basis_array.py

import scipy.signal as ss
import numpy as np
import scipy.misc as mi
import matplotlib.pyplot as plt

def deboor(k,t):
	m = len(t) - 1
	a, b, _k, _m = [], [], xrange(k + 1), xrange(m)
	for i in _m:
		a.append([]); b.append([])
		for k in _k:
			a[i].append(None)
			if k == 0: b[i].append(lambda t_, i = i: t[i] <= t_ < t[i + 1])
			elif m < i + k: b[i].append(lambda t_: False)
			else:
				if t[i] == t[i + k]: a[i][k] = lambda t_: False
				else:
					a[i][k] = lambda t_, i = i, k = k: ((t_ - t[i]) /
													   (t[i + k] - t[i]))
				b[i].append(lambda t_, i = i, k = k:
								a[i][k](t_) * b[i][k - 1](t_) +
								(1 - a[i + 1][k](t_)) * b[i + 1][k - 1](t_))
	return b# set b


for power in range(11):
    n=2**power+3-1
    print "Generating Basis with "+str(n+1)+" elements"
    k = 3                                                                   # degree of curve
    m = n + k + 1                                                           # property of b-splines: m = n + k + 1
    _t = 1.0 / (m - k * 2)                                                    # t between clamped ends will be evenly spaced (not a necessary condition, however)
                                                                # the endpoints of clamped splines have a multiplicity of k + 1 (the endpoint knots are repeated k + 1 times)
    t = k * [0] + [t_ * _t for t_ in xrange(m - (k * 2) + 1)] + [1] * k     # clamp ends and get the t between them (+1 in the xrange to iterate to index m - k * 2)
    
    b=deboor(3,t)
    _n=xrange(len(t)-1-k-1+1)
    t_=np.arange(0,1.0004,.0004)
    
    
    
    f_h=open("./basis_data_2500/basis_array_"+str(n+1)+".txt",'w')
    u_len=len(t_)
    at_first=1
    for i in t_:
        dummy=np.array([])
        for j in range(n+1):
            dummy=np.append(dummy,b[j][k](i))
        if at_first==1:
            at_first=0
            b_mat=dummy
        else:
            b_mat=np.vstack((b_mat,dummy))
    np.savetxt(f_h,b_mat)
    f_h.close()
    
    for i in range(n+1):
        plt.plot(t_,b_mat[:,i])
    plt.savefig("./basis_data_2500/basis_fig_"+str(n+1)+".png")
    plt.clf()
    print "Generation and Saving figure complete"
#plt.show()