def sift(x, ts):
"""One sifting iteration."""
tmin, tmax, xmin, xmax = boundary_conditions(x, ts)
tck = splrep(tmin, xmin)
lower_envelop = splev(ts, tck)
tck = splrep(tmax, xmax)
upper_envelop = splev(ts, tck)
mean_amplitude = np.abs(upper_envelop - lower_envelop) / 2
local_mean = (upper_envelop + lower_envelop) / 2
amplitude_error = np.abs(local_mean) / mean_amplitude
return x - local_mean, amplitude_error.sum()
def emd(x, ts, n_imfs):
imfs = np.zeros((n_imfs + 1, x.shape[0]))
for i in range(n_imfs):
ix = 0
mode = x - imfs.sum(0)
nmin, nmax, nzero = map(len, extr(mode))
tmin, tmax, xmin, xmax = boundary_conditions(mode, ts)
# while abs((nmin + nmax) - nzero) > 1 and (not (utils.judge_stop(mode))):
# mode, amplitude_error = sift(mode, ts)
# if amplitude_error <= tol or (utils.judge_stop(mode)):
# break
if abs((nmin + nmax) - nzero) > 1 and (not (
utils.judge_stop(mode))) and len(tmin) > 3 and len(tmax) > 3:
mode, amplitude_error = sift(mode, ts)
imfs[i, :] = mode
imfs[-1, :] = x - imfs.sum(0)
return imfs
def mean_and_amplitude(self, m):
if self.is_bivariate:
if self.bivariate_mode == 'centroid':
nem = []
nzm = []
envmin = np.zeros((self.ndirs, len(self.t)))
envmax = np.zeros((self.ndirs, len(self.t)))
for k in range(self.ndirs):
phi = k * pi / self.ndirs
y = np.real(np.exp(-1j * phi) * m)
indmin, indmax, indzer = extr(y)
nem.append(len(indmin) + len(indmax))
nzm.append(len(indzer))
if self.nbsym:
tmin, tmax, zmin, zmax = boundary_conditions(
y, self.t, m, self.nbsym)
else:
tmin = np.r_[self.t[0], self.t[indmin], self.t[-1]]
tmax = np.r_[self.t[0], self.t[indmax], self.t[-1]]
zmin, zmax = m[tmin], m[tmax]
f = splrep(tmin, zmin)
spl = splev(self.t, f)
envmin[k, :] = spl
f = splrep(tmax, zmax)
spl = splev(self.t, f)
envmax[k, :] = spl
envmoy = np.mean((envmin + envmax) / 2, axis=0)
amp = np.mean(abs(envmax - envmin), axis=0) / 2
elif self.bivariate_mode == 'bbox_center':
nem = []
nzm = []
envmin = np.zeros((self.ndirs, len(self.t)), dtype=complex)
envmax = np.zeros((self.ndirs, len(self.t)), dtype=complex)
for k in range(self.ndirs):
phi = k * pi / self.ndirs
y = np.real(np.exp(-1j * phi) * m)
indmin, indmax, indzer = extr(y)
nem.append(len(indmin) + len(indmax))
nzm.append(len(indzer))
if self.nbsym:
tmin, tmax, zmin, zmax = boundary_conditions(
y, self.t, m, self.nbsym)
else:
tmin = np.r_[self.t[0], self.t[indmin], self.t[-1]]
tmax = np.r_[self.t[0], self.t[indmax], self.t[-1]]
zmin, zmax = m[tmin], m[tmax]
f = splrep(tmin, zmin)
spl = splev(self.t, f)
envmin[k, ] = np.exp(1j * phi) * spl
f = splrep(tmax, zmax)
spl = splev(self.t, f)
envmax[k, ] = np.exp(1j * phi) * spl
envmoy = np.mean((envmin + envmax), axis=0)
amp = np.mean(abs(envmax - envmin), axis=0) / 2
else:
indmin, indmax, indzer = extr(m)
nem = len(indmin) + len(indmax)
nzm = len(indzer)
if self.nbsym:
tmin, tmax, mmin, mmax = boundary_conditions(
m, self.t, m, self.nbsym)
else:
tmin = np.r_[self.t[0], self.t[indmin], self.t[-1]]
tmax = np.r_[self.t[0], self.t[indmax], self.t[-1]]
mmin, mmax = m[tmin], m[tmax]
f = splrep(tmin, mmin)
envmin = splev(self.t, f)
f = splrep(tmax, mmax)
envmax = splev(self.t, f)
envmoy = (envmin + envmax) / 2
amp = np.abs(envmax - envmin) / 2.0
if self.is_bivariate:
nem = np.array(nem)
nzm = np.array(nzm)
return envmoy, nem, nzm, amp
def decompose(self):
if self.display_sifting:
fig_h = plt.figure()
A = not(self.stop_EMD())
B = (self.k<self.MAXMODES+1 or self.MAXMODES==0)
C = not(np.any(self.mask))
while (A and B and C):
# current mode
m = self.r
# mode at previous iteration
mp = m.copy()
# computing mean and stopping criterion
if self.FIXE:
stop_sift, moyenne = self.stop_sifting_fixe()
elif self.FIXE_H:
stop_count = 0
stop_sift, moyenne = self.stop_sifting_fixe_h()
else:
stop_sift, moyenne, _ = self.stop_sifting(m)
# in case current mode is small enough to cause spurious extrema
if np.max(np.abs(m)) < (1e-10)*np.max(np.abs(self.x)):
if not stop_sift:
warnings.warn("EMD Warning: Amplitude too small, stopping.")
else:
print "Force stopping EMD: amplitude too small."
return
# SIFTING LOOP:
while not(stop_sift) and (self.nbit<self.MAXITERATIONS):
print "iteration {}".format(self.nbit)
if (not(self.MODE_COMPLEX) and (self.nbit>self.MAXITERATIONS/5) \
and self.nbit%np.floor(self.MAXITERATIONS/10)==0 and \
not(self.FIXE) and self.nbit > 100):
print "Mode "+str(self.k) + ", Iteration " + str(self.nbit)
im, iM, _ = extr(m)
print str(np.sum(m[im]>0)) + " minima > 0; " + \
str(np.sum(m[im]<0)) + " maxima < 0."
# Sifting
m = m - moyenne
# Computing mean and stopping criterion
if self.FIXE:
stop_sift, moyenne = self.stop_sifting_fixe()
elif self.FIXE_H:
stop_sift, moyenne, stop_count = self.stop_sifting_fixe_h()
else:
stop_sift, moyenne, s = self.stop_sifting(m)
# Display
if self.display_sifting and self.MODE_COMPLEX:
indmin, indmax, _ = extr(m)
tmin, tmax, mmin, mmax = boundary_conditions(indmin,
indmax,
self.t, mp,
mp,
self.nbsym)
f = splrep(tmin,mmin)
envminp = splev(self.t,f)
f = splrep(tmax,mmax)
envmaxp = splev(self.t,f)
envmoyp = (envminp+envmaxp)/2;
if self.FIXE or self.FIXE_H:
self.display_emd_fixe(mp, envminp, envmaxp, envmoyp)
else:
sxp = 2*(np.abs(envmoyp))/np.abs(envmaxp-envminp)
sp = np.mean(sxp)
self.display_emd(mp, envminp, envmaxp, envmoyp, sp, sxp)
mp = m
self.nbit += 1
self.NbIt += 1
if (self.nbit==(self.MAXITERATIONS-1)) and not(self.FIXE) and (self.nbit>100):
warnings.warn("Emd:warning, Forced stop of sifting - "+
"too many iterations")
self.imf.append(m)
if self.display_sifting:
print "mode "+str(self.k)+ " stored"
self.nbits.append(self.nbit)
self.k += 1
self.r = self.r - m
ort = self.io()
self.ort = ort
return np.array(self.imf)
def mean_and_amplitude(self, m):
""" Computes the mean of the envelopes and the mode amplitudes."""
# FIXME: The spline interpolation may not be identical with the MATLAB
# implementation. Needs further investigation.
if self.MODE_COMPLEX:
if self.MODE_COMPLEX == 1:
nem = []
nzm = []
envmin = np.zeros((self.ndirs,len(self.t)))
envmax = np.zeros((self.ndirs,len(self.t)))
for k in range(self.ndirs):
phi = k*pi/self.ndirs
y = np.real(np.exp(-1j*phi)*m)
indmin, indmax, indzer = extr(y)
nem.append(len(indmin)+len(indmax))
nzm.append(len(indzer))
tmin, tmax, zmin, zmax = boundary_conditions(indmin,
indmax,
self.t, y, m,
self.nbsym)
f = splrep(tmin,zmin)
spl = splev(self.t,f)
envmin[k,:] = spl
f = splrep(tmax,zmax)
spl = splev(self.t,f)
envmax[k,:] = spl
envmoy = np.mean((envmin+envmax)/2,axis=0)
amp = np.mean(abs(envmax-envmin),axis=0)/2
elif self.MODE_COMPLEX == 2:
nem = []
nzm = []
envmin = np.zeros((self.ndirs,len(self.t)))
envmax = np.zeros((self.ndirs,len(self.t)))
for k in range(self.ndirs):
phi = k*pi/self.ndirs
y = np.real(np.exp(-1j*phi)*m)
indmin, indmax, indzer = extr(y)
nem.append(len(indmin)+len(indmax))
nzm.append(len(indzer))
tmin, tmax, zmin, zmax = boundary_conditions(indmin,
indmax,
self.t, y, m,
self.nbsym)
f = splrep(tmin, zmin)
spl = splev(self.t,f)
envmin[k,:] = np.exp(1j*phi)*spl
f = splrep(tmax, zmax)
spl = splev(self.t,f)
envmax[k,:] = np.exp(1j*phi)*spl
envmoy = np.mean((envmin+envmax),axis=0)
amp = np.mean(abs(envmax-envmin),axis=0)/2
else:
indmin, indmax, indzer = extr(m)
nem = len(indmin)+len(indmax)
nzm = len(indzer)
tmin, tmax, mmin, mmax = boundary_conditions(indmin, indmax,
self.t, m, m,
self.nbsym)
f = splrep(tmin, mmin)
envmin = splev(self.t,f)
f = splrep(tmax, mmax)
envmax = splev(self.t,f);
envmoy = (envmin+envmax)/2;
amp = np.abs(envmax-envmin)/2.0
return envmoy, nem, nzm, amp
def mean_and_amplitude(self, m):
""" Computes the mean of the envelopes and the mode amplitudes."""
# FIXME: The spline interpolation may not be identical with the MATLAB
# implementation. Needs further investigation.
if self.is_mode_complex:
if self.is_mode_complex == 1:
nem = []
nzm = []
envmin = np.zeros((self.ndirs, len(self.t)))
envmax = np.zeros((self.ndirs, len(self.t)))
for k in range(self.ndirs):
phi = k * pi / self.ndirs
y = np.real(np.exp(-1j * phi) * m)
indmin, indmax, indzer = extr(y)
nem.append(len(indmin) + len(indmax))
nzm.append(len(indzer))
tmin, tmax, zmin, zmax = boundary_conditions(
y, self.t, m, self.nbsym)
f = splrep(tmin, zmin)
spl = splev(self.t, f)
envmin[k, :] = spl
f = splrep(tmax, zmax)
spl = splev(self.t, f)
envmax[k, :] = spl
envmoy = np.mean((envmin + envmax) / 2, axis=0)
amp = np.mean(abs(envmax - envmin), axis=0) / 2
elif self.is_mode_complex == 2:
nem = []
nzm = []
envmin = np.zeros((self.ndirs, len(self.t)))
envmax = np.zeros((self.ndirs, len(self.t)))
for k in range(self.ndirs):
phi = k * pi / self.ndirs
y = np.real(np.exp(-1j * phi) * m)
indmin, indmax, indzer = extr(y)
nem.append(len(indmin) + len(indmax))
nzm.append(len(indzer))
tmin, tmax, zmin, zmax = boundary_conditions(
y, self.t, m, self.nbsym)
f = splrep(tmin, zmin)
spl = splev(self.t, f)
envmin[k, ] = np.exp(1j * phi) * spl
f = splrep(tmax, zmax)
spl = splev(self.t, f)
envmax[k, ] = np.exp(1j * phi) * spl
envmoy = np.mean((envmin + envmax), axis=0)
amp = np.mean(abs(envmax - envmin), axis=0) / 2
else:
indmin, indmax, indzer = extr(m)
nem = len(indmin) + len(indmax)
nzm = len(indzer)
tmin, tmax, mmin, mmax = boundary_conditions(
m, self.t, m, self.nbsym)
f = splrep(tmin, mmin)
envmin = splev(self.t, f)
f = splrep(tmax, mmax)
envmax = splev(self.t, f)
envmoy = (envmin + envmax) / 2
amp = np.abs(envmax - envmin) / 2.0
return envmoy, nem, nzm, amp