bpp-core  2.1.0
bpp::LowMemoryRescaledHmmLikelihood Class Reference

A modified implementation of the RescaledHmmLikelihood implementation, with lower memory usage. More...

#include <Bpp/Numeric/Hmm/LowMemoryRescaledHmmLikelihood.h>

+ Inheritance diagram for bpp::LowMemoryRescaledHmmLikelihood:
+ Collaboration diagram for bpp::LowMemoryRescaledHmmLikelihood:

List of all members.

Public Member Functions

 LowMemoryRescaledHmmLikelihood (HmmStateAlphabet *hiddenAlphabet, HmmTransitionMatrix *transitionMatrix, HmmEmissionProbabilities *emissionProbabilities, const std::string &prefix, size_t maxSize=1000000) throw (Exception)
 Build a new LowMemoryRescaledHmmLikelihood object.
 LowMemoryRescaledHmmLikelihood (const LowMemoryRescaledHmmLikelihood &lik)
LowMemoryRescaledHmmLikelihoodoperator= (const LowMemoryRescaledHmmLikelihood &lik)
virtual ~LowMemoryRescaledHmmLikelihood ()
LowMemoryRescaledHmmLikelihoodclone () const
 Create a copy of this object and send a pointer to it.
const HmmStateAlphabetgetHmmStateAlphabet () const
HmmStateAlphabetgetHmmStateAlphabet ()
const HmmTransitionMatrixgetHmmTransitionMatrix () const
HmmTransitionMatrixgetHmmTransitionMatrix ()
const HmmEmissionProbabilitiesgetHmmEmissionProbabilities () const
HmmEmissionProbabilitiesgetHmmEmissionProbabilities ()
void setBreakPoints (const std::vector< size_t > &breakPoints)
const std::vector< size_t > & getBreakPoints () const
void setParameters (const ParameterList &pl) throw (Exception)
 Set the point where the function must be computed.
double getValue () const throw (Exception)
 Get the value of the function at the current point.
double getLogLikelihood () const
void fireParameterChanged (const ParameterList &pl)
 Notify the class when one or several parameters have changed.
void getHiddenStatesPosteriorProbabilities (std::vector< std::vector< double > > &probs, bool append=false) const throw (NotImplementedException)
virtual double f (const ParameterList &parameters) throw (Exception)
 Get the value of the function according to a given set of parameters.
virtual bool hasParameter (const std::string &name) const =0
 Tell if there is a parameter with specified name.
virtual const ParameterListgetParameters () const =0
 Get all parameters available.
virtual const ParametergetParameter (const std::string &name) const =0 throw (ParameterNotFoundException)
 Get the parameter with specified name.
virtual double getParameterValue (const std::string &name) const =0 throw (ParameterNotFoundException)
 Get the value for parameter of name 'name'.
virtual void setAllParametersValues (const ParameterList &parameters)=0 throw (ParameterNotFoundException, ConstraintException)
 Set the parameters values to be equals to those of parameters.
virtual void setParameterValue (const std::string &name, double value)=0 throw (ParameterNotFoundException, ConstraintException)
 Set the value of parameter with name name to be equal to value.
virtual void setParametersValues (const ParameterList &parameters)=0 throw (ParameterNotFoundException, ConstraintException)
 Update the parameters from parameters.
virtual bool matchParametersValues (const ParameterList &parameters)=0 throw (ConstraintException)
 Update the parameters from parameters.
virtual size_t getNumberOfParameters () const =0
 Get the number of parameters.
virtual void setNamespace (const std::string &prefix)=0
 Set the namespace for the parameter names.
virtual std::string getNamespace () const =0
virtual std::string getParameterNameWithoutNamespace (const std::string &name) const =0
 Resolves a parameter name according to the current namespace.
bool hasParameter (const std::string &name) const
 Tell if there is a parameter with specified name.
const ParameterListgetParameters () const
 Get all parameters available.
const ParametergetParameter (const std::string &name) const throw (ParameterNotFoundException)
 Get the parameter with specified name.
double getParameterValue (const std::string &name) const throw (ParameterNotFoundException)
 Get the value for parameter of name 'name'.
void setAllParametersValues (const ParameterList &parameters) throw (ParameterNotFoundException, ConstraintException)
 Set the parameters values to be equals to those of parameters.
void setParameterValue (const std::string &name, double value) throw (ParameterNotFoundException, ConstraintException)
 Set the value of parameter with name name to be equal to value.
void setParametersValues (const ParameterList &parameters) throw (ParameterNotFoundException, ConstraintException)
 Update the parameters from parameters.
bool matchParametersValues (const ParameterList &parameters) throw (ConstraintException)
 Update the parameters from parameters.
size_t getNumberOfParameters () const
 Get the number of parameters.
void setNamespace (const std::string &prefix)
 Set the namespace for the parameter names.
std::string getNamespace () const
std::string getParameterNameWithoutNamespace (const std::string &name) const
 Resolves a parameter name according to the current namespace.

Protected Member Functions

void computeForward_ ()
void addParameter_ (Parameter *parameter)
void addParameters_ (const ParameterList &parameters)
void deleteParameter_ (size_t index) throw (IndexOutOfBoundsException)
void resetParameters_ ()
ParametergetParameter_ (const std::string &name) throw (ParameterNotFoundException)
ParametergetParameter_ (size_t index) throw (IndexOutOfBoundsException)
const ParametergetParameter_ (size_t index) const throw (IndexOutOfBoundsException)
ParametergetParameterWithNamespace_ (const std::string &name) throw (ParameterNotFoundException)
const ParametergetParameterWithNamespace_ (const std::string &name) const throw (ParameterNotFoundException)
ParameterListgetParameters_ ()

Private Attributes

std::auto_ptr< HmmStateAlphabethiddenAlphabet_
 The alphabet describing the hidden states.
std::auto_ptr
< HmmTransitionMatrix
transitionMatrix_
std::auto_ptr
< HmmEmissionProbabilities
emissionProbabilities_
std::vector< double > likelihood1_
 The likelihood array.
std::vector< double > likelihood2_
double logLik_
size_t maxSize_
std::vector< size_t > breakPoints_
size_t nbStates_
size_t nbSites_

Detailed Description

A modified implementation of the RescaledHmmLikelihood implementation, with lower memory usage.

This implementation is similar to the one used in the RescaledHmmLikelihood class, but does not store the full likelihood array. The benefit of it is a significantly reduced memory usage, allowing to compute likelihood for very large data sets. The drawback is that this class can't compute posterior probabilities, and can hence only be used to estimate parameters.

Definition at line 62 of file LowMemoryRescaledHmmLikelihood.h.


Constructor & Destructor Documentation

LowMemoryRescaledHmmLikelihood::LowMemoryRescaledHmmLikelihood ( HmmStateAlphabet hiddenAlphabet,
HmmTransitionMatrix transitionMatrix,
HmmEmissionProbabilities emissionProbabilities,
const std::string &  prefix,
size_t  maxSize = 1000000 
) throw (Exception)

Build a new LowMemoryRescaledHmmLikelihood object.

Warning:
the HmmTransitionMatrix and HmmEmissionProbabilities object passed as argument must be non-null and point toward the same HmmStateAlphabet instance. The three object will be copied if needed, and deleted when the hmm likelihood objet is deleted. You should secure a copy before if you don't want them to be destroyed with this object.
Parameters:
hiddenAlphabetThe hidden states alphabet to use.
transitionMatrixThe transition matrix to use.
emissionProbabilitiesThe emission probabilities to use.
prefixA namespace for parameter names.
maxSizethe maximum size of the vector of scales. If this size is exceeded, then a temporary likelihood computation is made and stored, and the vector is reset. the size of the vector specify the memory usage of the class. A two low value can lead to numerical precision errors.

Definition at line 48 of file LowMemoryRescaledHmmLikelihood.cpp.

Referenced by clone().


Member Function Documentation

void bpp::AbstractParametrizable::addParameters_ ( const ParameterList parameters) [inline, protected, inherited]

Create a copy of this object and send a pointer to it.

Returns:
A pointer toward the copy object.

Implements bpp::HmmLikelihood.

Definition at line 156 of file LowMemoryRescaledHmmLikelihood.h.

References LowMemoryRescaledHmmLikelihood().

Definition at line 105 of file LowMemoryRescaledHmmLikelihood.cpp.

Referenced by setBreakPoints().

Notify the class when one or several parameters have changed.

Parameters:
parametersA ParameterList object with parameters that changed.

Implements bpp::AbstractParametrizable.

Definition at line 89 of file LowMemoryRescaledHmmLikelihood.cpp.

const std::vector<size_t>& bpp::LowMemoryRescaledHmmLikelihood::getBreakPoints ( ) const [inline, virtual]

Implements bpp::HmmLikelihood.

Definition at line 173 of file LowMemoryRescaledHmmLikelihood.h.

References breakPoints_.

void bpp::LowMemoryRescaledHmmLikelihood::getHiddenStatesPosteriorProbabilities ( std::vector< std::vector< double > > &  probs,
bool  append = false 
) const throw (NotImplementedException) [inline, virtual]

Implements bpp::HmmLikelihood.

Definition at line 186 of file LowMemoryRescaledHmmLikelihood.h.

Implements bpp::HmmLikelihood.

Definition at line 159 of file LowMemoryRescaledHmmLikelihood.h.

References hiddenAlphabet_.

double bpp::LowMemoryRescaledHmmLikelihood::getLogLikelihood ( ) const [inline, virtual]

Implements bpp::HmmLikelihood.

Definition at line 182 of file LowMemoryRescaledHmmLikelihood.h.

References logLik_.

std::string bpp::AbstractParametrizable::getNamespace ( ) const [inline, virtual, inherited]
virtual std::string bpp::Parametrizable::getNamespace ( ) const [pure virtual, inherited]
Returns:
The current namespace used. This is an empty string if no namespace is currently defined.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::FunctionWrapper::getNamespace().

virtual size_t bpp::Parametrizable::getNumberOfParameters ( ) const [pure virtual, inherited]

Get the number of parameters.

See also:
getNumberOfIndependentParameters If some parameters are aliased.
Returns:
The number of parameters.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, bpp::AbstractParametrizable, and bpp::DirectionFunction.

Referenced by bpp::FunctionWrapper::getNumberOfParameters(), and bpp::BppODiscreteDistributionFormat::write().

const Parameter& bpp::AbstractParametrizable::getParameter ( const std::string &  name) const throw (ParameterNotFoundException) [inline, virtual, inherited]
virtual const Parameter& bpp::Parametrizable::getParameter ( const std::string &  name) const throw (ParameterNotFoundException) [pure virtual, inherited]

Get the parameter with specified name.

Parameters:
nameThe name of the parameter to look for.
Returns:
The parameter with given name.
Exceptions:
ParameterNotFoundExceptionif no parameter with this name is found.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::FunctionWrapper::getParameter().

const Parameter& bpp::AbstractParametrizable::getParameter_ ( size_t  index) const throw (IndexOutOfBoundsException) [inline, protected, inherited]
std::string AbstractParametrizable::getParameterNameWithoutNamespace ( const std::string &  name) const [virtual, inherited]

Resolves a parameter name according to the current namespace.

Returns:
The parameter name without the namespace prefix, if any.

Implements bpp::Parametrizable.

Definition at line 63 of file AbstractParametrizable.cpp.

References bpp::TextTools::startsWith().

virtual std::string bpp::Parametrizable::getParameterNameWithoutNamespace ( const std::string &  name) const [pure virtual, inherited]

Resolves a parameter name according to the current namespace.

Returns:
The parameter name without the namespace prefix, if any.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::FunctionWrapper::getParameterNameWithoutNamespace(), bpp::BppODiscreteDistributionFormat::read(), and bpp::BppOParametrizableFormat::write().

const ParameterList& bpp::AbstractParametrizable::getParameters ( ) const [inline, virtual, inherited]

Get all parameters available.

See also:
getIndependentParameters if some parameters are aliased.
Returns:
A list with all parameters available.

Implements bpp::Parametrizable.

Definition at line 77 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::parameters_.

Referenced by bpp::AbstractParameterAliasable::fireParameterChanged(), and bpp::MixtureOfDiscreteDistributions::MixtureOfDiscreteDistributions().

virtual const ParameterList& bpp::Parametrizable::getParameters ( ) const [pure virtual, inherited]
virtual double bpp::Parametrizable::getParameterValue ( const std::string &  name) const throw (ParameterNotFoundException) [pure virtual, inherited]

Get the value for parameter of name 'name'.

Parameters:
nameThe name of the parameter.
Returns:
the value of parameter name.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::FunctionWrapper::getParameterValue(), and bpp::BppODiscreteDistributionFormat::read().

Parameter& bpp::AbstractParametrizable::getParameterWithNamespace_ ( const std::string &  name) throw (ParameterNotFoundException) [inline, protected, inherited]
Parameters:
nameThe name of the parameter, including its namespace.
Returns:
A reference toward the corresponding parameter.
Exceptions:
ParameterNotFoundExceptionIf no parameter with that name is found in the list.

Definition at line 174 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::getParameter_().

const Parameter& bpp::AbstractParametrizable::getParameterWithNamespace_ ( const std::string &  name) const throw (ParameterNotFoundException) [inline, protected, inherited]
Parameters:
nameThe name of the parameter, including its namespace.
Returns:
A reference toward the corresponding parameter.
Exceptions:
ParameterNotFoundExceptionIf no parameter with that name is found in the list.

Definition at line 183 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::getParameter().

double bpp::LowMemoryRescaledHmmLikelihood::getValue ( ) const throw (Exception) [inline, virtual]

Get the value of the function at the current point.

Returns:
The value of the function.
Exceptions:
ExceptionIf no point is specified or if an error occured.

Implements bpp::Function.

Definition at line 180 of file LowMemoryRescaledHmmLikelihood.h.

References logLik_.

virtual bool bpp::Parametrizable::hasParameter ( const std::string &  name) const [pure virtual, inherited]

Tell if there is a parameter with specified name.

Parameters:
nameThe name of the parameter to look for.
Returns:
y/n.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::FunctionWrapper::hasParameter().

bool bpp::AbstractParametrizable::hasParameter ( const std::string &  name) const [inline, virtual, inherited]

Tell if there is a parameter with specified name.

Parameters:
nameThe name of the parameter to look for.
Returns:
y/n.

Implements bpp::Parametrizable.

Definition at line 75 of file AbstractParametrizable.h.

References bpp::ParameterList::hasParameter(), bpp::AbstractParametrizable::parameters_, and bpp::AbstractParametrizable::prefix_.

Referenced by bpp::ConstantDistribution::fireParameterChanged().

bool bpp::AbstractParametrizable::matchParametersValues ( const ParameterList parameters) throw (ConstraintException) [inline, virtual, inherited]

Update the parameters from parameters.

Only common parameters with parameters will be updated.

Parameters:
parametersA list of parameters.
Returns:
True if at least one parameter value has been changed.
Exceptions:
ConstraintExceptionIf a value in parameters does not match the constraint in the corresponding parameter in the list.

Implements bpp::Parametrizable.

Definition at line 111 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::fireParameterChanged(), bpp::ParameterList::matchParametersValues(), and bpp::AbstractParametrizable::parameters_.

Referenced by bpp::Simplex::setFrequencies(), bpp::ReparametrizationFunctionWrapper::setParameters(), and bpp::TestFunction::setParameters().

virtual bool bpp::Parametrizable::matchParametersValues ( const ParameterList parameters) throw (ConstraintException) [pure virtual, inherited]

Update the parameters from parameters.

Only common parameters with parameters will be updated.

Parameters:
parametersA list of parameters.
Returns:
True if at least one parameter value has been changed.
Exceptions:
ConstraintExceptionIf a value in parameters does not match the constraint in the corresponding parameter in the list.

Implemented in bpp::InfinityFunctionWrapper, bpp::FunctionWrapper, bpp::AbstractNumericalDerivative, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::InvariantMixedDiscreteDistribution::fireParameterChanged(), bpp::AbstractNumericalDerivative::matchParametersValues(), bpp::FunctionWrapper::matchParametersValues(), and bpp::InfinityFunctionWrapper::matchParametersValues().

Set the parameters values to be equals to those of parameters.

The list must contain exactly the same parameters (ie same names) than the parameters available.

Parameters:
parametersA list with all parameters.
Exceptions:
ParameterNotFoundExceptionIf a some parameter in the list is not in params.
ConstraintExceptionIf a value in parameters does not match the constraint in the corresponding parameter in the list.

Implements bpp::Parametrizable.

Definition at line 90 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::fireParameterChanged(), bpp::AbstractParametrizable::parameters_, and bpp::ParameterList::setAllParametersValues().

virtual void bpp::Parametrizable::setAllParametersValues ( const ParameterList parameters) throw (ParameterNotFoundException, ConstraintException) [pure virtual, inherited]

Set the parameters values to be equals to those of parameters.

The list must contain exactly the same parameters (ie same names) than the parameters available.

Parameters:
parametersA list with all parameters.
Exceptions:
ParameterNotFoundExceptionIf a some parameter in the list is not in params.
ConstraintExceptionIf a value in parameters does not match the constraint in the corresponding parameter in the list.

Implemented in bpp::InfinityFunctionWrapper, bpp::FunctionWrapper, bpp::AbstractNumericalDerivative, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::AbstractNumericalDerivative::setAllParametersValues(), bpp::FunctionWrapper::setAllParametersValues(), and bpp::InfinityFunctionWrapper::setAllParametersValues().

void bpp::LowMemoryRescaledHmmLikelihood::setBreakPoints ( const std::vector< size_t > &  breakPoints) [inline, virtual]

Implements bpp::HmmLikelihood.

Definition at line 168 of file LowMemoryRescaledHmmLikelihood.h.

References breakPoints_, and computeForward_().

void AbstractParametrizable::setNamespace ( const std::string &  prefix) [virtual, inherited]

Set the namespace for the parameter names.

Parameters:
prefixThe 'namespace', that is a prefix to add to all parameter names. If parameter names are already prefixed, the new prefix will be used instead.

Implements bpp::Parametrizable.

Reimplemented in bpp::AbstractParameterAliasable, bpp::MixtureOfDiscreteDistributions, and bpp::InvariantMixedDiscreteDistribution.

Definition at line 45 of file AbstractParametrizable.cpp.

References bpp::TextTools::startsWith().

virtual void bpp::Parametrizable::setNamespace ( const std::string &  prefix) [pure virtual, inherited]

Set the namespace for the parameter names.

Parameters:
prefixThe 'namespace', that is a prefix to add to all parameter names. If parameter names are already prefixed, the new prefix will be used instead.

Implemented in bpp::FunctionWrapper, bpp::ParametrizableAdapter, bpp::AbstractParameterAliasable, bpp::MixtureOfDiscreteDistributions, bpp::AbstractParametrizable, and bpp::InvariantMixedDiscreteDistribution.

Referenced by bpp::InvariantMixedDiscreteDistribution::InvariantMixedDiscreteDistribution(), bpp::InvariantMixedDiscreteDistribution::setNamespace(), and bpp::FunctionWrapper::setNamespace().

void bpp::LowMemoryRescaledHmmLikelihood::setParameters ( const ParameterList parameters) throw (Exception) [inline, virtual]

Set the point where the function must be computed.

Parameters:
parametersThe parameter set to pass to the function.

Implements bpp::Function.

Definition at line 175 of file LowMemoryRescaledHmmLikelihood.h.

References bpp::AbstractParametrizable::setParametersValues().

void bpp::AbstractParametrizable::setParametersValues ( const ParameterList parameters) throw (ParameterNotFoundException, ConstraintException) [inline, virtual, inherited]

Update the parameters from parameters.

parameters must be a subset of all parameters available.

Parameters:
parametersA list containing all parameters to update.
Exceptions:
ParameterNotFoundExceptionIf a some parameter in params is not in the list.
ConstraintExceptionIf a value in parameters does not match the constraint in the corresponding parameter in the list.

Implements bpp::Parametrizable.

Definition at line 104 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::fireParameterChanged(), bpp::AbstractParametrizable::parameters_, and bpp::ParameterList::setParametersValues().

Referenced by bpp::RescaledHmmLikelihood::setParameters(), bpp::LogsumHmmLikelihood::setParameters(), and setParameters().

virtual void bpp::Parametrizable::setParametersValues ( const ParameterList parameters) throw (ParameterNotFoundException, ConstraintException) [pure virtual, inherited]

Update the parameters from parameters.

parameters must be a subset of all parameters available.

Parameters:
parametersA list containing all parameters to update.
Exceptions:
ParameterNotFoundExceptionIf a some parameter in params is not in the list.
ConstraintExceptionIf a value in parameters does not match the constraint in the corresponding parameter in the list.

Implemented in bpp::InfinityFunctionWrapper, bpp::FunctionWrapper, bpp::AbstractNumericalDerivative, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::AbstractNumericalDerivative::setParametersValues(), bpp::FunctionWrapper::setParametersValues(), and bpp::InfinityFunctionWrapper::setParametersValues().

void bpp::AbstractParametrizable::setParameterValue ( const std::string &  name,
double  value 
) throw (ParameterNotFoundException, ConstraintException) [inline, virtual, inherited]

Set the value of parameter with name name to be equal to value.

Parameters:
namethe name of the parameter to set.
valueThe value of the parameter.
Exceptions:
ParameterNotFoundExceptionIf no parameter in the list has the name name.
ConstraintExceptionIf value does not match the constraint associated to parameter name.

Implements bpp::Parametrizable.

Definition at line 97 of file AbstractParametrizable.h.

References bpp::AbstractParametrizable::fireParameterChanged(), bpp::AbstractParametrizable::parameters_, bpp::AbstractParametrizable::prefix_, bpp::ParameterList::setParameterValue(), and bpp::ParameterList::subList().

virtual void bpp::Parametrizable::setParameterValue ( const std::string &  name,
double  value 
) throw (ParameterNotFoundException, ConstraintException) [pure virtual, inherited]

Set the value of parameter with name name to be equal to value.

Parameters:
namethe name of the parameter to set.
valueThe value of the parameter.
Exceptions:
ParameterNotFoundExceptionIf no parameter in the list has the name name.
ConstraintExceptionIf value does not match the constraint associated to parameter name.

Implemented in bpp::InfinityFunctionWrapper, bpp::FunctionWrapper, bpp::AbstractNumericalDerivative, bpp::ParametrizableAdapter, and bpp::AbstractParametrizable.

Referenced by bpp::AbstractNumericalDerivative::setParameterValue(), bpp::FunctionWrapper::setParameterValue(), and bpp::InfinityFunctionWrapper::setParameterValue().


Member Data Documentation

Definition at line 84 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by getBreakPoints(), operator=(), and setBreakPoints().

The alphabet describing the hidden states.

Definition at line 70 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by getHmmStateAlphabet(), LowMemoryRescaledHmmLikelihood(), and operator=().

The likelihood array.

Here we use two arrays for the i and i-1 positions

Definition at line 79 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by operator=().

Definition at line 80 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by operator=().

Definition at line 82 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by operator=().

Definition at line 86 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by operator=().

Definition at line 86 of file LowMemoryRescaledHmmLikelihood.h.

Referenced by operator=().


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