def setUp(self):
dt = 0.5
# process model
A = numpy.array([[1, 0, dt, 0],
[0, 1, 0, dt],
[0, 0, .5, 0],
[0, 0, 0, .5]],
dtype=numpy.float64)
# observation model
C = numpy.array([[1, 0, 0, 0],
[0, 1, 0, 0]],
dtype=numpy.float64)
# process covariance
Q = numpy.eye(4)
Q[:2,:2] = [[ 2, .1],[.1,2]]
# measurement covariance
R = numpy.array([[ 1, 0.2], [0.2, 1]],
dtype=numpy.float64)
Q = 0.001*Q
R = 0.001*R
N = 1000
numpy.random.seed(4)
x0 = numpy.random.randn( 4 )
P0 = numpy.random.randn( 4,4 )
process_noise = adskalman.rand_mvn( 0, Q, N )
observation_noise = adskalman.rand_mvn( 0, R, N )
X = []
Y = []
x = x0
for i in range(N):
X.append( x )
Y.append( numpy.dot(C,x) + observation_noise[i] )
x = numpy.dot(A,x) + process_noise[i] # for next time step
X = numpy.array(X)
Y = numpy.array(Y)
Abad = numpy.eye(4)
#Abad[0,0] = 0
#Abad[1,1] = 100
#Abad[0,2] = .0
#Abad[1,3] = .0
self.Y = Y
self.A = A
self.Abad = Abad
self.C = C
self.Q = Q
self.R = R
self.x0 = x0
self.P0 = P0
def setUp(self):
# process model
A = numpy.array([[1, 0],
[0, .5]],
dtype=numpy.float64)
# observation model
C = numpy.array([[1, 0],
[0, 1]],
dtype=numpy.float64)
# process covariance
Q = numpy.eye(2)
# measurement covariance
R = numpy.eye(2)
Q = 0.001*Q
R = 0.001*R
N = 1000
numpy.random.seed(4)
x0 = numpy.random.randn( 2 )
P0 = numpy.random.randn( 2,2 )
process_noise = adskalman.rand_mvn( 0, Q, N )
observation_noise = adskalman.rand_mvn( 0, R, N )
#pylab.hist( process_noise[:,0], bins=100)
#pylab.show()
X = []
Y = []
x = x0
for i in range(N):
X.append( x )
Y.append( numpy.dot(C,x) + observation_noise[i] )
x = numpy.dot(A,x) + process_noise[i] # for next time step
X = numpy.array(X)
Y = numpy.array(Y)
Abad = numpy.eye(2)
Abad[0,0] = .1
Abad[1,1] = 4
self.X = X
self.Y = Y
self.A = A
self.Abad = Abad
self.C = C
self.Q = Q
self.R = R
self.x0 = x0
self.P0 = P0
def test_rand_mvn2(self):
mu = numpy.array([1])
sigma = 2*numpy.eye(1)
N = 10000
Y = adskalman.rand_mvn(mu,sigma,N)
Y2 = numpy.random.standard_normal((N,1))*sigma[0]+mu[0]
assert Y.shape == (N,1)
assert Y2.shape == (N,1)
Y = Y[:,0] # drop an axis
Y2 = Y2[:,0] # drop an axis
meanY = numpy.mean(Y)
#print 'meanY',meanY
meanY2 = numpy.mean(Y2)
#print 'meanY2',meanY2
# according to z-test on wikipedia
SE = sigma[0]/numpy.sqrt(N)
SE2 = sigma[0]/numpy.sqrt(N)
z = (meanY-mu[0])/SE
z2 = (meanY2-mu[0])/SE2
if abs(z) > 3:
raise ValueError('Sample mean was three sigma away from true mean. This error is expected rarely.')
if abs(z2) > 3:
raise ValueError('Sample mean was three sigma away from true mean. This error is expected rarely.')
def test_rand_mvn1(self):
mu = numpy.array([1,2,3,4])
sigma = numpy.eye(4)
sigma[:2,:2] = [[2.0, 0.1],[0.1,0.2]]
N = 1000
Y = adskalman.rand_mvn(mu,sigma,N)
assert Y.shape==(N,4)
mu2 = numpy.mean(Y,axis=0)
eps = .2
assert numpy.sqrt(numpy.sum((mu-mu2)**2)) < eps # expect occasional failure here
sigma2 = adskalman.covar(Y)
eps = .3
assert numpy.sqrt(numpy.sum((sigma-sigma2)**2)) < eps # expect occasional failure here