def test_cf_hamilton_linear_to_quadratic_matrix(self):
"""Compare the results of (1) asking directly for the linear
matrix for a given Hamiltonian, and (2) forming Hamilton's
equations and then linearizing them."""
dof = 3
terms = {Powers((2, 0, 0, 0, 0, 0)): -0.3,
Powers((1, 1, 0, 0, 0, 0)): 0.33,
Powers((0, 1, 0, 1, 1, 0)): 7.2,
Powers((0, 1, 0, 0, 1, 0)): 7.12,
Powers((0, 0, 3, 0, 1, 0)): -4.0 }
h = Polynomial(2*dof, terms=terms)
alg = LieAlgebra(dof)
diag = Diagonalizer(alg)
lin = diag.linear_matrix(h)
rhs = diag.hamiltons_equations_rhs(h)
rhs_lin = tuple([alg.isograde(h_term, 1) for h_term in rhs])
for i, pol in enumerate(rhs_lin):
for m, c in pol.powers_and_coefficients():
mon = alg.monomial(m, c)
self.assertEquals(alg.grade(mon), 1)
for j, f in enumerate(m):
if f==1:
self.assertEquals(lin[i, j], c)
def test_cf_hamilton_linear_to_quadratic_matrix(self):
"""Compare the results of (1) asking directly for the linear
matrix for a given Hamiltonian, and (2) forming Hamilton's
equations and then linearizing them."""
dof = 3
terms = {
Powers((2, 0, 0, 0, 0, 0)): -0.3,
Powers((1, 1, 0, 0, 0, 0)): 0.33,
Powers((0, 1, 0, 1, 1, 0)): 7.2,
Powers((0, 1, 0, 0, 1, 0)): 7.12,
Powers((0, 0, 3, 0, 1, 0)): -4.0
}
h = Polynomial(2 * dof, terms=terms)
alg = LieAlgebra(dof)
diag = Diagonalizer(alg)
lin = diag.linear_matrix(h)
rhs = diag.hamiltons_equations_rhs(h)
rhs_lin = tuple([alg.isograde(h_term, 1) for h_term in rhs])
for i, pol in enumerate(rhs_lin):
for m, c in pol.powers_and_coefficients():
mon = alg.monomial(m, c)
self.assertEquals(alg.grade(mon), 1)
for j, f in enumerate(m):
if f == 1:
self.assertEquals(lin[i, j], c)
def test_eigensystem(self):
"""Multiply eigenvectors and the original matrix by the
eigenvalues in order to check the integrity of the
eigensystem."""
dof = 3
terms = {Powers((2, 0, 0, 0, 0, 0)): -0.3,
Powers((1, 1, 0, 0, 0, 0)): 0.33,
Powers((0, 0, 1, 0, 1, 0)): 7.2,
Powers((0, 0, 0, 0, 0, 2)): 7.2,
Powers((0, 0, 0, 1, 1, 0)): 7.12 }
g = Polynomial(2*dof, terms=terms)
alg = LieAlgebra(dof)
diag = Diagonalizer(alg)
lin = diag.linear_matrix(g)
val_vec_pairs = diag.eigenvalue_eigenvector_pairs(g)
for p in val_vec_pairs:
prod_s = p.vec*p.val
prod_v = matrixmultiply(lin, p.vec)
for x in prod_s-prod_v:
self.assert_(abs(x)<1.0e-15)
def test_eigensystem(self):
"""Multiply eigenvectors and the original matrix by the
eigenvalues in order to check the integrity of the
eigensystem."""
dof = 3
terms = {
Powers((2, 0, 0, 0, 0, 0)): -0.3,
Powers((1, 1, 0, 0, 0, 0)): 0.33,
Powers((0, 0, 1, 0, 1, 0)): 7.2,
Powers((0, 0, 0, 0, 0, 2)): 7.2,
Powers((0, 0, 0, 1, 1, 0)): 7.12
}
g = Polynomial(2 * dof, terms=terms)
alg = LieAlgebra(dof)
diag = Diagonalizer(alg)
lin = diag.linear_matrix(g)
val_vec_pairs = diag.eigenvalue_eigenvector_pairs(g)
for p in val_vec_pairs:
prod_s = p.vec * p.val
prod_v = matrixmultiply(lin, p.vec)
for x in prod_s - prod_v:
self.assert_(abs(x) < 1.0e-15)