插值

日期2007-05-03（最后修改），2006-01-29（创建）

在 scipy.signal 中使用 B 样条¶

示例展示了如何在 scipy.signal 中使用 B 样条进行插值。要使用这些例程，输入点必须等距分布。

在 [1]

from numpy import r_, sin
from scipy.signal import cspline1d, cspline1d_eval
%pylab inline

x = r_[0:10]
dx = x[1]-x[0]
newx = r_[-3:13:0.1]  # notice outside the original domain 
y = sin(x)
cj = cspline1d(y)
newy = cspline1d_eval(cj, newx, dx=dx,x0=x[0])
from pylab import plot, show
plot(newx, newy, x, y, 'o')
show()

Populating the interactive namespace from numpy and matplotlib

N 维等距数据的插值¶

scipy.ndimage 包还包含 spline_filter 和 map_coordinates，可用于对等距数据执行 N 维插值。下面给出了一个二维示例

在 [2]

from scipy import ogrid, sin, mgrid, ndimage, array
from matplotlib import pyplot as plt

x,y = ogrid[-1:1:5j,-1:1:5j]
fvals = sin(x)*sin(y)
newx,newy = mgrid[-1:1:100j,-1:1:100j]
x0 = x[0,0]
y0 = y[0,0]
dx = x[1,0] - x0
dy = y[0,1] - y0
ivals = (newx - x0)/dx
jvals = (newy - y0)/dy
coords = array([ivals, jvals])
newf1 = ndimage.map_coordinates(fvals, coords)

要预先计算权重（用于多个插值结果），可以使用

在 [3]

coeffs = ndimage.spline_filter(fvals)
newf2 = ndimage.map_coordinates(coeffs, coords, prefilter=False)

plt.subplot(1,2,1)
plt.imshow(newf1)
plt.subplot(1,2,2)
plt.imshow(newf2)
plt.show()

N 维曲线的插值¶

scipy.interpolate 包封装了 netlib FITPACK 例程（Dierckx），用于计算各种数据和几何形状的平滑样条。虽然本例中的数据是等距分布的，但使用此例程并不需要这样。

在 [4]

from numpy import arange, cos, linspace, pi, sin, random
from scipy.interpolate import splprep, splev

# make ascending spiral in 3-space
t=linspace(0,1.75*2*pi,100)

x = sin(t)
y = cos(t)
z = t

# add noise
x+= random.normal(scale=0.1, size=x.shape)
y+= random.normal(scale=0.1, size=y.shape)
z+= random.normal(scale=0.1, size=z.shape)

# spline parameters
s=3.0 # smoothness parameter
k=2 # spline order
nest=-1 # estimate of number of knots needed (-1 = maximal)

# find the knot points
tckp,u = splprep([x,y,z],s=s,k=k,nest=-1)

# evaluate spline, including interpolated points
xnew,ynew,znew = splev(linspace(0,1,400),tckp)

import pylab
pylab.subplot(2,2,1)
data,=pylab.plot(x,y,'bo-',label='data')
fit,=pylab.plot(xnew,ynew,'r-',label='fit')
pylab.legend()
pylab.xlabel('x')
pylab.ylabel('y')

pylab.subplot(2,2,2)
data,=pylab.plot(x,z,'bo-',label='data')
fit,=pylab.plot(xnew,znew,'r-',label='fit')
pylab.legend()
pylab.xlabel('x')
pylab.ylabel('z')

pylab.subplot(2,2,3)
data,=pylab.plot(y,z,'bo-',label='data')
fit,=pylab.plot(ynew,znew,'r-',label='fit')
pylab.legend()
pylab.xlabel('y')
pylab.ylabel('z')
plt.show()

章节作者：TravisOliphant，Unknown[63]，GaelVaroquaux，AndrewStraw，NickFotopoulos