使用径向基函数进行平滑/插值¶
| 日期 | 2020-06-09 (最后修改), 2007-02-08 (创建) |
|---|
径向基函数可用于平滑/插值 n 维散点数据，但在观察数据范围之外进行外推时应谨慎使用。
1d 示例¶
此示例比较了 scipy.interpolate 模块中 Rbf 和 UnivariateSpline 类的用法。
在 [ ]
import numpy as np
from scipy.interpolate import Rbf, InterpolatedUnivariateSpline
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
# setup data
x = np.linspace(0, 10, 9)
y = np.sin(x)
xi = np.linspace(0, 10, 101)
# use fitpack2 method
ius = InterpolatedUnivariateSpline(x, y)
yi = ius(xi)
plt.subplot(2, 1, 1)
plt.plot(x, y, 'bo')
plt.plot(xi, yi, 'g')
plt.plot(xi, np.sin(xi), 'r')
plt.title('Interpolation using univariate spline')
# use RBF method
rbf = Rbf(x, y)
fi = rbf(xi)
plt.subplot(2, 1, 2)
plt.plot(x, y, 'bo')
plt.plot(xi, fi, 'g')
plt.plot(xi, np.sin(xi), 'r')
plt.title('Interpolation using RBF - multiquadrics')
plt.tight_layout()
plt.savefig('rbf1d.png')
在 [ ]
import numpy as np
from scipy.interpolate import Rbf
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib import cm
# 2-d tests - setup scattered data
x = np.random.rand(100)*4.0-2.0
y = np.random.rand(100)*4.0-2.0
z = x*np.exp(-x**2-y**2)
ti = np.linspace(-2.0, 2.0, 100)
XI, YI = np.meshgrid(ti, ti)
# use RBF
rbf = Rbf(x, y, z, epsilon=2)
ZI = rbf(XI, YI)
# plot the result
n = plt.normalize(-2., 2.)
plt.subplot(1, 1, 1)
plt.pcolor(XI, YI, ZI, cmap=cm.jet)
plt.scatter(x, y, 100, z, cmap=cm.jet)
plt.title('RBF interpolation - multiquadrics')
plt.xlim(-2, 2)
plt.ylim(-2, 2)
plt.colorbar()
plt.savefig('rbf2d.png')
章节作者: Unknown[13], cassiasamp, Christian Gagnon
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