def welch_l2_estimator(appro, mask=None, lbda=1, consider_fBm=False):
"""
This function estimate the Hurst exponent of a signal based
on Detrend Fluctuation Analysis.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
lbda: weight used in regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1]) == 1
if appro.ndim > 2:
shape = (reduce(lambda a, b: a * b, (1, ) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
Hurst_exponent, dico = hurstexp_welchper(appro, consider_fBm=consider_fBm)
log2frq = dico['log2frq']
log2pwr = dico['log2pwr']
aest = dico['aest']
fg = lambda x, lbda, **kwargs: welch_squared_loss_l2pen(
x, aest, log2frq, log2pwr, mask, lbda, consider_fBm=consider_fBm)
l2_algo = lambda lbda: fmin_l_bfgs_b(lambda x: fg(x, lbda), Hurst_exponent)
Hmin = l2_algo(lbda)
return Hurst_exponent, Hmin[0]
def welch_l2_estimator(appro, mask=None, lbda=1, consider_fBm=False):
"""
This function estimate the Hurst exponent of a signal based
on Detrend Fluctuation Analysis.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
lbda: weight used in regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])==1
if appro.ndim > 2:
shape = (reduce(lambda a,b : a*b , (1,) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
Hurst_exponent, dico = hurstexp_welchper(appro, consider_fBm=consider_fBm)
log2frq = dico['log2frq']
log2pwr = dico['log2pwr']
aest = dico['aest']
fg = lambda x, lbda, **kwargs: welch_squared_loss_l2pen(x, aest, log2frq, log2pwr, mask, lbda, consider_fBm=consider_fBm)
l2_algo = lambda lbda: fmin_l_bfgs_b(lambda x: fg(x, lbda), Hurst_exponent)
Hmin = l2_algo(lbda)
return Hurst_exponent, Hmin[0]
def welch_tv_estimator(appro, mask=None, lbda=1, consider_fBm=False):
"""
This function estimate the Hurst exponent of a signal based
on Daubechies' Wavelet coeffecients.
It also allow l2 and tv regularisation.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
lbda: weight used in regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])==1
if appro.ndim > 2:
shape = (reduce(lambda a,b : a*b , (1,) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
Hurst_exponent, dico = hurstexp_welchper(appro, consider_fBm=consider_fBm)
log2frq = dico['log2frq']
log2pwr = dico['log2pwr']
aest = dico['aest']
lipschitz_constant = lipschitz_constant_grad_welch_square_loss(log2frq, consider_fBm=consider_fBm)
l1_ratio = 0
tv_algo = lambda lbda: tv_welch_solver(Hurst_exponent, aest,
log2frq, log2pwr, mask,
lipschitz_constant=lipschitz_constant,
l1_ratio = l1_ratio, l=lbda, verbose=0, consider_fBm=consider_fBm)
Hmin = tv_algo(lbda)
return Hurst_exponent, Hmin[0]
def welch_tv_estimator(appro, mask=None, lbda=1, consider_fBm=False):
"""
This function estimate the Hurst exponent of a signal based
on Daubechies' Wavelet coeffecients.
It also allow l2 and tv regularisation.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
lbda: weight used in regularisation
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1]) == 1
if appro.ndim > 2:
shape = (reduce(lambda a, b: a * b, (1, ) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
Hurst_exponent, dico = hurstexp_welchper(appro, consider_fBm=consider_fBm)
log2frq = dico['log2frq']
log2pwr = dico['log2pwr']
aest = dico['aest']
lipschitz_constant = lipschitz_constant_grad_welch_square_loss(
log2frq, consider_fBm=consider_fBm)
l1_ratio = 0
tv_algo = lambda lbda: tv_welch_solver(Hurst_exponent,
aest,
log2frq,
log2pwr,
mask,
lipschitz_constant=
lipschitz_constant,
l1_ratio=l1_ratio,
l=lbda,
verbose=0,
consider_fBm=consider_fBm)
Hmin = tv_algo(lbda)
return Hurst_exponent, Hmin[0]
def welch_estimator(appro, mask=None, consider_fBm=False):
"""
This function estimate the Hurst exponent of a signal based
on Detrend Fluctuation Analysis.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])
if appro.ndim > 2:
shape = (reduce(lambda a, b: a * b, (1, ) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
Hurst_exponent, dico = hurstexp_welchper(appro, consider_fBm=consider_fBm)
return Hurst_exponent
def welch_estimator(appro, mask=None, consider_fBm=False):
"""
This function estimate the Hurst exponent of a signal based
on Detrend Fluctuation Analysis.
-----------------------------------------------------------
Input:
appro: multidimensionnal signal as an np array (shape X Time)
mask: if the data are taken from a masked image
Output:
image (shape) of Hurst coefficient
"""
if mask is None:
mask = np.ones(appro.shape[:-1])
if appro.ndim > 2:
shape = (reduce(lambda a,b : a*b , (1,) + simulation.shape[:-1]))
appro = np.reshape(appro, (shape, appro.shape[-1]))
N = appro.shape[0]
l = appro.shape[-1]
Hurst_exponent, dico = hurstexp_welchper(appro, consider_fBm=consider_fBm)
return Hurst_exponent