def test_lagvander(self) :
# check for 1d x
x = np.arange(3)
v = lag.lagvander(x, 3)
assert_(v.shape == (3, 4))
for i in range(4) :
coef = [0]*i + [1]
assert_almost_equal(v[..., i], lag.lagval(x, coef))
# check for 2d x
x = np.array([[1, 2], [3, 4], [5, 6]])
v = lag.lagvander(x, 3)
assert_(v.shape == (3, 2, 4))
for i in range(4) :
coef = [0]*i + [1]
assert_almost_equal(v[..., i], lag.lagval(x, coef))
def test_lagvander(self):
# check for 1d x
x = np.arange(3)
v = lag.lagvander(x, 3)
assert_(v.shape == (3, 4))
for i in range(4):
coef = [0]*i + [1]
assert_almost_equal(v[..., i], lag.lagval(x, coef))
# check for 2d x
x = np.array([[1, 2], [3, 4], [5, 6]])
v = lag.lagvander(x, 3)
assert_(v.shape == (3, 2, 4))
for i in range(4):
coef = [0]*i + [1]
assert_almost_equal(v[..., i], lag.lagval(x, coef))
def test_100(self):
x, w = lag.laggauss(100)
# test orthogonality. Note that the results need to be normalized,
# otherwise the huge values that can arise from fast growing
# functions like Laguerre can be very confusing.
v = lag.lagvander(x, 99)
vv = np.dot(v.T * w, v)
vd = 1/np.sqrt(vv.diagonal())
vv = vd[:, None] * vv * vd
assert_almost_equal(vv, np.eye(100))
# check that the integral of 1 is correct
tgt = 1.0
assert_almost_equal(w.sum(), tgt)
def test_100(self):
x, w = lag.laggauss(100)
# test orthogonality. Note that the results need to be normalized,
# otherwise the huge values that can arise from fast growing
# functions like Laguerre can be very confusing.
v = lag.lagvander(x, 99)
vv = np.dot(v.T * w, v)
vd = 1 / np.sqrt(vv.diagonal())
vv = vd[:, None] * vv * vd
assert_almost_equal(vv, np.eye(100))
# check that the integral of 1 is correct
tgt = 1.0
assert_almost_equal(w.sum(), tgt)
def vandermonde(self, x):
V = lag.lagvander(x, self.N-1)
return V
def vandermonde(self, x):
V = lag.lagvander(x, int(self.N * self.padding_factor) - 1)
return V
