File:Ispline order3.svg
Summary
| Description |
English: Plot showing I-splines of order 3. |
| Date | |
| Source | Own work |
| Author | Skbkekas |
| SVG development | |
| Source code | Python codefrom __future__ import division
import numpy as np
import matplotlib.pyplot as plt
def mspline(x, k, i, T):
"""Evaluate the kth order m-spline at x.
Arguments:
----------
x : the point at which the spline is evaluated
k : the order of the spline (k>=1)
i : the interval on which the spline is defined (i<len(T)-k)
T : the knots
Returns:
--------
The value of the spline at x
Note: Use mspline_knots(...) to create T.
"""
if x<T[i]: return 0.
if x>=T[i+k]: return 0.
if k==1: return 1/(T[i+1]-T[i])
d1 = x-T[i]
d2 = T[i+k]-x
v = d1*mspline(x, k-1, i, T) + d2*mspline(x, k-1, i+1, T)
v *= k
v /= (k-1)*(T[i+k]-T[i])
return v
def ispline(x, k, i, T):
"""Evaluate the kth order i-spline at x.
Arguments:
----------
x : the point at which the spline is evaluated
k : the order of the spline
i : the interval on which the spline is defined (i<len(T)-k-1)
T : the knots
Returns:
--------
The value of the spline at x
Note: Use ispline_knots(...) to create T.
"""
j = np.flatnonzero(T<=x)[-1]
if j<i: return 0.
if j-k+1>i: return 1.
v = 0.
for m in range(i,j+1):
v += mspline(x, k+1, m, T)*(T[m+k+1]-T[m])/(k+1)
return v
def mspline_knots(xmin, xmax, k, m):
"""Create an order list of points in the inteval (xmin,xmax)
suitable for use as knots in m-splines and i-splines.
Arguments:
----------
xmin : the lower bound of the interval
xmax : the upper bount of the interval
k : the order of the m-spline for which the knots will be used
m : the number of intervals into which (xmin,xmax) will be partitioned
"""
T = [xmin]*(k-1)
h = (xmax-xmin)/m
T.extend(np.arange(xmin, xmax, h))
T.extend([xmax]*k)
return T
def ispline_knots(xmin, xmax, k, m):
"""Create an order list of points in the inteval (xmin,xmax)
suitable for use as knots in m-splines and i-splines.
Arguments:
----------
xmin : the lower bound of the interval
xmax : the upper bount of the interval
k : the order of the m-spline for which the knots will be used
m : the number of intervals into which (xmin,xmax) will be partitioned
"""
return mspline_knots(xmin, xmax, k+1, m)
def test_ispline():
plt.clf()
plt.axes([0.1,0.1,0.7,0.8])
k = 3
T = ispline_knots(0, 1, k, 5)
A = []
for i in range(1,len(T)-k-1):
F = []
for x in np.arange(0,1.01,0.01):
F.append([x,ispline(x, k, i, T)])
F = np.array(F)
a = plt.plot(F[:,0], F[:,1], '-')
A.append(a)
if i==0: print F
plt.hold(True)
b = plt.figlegend(A, ("i=1", "i=2", "i=3", "i=4", "i=5", "i=6", "i=7"),\
'center right')
b.draw_frame(False)
plt.xlabel(r"$x$")
plt.ylabel(r"$M_i(x
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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