def assertJacobian(self, f, Jf, x0, tol=1e-5, h=1e-8, verbose=False):
x0 = asarray(x0)
# if Jf is a function then just evaluate it once
if callable(Jf):
J_analytic = atleast_2d(Jf(x0))
else:
J_analytic = atleast_2d(Jf)
# Compute numeric jacobian
J_numeric = finite_differences.numeric_jacobian(f, x0, h)
# Check shape
self.assertEqual(J_analytic.shape, J_numeric.shape)
# Compute error
J_abserr = np.abs(J_analytic - J_numeric)
mask = np.abs(J_numeric) > 1.
J_abserr[mask] /= np.abs(J_numeric[mask])
# Check error
maxerr = np.max(J_abserr) # threshold should be independent of matrix size
if maxerr > tol:
raise JacobianAssertionError(J_numeric, J_analytic)
elif verbose:
print 'numeric:'
print J_numeric
print 'analytic:'
print J_analytic
def compute_posterior(x0, x1, R_mean, t_mean):
x = concatenate((x0,x1))
Fmat = lambda R,t: fundamental.make_fundamental(eye(3), R, t)
f_alg = lambda R,t: algebraic_cost(Fmat(R, t), x0, x1)
J_alg = lambda R,t: Jalgebraic_cost_x(Fmat(R, t), x0, x1)
# sampson errors
E_sampson = lambda R,t: ssq(sampson.firstorder_deviation(x, f_alg(R,t), J_alg(R,t)))
E_sampson_charted = lambda v: E_sampson(se3_chart((R_mean, t_mean), v))
# sampson reprojections
sampson_prediction = lambda (R,t): sampson.firstorder_reprojection(x, f_alg(R,t), J_alg(R,t))
sampson_prediction_charted = lambda v: sampson_prediction(se3_chart((R_mean,t_mean), v))
# prediction jacobian
Jprediction = finite_differences.numeric_jacobian(sampson_prediction_charted,
zeros(6))
# compute likelihood in terms of R and t
prediction = sampson_prediction((R_mean, t_mean))
print prediction
print Jprediction
print x
print SENSOR_INFO
v,L = beliefs.compute_likelihood(zeros(6), prediction, Jprediction, x, eye(6))
print 'R_mean:'
print R_mean
print 't_mean'
print t
# compute mean and variance
print 'v'
print v.round(2)
print 'L'
print L.round(2)
mean,cov = beliefs.normal_to_invnormal(v,L)
print 'mean:'
print mean
print 'cov:'
print cov