class Cov2KronSumLR(Covariance):
"""
Covariance class for sum of 2 Kronecker products with one low rank term:
K = Cr \kron GG.T + Cn \kron I
Notation:
- dim_c: dimension of col covariances
- dim_r: dimension of row covariances
- rank_c: rank of low-rank col covariance
- rank_r: rank of low-rank row covariance
"""
def __init__(self, Cn = None, G = None, rank = 1):
"""
Args:
Cn: Limix covariance matrix for Cn (dimension dim_c)
G: [dim_r, rank_r] numpy covariance matrix for G
rank: rank of column low-rank covariance (default = 1)
"""
Covariance.__init__(self)
self._Cr_act = True
self._Cn_act = True
self.setColCovars(Cn, rank = rank)
self.G = G
self.dim = self.dim_c * self.dim_r
self._use_to_predict = False
def G_has_changed(self):
self.clear_cache('row_cov')
self._notify('row_cov')
self.clear_all()
def col_covs_have_changed(self):
self.clear_cache('col_cov')
self._notify('col_cov')
self.clear_all()
#####################
# Properties
#####################
@property
def G(self):
return self._G
@property
def Cr(self):
return self._Cr
@property
def Cn(self):
return self._Cn
@property
def dim_r(self):
return self._dim_r
@property
def dim_c(self):
return self._dim_c
@property
def rank_r(self):
return self._rank_r
@property
def rank_c(self):
return self._rank_c
#####################
# Setters
#####################
@G.setter
def G(self,value):
assert value is not None, 'G cannot be set to None.'
self._dim_r = value.shape[0]
# perform svd on G
# excludes eigh < 1e-8 and recalcs G
_value, U, S, V = svd_reduce(value)
self._rank_r = _value.shape[1]
self._G = _value
self._Ug = U
self._Sg = S
self._Vg = V
self.G_has_changed()
# normal setter for col covars
def setColCovars(self, Cn = None, rank = 1):
assert Cn is not None, 'Cn has to be specified.'
self._rank_c = rank
self._dim_c = Cn.dim
self._Cr = LowRankCov(self._dim_c, rank)
self._Cn = Cn
# register
self._Cr.register(self.col_covs_have_changed)
self._Cn.register(self.col_covs_have_changed)
self.col_covs_have_changed()
#####################
# Activation handling
#####################
@property
def act_Cr(self):
return self._Cr_act
@act_Cr.setter
def act_Cr(self, act):
self._Cr_act = bool(act)
self._notify()
@property
def act_Cn(self):
return self._Cn_act
@act_Cn.setter
def act_Cn(self, act):
self._Cn_act = bool(act)
self._notify()
def _actindex2index(self, i):
nCr = self.Cr.getNumberParams()
i += nCr * int(not self._Cr_act)
return i
def _index2actindex(self, i):
nCr = self.Cr.getNumberParams()
i -= nCr * int(not self._Cr_act)
return i
#####################
# Params handling
#####################
def setParams(self, params):
nCr = int(self._Cr_act) * self.Cr.getNumberParams()
nCn = int(self._Cn_act) * self.Cn.getNumberParams()
if len(params) != self.getNumberParams():
raise ValueError("The number of parameters passed to setParams "
"differs from the number of active parameters.")
if self._Cr_act:
self.Cr.setParams(params[:nCr])
if self._Cn_act:
self.Cn.setParams(params[nCr:])
def getParams(self):
params = []
if self._Cr_act:
params.append(self.Cr.getParams())
if self._Cn_act:
params.append(self.Cn.getParams())
if len(params) == 0:
return np.array([])
return sp.concatenate(params)
def getNumberParams(self):
return (int(self._Cr_act) * self.Cr.getNumberParams() +
int(self._Cn_act) * self.Cn.getNumberParams())
#####################
# Cached
#####################
def Sg(self):
return self._Sg
def Ug(self):
return self._Ug
def Vg(self):
return self._Vg
@cached('row_cov')
def trSg(self):
return self.Sg().sum()
@cached('row_cov')
def logdetSg(self):
return sp.log(self.Sg()).sum()
@cached('row_cov')
def Wr(self):
return self.Ug().T
@cached('col_cov')
def Lc(self):
return self.Cn.USi2().T
@cached
def Lr(self):
return self.eye(N)
@cached('col_cov')
def Estar(self):
E = self.Cr.X
# for a general covariance matrix
# E = LA.chol(C.K())
# or based on eigh decomposition if this fails
return sp.dot(self.Lc(), E)
@cached('col_cov')
def Se(self):
Ue, Seh, Ve = nla.svd(self.Estar(), full_matrices=0)
self.fill_cache('Ue',Ue)
self.fill_cache('Ve',Ve)
return Seh**2
@cached('col_cov')
def Ue(self):
Ue, Seh, Ve = nla.svd(self.Estar(), full_matrices=0)
self.fill_cache('Se',Seh**2)
self.fill_cache('Ve',Ve)
return Ue
@cached('col_cov')
def Ve(self):
Ue, Seh, Ve = nla.svd(self.Estar(), full_matrices=0)
self.fill_cache('Ue',Ue)
self.fill_cache('Se',Seh**2)
return Ve
@cached('col_cov')
def Wc(self):
return self.Ue().T
@cached(['row_cov', 'col_cov'])
def SpI(self):
return sp.kron(1./self.Se(), 1./self.Sg()) + 1
@cached(['row_cov', 'col_cov'])
def d(self):
return 1./self.SpI()
@cached(['row_cov', 'col_cov'])
def D(self):
return self.d().reshape((self.rank_r, self.rank_c), order = 'F')
@cached(['col_cov'])
def Ctilde(self, i):
if i < self.Cr.getNumberParams():
C = self.Cr.K_grad_i(i)
else:
_i = i - self.Cr.getNumberParams()
C = self.Cn.K_grad_i(_i)
return sp.dot(self.Lc(), sp.dot(C, self.Lc().T))
@cached(['col_cov'])
def LcCtildeLc(self, i):
return sp.dot(self.Lc().T, sp.dot(self.Ctilde(i), self.Lc()))
@cached(['col_cov'])
def Cbar(self, i):
return sp.dot(self.Wc(), sp.dot(self.Ctilde(i), self.Wc().T))
#####################
# Debug quantities
#####################
def L(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
return sp.kron(self.Lc(), sp.eye(self.dim_r))
def W(self):
return sp.dot(self.Wc(), self.Wr())
def R(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
return sp.dot(self.G, self.G.T)
#####################
# Overwritten covar_base methods
#####################
@cached(['row_cov', 'col_cov', 'covar_base'])
def K(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
rv = sp.kron(self.Cr.K(), self.R()) + sp.kron(self.Cn.K(), sp.eye(self.dim_r))
return rv
@cached(['row_cov', 'col_cov', 'covar_base'])
def K_grad_i(self,i):
n = self.getNumberParams()
if i >= n:
raise ValueError("Trying to retrieve the gradient over a "
"parameter that is inactive.")
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
i = self._actindex2index(i)
nCr = self.Cr.getNumberParams()
if i < nCr:
rv= sp.kron(self.Cr.K_grad_i(i), self.R())
else:
_i = i - nCr
rv = sp.kron(self.Cn.K_grad_i(_i), sp.eye(self.dim_r))
return rv
@cached(['row_cov', 'col_cov', 'covar_base'])
def logdet(self):
rv = sp.sum(sp.log(self.Cn.S())) * self.dim_r
rv+= sp.log(self.SpI()).sum()
rv+= sp.log(self.Se()).sum() * self.rank_r
rv+= self.logdetSg() * self.rank_c
return rv
@cached(['row_cov', 'col_cov', 'covar_base'])
def logdet_grad_i(self,i):
if i >= self.getNumberParams():
raise ValueError("Trying to retrieve the gradient over a "
"parameter that is inactive.")
i = self._actindex2index(i)
if i < self.Cr.getNumberParams():
trR = self.trSg()
diagR = self.Sg()
else:
trR = self.dim_r
diagR = sp.ones(self.rank_r)
rv = self.Ctilde(i).diagonal().sum() * trR
rv-= (self.d() * sp.kron(sp.diag(self.Cbar(i)), diagR)).sum()
return rv
class Cov2KronSumLR(Covariance):
"""
Covariance class for sum of 2 Kronecker products with one low rank term:
K = Cr \kron GG.T + Cn \kron I
Notation:
- dim_c: dimension of col covariances
- dim_r: dimension of row covariances
- rank_c: rank of low-rank col covariance
- rank_r: rank of low-rank row covariance
"""
def __init__(self, Cn = None, G = None, rank = 1):
"""
Args:
Cn: Limix covariance matrix for Cn (dimension dim_c)
G: [dim_r, rank_r] numpy covariance matrix for G
rank: rank of column low-rank covariance (default = 1)
"""
Covariance.__init__(self)
self._Cr_act = True
self._Cn_act = True
self.setColCovars(Cn, rank = rank)
self.G = G
self.dim = self.dim_c * self.dim_r
self._use_to_predict = False
def G_has_changed(self):
self.clear_cache('row_cov')
self._notify('row_cov')
self.clear_all()
def col_covs_have_changed(self):
self.clear_cache('col_cov')
self._notify('col_cov')
self.clear_all()
#####################
# Properties
#####################
@property
def G(self):
return self._G
@property
def Cr(self):
return self._Cr
@property
def Cn(self):
return self._Cn
@property
def dim_r(self):
return self._dim_r
@property
def dim_c(self):
return self._dim_c
@property
def rank_r(self):
return self._rank_r
@property
def rank_c(self):
return self._rank_c
#####################
# Setters
#####################
@G.setter
def G(self,value):
assert value is not None, 'G cannot be set to None.'
self._dim_r = value.shape[0]
# perform svd on G
# excludes eigh < 1e-8 and recalcs G
_value, U, S, V = svd_reduce(value)
self._rank_r = _value.shape[1]
self._G = _value
self._Ug = U
self._Sg = S
self._Vg = V
self.G_has_changed()
# normal setter for col covars
def setColCovars(self, Cn = None, rank = 1):
assert Cn is not None, 'Cn has to be specified.'
self._rank_c = rank
self._dim_c = Cn.dim
self._Cr = LowRankCov(self._dim_c, rank)
self._Cn = Cn
# register
self._Cr.register(self.col_covs_have_changed)
self._Cn.register(self.col_covs_have_changed)
self.col_covs_have_changed()
#####################
# Activation handling
#####################
@property
def act_Cr(self):
return self._Cr_act
@act_Cr.setter
def act_Cr(self, act):
self._Cr_act = bool(act)
self._notify()
@property
def act_Cn(self):
return self._Cn_act
@act_Cn.setter
def act_Cn(self, act):
self._Cn_act = bool(act)
self._notify()
def _actindex2index(self, i):
nCr = self.Cr.getNumberParams()
i += nCr * int(not self._Cr_act)
return i
def _index2actindex(self, i):
nCr = self.Cr.getNumberParams()
i -= nCr * int(not self._Cr_act)
return i
#####################
# Params handling
#####################
def setParams(self, params):
nCr = int(self._Cr_act) * self.Cr.getNumberParams()
nCn = int(self._Cn_act) * self.Cn.getNumberParams()
if len(params) != self.getNumberParams():
raise ValueError("The number of parameters passed to setParams "
"differs from the number of active parameters.")
if self._Cr_act:
self.Cr.setParams(params[:nCr])
if self._Cn_act:
self.Cn.setParams(params[nCr:])
def getParams(self):
params = []
if self._Cr_act:
params.append(self.Cr.getParams())
if self._Cn_act:
params.append(self.Cn.getParams())
if len(params) == 0:
return np.array([])
return sp.concatenate(params)
def getNumberParams(self):
return (int(self._Cr_act) * self.Cr.getNumberParams() +
int(self._Cn_act) * self.Cn.getNumberParams())
#####################
# Cached
#####################
def Sg(self):
return self._Sg
def Ug(self):
return self._Ug
def Vg(self):
return self._Vg
@cached('row_cov')
def trSg(self):
return self.Sg().sum()
@cached('row_cov')
def logdetSg(self):
return sp.log(self.Sg()).sum()
@cached('row_cov')
def Wr(self):
return self.Ug().T
@cached('col_cov')
def Lc(self):
return self.Cn.USi2().T
@cached
def Lr(self):
return self.eye(N)
@cached('col_cov')
def Estar(self):
E = self.Cr.X
# for a general covariance matrix
# E = LA.chol(C.K())
# or based on eigh decomposition if this fails
return sp.dot(self.Lc(), E)
@cached('col_cov')
def Se(self):
Ue, Seh, Ve = nla.svd(self.Estar(), full_matrices=0)
self.fill_cache('Ue',Ue)
self.fill_cache('Ve',Ve)
return Seh**2
@cached('col_cov')
def Ue(self):
Ue, Seh, Ve = nla.svd(self.Estar(), full_matrices=0)
self.fill_cache('Se',Seh**2)
self.fill_cache('Ve',Ve)
return Ue
@cached('col_cov')
def Ve(self):
Ue, Seh, Ve = nla.svd(self.Estar(), full_matrices=0)
self.fill_cache('Ue',Ue)
self.fill_cache('Se',Seh**2)
return Ve
@cached('col_cov')
def Wc(self):
return self.Ue().T
@cached(['row_cov', 'col_cov'])
def SpI(self):
return sp.kron(1./self.Se(), 1./self.Sg()) + 1
@cached(['row_cov', 'col_cov'])
def d(self):
return 1./self.SpI()
@cached(['row_cov', 'col_cov'])
def D(self):
return self.d().reshape((self.rank_r, self.rank_c), order = 'F')
@cached(['col_cov'])
def Ctilde(self, i):
if i < self.Cr.getNumberParams():
C = self.Cr.K_grad_i(i)
else:
_i = i - self.Cr.getNumberParams()
C = self.Cn.K_grad_i(_i)
return sp.dot(self.Lc(), sp.dot(C, self.Lc().T))
@cached(['col_cov'])
def LcCtildeLc(self, i):
return sp.dot(self.Lc().T, sp.dot(self.Ctilde(i), self.Lc()))
@cached(['col_cov'])
def Cbar(self, i):
return sp.dot(self.Wc(), sp.dot(self.Ctilde(i), self.Wc().T))
#####################
# Debug quantities
#####################
def L(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
return sp.kron(self.Lc(), sp.eye(self.dim_r))
def W(self):
return sp.dot(self.Wc(), self.Wr())
def R(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
return sp.dot(self.G, self.G.T)
#####################
# Overwritten covar_base methods
#####################
@cached(['row_cov', 'col_cov', 'covar_base'])
def K(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
rv = sp.kron(self.Cr.K(), self.R()) + sp.kron(self.Cn.K(), sp.eye(self.dim_r))
return rv
@cached(['row_cov', 'col_cov', 'covar_base'])
def K_grad_i(self,i):
n = self.getNumberParams()
if i >= n:
raise ValueError("Trying to retrieve the gradient over a "
"parameter that is inactive.")
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
i = self._actindex2index(i)
nCr = self.Cr.getNumberParams()
if i < nCr:
rv= sp.kron(self.Cr.K_grad_i(i), self.R())
else:
_i = i - nCr
rv = sp.kron(self.Cn.K_grad_i(_i), sp.eye(self.dim_r))
return rv
@cached(['row_cov', 'col_cov', 'covar_base'])
def logdet(self):
rv = sp.sum(sp.log(self.Cn.S())) * self.dim_r
rv+= sp.log(self.SpI()).sum()
rv+= sp.log(self.Se()).sum() * self.rank_r
rv+= self.logdetSg() * self.rank_c
return rv
@cached(['row_cov', 'col_cov', 'covar_base'])
def logdet_grad_i(self,i):
if i >= self.getNumberParams():
raise ValueError("Trying to retrieve the gradient over a "
"parameter that is inactive.")
i = self._actindex2index(i)
if i < self.Cr.getNumberParams():
trR = self.trSg()
diagR = self.Sg()
else:
trR = self.dim_r
diagR = sp.ones(self.rank_r)
rv = self.Ctilde(i).diagonal().sum() * trR
rv-= (self.d() * sp.kron(sp.diag(self.Cbar(i)), diagR)).sum()
return rv
