我有一组数据点,想用样条函数来近似它们。
我使用了两个不同的函数:
-
splrep来自 scipy
- 和我发现的三次样条函数here http://en.literateprograms.org/Cubic_spline_%28Python%29.
结果看起来像this http://postimage.org/image/9wvq9gzdz/.
代码如下:
from matplotlib.pyplot import *
from numpy import *
from scipy import interpolate
#----------------------------------------------
s = arange(257)/256.0
z = s[::-1]
b = transpose(array((z*z*z,
3*z*z*s,
3*z*s*s,
s*s*s)))
def cubicspline(c,t):
return dot(b[t],c)
#----------------------------------------------
A = array([
[ -126.041 , 246.867004],
[ -113.745003, 92.083 ],
[ 208.518997, -183.796997],
[ 278.859009, -190.552994]])
a1 = A[:,0]
a2 = A[:,1]
cs = reshape(A, (-1, 4, 2))
X = []
Y = []
#spline with cubicspline()
for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
X.append(x)
Y.append(y)
# spline with splrep
tck = interpolate.splrep( a1, a2)
xnew = np.arange( min(a1), max(a1), 5)
ynew = interpolate.splev(xnew, tck)
plot(a1, a2, "--ob", ms = 9, label = "points")
plot(X, Y, "r", lw=2, label = "cubicspline")
plot(xnew, ynew, "g", lw=2, label = "splrep")
legend(); savefig("image.png"); show()
正如你可能看到的结果splrep还远远不能令人满意。
有人可以解释一下这种行为以及如何从splrep?