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Compute log-derivative of correlation matrix in reference prior computation #5

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5500535
Kriging: Implement Gu robust parameter estimation
jschueller Mar 1, 2019
3956067
Compute log-derivative of correlation matrix
josephmure Mar 17, 2020
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2 changes: 2 additions & 0 deletions lib/etc/openturns.conf.in
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Expand Up @@ -606,6 +606,8 @@
<GeneralLinearModelAlgorithm-StartingScaling value_float="1.0e-13" />
<GeneralLinearModelAlgorithm-DefaultOptimizationAlgorithm value_str="TNC" />
<GeneralLinearModelAlgorithm-LinearAlgebra value_str="LAPACK" />
<GeneralLinearModelAlgorithm-JointlyRobustPriorB0 value_float="1.0" />
<GeneralLinearModelAlgorithm-JointlyRobustPriorB1 value_float="0.2" />

<!-- OT::KrigingAlgorithm parameters -->
<KrigingAlgorithm-MaximalScaling value_float="1.0e5" />
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2 changes: 2 additions & 0 deletions lib/src/Base/Common/ResourceMap.cxx
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Expand Up @@ -1218,6 +1218,8 @@ void ResourceMap::loadDefaultConfiguration()
addAsScalar("GeneralLinearModelAlgorithm-StartingScaling", 1.0e-13);
addAsString("GeneralLinearModelAlgorithm-DefaultOptimizationAlgorithm", "TNC");
addAsString("GeneralLinearModelAlgorithm-LinearAlgebra", "LAPACK");
addAsScalar( "GeneralLinearModelAlgorithm-JointlyRobustPriorB0", 1.0);
addAsScalar( "GeneralLinearModelAlgorithm-JointlyRobustPriorB1", 0.2);

// KrigingAlgorithm parameters //
addAsScalar("KrigingAlgorithm-MaximalScaling", 1.0e5);
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37 changes: 35 additions & 2 deletions lib/src/Base/Stat/AbsoluteExponential.cxx
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Expand Up @@ -64,21 +64,54 @@ AbsoluteExponential * AbsoluteExponential::clone() const
Scalar AbsoluteExponential::computeStandardRepresentative(const Point & tau) const
{
if (tau.getDimension() != inputDimension_) throw InvalidArgumentException(HERE) << "Error: expected a shift of dimension=" << inputDimension_ << ", got dimension=" << tau.getDimension();

Point theta(scale_);
switch (scaleParametrization_)
{
case STANDARD:
// nothing to do
break;
case INVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = 1.0 / scale_[i];
break;
case LOGINVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = std::exp(- scale_[i]);
break;
}

Point tauOverTheta(inputDimension_);
for (UnsignedInteger i = 0; i < inputDimension_; ++i) tauOverTheta[i] = tau[i] / scale_[i];
for (UnsignedInteger i = 0; i < inputDimension_; ++i) tauOverTheta[i] = tau[i] / theta[i];
const Scalar tauOverThetaNorm = tauOverTheta.norm1();
return tauOverThetaNorm <= SpecFunc::ScalarEpsilon ? 1.0 + nuggetFactor_ : exp(-tauOverThetaNorm);
}

Scalar AbsoluteExponential::computeStandardRepresentative(const Collection<Scalar>::const_iterator & s_begin,
const Collection<Scalar>::const_iterator & t_begin) const
{
Point theta(scale_);
switch (scaleParametrization_)
{
case STANDARD:
// nothing to do
break;
case INVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = 1.0 / scale_[i];
break;
case LOGINVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = std::exp(- scale_[i]);
break;
}

Scalar tauOverThetaNorm = 0;
Collection<Scalar>::const_iterator s_it = s_begin;
Collection<Scalar>::const_iterator t_it = t_begin;
for (UnsignedInteger i = 0; i < inputDimension_; ++i, ++s_it, ++t_it)
{
tauOverThetaNorm += std::abs(*s_it - *t_it) / scale_[i];
tauOverThetaNorm += std::abs(*s_it - *t_it) / theta[i];
}
return tauOverThetaNorm <= SpecFunc::ScalarEpsilon ? 1.0 + nuggetFactor_ : exp(-tauOverThetaNorm);
}
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18 changes: 18 additions & 0 deletions lib/src/Base/Stat/CovarianceModel.cxx
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Expand Up @@ -221,6 +221,18 @@ void CovarianceModel::setScale(const Point & scale)
getImplementation()->setScale(scale);
}

/* Scale accessor */
CovarianceModel::ScaleParametrization CovarianceModel::getScaleParametrization() const
{
return getImplementation()->getScaleParametrization();
}

void CovarianceModel::setScaleParametrization(const ScaleParametrization scaleParametrization)
{
copyOnWrite();
getImplementation()->setScaleParametrization(scaleParametrization);
}

/* Spatial correlation accessor */
CorrelationMatrix CovarianceModel::getOutputCorrelation() const
{
Expand Down Expand Up @@ -304,6 +316,12 @@ Bool CovarianceModel::isDiagonal() const
return getImplementation()->isDiagonal();
}

/* Is it a composite covariance model ? */
Bool CovarianceModel::isComposite() const
{
return getImplementation()->isComposite();
}

/* Drawing method */
Graph CovarianceModel::draw(const UnsignedInteger rowIndex,
const UnsignedInteger columnIndex,
Expand Down
133 changes: 113 additions & 20 deletions lib/src/Base/Stat/CovarianceModelImplementation.cxx
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Expand Up @@ -45,6 +45,7 @@ static const Factory<CovarianceModelImplementation> Factory_CovarianceModelImple
CovarianceModelImplementation::CovarianceModelImplementation(const UnsignedInteger inputDimension)
: PersistentObject()
, scale_(inputDimension, 1.0)
, scaleParametrization_(STANDARD)
, inputDimension_(inputDimension)
, amplitude_(1, 1.0)
, outputDimension_(1)
Expand All @@ -65,6 +66,7 @@ CovarianceModelImplementation::CovarianceModelImplementation(const Point & scale
const Point & amplitude)
: PersistentObject()
, scale_(0)
, scaleParametrization_(STANDARD)
, inputDimension_(scale.getDimension())
, amplitude_(0)
, outputDimension_(amplitude.getDimension())
Expand All @@ -88,6 +90,7 @@ CovarianceModelImplementation::CovarianceModelImplementation(const Point & scale
const CorrelationMatrix & spatialCorrelation)
: PersistentObject()
, scale_(0)
, scaleParametrization_(STANDARD)
, inputDimension_(scale.getDimension())
, amplitude_(0)
, outputDimension_(amplitude.getDimension())
Expand All @@ -110,6 +113,7 @@ CovarianceModelImplementation::CovarianceModelImplementation(const Point & scale
const CovarianceMatrix & spatialCovariance)
: PersistentObject()
, scale_(0)
, scaleParametrization_(STANDARD)
, inputDimension_(scale.getDimension())
, amplitude_(0)
, outputDimension_(spatialCovariance.getDimension())
Expand Down Expand Up @@ -597,12 +601,84 @@ Point CovarianceModelImplementation::getScale() const
void CovarianceModelImplementation::setScale(const Point & scale)
{
if (scale.getDimension() != inputDimension_) throw InvalidArgumentException(HERE) << "In CovarianceModelImplementation::setScale: the given scale has a dimension=" << scale.getDimension() << " different from the input dimension=" << inputDimension_;
for (UnsignedInteger index = 0; index < inputDimension_; ++index)
if (!(scale[index] > 0.0))
throw InvalidArgumentException(HERE) << "In CovarianceModelImplementation::setScale: the component " << index << " of scale is non positive" ;
if ((scaleParametrization_ == STANDARD) || (scaleParametrization_ == INVERSE))
for (UnsignedInteger index = 0; index < inputDimension_; ++index)
if (!(scale[index] > 0.0))
throw InvalidArgumentException(HERE) << "In CovarianceModelImplementation::setScale: the component " << index << " of scale is non positive" ;
scale_ = scale;
}


// Scale parametrization accessor
CovarianceModelImplementation::ScaleParametrization CovarianceModelImplementation::getScaleParametrization() const
{
return scaleParametrization_;
}

void CovarianceModelImplementation::setScaleParametrization(const ScaleParametrization scaleParametrization)
{
Point scale(getScale());
switch (scaleParametrization_)
{
case STANDARD:
switch (scaleParametrization)
{
case STANDARD:
// nothing to do
break;
case INVERSE:
// STANDARD -> INVERSE
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
scale[i] = 1.0 / scale[i];
break;
case LOGINVERSE:
// STANDARD -> LOGINVERSE
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
scale[i] = -std::log(scale[i]);
break;
}
break;
case INVERSE:
switch (scaleParametrization)
{
case STANDARD:
// INVERSE -> STANDARD
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
scale[i] = 1.0 / scale[i];
break;
case INVERSE:
// nothing to do
break;
case LOGINVERSE:
// INVERSE -> LOGINVERSE
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
scale[i] = -std::log(1.0 / scale[i]);
break;
}
break;
case LOGINVERSE:
switch (scaleParametrization)
{
case STANDARD:
// LOGINVERSE -> STANDARD
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
scale[i] = std::exp(- scale[i]);
break;
case INVERSE:
// LOGINVERSE -> INVERSE
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
scale[i] = 1.0 / std::exp(- scale[i]);
break;
case LOGINVERSE:
// nothing to do
break;
}
break;
}
scaleParametrization_ = scaleParametrization;
setScale(scale);
}

/* Output correlation accessor */
CorrelationMatrix CovarianceModelImplementation::getOutputCorrelation() const
{
Expand Down Expand Up @@ -649,29 +725,23 @@ void CovarianceModelImplementation::setNuggetFactor(const Scalar nuggetFactor)
void CovarianceModelImplementation::setFullParameter(const Point & parameter)
{
// Here we manage only the generic parameters
// First the scale parameter
UnsignedInteger index = 0;
// Check the size
const UnsignedInteger totalSize = inputDimension_ + outputDimension_ * (outputDimension_ + 1) / 2;
if (parameter.getSize() < totalSize)
throw InvalidArgumentException(HERE) << "In CovarianceModelImplementation::setFullParameter, points have incompatible size. Point size = " << parameter.getSize()
<< " whereas expected size = " << totalSize ;

for (UnsignedInteger i = 0; i < inputDimension_; ++ i)
{
if (!(parameter[index] > 0.0))
throw InvalidArgumentException(HERE) << "In CovarianceModelImplementation::setParameter, the component " << index << " of scale is non positive" ;
scale_[i] = parameter[index];
++ index;
}
// First the scale parameter
Point scale(inputDimension_);
std::copy(parameter.begin(), parameter.begin() + inputDimension_, scale.begin());
setScale(scale);

// Second the amplitude parameter
for (UnsignedInteger i = 0; i < outputDimension_; ++ i)
{
if (!(parameter[index] > 0.0))
throw InvalidArgumentException(HERE) << "In CovarianceModelImplementation::setParameter, the component " << index << " of amplitude is non positive" ;
amplitude_[i] = parameter[index];
++ index;
}
Point amplitude(outputDimension_);
std::copy(parameter.begin() + inputDimension_, parameter.begin() + inputDimension_ + outputDimension_, amplitude.begin());
setAmplitude(amplitude);

UnsignedInteger index = inputDimension_ + outputDimension_;
CorrelationMatrix outputCorrelation(outputDimension_);
// Third the output correlation parameter, only the lower triangle
for (UnsignedInteger i = 0; i < outputDimension_; ++ i)
Expand Down Expand Up @@ -710,8 +780,21 @@ Description CovarianceModelImplementation::getFullParameterDescription() const
// First the scale parameter
Description description(0);
// First the scale parameter
String scalePrefix;
switch (scaleParametrization_)
{
case STANDARD:
// empty
break;
case INVERSE:
scalePrefix = "inverse_";
break;
case LOGINVERSE:
scalePrefix = "loginverse_";
break;
}
for (UnsignedInteger j = 0; j < inputDimension_; ++j)
description.add(OSS() << "scale_" << j);
description.add(OSS() << scalePrefix << "scale_" << j);
// Second the amplitude parameter
for (UnsignedInteger j = 0; j < outputDimension_; ++j)
description.add(OSS() << "amplitude_" << j);
Expand Down Expand Up @@ -791,6 +874,12 @@ Bool CovarianceModelImplementation::isDiagonal() const
return isDiagonal_;
}

/* Is it a composite model ? */
Bool CovarianceModelImplementation::isComposite() const
{
return false;
}

/* Marginal accessor */
CovarianceModel CovarianceModelImplementation::getMarginal(const UnsignedInteger index) const
{
Expand Down Expand Up @@ -937,6 +1026,7 @@ void CovarianceModelImplementation::save(Advocate & adv) const
{
PersistentObject::save(adv);
adv.saveAttribute("scale_", scale_);
adv.saveAttribute("scaleParametrization_", static_cast<UnsignedInteger>(scaleParametrization_));
adv.saveAttribute("inputDimension_", inputDimension_);
adv.saveAttribute("amplitude_", amplitude_);
adv.saveAttribute("outputDimension_", outputDimension_);
Expand All @@ -952,6 +1042,9 @@ void CovarianceModelImplementation::load(Advocate & adv)
{
PersistentObject::load(adv);
adv.loadAttribute("scale_", scale_);
UnsignedInteger scaleParametrization = 0;
adv.loadAttribute( "scaleParametrization_", scaleParametrization );
scaleParametrization_ = static_cast<ScaleParametrization>(scaleParametrization);
adv.loadAttribute("inputDimension_", inputDimension_);
adv.loadAttribute("amplitude_", amplitude_);
adv.loadAttribute("outputDimension_", outputDimension_);
Expand Down
36 changes: 34 additions & 2 deletions lib/src/Base/Stat/ExponentialModel.cxx
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Expand Up @@ -82,7 +82,23 @@ Scalar ExponentialModel::computeStandardRepresentative(const Point & tau) const
throw InvalidArgumentException(HERE) << "In ExponentialModel::computeStandardRepresentative: expected a shift of dimension=" << getInputDimension() << ", got dimension=" << tau.getDimension();
// Absolute value of tau / scale
Point tauOverTheta(getInputDimension());
for (UnsignedInteger i = 0; i < getInputDimension(); ++i) tauOverTheta[i] = tau[i] / scale_[i];
Point theta(scale_);
switch (scaleParametrization_)
{
case STANDARD:
// nothing to do
break;
case INVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = 1.0 / scale_[i];
break;
case LOGINVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = std::exp(- scale_[i]);
break;
}

for (UnsignedInteger i = 0; i < getInputDimension(); ++i) tauOverTheta[i] = tau[i] / theta[i];
const Scalar tauOverThetaNorm = tauOverTheta.norm();
// Return value
return (tauOverThetaNorm == 0.0 ? 1.0 + nuggetFactor_ : exp(- tauOverThetaNorm ));
Expand All @@ -91,12 +107,28 @@ Scalar ExponentialModel::computeStandardRepresentative(const Point & tau) const
Scalar ExponentialModel::computeStandardRepresentative(const Collection<Scalar>::const_iterator & s_begin,
const Collection<Scalar>::const_iterator & t_begin) const
{
Point theta(scale_);
switch (scaleParametrization_)
{
case STANDARD:
// nothing to do
break;
case INVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = 1.0 / scale_[i];
break;
case LOGINVERSE:
for(UnsignedInteger i = 0; i < inputDimension_; ++i)
theta[i] = std::exp(- scale_[i]);
break;
}

Scalar tauOverThetaNorm = 0;
Collection<Scalar>::const_iterator s_it = s_begin;
Collection<Scalar>::const_iterator t_it = t_begin;
for (UnsignedInteger i = 0; i < inputDimension_; ++i, ++s_it, ++t_it)
{
const Scalar dx = (*s_it - *t_it) / scale_[i];
const Scalar dx = (*s_it - *t_it) / theta[i];
tauOverThetaNorm += dx * dx;
}
tauOverThetaNorm = sqrt(tauOverThetaNorm);
Expand Down
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