def setdict(self, D=None, B=None):
"""Set dictionary array."""
if D is not None:
self.D = np.asarray(D, dtype=self.dtype)
if B is not None:
self.B = np.asarray(B, dtype=self.dtype)
if B is not None or not hasattr(self, 'Gamma'):
self.Gamma, self.Q = np.linalg.eigh(self.B.T.dot(self.B))
self.Gamma = np.abs(self.Gamma)
if D is not None or not hasattr(self, 'Df'):
self.Df = sl.rfftn(self.D, self.cri.Nv, self.cri.axisN)
self.DSf = np.conj(self.Df) * self.Sf
self.DSfBQ = sl.dot(self.B.dot(self.Q).T, self.DSf,
axis=self.cri.axisC)
# Fold square root of Gamma into the dictionary array to enable
# use of the solvedbi_sm solver
shpg = [1] * len(self.cri.shpD)
shpg[self.cri.axisC] = self.Gamma.shape[0]
Gamma2 = np.sqrt(self.Gamma).reshape(shpg)
self.gDf = Gamma2 * self.Df
if self.opt['HighMemSolve']:
self.c = sl.solvedbi_sm_c(self.gDf, np.conj(self.gDf), self.rho,
self.cri.axisM)
else:
self.c = None
def setdict(self, D=None, B=None):
"""Set dictionary array."""
if D is not None:
self.D = np.asarray(D, dtype=self.dtype)
if B is not None:
self.B = np.asarray(B, dtype=self.dtype)
if B is not None or not hasattr(self, 'Gamma'):
self.Gamma, self.Q = np.linalg.eigh(self.B.T.dot(self.B))
self.Gamma = np.abs(self.Gamma)
if D is not None or not hasattr(self, 'Df'):
self.Df = sl.rfftn(self.D, self.cri.Nv, self.cri.axisN)
self.DSf = np.conj(self.Df) * self.Sf
self.DSfBQ = sl.dot(self.B.dot(self.Q).T, self.DSf,
axis=self.cri.axisC)
# Fold square root of Gamma into the dictionary array to enable
# use of the solvedbi_sm solver
shpg = [1] * len(self.cri.shpD)
shpg[self.cri.axisC] = self.Gamma.shape[0]
Gamma2 = np.sqrt(self.Gamma).reshape(shpg)
self.gDf = Gamma2 * self.Df
if self.opt['HighMemSolve']:
self.c = sl.solvedbi_sm_c(self.gDf, np.conj(self.gDf), self.rho,
self.cri.axisM)
else:
self.c = None
def rhochange(self):
"""Updated cached c array when rho changes."""
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
self.c = sl.solvedbi_sm_c(self.Df, np.conj(self.Df),
self.rho * self.GHGf + self.rho,
self.cri.axisM)
def rhochange(self):
"""Updated cached c array when rho changes."""
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
self.c = sl.solvedbi_sm_c(
self.Df, np.conj(self.Df), self.rho*self.GHGf + self.rho,
self.cri.axisM)
def setdict(self, D=None):
"""Set dictionary array."""
if D is not None:
self.D = np.asarray(D, dtype=self.dtype)
self.Df = fftn(self.D, self.cri.Nv, self.cri.axisN)
# Compute D^H S
self.DSf = np.conj(self.Df) * self.Sf
if self.cri.Cd > 1:
self.DSf = np.sum(self.DSf, axis=self.cri.axisC, keepdims=True)
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
self.c = sl.solvedbi_sm_c(self.Df, np.conj(self.Df), self.rho,
self.cri.axisM)
else:
self.c = None
def setdict(self, D=None):
"""Set dictionary array."""
if D is not None:
self.D = np.asarray(D, dtype=self.dtype)
self.Df = sl.rfftn(self.D, self.cri.Nv, self.cri.axisN)
# Compute D^H S
self.DSf = np.conj(self.Df) * self.Sf
if self.cri.Cd > 1:
self.DSf = np.sum(self.DSf, axis=self.cri.axisC, keepdims=True)
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
self.c = sl.solvedbi_sm_c(
self.Df, np.conj(self.Df), self.rho*self.GHGf + self.rho,
self.cri.axisM)
else:
self.c = None
def setdict(self, D=None):
"""Set dictionary array."""
if D is not None:
self.D = np.asarray(D, dtype=self.dtype)
self.Df = rfftn(self.D, self.cri.Nv, self.cri.axisN)
if self.opt['DatFidNoDC']:
if self.cri.dimN == 1:
self.Df[0] = 0.0
else:
self.Df[0, 0] = 0.0
self.DSf = np.conj(self.Df) * self.Sf
if self.cri.Cd > 1: # NB: Not tested
self.DSf = np.sum(self.DSf, axis=self.cri.axisC, keepdims=True)
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
self.c = sl.solvedbi_sm_c(self.Df, np.conj(self.Df), self.rho,
self.cri.axisM)
else:
self.c = None
def __init__(self, D, S, lmbda=None, W=None, opt=None, nproc=None,
ngrp=None, dimK=None, dimN=2):
"""
Parameters
----------
D : array_like
Dictionary matrix
S : array_like
Signal vector or matrix
lmbda : float
Regularisation parameter
W : array_like
Mask array. The array shape must be such that the array is
compatible for multiplication with input array S (see
:func:`.cnvrep.mskWshape` for more details).
opt : :class:`ParConvBPDN.Options` object
Algorithm options
nproc : int
Number of processes
ngrp : int
Number of groups in partition of filter indices
dimK : 0, 1, or None, optional (default None)
Number of dimensions in input signal corresponding to multiple
independent signals
dimN : int, optional (default 2)
Number of spatial dimensions
"""
self.pool = None
# Set default options if none specified
if opt is None:
opt = ParConvBPDN.Options()
# Set dtype attribute based on S.dtype and opt['DataType']
self.set_dtype(opt, S.dtype)
# Set default lambda value if not specified
if lmbda is None:
cri = cr.CSC_ConvRepIndexing(D, S, dimK=dimK, dimN=dimN)
Df = sl.rfftn(D.reshape(cri.shpD), cri.Nv, axes=cri.axisN)
Sf = sl.rfftn(S.reshape(cri.shpS), axes=cri.axisN)
b = np.conj(Df) * Sf
lmbda = 0.1*abs(b).max()
# Set l1 term scaling and weight array
self.lmbda = self.dtype.type(lmbda)
# Set penalty parameter
self.set_attr('rho', opt['rho'], dval=(50.0*self.lmbda + 1.0),
dtype=self.dtype)
self.set_attr('alpha', opt['alpha'], dval=1.0,
dtype=self.dtype)
# Set rho_xi attribute (see Sec. VI.C of wohlberg-2015-adaptive)
# if self.lmbda != 0.0:
# rho_xi = (1.0 + (18.3)**(np.log10(self.lmbda) + 1.0))
# else:
# rho_xi = 1.0
# self.set_attr('rho_xi', opt['AutoRho', 'RsdlTarget'], dval=rho_xi,
# dtype=self.dtype)
# Call parent class __init__
super(ParConvBPDN, self).__init__(D, S, opt, dimK, dimN)
if nproc is None:
if ngrp is None:
self.nproc = min(mp.cpu_count(), self.cri.M)
self.ngrp = self.nproc
else:
self.nproc = min(mp.cpu_count(), ngrp, self.cri.M)
self.ngrp = ngrp
else:
if ngrp is None:
self.ngrp = nproc
self.nproc = nproc
else:
self.ngrp = ngrp
self.nproc = nproc
if W is None:
W = np.array([1.0], dtype=self.dtype)
self.W = np.asarray(W.reshape(cr.mskWshape(W, self.cri)),
dtype=self.dtype)
self.wl1 = np.asarray(opt['L1Weight'], dtype=self.dtype)
self.wl1 = self.wl1.reshape(cr.l1Wshape(self.wl1, self.cri))
self.xrrs = None
# Initialise global variables
# Conv Rep Indexing and parameter values for multiprocessing
global mp_nproc
mp_nproc = self.nproc
global mp_ngrp
mp_ngrp = self.ngrp
global mp_Nv
mp_Nv = self.cri.Nv
global mp_axisN
mp_axisN = tuple(i+1 for i in self.cri.axisN)
global mp_C
mp_C = self.cri.C
global mp_Cd
mp_Cd = self.cri.Cd
global mp_axisC
mp_axisC = self.cri.axisC+1
global mp_axisM
mp_axisM = 0
global mp_NonNegCoef
mp_NonNegCoef = self.opt['NonNegCoef']
global mp_NoBndryCross
mp_NoBndryCross = self.opt['NoBndryCross']
global mp_Dshp
mp_Dshp = self.D.shape
# Parameters for optimization
global mp_lmbda
mp_lmbda = self.lmbda
global mp_rho
mp_rho = self.rho
global mp_alpha
mp_alpha = self.alpha
global mp_rlx
mp_rlx = self.rlx
global mp_wl1
init_mpraw('mp_wl1', np.moveaxis(self.wl1, self.cri.axisM, mp_axisM))
# Matrices used in optimization
global mp_S
init_mpraw('mp_S', np.moveaxis(self.S*self.W**2, self.cri.axisM,
mp_axisM))
global mp_Df
init_mpraw('mp_Df', np.moveaxis(self.Df, self.cri.axisM, mp_axisM))
global mp_X
init_mpraw('mp_X', np.moveaxis(self.Y, self.cri.axisM, mp_axisM))
shp_X = list(mp_X.shape)
global mp_Xnr
mp_Xnr = mpraw_as_np(mp_X.shape, mp_X.dtype)
global mp_Y0
shp_Y0 = shp_X[:]
shp_Y0[0] = self.ngrp
shp_Y0[mp_axisC] = mp_C
if self.opt['Y0'] is not None:
init_mpraw('Y0', np.moveaxis(
self.opt['Y0'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_Y0 = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_Y0old
mp_Y0old = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_Y1
if self.opt['Y1'] is not None:
init_mpraw('Y1', np.moveaxis(
self.opt['Y1'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_Y1 = mpraw_as_np(shp_X, mp_X.dtype)
global mp_Y1old
mp_Y1old = mpraw_as_np(shp_X, mp_X.dtype)
global mp_U0
if self.opt['U0'] is not None:
init_mpraw('U0', np.moveaxis(
self.opt['U0'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_U0 = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_U1
if self.opt['U1'] is not None:
init_mpraw('U1', np.moveaxis(
self.opt['U1'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_U1 = mpraw_as_np(shp_X, mp_X.dtype)
global mp_DX
mp_DX = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_DXnr
mp_DXnr = mpraw_as_np(shp_Y0, mp_X.dtype)
# Variables used to solve the optimization efficiently
global mp_inv_off_diag
if self.W.ndim is self.cri.axisM+1:
init_mpraw('mp_inv_off_diag', np.moveaxis(
-self.W**2/(mp_rho*(mp_rho+self.W**2*mp_ngrp)),
self.cri.axisM, mp_axisM))
else:
init_mpraw('mp_inv_off_diag',
-self.W**2/(mp_rho*(mp_rho+self.W**2*mp_ngrp)))
global mp_grp
mp_grp = [np.min(i) for i in
np.array_split(np.array(range(self.cri.M)),
mp_ngrp)] + [self.cri.M, ]
global mp_cache
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
mp_cache = [sl.solvedbi_sm_c(mp_Df[k], np.conj(mp_Df[k]),
mp_alpha**2, mp_axisM) for k in
np.array_split(np.array(range(self.cri.M)), self.ngrp)]
else:
mp_cache = [None for k in mp_grp]
global mp_b
shp_b = shp_Y0[:]
shp_b[0] = 1
mp_b = mpraw_as_np(shp_b, mp_X.dtype)
# Residual and stopping criteria variables
global mp_ry0
mp_ry0 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_ry1
mp_ry1 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_sy0
mp_sy0 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_sy1
mp_sy1 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_nrmAx
mp_nrmAx = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_nrmBy
mp_nrmBy = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_nrmu
mp_nrmu = mpraw_as_np((self.ngrp,), mp_X.dtype)
def __init__(self, D, S, lmbda=None, W=None, opt=None, nproc=None,
ngrp=None, dimK=None, dimN=2):
"""
Parameters
----------
D : array_like
Dictionary matrix
S : array_like
Signal vector or matrix
lmbda : float
Regularisation parameter
W : array_like
Mask array. The array shape must be such that the array is
compatible for multiplication with input array S (see
:func:`.cnvrep.mskWshape` for more details).
opt : :class:`ParConvBPDN.Options` object
Algorithm options
nproc : int
Number of processes
ngrp : int
Number of groups in partition of filter indices
dimK : 0, 1, or None, optional (default None)
Number of dimensions in input signal corresponding to multiple
independent signals
dimN : int, optional (default 2)
Number of spatial dimensions
"""
self.pool = None
# Set default options if none specified
if opt is None:
opt = ParConvBPDN.Options()
# Set dtype attribute based on S.dtype and opt['DataType']
self.set_dtype(opt, S.dtype)
# Set default lambda value if not specified
if lmbda is None:
cri = cr.CSC_ConvRepIndexing(D, S, dimK=dimK, dimN=dimN)
Df = sl.rfftn(D.reshape(cri.shpD), cri.Nv, axes=cri.axisN)
Sf = sl.rfftn(S.reshape(cri.shpS), axes=cri.axisN)
b = np.conj(Df) * Sf
lmbda = 0.1*abs(b).max()
# Set l1 term scaling and weight array
self.lmbda = self.dtype.type(lmbda)
# Set penalty parameter
self.set_attr('rho', opt['rho'], dval=(50.0*self.lmbda + 1.0),
dtype=self.dtype)
self.set_attr('alpha', opt['alpha'], dval=1.0,
dtype=self.dtype)
# Set rho_xi attribute (see Sec. VI.C of wohlberg-2015-adaptive)
# if self.lmbda != 0.0:
# rho_xi = (1.0 + (18.3)**(np.log10(self.lmbda) + 1.0))
# else:
# rho_xi = 1.0
# self.set_attr('rho_xi', opt['AutoRho', 'RsdlTarget'], dval=rho_xi,
# dtype=self.dtype)
# Call parent class __init__
super(ParConvBPDN, self).__init__(D, S, opt, dimK, dimN)
if nproc is None:
if ngrp is None:
self.nproc = min(mp.cpu_count(), self.cri.M)
self.ngrp = self.nproc
else:
self.nproc = min(mp.cpu_count(), ngrp, self.cri.M)
self.ngrp = ngrp
else:
if ngrp is None:
self.ngrp = nproc
self.nproc = nproc
else:
self.ngrp = ngrp
self.nproc = nproc
if W is None:
W = np.array([1.0], dtype=self.dtype)
self.W = np.asarray(W.reshape(cr.mskWshape(W, self.cri)),
dtype=self.dtype)
self.wl1 = np.asarray(opt['L1Weight'], dtype=self.dtype)
self.wl1 = self.wl1.reshape(cr.l1Wshape(self.wl1, self.cri))
self.xrrs = None
# Initialise global variables
# Conv Rep Indexing and parameter values for multiprocessing
global mp_nproc
mp_nproc = self.nproc
global mp_ngrp
mp_ngrp = self.ngrp
global mp_Nv
mp_Nv = self.cri.Nv
global mp_axisN
mp_axisN = tuple(i+1 for i in self.cri.axisN)
global mp_C
mp_C = self.cri.C
global mp_Cd
mp_Cd = self.cri.Cd
global mp_axisC
mp_axisC = self.cri.axisC+1
global mp_axisM
mp_axisM = 0
global mp_NonNegCoef
mp_NonNegCoef = self.opt['NonNegCoef']
global mp_NoBndryCross
mp_NoBndryCross = self.opt['NoBndryCross']
global mp_Dshp
mp_Dshp = self.D.shape
# Parameters for optimization
global mp_lmbda
mp_lmbda = self.lmbda
global mp_rho
mp_rho = self.rho
global mp_alpha
mp_alpha = self.alpha
global mp_rlx
mp_rlx = self.rlx
global mp_wl1
init_mpraw('mp_wl1', np.moveaxis(self.wl1, self.cri.axisM, mp_axisM))
# Matrices used in optimization
global mp_S
init_mpraw('mp_S', np.moveaxis(self.S*self.W**2, self.cri.axisM,
mp_axisM))
global mp_Df
init_mpraw('mp_Df', np.moveaxis(self.Df, self.cri.axisM, mp_axisM))
global mp_X
init_mpraw('mp_X', np.moveaxis(self.Y, self.cri.axisM, mp_axisM))
shp_X = list(mp_X.shape)
global mp_Xnr
mp_Xnr = mpraw_as_np(mp_X.shape, mp_X.dtype)
global mp_Y0
shp_Y0 = shp_X[:]
shp_Y0[0] = self.ngrp
shp_Y0[mp_axisC] = mp_C
if self.opt['Y0'] is not None:
init_mpraw('Y0', np.moveaxis(
self.opt['Y0'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_Y0 = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_Y0old
mp_Y0old = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_Y1
if self.opt['Y1'] is not None:
init_mpraw('Y1', np.moveaxis(
self.opt['Y1'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_Y1 = mpraw_as_np(shp_X, mp_X.dtype)
global mp_Y1old
mp_Y1old = mpraw_as_np(shp_X, mp_X.dtype)
global mp_U0
if self.opt['U0'] is not None:
init_mpraw('U0', np.moveaxis(
self.opt['U0'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_U0 = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_U1
if self.opt['U1'] is not None:
init_mpraw('U1', np.moveaxis(
self.opt['U1'].astype(self.dtype, copy=True),
self.cri.axisM, mp_axisM))
else:
mp_U1 = mpraw_as_np(shp_X, mp_X.dtype)
global mp_DX
mp_DX = mpraw_as_np(shp_Y0, mp_X.dtype)
global mp_DXnr
mp_DXnr = mpraw_as_np(shp_Y0, mp_X.dtype)
# Variables used to solve the optimization efficiently
global mp_inv_off_diag
if self.W.ndim is self.cri.axisM+1:
init_mpraw('mp_inv_off_diag', np.moveaxis(
-self.W**2/(mp_rho*(mp_rho+self.W**2*mp_ngrp)),
self.cri.axisM, mp_axisM))
else:
init_mpraw('mp_inv_off_diag',
-self.W**2/(mp_rho*(mp_rho+self.W**2*mp_ngrp)))
global mp_grp
mp_grp = [np.min(i) for i in
np.array_split(np.array(range(self.cri.M)),
mp_ngrp)] + [self.cri.M, ]
global mp_cache
if self.opt['HighMemSolve'] and self.cri.Cd == 1:
mp_cache = [sl.solvedbi_sm_c(mp_Df[k], np.conj(mp_Df[k]),
mp_alpha**2, mp_axisM) for k in
np.array_split(np.array(range(self.cri.M)), self.ngrp)]
else:
mp_cache = [None for k in mp_grp]
global mp_b
shp_b = shp_Y0[:]
shp_b[0] = 1
mp_b = mpraw_as_np(shp_b, mp_X.dtype)
# Residual and stopping criteria variables
global mp_ry0
mp_ry0 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_ry1
mp_ry1 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_sy0
mp_sy0 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_sy1
mp_sy1 = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_nrmAx
mp_nrmAx = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_nrmBy
mp_nrmBy = mpraw_as_np((self.ngrp,), mp_X.dtype)
global mp_nrmu
mp_nrmu = mpraw_as_np((self.ngrp,), mp_X.dtype)
def rhochange(self):
"""Updated cached c array when rho changes."""
if self.opt['HighMemSolve']:
self.c = solvedbi_sm_c(self.gDf, np.conj(self.gDf), self.rho,
self.cri.axisM)
