def test_rsolve():
random = RandomState(0)
A = random.randn(1, 1)
b = random.randn(1)
assert_allclose(solve(A, b), npy_solve(A, b))
A = random.randn(2, 2)
b = random.randn(2)
assert_allclose(solve(A, b), npy_solve(A, b))
A = random.randn(3, 3)
b = random.randn(3)
assert_allclose(rsolve(A, b), npy_solve(A, b))
A[:] = 1e-10
assert_allclose(rsolve(A, b), zeros(A.shape[1]))
A = zeros((0, 0))
b = zeros((0, ))
assert_(rsolve(A, b).ndim == 1)
assert_(rsolve(A, b).shape[0] == 0)
A = zeros((0, 1))
b = zeros((0, ))
assert_(rsolve(A, b).ndim == 1)
assert_(rsolve(A, b).shape[0] == 1)
def test_solve_raise():
A = array([[2.05036632, 2.05036632], [2.05036632, 2.05036632]])
b = array([0.11260227, 0.11260227])
with pytest.raises(LinAlgError):
solve(A, b)
A = array([[0.0]])
b = array([1.0])
with pytest.raises(LinAlgError):
solve(A, b)
def test_solve():
random = RandomState(0)
A = random.randn(1, 1)
b = random.randn(1)
assert_allclose(solve(A, b), npy_solve(A, b))
A = random.randn(2, 2)
b = random.randn(2)
assert_allclose(solve(A, b), npy_solve(A, b))
A = random.randn(3, 3)
b = random.randn(3)
assert_allclose(solve(A, b), npy_solve(A, b))
def _optimal_tbeta(self):
self._update()
if all(abs(self._M) < 1e-15):
return zeros_like(self._tbeta)
u = dot(self._tM.T, self._optimal_beta_nom())
Z = self._optimal_tbeta_denom()
try:
with errstate(all='raise'):
self._tbeta = solve(Z, u)
except (LinAlgError, FloatingPointError):
self._logger.warning('Failed to compute the optimal beta.' +
' Zeroing it.')
self.__tbeta[:] = 0.
return self.__tbeta
def _update_fixed_effects(self):
nominator = self._b1 - self._b0
denominator = self._c1 - self._c0
self._tbeta = solve(denominator, nominator)
def beta(self):
r"""Returns :math:`\boldsymbol\beta`."""
return solve(self._svd_V.T, self._tbeta / self._svd_S12)
def fast_scan(self, markers):
r"""LMLs of markers by fitting scale and fixed-effect sizes parameters.
The likelihood is given by
.. math::
\mathcal N\big(~\mathbf y ~|~ \boldsymbol\beta^{\intercal}
[\mathrm M ~~ \tilde{\mathrm M}], s \mathrm K~\big),
where :math:`s` is the scale parameter and :math:`\boldsymbol\beta` is the
fixed-effect sizes; :math:`\tilde{\mathrm M}` is a marker to be scanned.
"""
assert markers.ndim == 2
nc = self.M.shape[1]
M = self.M
MTQ0 = dot(M.T, self.Q0)
mTQ0 = dot(markers.T, self.Q0)
MTQ1 = dot(M.T, self.Q1)
mTQ1 = dot(markers.T, self.Q1)
yTQ0diag0 = self.yTQ0 / self.diag0
yTQ1diag1 = self.yTQ1 / self.diag1
b0 = yTQ0diag0.dot(MTQ0.T)
b0m = yTQ0diag0.dot(mTQ0.T)
MTQ0diag0 = MTQ0 / self.diag0
MTQ1diag1 = MTQ1 / self.diag1
c0_00 = MTQ0diag0.dot(MTQ0.T)
c0_01 = MTQ0diag0.dot(mTQ0.T)
c0_11 = sum((mTQ0 / self.diag0) * mTQ0, axis=1)
b1 = yTQ1diag1.dot(MTQ1.T)
b1m = yTQ1diag1.dot(mTQ1.T)
c1_00 = MTQ1diag1.dot(MTQ1.T)
c1_01 = MTQ1diag1.dot(mTQ1.T)
c1_11 = sum((mTQ1 / self.diag1) * mTQ1, axis=1)
C0 = empty((nc + 1, nc + 1))
C0[:-1, :-1] = c0_00
C1 = empty((nc + 1, nc + 1))
C1[:-1, :-1] = c1_00
n = markers.shape[0]
lmls = empty(markers.shape[1])
effect_sizes = empty(markers.shape[1])
LOG2PI = 1.837877066409345339081937709124758839607238769531250
lmls[:] = -n * LOG2PI - n
lmls[:] += -sum(log(self.diag0)) - (n - len(self.diag0)) * log(
self.diag1)
for i in range(markers.shape[1]):
b11m = append(b1, b1m[i])
b00m = append(b0, b0m[i])
nominator = b11m - b00m
C0[:-1, -1] = c0_01[:, i]
C1[:-1, -1] = c1_01[:, i]
C0[-1, :-1] = C0[:-1, -1]
C1[-1, :-1] = C1[:-1, -1]
C0[-1, -1] = c0_11[i]
C1[-1, -1] = c1_11[i]
denominator = C1 - C0
beta = solve(denominator, nominator)
effect_sizes[i] = beta[-1]
p0 = self.a1 - 2 * b11m.dot(beta) + beta.dot(C1.dot(beta))
p1 = self.a0 - 2 * b00m.dot(beta) + beta.dot(C0).dot(beta)
scale = (p0 + p1) / n
lmls[i] -= n * log(scale)
lmls /= 2
return lmls, effect_sizes