def __get_collocation_nodes(self, m, kind):
"""Computes the collocation nodes."""
# basis coefs
coefs = np.zeros(m + 1)
coefs[-1] = 1
if kind == 'polynomial':
nodes = polynomial.Polynomial(coefs).roots()
elif kind == 'chebyshev':
domain = [self.a, self.b]
nodes = polynomial.Chebyshev(coefs, domain).roots()
elif kind == 'legendre':
domain = [self.a, self.b]
nodes = polynomial.Legendre(coefs, domain).roots()
elif kind == 'laguerre':
domain = [self.a, self.b]
nodes = polynomial.Laguerre(coefs, domain).roots()
elif kind == 'hermite':
domain = [self.a, self.b]
nodes = polynomial.Hermite(coefs, domain).roots()
else:
raise ValueError
return nodes
def __get_lege_yhat(self, coefs):
"""Constructs a Legendre polynomial approximation to the solution."""
# the solution y is in R^n
n = coefs.shape[0]
# create the approximation yhat
domain = [self.a, self.b]
yhat = [polynomial.Legendre(coefs[i], domain) for i in range(n)]
# create the approximation of yhat_prime
yhat_prime = [yhat[i].deriv() for i in range(n)]
return [yhat, yhat_prime]
def test_legendre_repr(self):
res = repr(poly.Legendre([0, 1]))
tgt = 'Legendre([0., 1.], domain=[-1, 1], window=[-1, 1])'
assert_equal(res, tgt)
def test_legendre_str(self):
res = str(poly.Legendre([0, 1]))
tgt = 'leg([0. 1.])'
assert_equal(res, tgt)
def test_legendre_repr(self):
res = repr(poly.Legendre([0,1]))
tgt = 'Legendre([0., 1.], [-1., 1.], [-1., 1.])'
assert_(res, tgt)
def test_legendre_str(self, inp, tgt):
res = str(poly.Legendre(inp))
assert_equal(res, tgt)
def test_legendre_repr(self):
res = repr(poly.Legendre([0, 1]))
tgt = ("Legendre([0., 1.], domain=[-1, 1], window=[-1, 1], "
"symbol='x')")
assert_equal(res, tgt)
