def evaluate_basis_derivative_all(self, x=None, k=0, argument=0):
if x is None:
x = self.mesh(False, False)
V = self.vandermonde(x)
M = V.shape[1]
if k == 1:
D = np.zeros((M, M))
D[:-1, :] = lag.lagder(np.eye(M), 1)
W = np.dot(V, D)
W -= 0.5*V
V = W*np.exp(-x/2)[:, np.newaxis]
elif k == 2:
D = np.zeros((M, M))
D[:-2, :] = lag.lagder(np.eye(M), 2)
D[:-1, :] -= lag.lagder(np.eye(M), 1)
W = np.dot(V, D)
W += 0.25*V
V = W*np.exp(-x/2)[:, np.newaxis]
elif k == 0:
V *= np.exp(-x/2)[:, np.newaxis]
else:
raise NotImplementedError
return self._composite_basis(V)
def evaluate_basis_derivative(self, x=None, i=0, k=0, output_array=None):
if x is None:
x = self.mesh(False, False)
x = np.atleast_1d(x)
v = eval_laguerre(i, x, out=output_array)
X = x[:, np.newaxis]
if k == 1:
D = np.zeros((self.N, self.N))
D[:-1, :] = lag.lagder(np.eye(self.N), 1)
V = np.dot(v, D)
V -= 0.5 * v
V *= np.exp(-X / 2)
v[:] = V
elif k == 2:
D = np.zeros((self.N, self.N))
D[:-2, :] = lag.lagder(np.eye(self.N), 2)
D[:-1, :] -= lag.lagder(np.eye(self.N), 1)
V = np.dot(v, D)
V += 0.25 * v
V *= np.exp(-X / 2)
v[:] = V
elif k == 0:
v *= np.exp(-X / 2)
else:
raise NotImplementedError
return v
def test_lagder_axis(self):
# check that axis keyword works
c2d = np.random.random((3, 4))
tgt = np.vstack([lag.lagder(c) for c in c2d.T]).T
res = lag.lagder(c2d, axis=0)
assert_almost_equal(res, tgt)
tgt = np.vstack([lag.lagder(c) for c in c2d])
res = lag.lagder(c2d, axis=1)
assert_almost_equal(res, tgt)
def test_lagder_axis(self):
# check that axis keyword works
c2d = np.random.random((3, 4))
tgt = np.vstack([lag.lagder(c) for c in c2d.T]).T
res = lag.lagder(c2d, axis=0)
assert_almost_equal(res, tgt)
tgt = np.vstack([lag.lagder(c) for c in c2d])
res = lag.lagder(c2d, axis=1)
assert_almost_equal(res, tgt)
def test_lagder(self) :
# check exceptions
assert_raises(ValueError, lag.lagder, [0], .5)
assert_raises(ValueError, lag.lagder, [0], -1)
# check that zeroth deriviative does nothing
for i in range(5) :
tgt = [0]*i + [1]
res = lag.lagder(tgt, m=0)
assert_equal(trim(res), trim(tgt))
# check that derivation is the inverse of integration
for i in range(5) :
for j in range(2, 5) :
tgt = [0]*i + [1]
res = lag.lagder(lag.lagint(tgt, m=j), m=j)
assert_almost_equal(trim(res), trim(tgt))
# check derivation with scaling
for i in range(5) :
for j in range(2, 5) :
tgt = [0]*i + [1]
res = lag.lagder(lag.lagint(tgt, m=j, scl=2), m=j, scl=.5)
assert_almost_equal(trim(res), trim(tgt))
def test_lagder(self):
# check exceptions
assert_raises(ValueError, lag.lagder, [0], .5)
assert_raises(ValueError, lag.lagder, [0], -1)
# check that zeroth deriviative does nothing
for i in range(5):
tgt = [0] * i + [1]
res = lag.lagder(tgt, m=0)
assert_equal(trim(res), trim(tgt))
# check that derivation is the inverse of integration
for i in range(5):
for j in range(2, 5):
tgt = [0] * i + [1]
res = lag.lagder(lag.lagint(tgt, m=j), m=j)
assert_almost_equal(trim(res), trim(tgt))
# check derivation with scaling
for i in range(5):
for j in range(2, 5):
tgt = [0] * i + [1]
res = lag.lagder(lag.lagint(tgt, m=j, scl=2), m=j, scl=.5)
assert_almost_equal(trim(res), trim(tgt))