def test_matrix(self):
knots = np.hstack((np.zeros(3), np.linspace(0,1,self.nrKnots-4),
np.ones(3)))
xi=(knots[1:-3]+knots[2:-2]+knots[3:-1])/3
nMatrix=np.zeros((len(xi),len(xi)))
for i in xrange(len(xi)):
fun = spline.basisFunction(i,knots)
nMatrix[:,i]=fun(xi,3)
revMatrix = nMatrix[::-1,::-1]
for i in xrange(nMatrix.size):
self.assertAlmostEqual(revMatrix.flat[i],nMatrix.flat[i])
def test_SumsUpToOne(self):
# the sum of the basis functions should add up to one
s = zeros([10,2])
u = linspace(0,1,10)
for i in range(10):
for j in range(12):
b = sp.basisFunction(u,j)
s[i] = s[i] + b(u[i])
b = abs(s[:,:] - 1.0) < finfo(double).eps #machine epsilon
# print b,s,sum(b)
assert(sum(b)==20)
def test_addsToOne(self):
knots = np.hstack((np.zeros(3), np.linspace(0,1,self.nrKnots-4),
np.ones(3)))
Ns = []
for i in xrange(len(knots)-4):
Ns.append(spline.basisFunction(i,knots))
x = np.random.random(1000)
y = np.zeros(len(x))
for n in Ns:
y += n(x)
for val in y:
self.assertAlmostEqual(val,1.)
def test_samefromblossomasfromrecursion(self):
cp = array([[0.,0.1], [0.3,0.6], [0.7,0.8],[1.0,0.2]]);
s = sp.Spline(cp);
N = [sp.basisFunction(s.getKnots()[2:-2], j) for j in range(len(cp))]
same = True;
for i in linspace(0,1,400):
s1 = s(i);
s2 = 0;
for j in range(len(cp)):
s2 += cp[j]*N[j](i);
# print s1
# print s2
self.assertAlmostEqual(s1.all(),s2.all());
