开发者

scipy.interpolate插值方法实例讲解

开发者 https://www.devze.com 2022-12-30 09:23 出处:网络 作者: tony365
目录scipy.interpolate插值方法1 一维插值2 multivariate data3 Multivariate data interpolation on a regular grid4 Rbf 插值方法scipy.interpolate插值方法
目录
  • scipy.interpolate插值方法
    • 1 一维插值
    • 2 multivariate data
    • 3 Multivariate data interpolation on a regular grid
    • 4 Rbf 插值方法

scipy.interpolate插值方法

1 一维插值

from scipy.interpolate import interp1d

1维插值算法

from scipy.interpolate import interp1d
x = np.linspace(0, 10, num=11, endpoint=True)
y = np.cos(-x**2/9.0)
f = interp1d(x, y)
f2 = interp1d(x, y, kind='cubic')
xnew = np.linspace(0, 10, num=41, endpoint=True)
import matplotlib.pyplot as plt
plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')
plt.legend(['data', 'linear', 'cubic'], loc='best')
plt.show()

数据点,线性插值结果,cubic插值结果:

scipy.interpolate插值方法实例讲解

2 multivariate data

from scipy.interpolate import interp2d

from scipy.interpolate import griddata

多为插值方法,可以应用在2Dlut,3Dlut的生成上面,比如当我们已经有了两组RGB映射数据, 可以插值得到一个查找表。

二维插值的例子如下:

import numpy as np
from scipy import interpolate
import matplotlib.pyplot as plt

from scipy.interpolate imphttp://www.devze.comort griddata, RegularGridInterpolator, Rbf

if __name__ == "__main__":
    x_edges, y_edges = np.mgrid[-1:1:21j, -1:1:21j]
    x = x_edges[:-1, :-1] + np.diff(x_edges[:2, 0])[0] / 2.
    y = y_edges[:-1, :-1] + np.diff(y_edges[0, :2])[0] / 2.

    # x_edges, y_edges 是 20个格的边缘的坐标, 尺寸 21 * 21
    # x, y 是 20个格的中心的坐标, 尺寸 20 * 20

    z = (x + y) * np.exp(-6.0 * (x * x + y * y))

    print(x_edges.shape, x.shape, z.shape)
    plt.figure()
    lims = dict(cmap='RdBu_r', vmin=-0.25, vmax=0.25)
    plt.pcolormesh(x_edges, y_edges, z, shading='flat', **lims) # plt.pcolormesh(), plt.colorbar() 画图
    plt.colorbar()
    plt.title("Sparsely sampled function.")
    plt.show()

    # 使用grid data
    xnew_edges, ynew_edges = np.mgrid[-1:1:71j, -1:1:71j]
    xnew = xnew_edges[:-1, :-1] + np.diff(xnew_edges[:2, 0])[0] / 2. # xnew其实是 height new
    ynew = ynew_edges[:-1, :-1] + np.diff(ynew_edges[0, :2])[0] / 2.
    grid_x, grid_y = xnew, ynew

    print(x.shape, y.shape, z.shape)
    points = np.hstack((x.reshape(-1, 1), y.reshape(-1, 1)))
    z1 = z.reshape(-1, 1)

    grid_z0 = griddata(points, z1, (grid_x, grid_y), method='nearest').squeeze()
    grid_z1 = griddata(points, z1, (grid_x, grid_y), method='lineaandroidr').squeeze()
    grid_z2 = griddata(points, z1, (grid_x, grid_y), method='cubic').squeeze()

    rbf = Rbf(points[:, 0], points[:, 1], z, epsilon=2)
    grid_z3 = rbf(grid_x, grid_y)

    plt.subplot(231)
    plt.imshow(z.T, extent=(-1, 1, -1, 1), origin='lower')
    plt.plot(points[:, 0], points[:, 1], 'k.', ms=1)
    plt.title('Original')
    plt.subplot(232)
    plt.imshow(grid_z0.T, extent=(-1, 1, -1, 1), origin='lower')
    plt.title('Nearest')
    plt.subplot(233)
    plt.imshow(gridhttp://www.devze.com_z1.T, extent=(-1, 1, -1, 1), origin='lower', cmap='RdBu_r')
    plt.title('Linear')
    plt.subplot(234)
    plt.imshow(grid_z2.T, extent=(-1, 1, -1, 1), origin='lower')
    plt.title('Cubic')
    plt.subplot(235)
    plt.imshow(grid_z3.T, extent=(-1, 1, -1, 1), origin='lower')
    plt.title('rbf')
    plt.gcf().set_size_inches(8, 6)
    plt.show()


scipy.interpolate插值方法实例讲解

示例2:

def func(x, y):
    return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2


grid_x, grid_y = np.mgrid[0:1:100j, 0:1:200j]


rng = np.random.default_rng()
points = rng.random((1000, 2))
values = func(points[:,0], points[:,1])

from scipy.interpolate import griddata
grid_z0 = griddata(points, values, (grid_x, grid_y), method='nearest')
grid_z1 = griddata(points, values, (grid_x, grid_y), method='linear')
grid_z2 = griddata(points, values, (grid_x, grid_y), method='cubic')

import matplotlib.pyplot as plt
plt.subplot(221)
plt.imshow(func(grid_x, grid_y).T, extent=(0,1,0,1), origin='lower')
plt.plot(points[:,0], points[:,1], 'k.', ms=1)
plt.title('Original')
plt.subplot(222)
plt.imshow(grid_z0.T, extent=(0,1,0,1), origin='lower')
plt.title('Nearest')
plt.subplot(223)
plt.imshow(grid_z1.T, extent=(0,1,0,1), origin='lower')
plt.title('Linear')
plt.subplot(224)
plt.imshow(grid_z2.T, extent=(0,1,0,1), origin='lower')
plt.title('Cubic')
plt.gcf().set_size_inches(6, 6)
plt.show()

scipy.interpolate插值方法实例讲解

3 Multivariate data interpolation on a regular grid

from scipy.interpolate import RegularGridInterpolator

已知一些grid上的值。

可以应用在2Dlut,3Dlut,当我们已经有了一个多维查找表,然后整个图像作为输入,得到查找和插值后的输出。

二维网格插值方法(好像和resize的功能比较一致)

# 使用RegularGridInterpolator
import matplotlib.pyplot as plt
from scipy.interpolate import RegularGridInterpolator

def F(u, v):
    return u * np.cos(u * v) + v * np.sin(u * v)

fit_points = [np.linspace(0, 3, 8), np.linspace(0, 3, 8)]
values = F(*np.meshgrid(*fit_points, indexing='ij'))

ut, vt = np.meshgrid(np.linspace(0, 3, 80), np.linspace(0, 3, 80), indexing='ij')
true_values = F(ut, vt)
test_points = np.array([ut.ravel(), vt.ravel()]).T

interp = RegularGridInterpolator(fit_points, values)
fig, axes = plt.subplots(2, 3, figsize=(10, 6))
axes = axes.ravel()
fig_index = 0
for method in ['linear', 'nearest', 'linear', 'cubic', 'quintic']:
    im = interp(test_points, method=method).reshape(80, 80)
    axes[fig_index].imshow(im)
    axes[fig_index].set_title(method)
    axes[fig_index].axis("off")
    fig_index += 1
axes[fig_index].imshow(true_values)
axes[fig_index].set_title("True values")
fig.tight_layout()
fig.show()
plt.show()

scipy.interpolate插值方法实例讲解

4 Rbf 插值方法

interpolate scattered 2-D data

import numpy as np
from scipy.interpolate import Rbf
import matplotlib.pyplot as plt
from matplotlib import cm

# 2-d tests - setup scattered data
rng = np.random.default_rng()
x = rng.random(100) * 4.0 - 2.0
androidy = rng.random(100) * 4.0 - 2.0
z = x * np.exp(-x ** 2 - y ** 2)


edges = np.linspace(-2.0, 2.0, 101)
centers = edges[:-1] + np.diff(edges[:2])[0] / 2.

XI, YI = np.meshgrid(centers, centers)
# use RBF
rbf = Rbf(x, y, z, epsilon=2)
Z1 = rbf(XI, YI)

points = np.hstack((x.reshape(-1, 1), y.reshape(-1, 1)))
Z2 = griddata(points, z, (XI, YI), method='cubic').squeeze()

# plot thejavascript result
plt.figure(figsize=(20,8))
plt.subplot(1, 2, 1)
X_edges, Y_edges = np.meshgrid(edges, edges)
lims = dict(cmap='RdBu_r', vmin=-0.4, vmax=0.4)
plt.pcolormesh(X_edges, Y_edges, Z1, shading='flat', **lims)
plt.scatter(x, y, 100, z, edgecolor='w', lw=0.1, **lims)
plt.title('RBF interpolation - multiquadrics')
plt.xlim(-2, 2)
plt.ylim(-2, 2)
pl开发者_开发入门t.colorbar()

plt.subplot(1, 2, 2)
X_edges, Y_edges = np.meshgrid(edges, edges)
lims = dict(cmap='RdBu_r', vmin=-0.4, vmax=0.4)
plt.pcolormesh(X_edges, Y_edges, Z2, shading='flat', **lims)
plt.scatter(x, y, 100, z, edgecolor='w', lw=0.1, **lims)
plt.title('griddata - cubic')
plt.xlim(-2, 2)
plt.ylim(-2, 2)
plt.colorbar()
plt.show()

得到结果如下, RBF一定程度上和 griddata可以互用, griddata方法比较通用

scipy.interpolate插值方法实例讲解

[1]https://docs.scipy.org/doc/scipy/tutorial/interpolate.html

到此这篇关于scipy.interpolate插值方法介绍的文章就介绍到这了,更多相关scipy.interpolate插值内容请搜索我们以前的文章或继续浏览下面的相关文章希望大家以后多多支持我们!

0

精彩评论

暂无评论...
验证码 换一张
取 消

关注公众号