def test_08(self):
N = 16
M = 4
Nd = 8
X = np.random.randn(N, N, 1, 1, M)
S = np.random.randn(N, N, 1)
dt = np.float64
opt = ccmod.ConvCnstrMODOptions(
{'Verbose': False, 'MaxMainIter': 20,
'BackTrack': {'Enabled': True},
'DataType': dt})
c = ccmod.ConvCnstrMOD(X, S, (Nd, Nd, M), opt=opt)
c.solve()
assert(c.X.dtype == dt)
assert(c.Xf.dtype == sl.complex_dtype(dt))
assert(c.Yf.dtype == sl.complex_dtype(dt))
def test_05(self):
N = 16
M = 4
Nd = 8
X = np.random.randn(N, N, 1, 1, M)
S = np.random.randn(N, N, 1)
dt = np.float64
opt = ccmod.ConvCnstrMOD.Options(
{'Verbose': False, 'MaxMainIter': 20,
'BackTrack': {'Enabled': True},
'DataType': dt})
c = ccmod.ConvCnstrMOD(X, S, (Nd, Nd, M), opt=opt)
c.solve()
assert c.X.dtype == dt
assert c.Xf.dtype == sl.complex_dtype(dt)
assert c.Yf.dtype == sl.complex_dtype(dt)
def test_06(self):
N = 16
Nd = 5
K = 2
M = 4
D = np.random.randn(Nd, Nd, M)
s = np.random.randn(N, N, K)
dt = np.float32
opt = cbpdn.ConvBPDN.Options({'Verbose': False, 'MaxMainIter': 20,
'BackTrack': {'Enabled': True},
'DataType': dt})
lmbda = 1e-1
b = cbpdn.ConvBPDN(D, s, lmbda, opt=opt)
b.solve()
assert b.X.dtype == dt
assert b.Xf.dtype == sl.complex_dtype(dt)
assert b.Yf.dtype == sl.complex_dtype(dt)
def __init__(self, D, S, lmbda, mu=0.0, opt=None, dimK=None, dimN=2):
if opt is None:
opt = ConvBPDNRecTV.Options()
# Infer problem dimensions and set relevant attributes of self
self.cri = cbpdn.ConvRepIndexing(D, S, dimK=dimK, dimN=dimN)
# Call parent class __init__
Nx = np.product(self.cri.shpX)
yshape = list(self.cri.shpX)
yshape[self.cri.axisM] += len(self.cri.axisN) * self.cri.Cd
super(ConvBPDNRecTV, self).__init__(Nx, yshape, yshape,
S.dtype, opt)
# Set l1 term scaling and weight array
self.lmbda = self.dtype.type(lmbda)
self.Wl1 = np.asarray(opt['L1Weight'], dtype=self.dtype)
self.mu = self.dtype.type(mu)
if hasattr(opt['TVWeight'], 'ndim') and opt['TVWeight'].ndim > 0:
self.Wtv = np.asarray(opt['TVWeight'].reshape((1,)*(dimN+2) +
opt['TVWeight'].shape), dtype=self.dtype)
else:
# Wtv is a scalar: no need to change shape
self.Wtv = self.dtype.type(opt['TVWeight'])
# Set penalty parameter
self.set_attr('rho', opt['rho'], dval=(50.0*self.lmbda + 1.0),
dtype=self.dtype)
# Set rho_xi attribute
self.set_attr('rho_xi', opt['AutoRho','RsdlTarget'], dval=1.0,
dtype=self.dtype)
# Reshape D and S to standard layout
self.D = np.asarray(D.reshape(self.cri.shpD), dtype=self.dtype)
self.S = np.asarray(S.reshape(self.cri.shpS), dtype=self.dtype)
# Compute signal in DFT domain
self.Sf = sl.rfftn(self.S, None, self.cri.axisN)
self.Gf, GHGf = sl.GradientFilters(self.cri.dimN+3, self.cri.axisN,
self.cri.Nv, dtype=self.dtype)
# Initialise byte-aligned arrays for pyfftw
self.YU = sl.pyfftw_empty_aligned(self.Y.shape, dtype=self.dtype)
xfshp = list(self.cri.shpX)
xfshp[dimN-1] = xfshp[dimN-1]//2 + 1
self.Xf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
self.setdict()
def test_06(self):
N = 16
Nd = 5
K = 2
M = 4
D = np.random.randn(Nd, Nd, M)
s = np.random.randn(N, N, K)
dt = np.float32
opt = cbpdn.ConvBPDN.Options({
'Verbose': False,
'MaxMainIter': 20,
'BackTrack': {
'Enabled': True
},
'DataType': dt
})
lmbda = 1e-1
b = cbpdn.ConvBPDN(D, s, lmbda, opt=opt)
b.solve()
assert (b.X.dtype == dt)
assert (b.Xf.dtype == sl.complex_dtype(dt))
assert (b.Yf.dtype == sl.complex_dtype(dt))
def __init__(self, D, S, lmbda=None, opt=None, dimK=None, dimN=2):
"""
Initialise a ConvBPDN object with problem parameters.
This class supports an arbitrary number of spatial dimensions,
`dimN`, with a default of 2. The input dictionary `D` is either
`dimN` + 1 dimensional, in which case each spatial component
(image in the default case) is assumed to consist of a single
channel, or `dimN` + 2 dimensional, in which case the final
dimension is assumed to contain the channels (e.g. colour
channels in the case of images). The input signal set `S` is
either `dimN` dimensional (no channels, only one signal), `dimN` + 1
dimensional (either multiple channels or multiple signals), or
`dimN` + 2 dimensional (multiple channels and multiple signals).
Determination of problem dimensions is handled by
:class:`.cnvrep.CSC_ConvRepIndexing`.
|
**Call graph**
.. image:: _static/jonga/fista_cbpdn_init.svg
:width: 20%
:target: _static/jonga/fista_cbpdn_init.svg
|
Parameters
----------
D : array_like
Dictionary array
S : array_like
Signal array
lmbda : float
Regularisation parameter
opt : :class:`ConvBPDN.Options` object
Algorithm options
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/temporal dimensions
"""
# Set default options if none specified
if opt is None:
opt = ConvBPDN.Options()
# Infer problem dimensions and set relevant attributes of self
if not hasattr(self, 'cri'):
self.cri = cr.CSC_ConvRepIndexing(D, S, dimK=dimK, dimN=dimN)
# 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)
self.wl1 = np.asarray(opt['L1Weight'], dtype=self.dtype)
# Call parent class __init__
xshape = self.cri.shpX
super(ConvBPDN, self).__init__(xshape, S.dtype, opt)
if self.opt['BackTrack', 'Enabled']:
self.L /= self.lmbda
# Reshape D and S to standard layout
self.D = np.asarray(D.reshape(self.cri.shpD), dtype=self.dtype)
self.S = np.asarray(S.reshape(self.cri.shpS), dtype=self.dtype)
# Compute signal in DFT domain
self.Sf = sl.rfftn(self.S, None, self.cri.axisN)
# Create byte aligned arrays for FFT calls
xfshp = list(self.X.shape)
xfshp[dimN - 1] = xfshp[dimN - 1] // 2 + 1
self.Xf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
# Initialise auxiliary variable Yf
self.Yf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
self.Ryf = -self.Sf
self.Xf = sl.rfftn(self.X, None, self.cri.axisN)
self.Yf = self.Xf
self.store_prev()
self.setdict()
def __init__(self, Z, S, W, dsz, opt=None, dimK=None, dimN=2):
"""
Initialise a ConvCnstrMODMaskDcplBase object with problem size
and options.
Parameters
----------
Z : array_like
Coefficient map array
S : array_like
Signal array
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).
dsz : tuple
Filter support size(s)
opt : :class:`ConvCnstrMODMaskDcplBase.Options` object
Algorithm options
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
"""
# Set default options if none specified
if opt is None:
opt = ConvCnstrMODMaskDcplBase.Options()
# Infer problem dimensions and set relevant attributes of self
self.cri = cr.CDU_ConvRepIndexing(dsz, S, dimK=dimK, dimN=dimN)
# Convert W to internal shape
W = np.asarray(W.reshape(cr.mskWshape(W, self.cri)), dtype=S.dtype)
# Reshape W if necessary (see discussion of reshape of S below)
if self.cri.Cd == 1 and self.cri.C > 1:
# In most cases broadcasting rules make it possible for W
# to have a singleton dimension corresponding to a non-singleton
# dimension in S. However, when S is reshaped to interleave axisC
# and axisK on the same axis, broadcasting is no longer sufficient
# unless axisC and axisK of W are either both singleton or both
# of the same size as the corresponding axes of S. If neither of
# these cases holds, it is necessary to replicate the axis of W
# (axisC or axisK) that does not have the same size as the
# corresponding axis of S.
shpw = list(W.shape)
swck = shpw[self.cri.axisC] * shpw[self.cri.axisK]
if swck > 1 and swck < self.cri.C * self.cri.K:
if W.shape[self.cri.axisK] == 1 and self.cri.K > 1:
shpw[self.cri.axisK] = self.cri.K
else:
shpw[self.cri.axisC] = self.cri.C
W = np.broadcast_to(W, shpw)
self.W = W.reshape(W.shape[0:self.cri.dimN] +
(1, W.shape[self.cri.axisC] *
W.shape[self.cri.axisK], 1))
else:
self.W = W
# Call parent class __init__
Nx = self.cri.N * self.cri.Cd * self.cri.M
CK = (self.cri.C if self.cri.Cd == 1 else 1) * self.cri.K
shpY = list(self.cri.shpX)
shpY[self.cri.axisC] = self.cri.Cd
shpY[self.cri.axisK] = 1
shpY[self.cri.axisM] += CK
super(ConvCnstrMODMaskDcplBase,
self).__init__(Nx, shpY, self.cri.axisM, CK, S.dtype, opt)
# Reshape S to standard layout (Z, i.e. X in cbpdn, is assumed
# to be taken from cbpdn, and therefore already in standard
# form). If the dictionary has a single channel but the input
# (and therefore also the coefficient map array) has multiple
# channels, the channel index and multiple image index have
# the same behaviour in the dictionary update equation: the
# simplest way to handle this is to just reshape so that the
# channels also appear on the multiple image index.
if self.cri.Cd == 1 and self.cri.C > 1:
self.S = S.reshape(self.cri.Nv + (1, self.cri.C * self.cri.K, 1))
else:
self.S = S.reshape(self.cri.shpS)
self.S = np.asarray(self.S, dtype=self.dtype)
# Create constraint set projection function
self.Pcn = cr.getPcn(dsz,
self.cri.Nv,
self.cri.dimN,
self.cri.dimCd,
zm=opt['ZeroMean'])
# Initialise byte-aligned arrays for pyfftw
self.YU = sl.pyfftw_empty_aligned(self.Y.shape, dtype=self.dtype)
xfshp = list(self.cri.Nv + (self.cri.Cd, 1, self.cri.M))
xfshp[dimN - 1] = xfshp[dimN - 1] // 2 + 1
self.Xf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
if Z is not None:
self.setcoef(Z)
def __init__(self, Z, S, dsz, opt=None, dimK=1, dimN=2):
"""Initialise a ConvCnstrMOD_Consensus object with problem
parameters. See :meth:`.ConvCnstrMODBase.__init__` for
interface details.
|
**Call graph**
.. image:: _static/jonga/ccmodcnsns_init.svg
:width: 20%
:target: _static/jonga/ccmodcnsns_init.svg
"""
# Set default options if none specified
if opt is None:
opt = ConvCnstrMOD_Consensus.Options()
# Infer problem dimensions and set relevant attributes of self
self.cri = cr.CDU_ConvRepIndexing(dsz, S, dimK=dimK, dimN=dimN)
# Handle possible reshape of channel axis onto multiple image axis
# (see comment below)
Nb = self.cri.K if self.cri.C == self.cri.Cd else \
self.cri.C * self.cri.K
admm.ADMMConsensus.__init__(self, Nb, self.cri.shpD, S.dtype, opt)
# Set penalty parameter
self.set_attr('rho', opt['rho'], dval=self.cri.K, dtype=self.dtype)
# Reshape S to standard layout (Z, i.e. X in cbpdn, is assumed
# to be taken from cbpdn, and therefore already in standard
# form). If the dictionary has a single channel but the input
# (and therefore also the coefficient map array) has multiple
# channels, the channel index and multiple image index have
# the same behaviour in the dictionary update equation: the
# simplest way to handle this is to just reshape so that the
# channels also appear on the multiple image index.
if self.cri.Cd == 1 and self.cri.C > 1:
self.S = S.reshape(self.cri.Nv + (1, ) +
(self.cri.C * self.cri.K, ) + (1, ))
else:
self.S = S.reshape(self.cri.shpS)
self.S = np.asarray(self.S, dtype=self.dtype)
# Compute signal S in DFT domain
self.Sf = sl.rfftn(self.S, None, self.cri.axisN)
# Create constraint set projection function
self.Pcn = cr.getPcn(dsz,
self.cri.Nv,
self.cri.dimN,
self.cri.dimCd,
zm=opt['ZeroMean'])
if Z is not None:
self.setcoef(Z)
self.X = sl.pyfftw_empty_aligned(self.xshape, dtype=self.dtype)
# See comment on corresponding test in xstep method
if self.cri.Cd > 1:
self.YU = sl.pyfftw_empty_aligned(self.yshape, dtype=self.dtype)
else:
self.YU = sl.pyfftw_empty_aligned(self.xshape, dtype=self.dtype)
xfshp = list(self.xshape)
xfshp[dimN - 1] = xfshp[dimN - 1] // 2 + 1
self.Xf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
def __init__(self, Z, S, dsz, opt=None, dimK=1, dimN=2):
"""Initialise a ConvCnstrMODBase object with problem parameters.
This class supports an arbitrary number of spatial dimensions,
`dimN`, with a default of 2. The input coefficient map array `Z`
(usually labelled X, but renamed here to avoid confusion with
the X and Y variables in the ADMM base class) is expected to
be in standard form as computed by the ConvBPDN class.
The input signal set `S` is either `dimN` dimensional (no
channels, only one signal), `dimN` +1 dimensional (either
multiple channels or multiple signals), or `dimN` +2 dimensional
(multiple channels and multiple signals). Parameter `dimK`, with
a default value of 1, indicates the number of multiple-signal
dimensions in `S`:
::
Default dimK = 1, i.e. assume input S is of form
S(N0, N1, C, K) or S(N0, N1, K)
If dimK = 0 then input S is of form
S(N0, N1, C, K) or S(N0, N1, C)
The internal data layout for S, D (X here), and X (Z here) is:
::
dim<0> - dim<Nds-1> : Spatial dimensions, product of N0,N1,... is N
dim<Nds> : C number of channels in S and D
dim<Nds+1> : K number of signals in S
dim<Nds+2> : M number of filters in D
sptl. chn sig flt
S(N0, N1, C, K, 1)
D(N0, N1, C, 1, M) (X here)
X(N0, N1, 1, K, M) (Z here)
The `dsz` parameter indicates the desired filter supports in the
output dictionary, since this cannot be inferred from the
input variables. The format is the same as the `dsz` parameter
of :func:`.cnvrep.bcrop`.
Parameters
----------
Z : array_like
Coefficient map array
S : array_like
Signal array
dsz : tuple
Filter support size(s)
opt : ccmod.Options object
Algorithm options
dimK : int, optional (default 1)
Number of dimensions for multiple signals in input S
dimN : int, optional (default 2)
Number of spatial dimensions
"""
# Set default options if none specified
if opt is None:
opt = ConvCnstrMODBase.Options()
# Infer problem dimensions and set relevant attributes of self
self.cri = cr.CDU_ConvRepIndexing(dsz, S, dimK=dimK, dimN=dimN)
# Call parent class __init__
super(ConvCnstrMODBase, self).__init__(self.cri.shpD, S.dtype, opt)
# Set penalty parameter
self.set_attr('rho', opt['rho'], dval=self.cri.K, dtype=self.dtype)
# Reshape S to standard layout (Z, i.e. X in cbpdn, is assumed
# to be taken from cbpdn, and therefore already in standard
# form). If the dictionary has a single channel but the input
# (and therefore also the coefficient map array) has multiple
# channels, the channel index and multiple image index have
# the same behaviour in the dictionary update equation: the
# simplest way to handle this is to just reshape so that the
# channels also appear on the multiple image index.
if self.cri.Cd == 1 and self.cri.C > 1:
self.S = S.reshape(self.cri.Nv + (1, ) +
(self.cri.C * self.cri.K, ) + (1, ))
else:
self.S = S.reshape(self.cri.shpS)
self.S = np.asarray(self.S, dtype=self.dtype)
# Compute signal S in DFT domain
self.Sf = sl.rfftn(self.S, None, self.cri.axisN)
# Create constraint set projection function
self.Pcn = cr.getPcn(dsz,
self.cri.Nv,
self.cri.dimN,
self.cri.dimCd,
zm=opt['ZeroMean'])
# Create byte aligned arrays for FFT calls
self.YU = sl.pyfftw_empty_aligned(self.Y.shape, dtype=self.dtype)
xfshp = list(self.Y.shape)
xfshp[dimN - 1] = xfshp[dimN - 1] // 2 + 1
self.Xf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
if Z is not None:
self.setcoef(Z)
def rfftn_empty(shape, axes, dtype, order='C', n=None):
ashp = list(shape)
raxis = axes[-1]
ashp[raxis] = ashp[raxis] // 2 + 1
cdtype = spl.complex_dtype(dtype)
return np.zeros(ashp, dtype=cdtype)
def __init__(self, D, S, lmbda, mu=0.0, opt=None, dimK=None, dimN=2):
"""
Initialise a ConvBPDNRecTV object with problem parameters.
|
**Call graph**
.. image:: _static/jonga/cbpdnrtv_init.svg
:width: 20%
:target: _static/jonga/cbpdnrtv_init.svg
|
Parameters
----------
D : array_like
Dictionary matrix
S : array_like
Signal vector or matrix
lmbda : float
Regularisation parameter (l1)
mu : float
Regularisation parameter (gradient)
opt : :class:`ConvBPDNRecTV.Options` object
Algorithm options
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
"""
if opt is None:
opt = ConvBPDNRecTV.Options()
# Infer problem dimensions and set relevant attributes of self
self.cri = cr.CSC_ConvRepIndexing(D, S, dimK=dimK, dimN=dimN)
# Call parent class __init__
Nx = np.product(self.cri.shpX)
yshape = list(self.cri.shpX)
yshape[self.cri.axisM] += len(self.cri.axisN) * self.cri.Cd
super(ConvBPDNRecTV, self).__init__(Nx, yshape, yshape, S.dtype, opt)
# Set l1 term scaling and weight array
self.lmbda = self.dtype.type(lmbda)
self.Wl1 = np.asarray(opt['L1Weight'], dtype=self.dtype)
self.Wl1 = self.Wl1.reshape(cr.l1Wshape(self.Wl1, self.cri))
self.mu = self.dtype.type(mu)
if hasattr(opt['TVWeight'], 'ndim') and opt['TVWeight'].ndim > 0:
self.Wtv = np.asarray(
opt['TVWeight'].reshape((1, ) * (dimN + 2) +
opt['TVWeight'].shape),
dtype=self.dtype)
else:
# Wtv is a scalar: no need to change shape
self.Wtv = self.dtype.type(opt['TVWeight'])
# Set penalty parameter
self.set_attr('rho',
opt['rho'],
dval=(50.0 * self.lmbda + 1.0),
dtype=self.dtype)
# Set rho_xi attribute
self.set_attr('rho_xi',
opt['AutoRho', 'RsdlTarget'],
dval=1.0,
dtype=self.dtype)
# Reshape D and S to standard layout
self.D = np.asarray(D.reshape(self.cri.shpD), dtype=self.dtype)
self.S = np.asarray(S.reshape(self.cri.shpS), dtype=self.dtype)
# Compute signal in DFT domain
self.Sf = sl.rfftn(self.S, None, self.cri.axisN)
self.Gf, GHGf = sl.GradientFilters(self.cri.dimN + 3,
self.cri.axisN,
self.cri.Nv,
dtype=self.dtype)
# Initialise byte-aligned arrays for pyfftw
self.YU = sl.pyfftw_empty_aligned(self.Y.shape, dtype=self.dtype)
xfshp = list(self.cri.shpX)
xfshp[dimN - 1] = xfshp[dimN - 1] // 2 + 1
self.Xf = sl.pyfftw_empty_aligned(xfshp,
dtype=sl.complex_dtype(self.dtype))
self.setdict()
