。在二维情况下，RBF 插值可以用于构建一个平滑的曲面，该曲面可以近似原始数据点的值。此外，RBF 插值还支持外推，即预测超出原始数据范围的值。

RBFInterpolator 的使用

RBFInterpolator 是 scipy.interpolate 中用于 RBF 插值的类，它提供了比旧的 Rbf 类更强大的功能和更好的性能。它特别适合处理大型数据集和需要外推的情况。

以下是一个使用 RBFInterpolator 进行二维样条插值和外推的示例：

import io
import numpy as np
import pandas as pd
from scipy.interpolate import RBFInterpolator
from numpy import ma
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D  # 导入 Axes3D

# 假设 data_str 包含你的数据
data_str = """dte,4500,4510,4520,4530,4540,4550,4560,4570,4580,4590,4600
0.015,0.218,0.209,0.201,0.194,0.187,0.181,0.175,0.17,0.165,0.16,0.156
0.041,0.217,0.208,0.2,0.193,0.186,0.18,0.174,0.169,0.164,0.159,0.155
0.068,0.216,0.207,0.199,0.192,0.185,0.179,0.173,0.168,0.163,0.158,0.154
0.096,0.215,0.206,0.198,0.191,0.184,0.178,0.172,0.167,0.162,0.157,0.153
0.123,0.214,0.205,0.197,0.19,0.183,0.177,0.171,0.166,0.161,0.156,0.152
0.151,0.213,0.204,0.196,0.189,0.182,0.176,0.17,0.165,0.16,0.155,0.151
0.178,0.212,0.203,0.195,0.188,0.181,0.175,0.169,0.164,0.159,0.154,0.15
0.206,0.211,0.202,0.194,0.187,0.18,0.174,0.168,0.163,0.158,0.153,0.149
0.233,0.21,0.201,0.193,0.186,0.179,0.173,0.167,0.162,0.157,0.152,0.148
0.26,0.209,0.2,0.192,0.185,0.178,0.172,0.166,0.161,0.156,0.151,0.147
0.288,0.208,0.199,0.191,0.184,0.177,0.171,0.165,0.16,0.155,0.15,0.146
0.315,0.207,0.198,0.19,0.183,0.176,0.17,0.164,0.159,0.154,0.149,0.145
0.342,0.206,0.197,0.189,0.182,0.175,0.169,0.163,0.158,0.153,0.148,0.144
0.37,0.205,0.196,0.188,0.181,0.174,0.168,0.162,0.157,0.152,0.147,0.143
0.397,0.204,0.195,0.187,0.18,0.173,0.167,0.161,0.156,0.151,0.146,0.142
"""

vol = pd.read_csv(io.StringIO(data_str))
vol.set_index('dte', inplace=True)
valid_vol = ma.masked_invalid(vol).T

Ti = np.linspace(float((vol.index).min()), float((vol.index).max()), len(vol.index))
Ki = np.linspace(float((vol.columns).min()), float((vol.columns).max()), len(vol.columns))

Ti, Ki = np.meshgrid(Ti, Ki)

valid_Ti = Ti[~valid_vol.mask]
valid_Ki = Ki[~valid_vol.mask]
valid_vol = valid_vol[~valid_vol.mask]

points = np.column_stack((valid_Ti, valid_Ki))
values = valid_vol.ravel()

# 使用 RBFInterpolator
rbf = RBFInterpolator(points, values, kernel='linear')

# 在原始数据范围之外进行插值
interp_value = rbf(np.array([0.0, 4500]))  # 示例：在 Ti=0, Ki=4500 处插值
print(f"外推值: {interp_value}")

# 可视化
fig = plt.figure(figsize=(12, 6))
ax = fig.add_subplot(111, projection='3d')

# 创建用于可视化的网格
x = np.linspace(Ti.min(), Ti.max(), 100)
y = np.linspace(Ki.min(), Ki.max(), 100)
x, y = np.meshgrid(x, y)

# 使用 RBFInterpolator 进行插值
z = rbf(np.column_stack((x.ravel(), y.ravel()))).reshape(x.shape)

# 绘制曲面
surf = ax.plot_surface(x, y, z, cmap='viridis')

# 设置坐标轴标签
ax.set_xlabel('Ti')
ax.set_ylabel('Ki')
ax.set_zlabel('Vol')

# 添加颜色条
fig.colorbar(surf)

plt.title('RBF Interpolation with Extrapolation')
plt.show()

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数据准备: 从字符串读取数据，并使用 numpy.ma 处理缺失值。
创建网格: 使用 np.meshgrid 创建二维网格，用于插值。
数据清洗: 移除无效值。
RBFInterpolator: 使用清洗后的数据创建 RBFInterpolator 对象。kernel='linear' 指定使用线性径向基函数。其他可用的核函数包括 'gaussian', 'multiquadric', 'inverse_quadratic', 'inverse_multiquadric', 'thin_plate_spline'。
外推: 调用 rbf 对象，传入要插值的点的坐标。
可视化: 使用 Matplotlib 绘制插值结果。