def test_van_loan_integrating_exponentiator(self):
"""VanLoanIntegratingExponentiator should reproduce Felsenstein
analytic result, should throw if we pass it a defected matrix and ask
it to use CheckedExponentiator, will work with a defective matrix (that
we can integrate by hand) if we use the default RobustExponentiator,
and should work for different choices of R and exponentiatior."""
# Result from Von Bing's R code
I = expm.VanLoanIntegratingExponentiator(self.q, -diag(self.q))(1.0)
assert_allclose(dot(self.p0, I), self.result)
self.assertRaises(
ArithmeticError,
expm.VanLoanIntegratingExponentiator,
self.q,
-diag(self.q),
cmme.CheckedExponentiator,
)
Q = array([[1.0, 1.0], [0.0, 1.0]])
def integral(t):
return array(
[[exp(t) - 1.0, exp(t) * (t - 1.0) + 1.0], [0.0, exp(t) - 1.0]]
)
assert_allclose(expm.VanLoanIntegratingExponentiator(Q)(1.0), integral(1.0))
assert_allclose(expm.VanLoanIntegratingExponentiator(Q)(2.0), integral(2.0))
R = array([[1.0], [1.0]])
assert_allclose(
expm.VanLoanIntegratingExponentiator(Q, R, cmme.TaylorExponentiator)(1.0),
dot(integral(1.0), R),
)
def test_von_bing_integrating_exponentiator(self):
"""VonBingIntegratingExponentiator should reproduce Felsenstein
analytic result, should throw if we pass it a defective matrix, and
should match results obtained from VanLoanIntegratingExponentiator for
a diagonisable matrix."""
# Result from Von Bing's R code.
result = 0.7295333
q = array([[0.5, 0.2, 0.1, 0.2]] * 4)
for i in range(4):
q[i, i] = 0.0
q[i, i] = -sum(
q[
i,
]
)
p0 = array([0.2, 0.3, 0.3, 0.2])
I = expm.VonBingIntegratingExponentiator(q)(1.0)
assert_allclose(dot(dot(p0, I), -diag(q)), result)
self.assertRaises(
ArithmeticError,
expm.VonBingIntegratingExponentiator,
array([[1.0, 1.0], [0.0, 1.0]]),
)
p = array(
[
[0.86758487, 0.05575623, 0.0196798, 0.0569791],
[0.01827347, 0.93312148, 0.02109664, 0.02750842],
[0.04782582, 0.1375742, 0.80046869, 0.01413129],
[0.23022035, 0.22306947, 0.06995306, 0.47675713],
]
)
assert_allclose(
expm.VonBingIntegratingExponentiator(p)(1.0),
expm.VanLoanIntegratingExponentiator(
p, exponentiator=cmme.FastExponentiator
)(1.0),
)
assert_allclose(
expm.VonBingIntegratingExponentiator(p)(2.0),
expm.VanLoanIntegratingExponentiator(
p, exponentiator=cmme.FastExponentiator
)(2.0),
)
def test_van_loan_integrating_exponentiator(self):
"""VanLoanIntegratingExponentiator should reproduce Felsenstein
analytic result, should throw if we pass it a defected matrix and ask
it to use CheckedExponentiator, will work with a defective matrix (that
we can integrate by hand) if we use the default RobustExponentiator,
and should work for different choices of R and exponentiatior."""
# Result from Von Bing's R code
result = 0.7295333
q = array([[0.5, 0.2, 0.1, 0.2]] * 4)
for i in range(4):
q[i, i] = 0.0
q[i, i] = -sum(q[i,])
p0 = array([0.2, 0.3, 0.3, 0.2])
I = expm.VanLoanIntegratingExponentiator(q, -diag(q))(1.0)
self.assertFloatEqual(dot(p0, I), result)
self.assertRaises(
ArithmeticError,
expm.VanLoanIntegratingExponentiator,
q,
-diag(q),
cmme.CheckedExponentiator,
)
Q = array([[1.0, 1.0], [0.0, 1.0]])
def integral(t):
return array(
[[exp(t) - 1.0, exp(t) * (t - 1.0) + 1.0], [0.0, exp(t) - 1.0]]
)
self.assertFloatEqual(
expm.VanLoanIntegratingExponentiator(Q)(1.0), integral(1.0)
)
self.assertFloatEqual(
expm.VanLoanIntegratingExponentiator(Q)(2.0), integral(2.0)
)
R = array([[1.0], [1.0]])
self.assertFloatEqual(
expm.VanLoanIntegratingExponentiator(Q, R, cmme.TaylorExponentiator)(1.0),
dot(integral(1.0), R),
)
