def test_ywcoef():
assert_array_almost_equal(
mlywar.arcoef100[1:],
-regression.yule_walker(x100, 10, method="mle")[0],
8,
)
assert_array_almost_equal(
mlywar.arcoef1000[1:],
-regression.yule_walker(x1000, 20, method="mle")[0],
8,
)
def apply(self, chunk):
if chunk.shape[0] <= self.max_chunk_size:
x = self.buffer.update_buffer(chunk)
y = sg.filtfilt(*self.ba_bandpass, x)
if self.delay < self.n_taps_edge_left:
ar, s = yule_walker(y.real[:-self.n_taps_edge_left], self.ar_order, 'mle')
pred = y.real[:-self.n_taps_edge_left].tolist()
for _ in range(self.n_taps_edge_left + self.n_taps_edge_right):
pred.append(ar[::-1].dot(pred[-self.ar_order:]))
an_signal = sg.hilbert(pred)
env = an_signal[-self.n_taps_edge_right-self.delay-len(chunk)+1:-self.n_taps_edge_right-self.delay+1]*np.ones(len(chunk))
#
# plt.plot(x, alpha=0.1)
# plt.plot(pred, alpha=0.9)
# plt.plot(np.abs(an_signal))
# plt.plot(y[:-self.n_taps_edge_left], 'k')
# plt.plot(y, 'k--')
#
# plt.show()
else:
env = sg.hilbert(y)[-self.delay-len(chunk)+1:-self.delay+1] * np.ones(len(chunk))
return env, y, pred
else:
return rt_emulate(self, chunk, self.max_chunk_size)
if __name__ == '__main__':
nobs = 50
ar = [1.0, -0.8, 0.1]
ma = [1.0, 0.1, 0.2]
#ma = [1]
np.random.seed(9875789)
y = arma_generate_sample(ar, ma, nobs, 2)
y -= y.mean() #I have not checked treatment of mean yet, so remove
mod = MLEGLS(y)
mod.nar, mod.nma = 2, 2 #needs to be added, no init method
mod.nobs = len(y)
res = mod.fit(start_params=[0.1, -0.8, 0.2, 0.1, 1.])
print('DGP', ar, ma)
print(res.params)
from statsmodels.regression import yule_walker
print(yule_walker(y, 2))
#resi = mod.fit_invertible(start_params=[0.1,0,0.2,0, 0.5])
#print(resi.params
arpoly, mapoly = getpoly(mod, res.params[:-1])
data = sm.datasets.sunspots.load(as_pandas=False)
#ys = data.endog[-100:]
## ys = data.endog[12:]-data.endog[:-12]
## ys -= ys.mean()
## mods = MLEGLS(ys)
## mods.nar, mods.nma = 13, 1 #needs to be added, no init method
## mods.nobs = len(ys)
## ress = mods.fit(start_params=np.r_[0.4, np.zeros(12), [0.2, 5.]],maxiter=200)
## print(ress.params
## import matplotlib.pyplot as plt
def genelwwLOCwithoutdelay(one_signal, orderLPC,
Fs_Hz, az_deg, el_deg, velocity_mps, Sigma_aec, xsensors_m):
"""
# Generate loss of coherence with noise
# Synopsis:
# genelwwLOCwithoutdelay(one_signal, orderLPC,
# Fs_Hz, az_deg,el_deg, velocity_mps, Sigma_aec, xsensors_m)
# Inputs
# ones_signal: one SOI
# orderLPC:
# Fs_Hz: sampling frequency in Hz
# az_deg, el_deg, velocity_mps:
# deterministic part of the DOA
#
# Sigma_aec : 3 array of the varaince of the random part of the DOA
# Sigma_aec[0] = std of the azimuth in rd
# Sigma_aec[1] = std of the elevation in rd
# Sigma_aec[2] = std of the velocity in m/s
#
# xsensor_m: M x 3
# 3D locations of the M sensors
#
#=======
# Outputs:
# signal_withLOC:
# M-ary signal (with delays and LOC)
#
# tau_s: TDOA on the C=M(M-1)/2 sensor pairs
# tau_s = (r_m-r_k)' x theta
# where theta is the wavenumber (in s/m)
#
# signal_withoutLOC:
# M-ary signal (with delays but without LOC)
#
# Gamma2_epsilon:
# positive matrix en s2/m2Ctrl+S (LOC)
#=====================================================================
"""
M = size(xsensors_m,0);
az_rd = az_deg*pi/180;
el_rd = el_deg*pi/180;
cosa = cos(az_rd);
sina = sin(az_rd);
cose = cos(el_rd);
sine = sin(el_rd);
##===== deterministic part
theta0_spm = array([-sina*cose, -cosa*cosa, sine]/velocity_mps);
##===== random part
Jacobian = zeros([3,3])
Jacobian[:,0] = array([-cosa*cose, sina*sine, \
sina*cose/velocity_mps]/velocity_mps);
Jacobian[:,1] = array([sina*cose, cosa*sine, \
cosa*cose/velocity_mps]/velocity_mps);
Jacobian[:,2] = array([0, cose, \
-sine/velocity_mps]/velocity_mps);
Gamma2_epsilon = dot(transpose(Jacobian), \
dot((Sigma_aec*Sigma_aec),Jacobian));
## AR analysis
#%%
N = len(one_signal);
theta_lp, sigma_AR = yule_walker(one_signal,orderLPC);
theta_AR = append(1,theta_lp)
residue = lfilter(theta_AR,[1.0],one_signal)/sigma_AR;
F_Hz = Fs_Hz*array(range(N))/N;
F2_Hz2 = F_Hz ** 2;
pi2 = pi*pi;
#==== extract M random sequences from residue by permutation
wwhite = zeros([N,M]);
wwhite[:,0] = residue[:,0];
for im in range(1,M):
wwhite[:,im] = residue[random.permutation(N),0];
#=== innovation generation
cf = ones([M,M,N]);
cp = 0;
for im1 in range(M-1):
for im2 in range(im1+1,M):
cp = cp+1;
sigma2_s2 = dot(dot((xsensors_m[im2,:]-xsensors_m[im1,:]),
Gamma2_epsilon),(xsensors_m[im2,:]-xsensors_m[im1,:]));
# LOC WITHOUT delays
cf[im1,im2,:] = exp(-2*pi2*F2_Hz2*sigma2_s2);
cf[im2,im1,:] = conj(cf[im1,im2,:]);
Wf = fft(wwhite);
Xf = zeros([N,M])+ complex(0,1)*zeros([N,M])
#=== GG = zeros([M,M,N]);
for indf in range(N/2): # 1:N/2+1,
GGaux = cf[:,:,indf];
UG,GGauxsvd,VG = svd(GGaux);
sqrtmGGaux = dot(dot(UG,diag(sqrt(GGauxsvd))),VG);
Xf[indf,:] = dot(Wf[indf,:],sqrtmGGaux);
Xf[range(N/2+1,N),:] = conj(Xf[range(N-N/2-1,0,-1),:]);
Xf[N/2,:] = real(Xf[N/2,:])/2.0;
Xf[0,:] = real(Xf[0,:])/2.0;
xt = ifft(Xf, axis=0);
signal_out_aux = real(xt);
signal_out_aux = signal_out_aux-ones([N,1])\
*mean(signal_out_aux);
#=== synthesis of signal
signal_out_with = signal_out_aux;
signal_withLOC = signal_out_aux;
for im in range(M):
xe = signal_out_aux[:,im];
signal_out_with[:,im] = lfilter([1.0], theta_AR, xe);
signal_withLOC[:,im] = signal_out_with[:,im]\
/ std(signal_out_with[:,im]);
return signal_withLOC, theta0_spm, Gamma2_epsilon, cf
if __name__ == '__main__':
nobs = 50
ar = [1.0, -0.8, 0.1]
ma = [1.0, 0.1, 0.2]
#ma = [1]
np.random.seed(9875789)
y = arma_generate_sample(ar,ma,nobs,2)
y -= y.mean() #I haven't checked treatment of mean yet, so remove
mod = MLEGLS(y)
mod.nar, mod.nma = 2, 2 #needs to be added, no init method
mod.nobs = len(y)
res = mod.fit(start_params=[0.1, -0.8, 0.2, 0.1, 1.])
print('DGP', ar, ma)
print(res.params)
from statsmodels.regression import yule_walker
print(yule_walker(y, 2))
#resi = mod.fit_invertible(start_params=[0.1,0,0.2,0, 0.5])
#print(resi.params
arpoly, mapoly = getpoly(mod, res.params[:-1])
data = sm.datasets.sunspots.load(as_pandas=False)
#ys = data.endog[-100:]
## ys = data.endog[12:]-data.endog[:-12]
## ys -= ys.mean()
## mods = MLEGLS(ys)
## mods.nar, mods.nma = 13, 1 #needs to be added, no init method
## mods.nobs = len(ys)
## ress = mods.fit(start_params=np.r_[0.4, np.zeros(12), [0.2, 5.]],maxiter=200)
## print(ress.params
## import matplotlib.pyplot as plt
if __name__ == '__main__':
nobs = 50
ar = [1.0, -0.8, 0.1]
ma = [1.0, 0.1, 0.2]
#ma = [1]
np.random.seed(9875789)
y = arma_generate_sample(ar,ma,nobs,2)
y -= y.mean() #I haven't checked treatment of mean yet, so remove
mod = MLEGLS(y)
mod.nar, mod.nma = 2, 2 #needs to be added, no init method
mod.nobs = len(y)
res = mod.fit(start_params=[0.1, -0.8, 0.2, 0.1, 1.])
print 'DGP', ar, ma
print res.params
from statsmodels.regression import yule_walker
print yule_walker(y, 2)
#resi = mod.fit_invertible(start_params=[0.1,0,0.2,0, 0.5])
#print resi.params
arpoly, mapoly = getpoly(mod, res.params[:-1])
data = sm.datasets.sunspots.load()
#ys = data.endog[-100:]
## ys = data.endog[12:]-data.endog[:-12]
## ys -= ys.mean()
## mods = MLEGLS(ys)
## mods.nar, mods.nma = 13, 1 #needs to be added, no init method
## mods.nobs = len(ys)
## ress = mods.fit(start_params=np.r_[0.4, np.zeros(12), [0.2, 5.]],maxiter=200)
## print ress.params
## #from statsmodels.sandbox.tsa import arima as tsaa
def arCoeff(array):
sigma, rho = regression.yule_walker(array, order=4)
return sigma, rho
if __name__ == '__main__':
nobs = 50
ar = [1.0, -0.8, 0.1]
ma = [1.0, 0.1, 0.2]
#ma = [1]
np.random.seed(9875789)
y = arma_generate_sample(ar, ma, nobs, 2)
y -= y.mean() #I haven't checked treatment of mean yet, so remove
mod = MLEGLS(y)
mod.nar, mod.nma = 2, 2 #needs to be added, no init method
mod.nobs = len(y)
res = mod.fit(start_params=[0.1, -0.8, 0.2, 0.1, 1.])
print 'DGP', ar, ma
print res.params
from statsmodels.regression import yule_walker
print yule_walker(y, 2)
#resi = mod.fit_invertible(start_params=[0.1,0,0.2,0, 0.5])
#print resi.params
arpoly, mapoly = getpoly(mod, res.params[:-1])
data = sm.datasets.sunspots.load()
#ys = data.endog[-100:]
## ys = data.endog[12:]-data.endog[:-12]
## ys -= ys.mean()
## mods = MLEGLS(ys)
## mods.nar, mods.nma = 13, 1 #needs to be added, no init method
## mods.nobs = len(ys)
## ress = mods.fit(start_params=np.r_[0.4, np.zeros(12), [0.2, 5.]],maxiter=200)
## print ress.params
## #from statsmodels.sandbox.tsa import arima as tsaa
def genelwwLOCwithoutdelay(one_signal, orderLPC, Fs_Hz, az_deg, el_deg,
velocity_mps, Sigma_aec, xsensors_m):
"""
# Generate loss of coherence with noise
# Synopsis:
# genelwwLOCwithoutdelay(one_signal, orderLPC,
# Fs_Hz, az_deg,el_deg, velocity_mps, Sigma_aec, xsensors_m)
# Inputs
# ones_signal: one SOI
# orderLPC:
# Fs_Hz: sampling frequency in Hz
# az_deg, el_deg, velocity_mps:
# deterministic part of the DOA
#
# Sigma_aec : 3 array of the varaince of the random part of the DOA
# Sigma_aec[0] = std of the azimuth in rd
# Sigma_aec[1] = std of the elevation in rd
# Sigma_aec[2] = std of the velocity in m/s
#
# xsensor_m: M x 3
# 3D locations of the M sensors
#
#=======
# Outputs:
# signal_withLOC:
# M-ary signal (with delays and LOC)
#
# tau_s: TDOA on the C=M(M-1)/2 sensor pairs
# tau_s = (r_m-r_k)' x theta
# where theta is the wavenumber (in s/m)
#
# signal_withoutLOC:
# M-ary signal (with delays but without LOC)
#
# Gamma2_epsilon:
# positive matrix en s2/m2Ctrl+S (LOC)
#=====================================================================
"""
M = size(xsensors_m, 0)
az_rd = az_deg * pi / 180
el_rd = el_deg * pi / 180
cosa = cos(az_rd)
sina = sin(az_rd)
cose = cos(el_rd)
sine = sin(el_rd)
##===== deterministic part
theta0_spm = array([-sina * cose, -cosa * cosa, sine] / velocity_mps)
##===== random part
Jacobian = zeros([3, 3])
Jacobian[:,0] = array([-cosa*cose, sina*sine, \
sina*cose/velocity_mps]/velocity_mps)
Jacobian[:,1] = array([sina*cose, cosa*sine, \
cosa*cose/velocity_mps]/velocity_mps)
Jacobian[:,2] = array([0, cose, \
-sine/velocity_mps]/velocity_mps)
Gamma2_epsilon = dot(transpose(Jacobian), \
dot((Sigma_aec*Sigma_aec),Jacobian))
## AR analysis
#%%
N = len(one_signal)
theta_lp, sigma_AR = yule_walker(one_signal, orderLPC)
theta_AR = append(1, theta_lp)
residue = lfilter(theta_AR, [1.0], one_signal) / sigma_AR
F_Hz = Fs_Hz * array(range(N)) / N
F2_Hz2 = F_Hz**2
pi2 = pi * pi
#==== extract M random sequences from residue by permutation
wwhite = zeros([N, M])
wwhite[:, 0] = residue[:, 0]
for im in range(1, M):
wwhite[:, im] = residue[random.permutation(N), 0]
#=== innovation generation
cf = ones([M, M, N])
cp = 0
for im1 in range(M - 1):
for im2 in range(im1 + 1, M):
cp = cp + 1
sigma2_s2 = dot(
dot((xsensors_m[im2, :] - xsensors_m[im1, :]), Gamma2_epsilon),
(xsensors_m[im2, :] - xsensors_m[im1, :]))
# LOC WITHOUT delays
cf[im1, im2, :] = exp(-2 * pi2 * F2_Hz2 * sigma2_s2)
cf[im2, im1, :] = conj(cf[im1, im2, :])
Wf = fft(wwhite)
Xf = zeros([N, M]) + complex(0, 1) * zeros([N, M])
#=== GG = zeros([M,M,N]);
for indf in range(N / 2): # 1:N/2+1,
GGaux = cf[:, :, indf]
UG, GGauxsvd, VG = svd(GGaux)
sqrtmGGaux = dot(dot(UG, diag(sqrt(GGauxsvd))), VG)
Xf[indf, :] = dot(Wf[indf, :], sqrtmGGaux)
Xf[range(N / 2 + 1, N), :] = conj(Xf[range(N - N / 2 - 1, 0, -1), :])
Xf[N / 2, :] = real(Xf[N / 2, :]) / 2.0
Xf[0, :] = real(Xf[0, :]) / 2.0
xt = ifft(Xf, axis=0)
signal_out_aux = real(xt)
signal_out_aux = signal_out_aux-ones([N,1])\
*mean(signal_out_aux)
#=== synthesis of signal
signal_out_with = signal_out_aux
signal_withLOC = signal_out_aux
for im in range(M):
xe = signal_out_aux[:, im]
signal_out_with[:, im] = lfilter([1.0], theta_AR, xe)
signal_withLOC[:,im] = signal_out_with[:,im]\
/ std(signal_out_with[:,im])
return signal_withLOC, theta0_spm, Gamma2_epsilon, cf
def test_yule_walker_inter():
# see 1869
x = np.array([1, -1, 2, 2, 0, -2, 1, 0, -3, 0, 0])
# it works
regression.yule_walker(x, 3)
print "\nExample 1"
ar = [1., -0.8]
ma = [1., 0.5]
y1 = arma.generate_sample(ar, ma, 1000,0.1)
arma = ARMA(x=y1, p=1, q=1)
rhohat1, cov_x1, infodict, mesg, ier = arma.fit(y1, 1, 1)
print 'estimate'
print rhohat1
print 'covariance'
print cov_x1
err1 = arma.errfn(x=y1)
print 'error'
print np.var(err1)
print regression.yule_walker(y1, order=2, inv=True)
print "\nExample 2"
arma2 = ARMA()
nsample = 1000
ar = [1.0, -0.6, -0.1]
ma = [1.0, 0.3, 0.2]
y2 = arma2.generate_sample(ar,ma,nsample,0.1)
rhohat2, cov_x2, infodict, mesg, ier = arma2.fit(y2,1,2)
print rhohat2
print cov_x2
err2 = arma2.errfn(x=y2)
print 'error = %s' % np.var(err2)
print "estimated b, a"
print arma2.b
print arma2.a
res = arma.fit((4, 0, 0)) print(res[0]) acf1 = acf(arrvs[0]) acovf1b = acovf(arrvs[0], unbiased=False) acf2 = autocorr(arrvs[0]) acf2m = autocorr(arrvs[0] - arrvs[0].mean()) print(acf1[:10]) print(acovf1b[:10]) print(acf2[:10]) print(acf2m[:10]) x = arma_generate_sample([1.0, -0.8], [1.0], 500) print(acf(x)[:20]) print(regression.yule_walker(x, 10)) #ax = plt.axes() plt.plot(x) #plt.show() plt.figure() pltxcorr(plt, x, x) plt.figure() pltxcorr(plt, x, x, usevlines=False) plt.figure() #FIXME: plotacf was moved to graphics/tsaplots.py, and interface changed plot_acf(plt, acf1[:20], np.arange(len(acf1[:20])), usevlines=True) plt.figure() ax = plt.subplot(211) plot_acf(ax, acf1[:20], usevlines=True)
print "\nExample 1"
ar = [1., -0.8]
ma = [1., 0.5]
y1 = arma.generate_sample(ar, ma, 1000, 0.1)
arma = ARMA(x=y1, p=1, q=1)
rhohat1, cov_x1, infodict, mesg, ier = arma.fit(y1, 1, 1)
print 'estimate'
print rhohat1
print 'covariance'
print cov_x1
err1 = arma.errfn(x=y1)
print 'error'
print np.var(err1)
print regression.yule_walker(y1, order=2, inv=True)
print "\nExample 2"
arma2 = ARMA()
nsample = 1000
ar = [1.0, -0.6, -0.1]
ma = [1.0, 0.3, 0.2]
y2 = arma2.generate_sample(ar, ma, nsample, 0.1)
rhohat2, cov_x2, infodict, mesg, ier = arma2.fit(y2, 1, 2)
print rhohat2
print cov_x2
err2 = arma2.errfn(x=y2)
print 'error = %s' % np.var(err2)
print "estimated b, a"
print arma2.b
print arma2.a