def test_smooth_missing(self):
kpm=scipy.io.loadmat(pkg_resources.resource_filename(__name__,'kpm_learn_results'))
y = kpm['y'].T # data vector is transposed from KPM
F1 = kpm['F1']
H1 = kpm['H1']
Q1 = kpm['Q1']
R1 = kpm['R1']
initx1 = kpm['initx']
initV1 = kpm['initV']
T,os = y.shape
# build data with missing observations specified by nan
if T>2:
y[2,:] = numpy.nan * numpy.ones( (os,) )
if T>12:
y[12,:] = numpy.nan * numpy.ones( (os,) )
# build data with missing observations specified by None
y_none = []
for yy in y:
if numpy.any( numpy.isnan( yy ) ):
y_none.append( None )
else:
y_none.append( yy )
# get results
xsmooth_nan, Vsmooth_nan = adskalman.kalman_smoother(y,F1,H1,Q1,R1,initx1,initV1)
xsmooth_none, Vsmooth_none = adskalman.kalman_smoother(y_none,F1,H1,Q1,R1,initx1,initV1)
# compare
assert numpy.allclose(xsmooth_nan, xsmooth_none)
assert numpy.allclose(Vsmooth_nan, Vsmooth_none)
def test_filt_KPM(self):
kpm=scipy.io.loadmat(pkg_resources.resource_filename(__name__,'kpm_results'))
# process model
A = numpy.array([[1, 0, 1, 0],
[0, 1, 0, 1],
[0, 0, 1, 0],
[0, 0, 0, 1]],
dtype=numpy.float64)
# observation model
C = numpy.array([[1, 0, 0, 0],
[0, 1, 0, 0]],
dtype=numpy.float64)
ss=4; os=2
# process covariance
Q = 0.1*numpy.eye(ss)
# measurement covariance
R = 1.0*numpy.eye(os)
initx = numpy.array([10, 10, 1, 0],dtype=numpy.float64)
initV = 10.0*numpy.eye(ss)
x = kpm['x'].T
y = kpm['y'].T
xfilt, Vfilt = adskalman.kalman_filter(y, A, C, Q, R, initx, initV)
assert numpy.allclose(xfilt.T,kpm['xfilt'])
assert_3d_vs_kpm_close(Vfilt,kpm['Vfilt'])
xsmooth, Vsmooth = adskalman.kalman_smoother(y,A,C,Q,R,initx,initV)
assert numpy.allclose(xsmooth.T,kpm['xsmooth'])
assert_3d_vs_kpm_close(Vsmooth,kpm['Vsmooth'])
def _test_kalman_murphy_smooth(self,missing_type):
Ymissing = numpy.array(self.Y, copy=True)
if missing_type=='nan':
valid_idx = None
elif missing_type=='large':
valid_idx = range(len(Ymissing))
else:
raise ValueError('unknown missing_type "%s"'%missing_type)
bad_idx = range(5,len(Ymissing),10)
for i in bad_idx:
if missing_type=='nan':
Ymissing[i] = numpy.nan*Ymissing[i]
elif missing_type=='large':
valid_idx.remove(i)
Ymissing[i] = 9e999*Ymissing[i]
assert len(bad_idx)>5 # make sure some data are actually missing!
xsmooth, Vsmooth = adskalman.kalman_smoother(Ymissing,self.A,self.C,self.Q,self.R,self.x0,self.P0,
valid_data_idx=valid_idx)
dist = numpy.sqrt(numpy.sum((xsmooth-self.X)**2,axis=1))
mean_dist = numpy.mean(dist)
#print 'mean_dist',missing_type,mean_dist
assert mean_dist < 0.1 # Not sure of exact value, but shouldn't be too large
def kalman_smoother(data, F, H, Q, R, initx, initv, plot=False):
os = H.shape[0]
ss = F.shape[0]
interpolated_data = np.zeros_like(data)
for c in range(os):
interpolated_data[:,c] = floris_math.interpolate_nan(data[:,c])
y = interpolated_data
xsmooth,Vsmooth = adskalman.kalman_smoother(y,F,H,Q,R,initx,initv)
if plot:
plt.plot(xsmooth[:,0])
plt.plot(y[:,0], '*')
return xsmooth,Vsmooth
def test_DRO_smooth(self):
kpm=scipy.io.loadmat(pkg_resources.resource_filename(__name__,'kpm_results'))
# process model
A = numpy.array([[1, 0, 1, 0],
[0, 1, 0, 1],
[0, 0, 1, 0],
[0, 0, 0, 1]],
dtype=numpy.float64)
# observation model
C = numpy.array([[1, 0, 0, 0],
[0, 1, 0, 0]],
dtype=numpy.float64)
ss=4; os=2
# process covariance
Q = 0.1*numpy.eye(ss)
# measurement covariance
R = 1.0*numpy.eye(os)
initx = numpy.array([10, 10, 1, 0],dtype=numpy.float64)
initV = 10.0*numpy.eye(ss)
x = kpm['x'].T
y = kpm['y'].T
xfilt, Vfilt = adskalman.DROsmooth(y,A,C,Q,R,initx,initV,mode='forward_only')
if 0:
xfilt_kpm, Vfilt_kpm = adskalman.kalman_filter(y, A, C, Q, R, initx, initV)
print 'xfilt.T',xfilt.T
print 'xfilt_kpm.T',xfilt_kpm.T
print "kpm['xfilt']",kpm['xfilt']
assert numpy.allclose(xfilt.T,kpm['xfilt'])
assert_3d_vs_kpm_close(Vfilt,kpm['Vfilt'])
xsmooth, Vsmooth = adskalman.DROsmooth(y,A,C,Q,R,initx,initV)
if 0:
xsmooth_kpm, Vsmooth_kpm = adskalman.kalman_smoother(y,A,C,Q,R,initx,initV)
print 'xsmooth.T',xsmooth.T
print 'xsmooth_kpm.T',xsmooth_kpm.T
print "kpm['xsmooth']",kpm['xsmooth']
print 'Vsmooth',Vsmooth
assert numpy.allclose(xsmooth.T[:,:-1],kpm['xsmooth'][:,:-1]) # KPM doesn't update last timestep
assert_3d_vs_kpm_close(Vsmooth[:-1],kpm['Vsmooth'][:,:,:-1])
def _test_kalman_murphy_EM(self): # temporarily disabled
def returnC(orig):
return self.C
def returnQ(orig):
return self.Q
def returnR(orig):
return self.R
constr_fun_dict = {
'C':returnC,
#'Q':returnQ,
#'R':returnR,
}
if 1:
print '-'*80,'Murphy'
Alearn, Clearn, Qlearn, Rlearn, initx2, initV2, LL = adskalman.learn_kalman(
self.Y, self.Abad, self.C, self.Q, self.R, self.x0,
self.P0, max_iter=500, verbose=2,
constr_fun_dict=constr_fun_dict,
thresh=1e-5,
)
xsmooth, Vsmooth, VVsmooth, loglik = adskalman.kalman_smoother(
self.Y,self.A,self.C,self.Q,self.R,self.x0,self.P0,
full_output=True)
if 1:
print 'best LL',loglik
print
print '*'*80,'Murphy'
print 'A'
print self.A
print 'Alearn'
print Alearn
print 'Clearn'
print Clearn
print 'Qlearn'
print Qlearn
print 'Rlearn'
print Rlearn
print '*'*80,'Murphy'
def test_loglik_KPM(self):
# this test broke the loglik calculation
kpm=scipy.io.loadmat(pkg_resources.resource_filename(__name__,'kpm_learn_results'))
y = kpm['y'].T # data vector is transposed from KPM
F1 = kpm['F1']
H1 = kpm['H1']
Q1 = kpm['Q1']
R1 = kpm['R1']
initx1 = kpm['initx']
initV1 = kpm['initV']
xfilt, Vfilt, VVfilt, loglik_filt = adskalman.kalman_filter(
y, F1, H1, Q1, R1, initx1, initV1,full_output=True)
assert numpy.allclose(xfilt, kpm['xfilt'].T)
assert_3d_vs_kpm_close(Vfilt, kpm['Vfilt'])
assert_3d_vs_kpm_close(VVfilt, kpm['VVfilt'])
assert numpy.allclose(loglik_filt, kpm['loglik_filt'])
xsmooth, Vsmooth, VVsmooth, loglik_smooth = adskalman.kalman_smoother(
y, F1, H1, Q1, R1, initx1, initV1,full_output=True)
assert numpy.allclose(xsmooth, kpm['xsmooth'].T)
assert_3d_vs_kpm_close(Vsmooth, kpm['Vsmooth'])
assert_3d_vs_kpm_close(VVsmooth, kpm['VVsmooth'])
assert numpy.allclose(loglik_smooth, kpm['loglik_smooth'])
def test_kalman__murphy1(self):
def returnC(orig):
return self.C
def returnQ(orig):
return self.Q
def returnR(orig):
return self.R
constr_fun_dict = {
'C':returnC,
'Q':returnQ,
'R':returnR,
}
print '-'*80,'Murphy'
Alearn, Clearn, Qlearn, Rlearn, initx2, initV2, LL = adskalman.learn_kalman(
self.Y, self.Abad, self.C, self.Q, self.R, self.x0,
self.P0, max_iter=150, verbose=2,
constr_fun_dict=constr_fun_dict,
)
xsmooth, Vsmooth, VVsmooth, loglik = adskalman.kalman_smoother(
self.Y,self.A,self.C,self.Q,self.R,self.x0,self.P0,
full_output=True)
print 'best LL',loglik
print
print '*'*80,'Murphy'
print 'A'
print self.A
print 'Alearn'
print Alearn
print 'Clearn'
print Clearn
print 'Qlearn'
print Qlearn
print 'Rlearn'
print Rlearn
print '*'*80,'Murphy'
[0,1,0,1],
[0,0,1,0],
[0,0,0,1]],
dtype=numpy.float)
H = numpy.array([[1,0,0,0], # observation matrix
[0,1,0,0]],
dtype=numpy.float)
Q = 0.1*numpy.eye(ss) # process noise
R = 1.0*numpy.eye(os) # observation noise
initx = numpy.array([10,10,1,0],dtype=numpy.float)
initV = 10*numpy.eye(ss)
T = 15
# This is the data that is generated by Murphy's demo.
#seed = 9
#numpy.random.seed(seed)
#x,y = adskalman.sample_lds(F,H,Q,R,initx,T)
x = numpy.array([[ 10. , 10.78562922, 12.14884733, 13.37768744, 14.70391646, 15.0972105 , 15.27100392, 16.02603256, 16.77868535, 17.35367989, 17.60693265, 17.90492854, 18.8527745 , 19.0826357 , 19.50682031],
[ 10. , 10.2018565 , 10.37289444, 10.24726726, 9.41747009, 9.23049962, 8.25498444, 7.93055042, 7.74377694, 6.57500322, 6.09083901, 6.04183098, 6.25299483, 5.86752675, 5.63880611],
[ 1. , 1.32750793, 0.89718228, 1.04323621, 0.6012368 , 0.38607908, 0.10314957, 0.58612548, 0.64803301, 0.31990456, 0.51884579, 1.12411301, 0.9584339 , 0.89764825, 0.99435954],
[ 0. , -0.13645972, -0.41671164, -0.91084177, -0.29670515, -0.80974329, -0.75982391, -0.28591924, -0.76442545, -0.16191313, 0.32366389, 0.19091798, -0.11169736, -0.20569391, 0.08488225]]).T
y = numpy.array([[ 11.49746646, 8.34917862, 12.2345992 , 13.01971219, 12.93696592, 14.91080222, 17.03870584, 14.63065253, 18.12204124, 16.81571886, 18.08187941, 17.91986286, 20.4956051 , 18.90627217, 19.40367059],
[ 10.37519837, 11.74461097, 10.10072462, 9.07503471, 9.47889654, 9.65741996, 9.11313015, 7.58503774, 6.4678298 , 5.02218694, 5.79485744, 4.45538921, 6.42789419, 6.45878971, 2.74446057]]).T
xsmooth,Vsmooth = adskalman.kalman_smoother(y,F,H,Q,R,initx,initV)
print 'xsmooth',xsmooth
print 'Vsmooth',Vsmooth
