pyhrf.jde.beta module¶

class pyhrf.jde.beta.BetaSampler(do_sampling=True, use_true_value=False, val_ini=array([ 0.7]), sigma=0.05, pr_beta_cut=1.2, pf_method='es', pf=None)¶

Bases: pyhrf.xmlio.Initable, pyhrf.jde.samplerbase.GibbsSamplerVariable

checkAndSetInitValue(variables)¶

getOutputs()¶

get_string_value(v)¶

linkToData(dataInput)¶

loadBetaGrid()¶

parametersComments = {'pf_method': 'either "es" (extrapolation scheme) or "ps" (path sampling)'}¶

parametersToShow = ['do_sampling', 'val_ini']¶

sampleNextInternal(variables)¶: Define the behaviour of the variable at each sampling step when its sampling is not activated. Must be overriden in child classes.

samplingWarmUp(variables)¶: Called before the launch of the main sampling loop by the sampler engine. Should be overriden and perform precalculations.

saveCurrentValue(it)¶

pyhrf.jde.beta.Cpt_AcceptNewBeta_Graph(RefGraph, GraphNodesLabels, VecEstim_lnZ, VecBetaVal, CurrentBeta, sigma, thresh=1.2, GraphWeight=None)¶

Starting from a given Beta vector (1 value for each condition) CurrentBeta, computes new Beta values in NewBeta using a Metropolis-Hastings step.

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0. GraphNodesLabels – Nodes labels. GraphNodesLabels[i] is the node i label. VecEstim_lnZ – Vector containing the ln(Z(beta,mask)) estimates (in accordance with the defined mask). VecBetaVal – Vector of the same size as VecExpectZ containing the corresponding beta value (in accordance with the defined mask). CurrentBeta – Beta at the current iteration sigma – such as NewBeta = CurrentBeta + N(0,sigma) thresh – the prior on beta is uniform between 0 and thresh and linearly decrease between thresh and VecBetaVal[-1] GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.
Returns:	Contains the accepted beta value at the next iteration
Return type:	NewBeta

pyhrf.jde.beta.Cpt_Distrib_P_beta_graph(RefGraph, GraphNodesLabels, VecEstim_lnZ, VecBetaVal, thresh=1.5, GraphWeight=None)¶

Computes the distribution $P(beta|q)$

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 GraphNodesLabels – Nodes labels. GraphNodesLabels[i] is the node i label. VecEstim_lnZ – Vector containing the $ln(Z(beta,mask))$ estimates (in accordance with the defined graph). VecBetaVal – Vector of the same size as VecExpectZ containing the corresponding beta value (in accordance with the defined graph). thresh – the prior on beta is uniform between 0 and thresh and linearly decrease between thresh and VecBetaVal[-1] GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.
Returns:	contains the $P(beta\|q)$ values (consistent with VecBetaVal).
Return type:	Vec_P_Beta

pyhrf.jde.beta.Cpt_Exact_lnZ_graph(RefGraph, beta, LabelsNb, GraphWeight=None)¶

Computes the logarithm of the exact partition function $Z(\beta)$ .

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 beta – spatial regularization parameter LabelsNb – number of labels in each site (typically 2 or 3) GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.
Returns:	exact value of ln(Z)
Return type:	exact_lnZ

pyhrf.jde.beta.Cpt_Expected_U_graph(RefGraph, beta, LabelsNb, SamplesNb, GraphWeight=None, GraphNodesLabels=None, GraphLinks=None, RefGrphNgbhPosi=None)¶

Useless now!

Estimates the expectation of U for a given normalization constant Beta and a given mask shape. Swendsen-Wang sampling is used to assess the expectation on significant images depending of beta.

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 beta – normalization constant LabelsNb – Labels number SamplesNb – Samples number for the U expectation estimation GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0. GraphNodesLabels – Optional list containing the nodes labels. The sampler aims to modify its values in function of beta and NbLabels. At this level this variable is seen as temporary and will be modified. Defining it slightly increases the calculation times. GraphLinks – Same shape as RefGraph. Each entry indicates if the link of the corresponding edge in RefGraph is considered (if yes …=1 else …=0). At this level this variable is seen as temporary and will be modified. Defining it slightly increases the calculation times. RefGrphNgbhPosi – Same shape as RefGraph. RefGrphNgbhPosi[i][j] indicates for which k is the link to i in RefGraph[RefGraph[i][j]][k]. This optional list is never modified.
Returns:	U expectation
Return type:	ExpectU

pyhrf.jde.beta.Cpt_Vec_Estim_lnZ_Graph(RefGraph, LabelsNb, SamplesNb=40, BetaMax=1.4, BetaStep=0.05, GraphWeight=None)¶

Estimates ln(Z) for fields of a given size and Beta values between 0 and BetaMax. Estimates of ln(Z) are first computed on a coarse grid of Beta values. They are then computed and returned on a fine grid. No approximation using precomputed partition function is performed here.

Parameters:

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 LabelsNb – number of labels SamplesNb – number of fields estimated for each beta BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax BetaStep – gap between two considered values of beta (…in the fine grid. This gap in the coarse grid is automatically fixed and depends on the graph size.) GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.
Returns:	VecEstim_lnZ – Vector containing the ln(Z(beta,mask)) estimates VecBetaVal – Vector of the same size as VecExpectZ containing the corresponding beta value

RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2
LabelsNb – number of labels
SamplesNb – number of fields estimated for each beta
BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax
BetaStep – gap between two considered values of beta (…in the fine grid. This gap in the coarse grid is automatically fixed and depends on the graph size.)
GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.

Returns:

VecEstim_lnZ – Vector containing the ln(Z(beta,mask)) estimates
VecBetaVal – Vector of the same size as VecExpectZ containing the corresponding beta value

pyhrf.jde.beta.Cpt_Vec_Estim_lnZ_Graph_fast(RefGraph, LabelsNb, MaxErrorAllowed=5, BetaMax=1.4, BetaStep=0.05)¶

Estimate ln(Z(beta)) of Potts fields. The default Beta grid is between 0. and 1.4 with a step of 0.05. Extrapolation algorithm is used. Fast estimates are only performed for Ising fields (2 labels). Reference partition functions were pre-computed on Ising fields designed on regular and non-regular grids. They all respect a 6-connectivity system.

Parameters:

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 LabelsNb – possible number of labels in each site of the graph MaxErrorAllowed – maximum error allowed in the graph estimation (in percents). BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.4 BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.
Returns:	Est_lnZ – Vector containing the ln(Z(beta)) estimates V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2
LabelsNb – possible number of labels in each site of the graph
MaxErrorAllowed – maximum error allowed in the graph estimation (in percents).
BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.4
BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.

Returns:

Est_lnZ – Vector containing the ln(Z(beta)) estimates
V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

pyhrf.jde.beta.Cpt_Vec_Estim_lnZ_Graph_fast2(RefGraph, BetaMax=1.4, BetaStep=0.05)¶

Estimate ln(Z(beta)) of Ising fields (2 labels). The default Beta grid is between 0. and 1.4 with a step of 0.05. Bilinar estimation with the number of sites and cliques is used. The bilinear functions were estimated using bilinear regression on reference partition functions on 240 non-regular grids and with respect to a 6-connectivity system. (Pfs are found in LoadBaseLogPartFctRef -> PFs 0:239)

Parameters:

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.4 BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.
Returns:	Est_lnZ – Vector containing the ln(Z(beta)) estimates V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2
BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.4
BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.

Returns:

Est_lnZ – Vector containing the ln(Z(beta)) estimates
V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

pyhrf.jde.beta.Cpt_Vec_Estim_lnZ_Graph_fast3(RefGraph, LabelsNb, MaxErrorAllowed=5, BetaMax=1.4, BetaStep=0.05)¶

Parameters:

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 LabelsNb – possible number of labels in each site of the graph MaxErrorAllowed – maximum error allowed in the graph estimation (in percents). BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.4 BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.
Returns:	Est_lnZ – Vector containing the ln(Z(beta)) estimates V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2
LabelsNb – possible number of labels in each site of the graph
MaxErrorAllowed – maximum error allowed in the graph estimation (in percents).
BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.4
BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.

Returns:

Est_lnZ – Vector containing the ln(Z(beta)) estimates
V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

pyhrf.jde.beta.Cpt_Vec_Estim_lnZ_OLD_Graph(RefGraph, LabelsNb, SamplesNb=50, BetaMax=1.0, BetaStep=0.01, GraphWeight=None)¶

Useless now!

Estimates ln(Z) for fields of a given size and Beta values between 0 and BetaMax.

Parameters:

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 LabelsNb – number of labels BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax BetaStep – gap between two considered values of bseta GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.
Returns:	VecEstim_lnZ – Vector containing the ln(Z(beta,mask)) estimates VecBetaVal – Vector of the same size as VecExpectZ containing the corresponding beta value

RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2
LabelsNb – number of labels
BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax
BetaStep – gap between two considered values of bseta
GraphWeight – Same shape as RefGraph. Each entry is the weight of the corresponding edge in RefGraph. If not defined the weights are set to 1.0.

Returns:

VecEstim_lnZ – Vector containing the ln(Z(beta,mask)) estimates
VecBetaVal – Vector of the same size as VecExpectZ containing the corresponding beta value

pyhrf.jde.beta.Cpt_Vec_Estim_lnZ_Onsager(n, BetaMax=1.2, BetaStep=0.05)¶

Estimate ln(Z(beta)) Onsager using Onsager technique (2D periodic fields - 2 labels - 4 connectivity)

Parameters:

Parameters:	n – number of sites BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.2. BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.
Returns:	Est_lnZ – Vector containing the ln(Z(beta)) estimates V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

n – number of sites
BetaMax – Z(beta,mask) will be computed for beta between 0 and BetaMax. Maximum considered value is 1.2.
BetaStep – gap between two considered values of beta. Actual gaps are not exactly those asked but very close.

Returns:

Est_lnZ – Vector containing the ln(Z(beta)) estimates
V_Beta – Vector of the same size as VecExpectZ containing the corresponding beta value

pyhrf.jde.beta.Estim_lnZ_Onsager(n, beta)¶

Estimate ln(Z(beta)) using Onsager technique (2D periodic fields - 2 labels - 4 connectivity)

Parameters:	n – number of sites beta – beta
Returns:	ln(Z(beta)) estimate
Return type:	LogZ

pyhrf.jde.beta.Estim_lnZ_ngbhd_graph(RefGraph, beta_Ngbhd, beta_Ref, lnZ_ref, VecU_ref, LabelsNb)¶

Estimates ln(Z) for beta=betaNgbhd. beta_Ngbhd is supposed close to beta_Ref for which ln(Z) is known (lnZ_ref) and the energy U of fields generated according to it have already been computed (VecU_ref).

Parameters:	RefGraph – List which contains the connectivity graph. Each entry represents a node of the graph and contains the list of its neighbors entry location in the graph. Ex: RefGraph[2][3]=10 means 3rd neighbour of the 2nd node is the 10th node. => There exists i such that RefGraph[10][i]=2 beta_Ngbhd – normalization constant for which ln(Z) will be estimated beta_Ref – normalization constant close to beta_Ngbhd for which ln(Z) already known lnZ_ref – ln(Z) for beta=beta_Ref VecU_ref – energy U of fields generated according to beta_Ref LabelsNb – Labels number
Returns:	ln(Z) for beta=beta_Ngbhd
Return type:	lnZ_Ngbhd

pyhrf.jde.beta.LoadBaseLogPartFctRef()¶

output:

BaseLogPartFctRef: dictionnary that contains the data base of log-PF (first value = nb labels / second value = nb. sites / third value = nb. cliques)
V_Beta_Ref: Beta grid corresponding to the log-PF values in ‘Est_lnZ_Ref’

pyhrf.jde.beta.beta_estim_obs_field(graph, labels, gridLnz, method='MAP', weights=None)¶

Estimate the amount of spatial correlation of an Ising observed field. graph is the neighbours list defining the topology labels is the field realisation gridLnz is the log-partition function associated to the topology, ie a grid where gridLnz[0] stores values of lnz and gridLnz[1] stores corresponding values of beta.

Returns:	estimated beta tabulated distribution p(beta\|labels)

pyhrf.jde.beta.logpf_ising_onsager(size, beta)¶: Calculate log partition function in terms of beta for an Ising field of size ‘size’. ‘beta’ can be scalar or numpy.array. Assumptions: the field is 2D, squared, toroidal and has 4-connectivity