lsst::afw::math::GaussianProcess< T > Class Template Reference

Stores values of a function sampled on an image and allows you to interpolate the function to unsampled points. More...

#include <GaussianProcess.h>

Inheritance diagram for lsst::afw::math::GaussianProcess< T >:

Public Member Functions
	GaussianProcess (ndarray::Array< T, 2, 2 > const &dataIn, ndarray::Array< T, 1, 1 > const &ff, boost::shared_ptr< Covariogram< T > > const &covarIn)
	This is the constructor you call if you do not wish to normalize the positions of your data points and you have only one function. More...
	GaussianProcess (ndarray::Array< T, 2, 2 > const &dataIn, ndarray::Array< T, 1, 1 > const &mn, ndarray::Array< T, 1, 1 > const &mx, ndarray::Array< T, 1, 1 > const &ff, boost::shared_ptr< Covariogram< T > > const &covarIn)
	This is the constructor you call if you want the positions of your data points normalized by the span of each dimension and you have only one function. More...
	GaussianProcess (ndarray::Array< T, 2, 2 > const &dataIn, ndarray::Array< T, 2, 2 > const &ff, boost::shared_ptr< Covariogram< T > > const &covarIn)
	this is the constructor to use in the case of a vector of input functions and an unbounded/unnormalized parameter space More...
	GaussianProcess (ndarray::Array< T, 2, 2 > const &dataIn, ndarray::Array< T, 1, 1 > const &mn, ndarray::Array< T, 1, 1 > const &mx, ndarray::Array< T, 2, 2 > const &ff, boost::shared_ptr< Covariogram< T > > const &covarIn)
	this is the constructor to use in the case of a vector of input functions using minima and maxima in parameter space More...
T	interpolate (ndarray::Array< T, 1, 1 > variance, ndarray::Array< T, 1, 1 > const &vin, int numberOfNeighbors) const
	Interpolate the function value at one point using a specified number of nearest neighbors. More...
void	interpolate (ndarray::Array< T, 1, 1 > mu, ndarray::Array< T, 1, 1 > variance, ndarray::Array< T, 1, 1 > const &vin, int numberOfNeighbors) const
	This is the version of GaussianProcess::interpolate for a vector of functions. More...
T	selfInterpolate (ndarray::Array< T, 1, 1 > variance, int dex, int numberOfNeighbors) const
	This method will interpolate the function on a data point for purposes of optimizing hyper parameters. More...
void	selfInterpolate (ndarray::Array< T, 1, 1 > mu, ndarray::Array< T, 1, 1 > variance, int dex, int numberOfNeighbors) const
	The version of selfInterpolate called for a vector of functions. More...
void	batchInterpolate (ndarray::Array< T, 1, 1 > mu, ndarray::Array< T, 1, 1 > variance, ndarray::Array< T, 2, 2 > const &queries) const
	Interpolate a list of query points using all of the input data (rather than nearest neighbors) More...
void	batchInterpolate (ndarray::Array< T, 1, 1 > mu, ndarray::Array< T, 2, 2 > const &queries) const
	Interpolate a list of points using all of the data. Do not return variances for the interpolation. More...
void	batchInterpolate (ndarray::Array< T, 2, 2 > mu, ndarray::Array< T, 2, 2 > variance, ndarray::Array< T, 2, 2 > const &queries) const
	This is the version of batchInterpolate (with variances) that is called for a vector of functions. More...
void	batchInterpolate (ndarray::Array< T, 2, 2 > mu, ndarray::Array< T, 2, 2 > const &queries) const
	This is the version of batchInterpolate (without variances) that is called for a vector of functions. More...
void	addPoint (ndarray::Array< T, 1, 1 > const &vin, T f)
	Add a point to the pool of data used by GaussianProcess for interpolation. More...
void	addPoint (ndarray::Array< T, 1, 1 > const &vin, ndarray::Array< T, 1, 1 > const &f)
	This is the version of addPoint that is called for a vector of functions. More...
void	removePoint (int dex)
	This will remove a point from the data set. More...
void	setKrigingParameter (T kk)
	Assign a value to the Kriging paramter. More...
void	setCovariogram (boost::shared_ptr< Covariogram< T > > const &covar)
	Assign a different covariogram to this GaussianProcess. More...
void	setLambda (T lambda)
	set the value of the hyperparameter _lambda More...
GaussianProcessTimer &	getTimes () const
	Give the user acces to _timer, an object keeping track of the time spent on various processes within interpolate. More...

Private Attributes
int	_pts
int	_useMaxMin
int	_dimensions
int	_room
int	_roomStep
int	_nFunctions
T	_krigingParameter
T	_lambda
ndarray::Array< T, 1, 1 >	_max
ndarray::Array< T, 1, 1 >	_min
ndarray::Array< T, 2, 2 >	_function
KdTree< T >	_kdTree
boost::shared_ptr< Covariogram < T > >	_covariogram
GaussianProcessTimer	_timer

Detailed Description

template<typename T>
class lsst::afw::math::GaussianProcess< T >

Stores values of a function sampled on an image and allows you to interpolate the function to unsampled points.

The data will be stored in a KD Tree for easy nearest neighbor searching when interpolating.

The array _function[] will contain the values of the function being interpolated. You can provide a two dimensional array _function[][] if you wish to interpolate a vector of functions. In this case _function[i][j] is the jth function associated with the ith data point. Note: presently, the covariance matrices do not relate elements of _function[i][] to each other, so the variances returned will be identical for all functions evaluated at the same point in parameter space.

_data[i][j] will be the jth component of the ith data point.

_max and _min contain the maximum and minimum values of each dimension in parameter space (if applicable) so that data points can be normalized by _max-_min to keep distances between points reasonable. This is an option specified by calling the relevant constructor.

Definition at line 499 of file GaussianProcess.h.

Constructor & Destructor Documentation

template<typename T >

lsst::afw::math::GaussianProcess< T >::GaussianProcess	(	ndarray::Array< T, 2, 2 > const &	dataIn,
		ndarray::Array< T, 1, 1 > const &	ff,
		boost::shared_ptr< Covariogram< T > > const &	covarIn
	)

This is the constructor you call if you do not wish to normalize the positions of your data points and you have only one function.

Parameters

[in]	dataIn	an ndarray containing the data points; the ith row of datain is the ith data point
[in]	ff	a one-dimensional ndarray containing the values of the scalar function associated with each data point. This is the function you are interpolating
[in]	covarIn	is the input covariogram

Definition at line 745 of file GaussianProcess.cc.

{
    int i;

    _covariogram = covarIn;

    _pts = dataIn.template getSize < 0 > ();
    _dimensions = dataIn.template getSize < 1 > ();

    _room = _pts;
    _roomStep = 5000;

    _nFunctions = 1;
    _function = allocate(ndarray::makeVector(_pts,1));

    for(i = 0; i < _pts; i++ ) _function[i][0] = ff[i];

    _krigingParameter = T(1.0);
    _lambda = T(1.0e-5);

    _useMaxMin = 0;


    _kdTree.Initialize(dataIn);

    _pts = _kdTree.getPoints();

}

template<typename T >

lsst::afw::math::GaussianProcess< T >::GaussianProcess	(	ndarray::Array< T, 2, 2 > const &	dataIn,
		ndarray::Array< T, 1, 1 > const &	mn,
		ndarray::Array< T, 1, 1 > const &	mx,
		ndarray::Array< T, 1, 1 > const &	ff,
		boost::shared_ptr< Covariogram< T > > const &	covarIn
	)

This is the constructor you call if you want the positions of your data points normalized by the span of each dimension and you have only one function.

Parameters

[in]	dataIn	an ndarray containing the data points; the ith row of datain is the ith data point
[in]	mn	a one-dimensional ndarray containing the minimum values of each dimension (for normalizing the positions of data points)
[in]	mx	a one-dimensional ndarray containing the maximum values of each dimension (for normalizing the positions of data points)
[in]	ff	a one-dimensional ndarray containing the values of the scalar function associated with each data point. This is the function you are interpolating
[in]	covarIn	is the input covariogram

Note: the member variable _useMaxMin will allow the code to remember which constructor you invoked

Definition at line 778 of file GaussianProcess.cc.

{

    int i,j;
    ndarray::Array < T,2,2 >  normalizedData;

    _covariogram = covarIn;

    _pts = dataIn.template getSize < 0 > ();
    _dimensions = dataIn.template getSize < 1 > ();
    _room = _pts;
    _roomStep = 5000;

    _krigingParameter = T(1.0);

    _lambda = T(1.0e-5);
    _krigingParameter = T(1.0);

    _max = allocate(ndarray::makeVector(_dimensions));
    _min = allocate(ndarray::makeVector(_dimensions)); 
    _max.deep() = mx;
    _min.deep() = mn;
    _useMaxMin = 1;
    normalizedData = allocate(ndarray::makeVector(_pts, _dimensions));
    for(i = 0; i < _pts; i++ ) {
        for(j = 0; j < _dimensions; j++ ) {
            normalizedData[i][j] = (dataIn[i][j] - _min[j])/(_max[j] - _min[j]);
            //note the normalization by _max - _min in each dimension
        }
    }

    _kdTree.Initialize(normalizedData);

    _pts = _kdTree.getPoints();
    _nFunctions = 1;
    _function = allocate(ndarray::makeVector(_pts, 1));
    for(i = 0; i < _pts; i++ )_function[i][0] = ff[i];
}

template<typename T >

lsst::afw::math::GaussianProcess< T >::GaussianProcess	(	ndarray::Array< T, 2, 2 > const &	dataIn,
		ndarray::Array< T, 2, 2 > const &	ff,
		boost::shared_ptr< Covariogram< T > > const &	covarIn
	)

this is the constructor to use in the case of a vector of input functions and an unbounded/unnormalized parameter space

Parameters

[in]	dataIn	contains the data points, as in other constructors
[in]	ff	contains the functions. Each row of ff corresponds to a datapoint. Each column corresponds to a function (ff[i][j] is the jth function associated with the ith data point)
[in]	covarIn	is the input covariogram

Definition at line 823 of file GaussianProcess.cc.

{

    _covariogram = covarIn;

    _pts = dataIn.template getSize < 0 > ();
    _dimensions = dataIn.template getSize < 1 > ();

    _room = _pts;
    _roomStep = 5000;

    _nFunctions = ff.template getSize < 1 > ();
    _function = allocate(ndarray::makeVector(_pts, _nFunctions));
    _function.deep() = ff;

    _krigingParameter = T(1.0);

    _lambda = T(1.0e-5);

    _useMaxMin = 0;


    _kdTree.Initialize(dataIn);

    _pts = _kdTree.getPoints();
}

template<typename T >

lsst::afw::math::GaussianProcess< T >::GaussianProcess	(	ndarray::Array< T, 2, 2 > const &	dataIn,
		ndarray::Array< T, 1, 1 > const &	mn,
		ndarray::Array< T, 1, 1 > const &	mx,
		ndarray::Array< T, 2, 2 > const &	ff,
		boost::shared_ptr< Covariogram< T > > const &	covarIn
	)

this is the constructor to use in the case of a vector of input functions using minima and maxima in parameter space

Parameters

[in]	dataIn	contains the data points, as in other constructors
[in]	mn	contains the minimum allowed values of the parameters in parameter space
[in]	mx	contains the maximum allowed values of the parameters in parameter space
[in]	ff	contains the functions. Each row of ff corresponds to a datapoint. Each column corresponds to a function (ff[i][j] is the jth function associated with the ith data point)
[in]	covarIn	is the input covariogram

Definition at line 853 of file GaussianProcess.cc.

{

    int i,j;
    ndarray::Array < T,2,2 >  normalizedData;

    _covariogram = covarIn;

    _pts = dataIn.template getSize < 0 > ();
    _dimensions = dataIn.template getSize < 1 > ();

    _room = _pts;
    _roomStep = 5000;

    _krigingParameter = T(1.0);

    _lambda = T(1.0e-5);
    _krigingParameter = T(1.0);

    _max = allocate(ndarray::makeVector(_dimensions));
    _min = allocate(ndarray::makeVector(_dimensions));
    _max.deep() = mx;
    _min.deep() = mn;
    _useMaxMin = 1;
    normalizedData = allocate(ndarray::makeVector(_pts,_dimensions));
    for(i = 0; i < _pts; i++ ) {
        for(j = 0; j < _dimensions; j++ ) {
            normalizedData[i][j] = (dataIn[i][j] - _min[j])/(_max[j] - _min[j]);
            //note the normalization by _max - _min in each dimension
        }
    }

    _kdTree.Initialize(normalizedData);
    _pts = _kdTree.getPoints();
    _nFunctions = ff.template getSize < 1 > ();
    _function = allocate(ndarray::makeVector(_pts, _nFunctions));
    _function.deep() = ff;
}

Member Function Documentation

template<typename T >

void lsst::afw::math::GaussianProcess< T >::addPoint	(	ndarray::Array< T, 1, 1 > const &	vin,
		T	f
	)

Add a point to the pool of data used by GaussianProcess for interpolation.

Parameters

[in]	vin	a one-dimensional ndarray storing the point in parameter space that you are adding
[in]	f	the value of the function at that point

Exceptions

pex_exceptions	RuntimeError if you call this when you should have called the version taking a vector of functions (below)
pex_exceptions	RuntimeError if the tree does not end up properly constructed (the exception is actually thrown by KdTree<T>::addPoint() )

Note: excessive use of addPoint and removePoint can result in an unbalanced KdTree, which will slow down nearest neighbor searches

Definition at line 1697 of file GaussianProcess.cc.

{

    int i,j;

    if(_nFunctions!= 1){

        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
        "You are calling the wrong addPoint; you need a vector of functions\n");

    }

    ndarray::Array < T,1,1 >  v;
    v = allocate(ndarray::makeVector(_dimensions));

    for(i = 0; i < _dimensions; i++ ){
        v[i] = vin[i];
        if(_useMaxMin == 1){
            v[i] = (v[i] - _min[i])/(_max[i] - _min[i]);
        }
    }

    if(_pts == _room){
        ndarray::Array < T,2,2 >  buff;
        buff = allocate(ndarray::makeVector(_pts, _nFunctions));
        buff.deep() = _function;

        _room += _roomStep;
        _function = allocate(ndarray::makeVector(_room, _nFunctions));
        for(i = 0; i < _pts; i++ ) {

            for(j = 0; j < _nFunctions; j++ ) {
                _function[i][j] = buff[i][j];
            }

        }
    }

    _function[_pts][0] = f;

    _kdTree.addPoint(v);
    _pts = _kdTree.getPoints();

}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::addPoint	(	ndarray::Array< T, 1, 1 > const &	vin,
		ndarray::Array< T, 1, 1 > const &	f
	)

This is the version of addPoint that is called for a vector of functions.

Exceptions

pex_exceptions

RuntimeError if the tree does not end up properly constructed (the exception is actually thrown by KdTree<T>::addPoint() )

Note: excessive use of addPoint and removePoint can result in an unbalanced KdTree, which will slow down nearest neighbor searches

Definition at line 1743 of file GaussianProcess.cc.

{

    int i,j;

    ndarray::Array < T,1,1 >  v;
    v = allocate(ndarray::makeVector(_dimensions));

    for(i = 0; i < _dimensions; i++ ) {
        v[i] = vin[i];
        if(_useMaxMin == 1) {
            v[i] = (v[i] - _min[i])/(_max[i] - _min[i]);
        }
    }

    if(_pts == _room) {
        ndarray::Array < T,2,2 >  buff;
        buff = allocate(ndarray::makeVector(_pts, _nFunctions));
        buff.deep() = _function;

        _room += _roomStep;
        _function = allocate(ndarray::makeVector(_room, _nFunctions));
        for(i = 0; i < _pts; i++ ) {
            for(j = 0; j < _nFunctions; j++ ) {
                 _function[i][j] = buff[i][j];
            }
        }

    }
    for(i = 0; i < _nFunctions; i++ )_function[_pts][i] = f[i];

    _kdTree.addPoint(v);
    _pts = _kdTree.getPoints();


}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::batchInterpolate	(	ndarray::Array< T, 1, 1 >	mu,
		ndarray::Array< T, 1, 1 >	variance,
		ndarray::Array< T, 2, 2 > const &	queries
	)		const

Interpolate a list of query points using all of the input data (rather than nearest neighbors)

Parameters

[out]	mu	a 1-dimensional ndarray where the interpolated function values will be stored
[out]	variance	a 1-dimensional ndarray where the corresponding variances in the function value will be stored
[in]	queries	a 2-dimensional ndarray containing the points to be interpolated. queries[i][j] is the jth component of the ith point

This method will attempt to construct a _pts X _pts covariance matrix C and solve the problem Cx=b. Be wary of using it in the case where _pts is very large.

This version of the method will also return variances for all of the query points. That is a very time consuming calculation relative to just returning estimates for the function. Consider calling the version of this method that does not calculate variances (below). The difference in time spent is an order of magnitude for 189 data points and 1,000,000 interpolations.

Definition at line 1365 of file GaussianProcess.cc.

{

    int i,j,ii,nQueries;

    T fbar;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  batchCovariance,batchbb,batchxx;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  queryCovariance;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    ndarray::Array < T,1,1 >  v1;

    _timer.start();

    nQueries = queries.template getSize < 0 > ();


    v1 = allocate(ndarray::makeVector(_dimensions));
    batchbb.resize(_pts, 1);
    batchxx.resize(_pts, 1);
    batchCovariance.resize(_pts, _pts);
    queryCovariance.resize(_pts, 1);

  
    for(i = 0; i < _pts; i++ ) {

        batchCovariance(i, i) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(i)) + _lambda;
        for(j = i + 1; j < _pts; j++ ) {
            batchCovariance(i, j) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(j));
            batchCovariance(j, i) = batchCovariance(i, j);
        }
    }
    _timer.addToIteration();

    ldlt.compute(batchCovariance);

    fbar = 0.0;
    for(i = 0; i < _pts; i++ ) {
        fbar += _function[i][0];
    }
    fbar = fbar/T(_pts);

    for(i = 0; i < _pts; i++ ){
        batchbb(i, 0) = _function[i][0] - fbar;
    }
    batchxx = ldlt.solve(batchbb);
    _timer.addToEigen();


    for(ii = 0; ii < nQueries; ii++ ) {
        for(i = 0; i < _dimensions; i++ )v1[i] = queries[ii][i];
        if(_useMaxMin == 1) {
            for(i = 0; i < _dimensions; i++ )v1[i] = (v1[i] - _min[i])/(_max[i] - _min[i]);
        }
        mu(ii) = fbar;
        for(i = 0; i < _pts; i++ ){
            mu(ii) += batchxx(i)*(*_covariogram)(v1, _kdTree.getData(i));
        }
    }
    _timer.addToIteration();

    for(ii = 0; ii < nQueries; ii++ ) {
        for(i = 0; i < _dimensions; i++ )v1[i] = queries[ii][i];
        if(_useMaxMin == 1) {
            for(i = 0; i < _dimensions; i++ )v1[i] = (v1[i] - _min[i])/(_max[i] - _min[i]);
        }

        for(i = 0; i < _pts; i++ ) {
            batchbb(i, 0) = (*_covariogram)(v1, _kdTree.getData(i));
            queryCovariance(i, 0) = batchbb(i, 0);
        }
        batchxx = ldlt.solve(batchbb);

        variance[ii] = (*_covariogram)(v1, v1) + _lambda;

        for(i = 0; i < _pts; i++ ){
            variance[ii] -= queryCovariance(i, 0)*batchxx(i);
        }

        variance[ii] = variance[ii]*_krigingParameter;

    }

    _timer.addToVariance();
    _timer.addToTotal(nQueries);
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::batchInterpolate	(	ndarray::Array< T, 1, 1 >	mu,
		ndarray::Array< T, 2, 2 > const &	queries
	)		const

Interpolate a list of points using all of the data. Do not return variances for the interpolation.

Parameters

[out]	mu	a 1-dimensional ndarray where the interpolated function values will be stored
[in]	queries	a 2-dimensional ndarray containing the points to be interpolated. queries[i][j] is the jth component of the ith point

This method will attempt to construct a _pts X _pts covariance matrix C and solve the problem Cx=b. Be wary of using it in the case where _pts is very large.

This version of the method does not return variances. It is an order of magnitude faster than the version of the method that does return variances (timing done on a case with 189 data points and 1 million query points).

Definition at line 1552 of file GaussianProcess.cc.

{

    int i,j,ii,nQueries;

    T fbar;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  batchCovariance,batchbb,batchxx;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  queryCovariance;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    ndarray::Array < T,1,1 >  v1;

    _timer.start();

    nQueries = queries.template getSize < 0 > ();

    v1 = allocate(ndarray::makeVector(_dimensions));

    batchbb.resize(_pts, 1);
    batchxx.resize(_pts, 1);
    batchCovariance.resize(_pts, _pts);
    queryCovariance.resize(_pts, 1);


    for(i = 0; i < _pts; i++ ) {
        batchCovariance(i, i) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(i)) + _lambda;
        for(j = i + 1; j < _pts; j++ ) {
            batchCovariance(i, j) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(j));
            batchCovariance(j, i) = batchCovariance(i, j);
        }
    }
    _timer.addToIteration();

    ldlt.compute(batchCovariance);

    fbar = 0.0;
    for(i = 0; i < _pts; i++ ) {
        fbar += _function[i][0];
    }
    fbar = fbar/T(_pts);

    for(i = 0; i < _pts; i++ ) {
        batchbb(i, 0) = _function[i][0] - fbar;
    }
    batchxx = ldlt.solve(batchbb);
    _timer.addToEigen();

    for(ii = 0; ii < nQueries; ii++ ) {

        for(i = 0; i < _dimensions; i++ ) v1[i] = queries[ii][i];
        if(_useMaxMin == 1) {
            for(i = 0; i < _dimensions; i++ )v1[i] = (v1[i] - _min[i])/(_max[i] - _min[i]);
        }

        mu(ii) = fbar;
        for(i = 0; i < _pts; i++ ) {
            mu(ii) += batchxx(i)*(*_covariogram)(v1, _kdTree.getData(i));
        }
    }
    _timer.addToIteration();
    _timer.addToTotal(nQueries);

}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::batchInterpolate	(	ndarray::Array< T, 2, 2 >	mu,
		ndarray::Array< T, 2, 2 >	variance,
		ndarray::Array< T, 2, 2 > const &	queries
	)		const

This is the version of batchInterpolate (with variances) that is called for a vector of functions.

Definition at line 1455 of file GaussianProcess.cc.

{

    int i,j,ii,nQueries,ifn;

    T fbar;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  batchCovariance,batchbb,batchxx;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  queryCovariance;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    ndarray::Array < T,1,1 >  v1; 

    _timer.start();

    nQueries = queries.template getSize < 0 > ();
  


    v1 = allocate(ndarray::makeVector(_dimensions));
    batchbb.resize(_pts, 1);
    batchxx.resize(_pts, 1);
    batchCovariance.resize(_pts, _pts);
    queryCovariance.resize(_pts, 1);

    for(i = 0; i < _pts; i++ ){
        batchCovariance(i, i) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(i)) + _lambda;
        for(j = i + 1; j < _pts; j++ ) {
            batchCovariance(i, j) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(j));
            batchCovariance(j, i) = batchCovariance(i, j);
        }
    }

    _timer.addToIteration();

    ldlt.compute(batchCovariance);

    _timer.addToEigen();

    for(ifn = 0; ifn < _nFunctions; ifn++ ) {

        fbar = 0.0;
        for(i = 0; i < _pts; i++ ){
            fbar += _function[i][ifn];
        }
        fbar = fbar/T(_pts);
        _timer.addToIteration();

        for(i = 0; i < _pts; i++ ){
            batchbb(i,0) = _function[i][ifn] - fbar;
        }
        batchxx = ldlt.solve(batchbb);
        _timer.addToEigen();


        for(ii = 0; ii < nQueries; ii++ ){
            for(i = 0; i < _dimensions; i++ ) v1[i] = queries[ii][i];
            if(_useMaxMin == 1) {
                for(i = 0; i < _dimensions; i++ ) v1[i] = (v1[i] - _min[i])/(_max[i] - _min[i]);
            }
            mu[ii][ifn] = fbar;
            for(i = 0; i < _pts; i++ ){
                mu[ii][ifn] += batchxx(i)*(*_covariogram)(v1, _kdTree.getData(i));
            }
        }

    }//ifn = 0 to _nFunctions

    _timer.addToIteration();
    for(ii = 0; ii < nQueries; ii++ ){
        for(i = 0; i < _dimensions; i++ ) v1[i] = queries[ii][i];
        if(_useMaxMin == 1){
            for(i = 0; i < _dimensions; i++ ) v1[i] = (v1[i] - _min[i])/(_max[i] - _min[i]);
        }

        for(i = 0;i < _pts;i++ ) {
            batchbb(i,0) = (*_covariogram)(v1,_kdTree.getData(i));
            queryCovariance(i,0) = batchbb(i,0);
        }
        batchxx = ldlt.solve(batchbb);

        variance[ii][0] = (*_covariogram)(v1, v1) + _lambda;

        for(i = 0; i < _pts; i++ ) {
              variance[ii][0] -= queryCovariance(i, 0)*batchxx(i);
        }

        variance[ii][0] = variance[ii][0]*_krigingParameter;
        for(i = 1; i < _nFunctions; i++ ) variance[ii][i] = variance[ii][0];

    }
    _timer.addToVariance();
    _timer.addToTotal(nQueries);
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::batchInterpolate	(	ndarray::Array< T, 2, 2 >	mu,
		ndarray::Array< T, 2, 2 > const &	queries
	)		const

This is the version of batchInterpolate (without variances) that is called for a vector of functions.

Definition at line 1618 of file GaussianProcess.cc.

{

    int i,j,ii,nQueries,ifn;


    T fbar;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  batchCovariance,batchbb,batchxx;
    Eigen::Matrix  < T,Eigen::Dynamic,Eigen::Dynamic >  queryCovariance;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    ndarray::Array < T,1,1 >  v1;

    _timer.start();

    nQueries = queries.template getSize < 0 > ();


    v1 = allocate(ndarray::makeVector(_dimensions));

    batchbb.resize(_pts, 1);
    batchxx.resize(_pts, 1);
    batchCovariance.resize(_pts, _pts);
    queryCovariance.resize(_pts, 1);


    for(i = 0; i < _pts; i++ ){
        batchCovariance(i, i) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(i)) + _lambda;
        for(j = i + 1; j < _pts; j++ ){
            batchCovariance(i, j) = (*_covariogram)(_kdTree.getData(i), _kdTree.getData(j));
            batchCovariance(j, i) = batchCovariance(i, j);
        }
    }

    _timer.addToIteration();

    ldlt.compute(batchCovariance);

    _timer.addToEigen();

    for(ifn = 0; ifn < _nFunctions; ifn++ ){

        fbar = 0.0;
        for(i = 0; i < _pts; i++ ){
            fbar += _function[i][ifn];
        }
        fbar = fbar/T(_pts);

        _timer.addToIteration();

        for(i = 0; i < _pts; i++ ){
            batchbb(i, 0) = _function[i][ifn] - fbar;
        }
        batchxx = ldlt.solve(batchbb);
        _timer.addToEigen();


        for(ii = 0; ii < nQueries; ii++ ){
            for(i = 0; i < _dimensions; i++ )v1[i] = queries[ii][i];
            if(_useMaxMin == 1){
                for(i = 0;i < _dimensions;i++ )v1[i] = (v1[i] - _min[i])/(_max[i] - _min[i]);
            }

            mu[ii][ifn] = fbar;
            for(i = 0; i < _pts; i++ ){
                 mu[ii][ifn] += batchxx(i)*(*_covariogram)(v1, _kdTree.getData(i));
            }
        }

      
    }//ifn = 0 through _nFunctions

    _timer.addToTotal(nQueries);

}

template<typename T >

GaussianProcessTimer & lsst::afw::math::GaussianProcess< T >::getTimes

(

)

const

Give the user acces to _timer, an object keeping track of the time spent on various processes within interpolate.

This will return a GaussianProcessTimer object. The user can, for example, see how much time has been spent on Eigen's linear algebra package (see the comments on the GaussianProcessTimer class) using code like

gg=GaussianProcess(....)

ticktock=gg.getTimes()

ticktock.display()

Definition at line 1815 of file GaussianProcess.cc.

{
    return _timer;
}

template<typename T >

T lsst::afw::math::GaussianProcess< T >::interpolate	(	ndarray::Array< T, 1, 1 >	variance,
		ndarray::Array< T, 1, 1 > const &	vin,
		int	numberOfNeighbors
	)		const

Interpolate the function value at one point using a specified number of nearest neighbors.

Parameters

[out]	variance	a one-dimensional ndarray. The value of the variance predicted by the Gaussian process will be stored in the zeroth element
[in]	vin	a one-dimensional ndarray representing the point at which you want to interpolate the function
[in]	numberOfNeighbors	the number of nearest neighbors to be used in the interpolation

the interpolated value of the function will be returned at the end of this method

Note: if you used a normalized parameter space, you should not normalize vin before inputting. The code will remember that you want a normalized parameter space, and will apply the normalization when you call interpolate

Definition at line 899 of file GaussianProcess.cc.

{
    
    if(numberOfNeighbors <= 0){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for zero or negative number of neighbors\n");
    }
    
    if(numberOfNeighbors > _kdTree.getPoints()){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for more neighbors than you have data points\n");
    }
    
    int i,j;
    T fbar,mu;

    ndarray::Array < T,1,1 >  covarianceTestPoint;
    ndarray::Array < int,1,1 >  neighbors;
    ndarray::Array < double,1,1 >  neighborDistances,vv;

    Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >  covariance,bb,xx;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;


    _timer.start();

    bb.resize(numberOfNeighbors, 1);
    xx.resize(numberOfNeighbors, 1);

    covariance.resize(numberOfNeighbors,numberOfNeighbors);

    covarianceTestPoint = allocate(ndarray::makeVector(numberOfNeighbors));

    neighbors = allocate(ndarray::makeVector(numberOfNeighbors));

    neighborDistances = allocate(ndarray::makeVector(numberOfNeighbors));

    vv = allocate(ndarray::makeVector(_dimensions));
    if(_useMaxMin == 1){
        //if you constructed this Gaussian process with minimum and maximum 
        //values for the dimensions of your parameter space,
        //the point you are interpolating must be scaled to match the data so 
        //that the selected nearest neighbors are appropriate

        for(i = 0; i < _dimensions; i++ ) vv[i] = (vin[i] - _min[i])/(_max[i] - _min[i]);
    }
    else{
        vv = vin;
    }


    _kdTree.findNeighbors(neighbors, neighborDistances, vv, numberOfNeighbors);

    _timer.addToSearch();

    fbar = 0.0;
    for(i = 0; i < numberOfNeighbors; i++ )fbar += _function[neighbors[i]][0];
    fbar = fbar/double(numberOfNeighbors);

    for(i = 0; i < numberOfNeighbors; i++ ){
        covarianceTestPoint[i] = (*_covariogram)(vv, _kdTree.getData(neighbors[i]));

        covariance(i,i) = (*_covariogram)(_kdTree.getData(neighbors[i]), _kdTree.getData(neighbors[i]))
                         + _lambda;

        for(j = i + 1; j < numberOfNeighbors; j++ ){
            covariance(i,j) = (*_covariogram)(_kdTree.getData(neighbors[i]),
                                              _kdTree.getData(neighbors[j]));
            covariance(j,i) = covariance(i, j);
        }
    }

    _timer.addToIteration();

    //use Eigen's ldlt solver in place of matrix inversion (for speed purposes)
    ldlt.compute(covariance);

    for(i = 0; i < numberOfNeighbors; i++) bb(i,0) = _function[neighbors[i]][0] - fbar;

    xx = ldlt.solve(bb);
    _timer.addToEigen();

    mu = fbar;

    for(i = 0; i < numberOfNeighbors; i++ ){
        mu += covarianceTestPoint[i]*xx(i, 0);
    }

    _timer.addToIteration();

    variance(0) = (*_covariogram)(vv, vv) + _lambda;

    for(i = 0; i < numberOfNeighbors; i++ ) bb(i) = covarianceTestPoint[i];

    xx = ldlt.solve(bb);

    for(i = 0; i < numberOfNeighbors; i++ ){
        variance(0) -= covarianceTestPoint[i]*xx(i, 0);
    }

    variance(0) = variance(0)*_krigingParameter;

    _timer.addToVariance();
    _timer.addToTotal(1);

    return mu;
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::interpolate	(	ndarray::Array< T, 1, 1 >	mu,
		ndarray::Array< T, 1, 1 >	variance,
		ndarray::Array< T, 1, 1 > const &	vin,
		int	numberOfNeighbors
	)		const

This is the version of GaussianProcess::interpolate for a vector of functions.

Parameters

[out]	mu	will store the vector of interpolated function values
[out]	variance	will store the vector of interpolated variances on mu
[in]	vin	the point at which you wish to interpolate the functions
[in]	numberOfNeighbors	is the number of nearest neighbor points to use in the interpolation

Note: Because the variance currently only depends on the covariance function and the covariance function currently does not include any terms relating different elements of mu to each other, all of the elements of variance will be identical

Definition at line 1010 of file GaussianProcess.cc.

{


    if(numberOfNeighbors <= 0){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for zero or negative number of neighbors\n");
    }
    
    if(numberOfNeighbors > _kdTree.getPoints()){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for more neighbors than you have data points\n");
    }


    int i,j,ii;
    T fbar;

    ndarray::Array < T,1,1 >  covarianceTestPoint;
    ndarray::Array < int,1,1 >  neighbors;
    ndarray::Array < double,1,1 >  neighborDistances,vv;

    Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >  covariance,bb,xx;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    _timer.start();


     bb.resize(numberOfNeighbors,1);
     xx.resize(numberOfNeighbors,1);
     covariance.resize(numberOfNeighbors,numberOfNeighbors);
     covarianceTestPoint = allocate(ndarray::makeVector(numberOfNeighbors));
     neighbors = allocate(ndarray::makeVector(numberOfNeighbors));
     neighborDistances = allocate(ndarray::makeVector(numberOfNeighbors));

     vv = allocate(ndarray::makeVector(_dimensions));


    if(_useMaxMin == 1) {
        //if you constructed this Gaussian process with minimum and maximum 
        //values for the dimensions of your parameter space,
        //the point you are interpolating must be scaled to match the data so 
        //that the selected nearest neighbors are appropriate

        for(i = 0; i < _dimensions; i++ )vv[i] = (vin[i] - _min[i])/(_max[i] - _min[i]);
    }
    else {
        vv = vin;
    }


    _kdTree.findNeighbors(neighbors, neighborDistances, vv, numberOfNeighbors);

    _timer.addToSearch();

    for(i = 0; i < numberOfNeighbors; i++ ) {
        covarianceTestPoint[i] = (*_covariogram)(vv, _kdTree.getData(neighbors[i]));

        covariance(i,i) = (*_covariogram)(_kdTree.getData(neighbors[i]), _kdTree.getData(neighbors[i]))
                           + _lambda;

        for(j = i + 1; j < numberOfNeighbors; j++ ){
            covariance(i,j) = (*_covariogram)(_kdTree.getData(neighbors[i]),
                                              _kdTree.getData(neighbors[j]));
            covariance(j,i) = covariance(i, j);
        }
    }

    _timer.addToIteration();

    //use Eigen's ldlt solver in place of matrix inversion (for speed purposes)
    ldlt.compute(covariance);

    for(ii = 0; ii < _nFunctions; ii++ ) {

          fbar = 0.0;
          for(i = 0; i < numberOfNeighbors; i++ )fbar += _function[neighbors[i]][ii];
          fbar = fbar/double(numberOfNeighbors);

          for(i = 0; i < numberOfNeighbors; i++ )bb(i,0) = _function[neighbors[i]][ii] - fbar;
          xx = ldlt.solve(bb);

          mu[ii] = fbar;

          for(i = 0; i < numberOfNeighbors; i++ ) {
            mu[ii] += covarianceTestPoint[i]*xx(i, 0);
          }

    }//ii = 0 through _nFunctions

    _timer.addToEigen();

    variance[0] = (*_covariogram)(vv, vv) + _lambda;

    for(i = 0; i < numberOfNeighbors; i++ )bb(i) = covarianceTestPoint[i];

    xx = ldlt.solve(bb);

    for(i = 0; i < numberOfNeighbors; i++ ) {
        variance[0] -= covarianceTestPoint[i]*xx(i, 0);
    }
    variance[0] = variance[0]*_krigingParameter;


    for(i = 1; i < _nFunctions; i++ )variance[i] = variance[0];

    _timer.addToVariance();
    _timer.addToTotal(1);
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::removePoint

(

int

dex

)

This will remove a point from the data set.

Parameters

[in]

dex

the index of the point you want to remove from your data set

Exceptions

pex_exceptions

RuntimeError if the tree does not end up properly constructed (the exception is actually thrown by KdTree<T>::removePoint() )

Note: excessive use of addPoint and removePoint can result in an unbalanced KdTree, which will slow down nearest neighbor searches

Definition at line 1782 of file GaussianProcess.cc.

{

    int i,j;

    _kdTree.removePoint(dex);

    for(i = dex; i < _pts; i++ ) {
        for(j = 0; j < _nFunctions; j++ ) {
             _function[i][j] = _function[i + 1][j];
        }
    }
    _pts = _kdTree.getPoints();
}

template<typename T >

T lsst::afw::math::GaussianProcess< T >::selfInterpolate	(	ndarray::Array< T, 1, 1 >	variance,
		int	dex,
		int	numberOfNeighbors
	)		const

This method will interpolate the function on a data point for purposes of optimizing hyper parameters.

Parameters

[out]	variance	a one-dimensional ndarray. The value of the variance predicted by the Gaussian process will be stored in the zeroth element
[in]	dex	the index of the point you wish to self interpolate
[in]	numberOfNeighbors	the number of nearest neighbors to be used in the interpolation

Exceptions

pex_exceptions

RuntimeError if the nearest neighbor search does not find the data point itself as the nearest neighbor

The interpolated value of the function will be returned at the end of this method

This method ignores the point on which you are interpolating when requesting nearest neighbors

Definition at line 1125 of file GaussianProcess.cc.

{

    if(numberOfNeighbors <= 0){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for zero or negative number of neighbors\n");
    }
    
    if(numberOfNeighbors > _kdTree.getPoints()){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for more neighbors than you have data points\n");
    }

    int i,j;
    T fbar,mu;

    ndarray::Array < T,1,1 >  covarianceTestPoint;
    ndarray::Array < int,1,1 >  selfNeighbors;
    ndarray::Array < double,1,1 >  selfDistances;
    ndarray::Array < int,1,1 >  neighbors;
    ndarray::Array < double,1,1 >  neighborDistances;

    Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >  covariance,bb,xx;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    _timer.start();

    bb.resize(numberOfNeighbors, 1);
    xx.resize(numberOfNeighbors, 1);
    covariance.resize(numberOfNeighbors,numberOfNeighbors);
    covarianceTestPoint = allocate(ndarray::makeVector(numberOfNeighbors));
    neighbors = allocate(ndarray::makeVector(numberOfNeighbors));
    neighborDistances = allocate(ndarray::makeVector(numberOfNeighbors));

    selfNeighbors = allocate(ndarray::makeVector(numberOfNeighbors + 1));
    selfDistances = allocate(ndarray::makeVector(numberOfNeighbors + 1));

    //we don't use _useMaxMin because the data has already been normalized


    _kdTree.findNeighbors(selfNeighbors, selfDistances, _kdTree.getData(dex),
                          numberOfNeighbors + 1);

    _timer.addToSearch();

    if(selfNeighbors[0]!= dex) {
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
        "Nearest neighbor search in selfInterpolate did not find self\n");
    }

    //SelfNeighbors[0] will be the point itself (it is its own nearest neighbor)
    //We discard that for the interpolation calculation
    //
    //If you do not wish to do this, simply call the usual ::interpolate() method instead of
    //::selfInterpolate()
    for(i = 0; i < numberOfNeighbors; i++ ){
        neighbors[i] = selfNeighbors[i + 1];
        neighborDistances[i] = selfDistances[i + 1];
    }

    fbar = 0.0;
    for(i = 0; i < numberOfNeighbors; i++ ) fbar += _function[neighbors[i]][0];
    fbar = fbar/double(numberOfNeighbors);

    for(i = 0; i < numberOfNeighbors; i++ ){
        covarianceTestPoint[i] = (*_covariogram)(_kdTree.getData(dex),
                                                 _kdTree.getData(neighbors[i]));

        covariance(i, i) = (*_covariogram)(_kdTree.getData(neighbors[i]),
                                           _kdTree.getData(neighbors[i])) + _lambda;

      for(j = i + 1; j < numberOfNeighbors; j++ ) {
          covariance(i, j) = (*_covariogram)(_kdTree.getData(neighbors[i]),
                                             _kdTree.getData(neighbors[j]));
          covariance(j, i) = covariance(i ,j);
        }
    }
    _timer.addToIteration();

    //use Eigen's ldlt solver in place of matrix inversion (for speed purposes)
    ldlt.compute(covariance);


    for(i = 0; i < numberOfNeighbors;i++ ) bb(i, 0) = _function[neighbors[i]][0] - fbar;
    xx = ldlt.solve(bb);
    _timer.addToEigen();

    mu = fbar;

    for(i = 0; i < numberOfNeighbors; i++ ) {
        mu += covarianceTestPoint[i]*xx(i, 0);
    }


    variance(0) = (*_covariogram)(_kdTree.getData(dex), _kdTree.getData(dex)) + _lambda;

    for(i = 0; i < numberOfNeighbors; i++ )bb(i) = covarianceTestPoint[i];

    xx = ldlt.solve(bb);
  
    for(i = 0; i < numberOfNeighbors; i++ ){
        variance(0) -= covarianceTestPoint[i]*xx(i,0);
    }

    variance(0) = variance(0)*_krigingParameter;
    _timer.addToVariance();
    _timer.addToTotal(1);

    return mu;
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::selfInterpolate	(	ndarray::Array< T, 1, 1 >	mu,
		ndarray::Array< T, 1, 1 >	variance,
		int	dex,
		int	numberOfNeighbors
	)		const

The version of selfInterpolate called for a vector of functions.

Parameters

[out]	mu	this is where the interpolated function values will be stored
[out]	variance	the variance on mu will be stored here
[in]	dex	the index of the point you wish to interpolate
[in]	numberOfNeighbors	the number of nearest neighbors to use in the interpolation

Exceptions

pex_exceptions

RuntimeError if the nearest neighbor search does not find the data point itself as the nearest neighbor

Definition at line 1239 of file GaussianProcess.cc.

                                                                         {

    if(numberOfNeighbors <= 0){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for zero or negative number of neighbors\n");
    }
    
    if(numberOfNeighbors + 1 > _kdTree.getPoints()){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked for more neighbors than you have data points\n");
    }
    
    if(dex < 0 || dex >=_kdTree.getPoints()){
        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
                          "Asked to self interpolate on a point that does not exist\n");
    }
    
    int i,j,ii;
    T fbar;

    ndarray::Array < T,1,1 >  covarianceTestPoint;
    ndarray::Array < int,1,1 >  selfNeighbors;
    ndarray::Array < double,1,1 >  selfDistances;
    ndarray::Array < int,1,1 >  neighbors;
    ndarray::Array < double,1,1 >  neighborDistances;

    Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >  covariance,bb,xx;
    Eigen::LDLT < Eigen::Matrix < T,Eigen::Dynamic,Eigen::Dynamic >   >  ldlt;

    _timer.start();

    bb.resize(numberOfNeighbors, 1);
    xx.resize(numberOfNeighbors, 1);
    covariance.resize(numberOfNeighbors,numberOfNeighbors);
    covarianceTestPoint = allocate(ndarray::makeVector(numberOfNeighbors));
    neighbors = allocate(ndarray::makeVector(numberOfNeighbors));
    neighborDistances = allocate(ndarray::makeVector(numberOfNeighbors));

    selfNeighbors = allocate(ndarray::makeVector(numberOfNeighbors + 1));
    selfDistances = allocate(ndarray::makeVector(numberOfNeighbors + 1));

    //we don't use _useMaxMin because the data has already been normalized


    _kdTree.findNeighbors(selfNeighbors, selfDistances, _kdTree.getData(dex),
                          numberOfNeighbors + 1);

    _timer.addToSearch();

    if(selfNeighbors[0]!= dex) {

        throw LSST_EXCEPT(lsst::pex::exceptions::RuntimeError,
        "Nearest neighbor search in selfInterpolate did not find self\n");
    }

    //SelfNeighbors[0] will be the point itself (it is its own nearest neighbor)
    //We discard that for the interpolation calculation
    //
    //If you do not wish to do this, simply call the usual ::interpolate() method instead of
    //::selfInterpolate()
    for(i = 0; i < numberOfNeighbors; i++ ) {
        neighbors[i] = selfNeighbors[i + 1];
        neighborDistances[i] = selfDistances[i + 1];
    }



    for(i = 0; i < numberOfNeighbors; i++ ) {
        covarianceTestPoint[i] = (*_covariogram)(_kdTree.getData(dex),_kdTree.getData(neighbors[i]));

        covariance(i, i) = (*_covariogram)(_kdTree.getData(neighbors[i]), _kdTree.getData(neighbors[i]))
                           + _lambda;

        for(j = i + 1; j < numberOfNeighbors; j++ ) {
            covariance(i, j) = (*_covariogram)(_kdTree.getData(neighbors[i]),
                                               _kdTree.getData(neighbors[j]));
            covariance(j, i) = covariance(i, j);
        }
    }
    _timer.addToIteration();


    //use Eigen's ldlt solver in place of matrix inversion (for speed purposes)
    ldlt.compute(covariance);

    for(ii = 0; ii < _nFunctions; ii++ ) {

        fbar = 0.0;
        for(i = 0; i < numberOfNeighbors; i++ )fbar += _function[neighbors[i]][ii];
        fbar = fbar/double(numberOfNeighbors);

        for(i = 0; i < numberOfNeighbors; i++ )bb(i,0) = _function[neighbors[i]][ii] - fbar;
        xx = ldlt.solve(bb);

        mu[ii] = fbar;

        for(i = 0; i < numberOfNeighbors; i++ ){
            mu[ii] += covarianceTestPoint[i]*xx(i,0);
        }
    }//ii = 0 through _nFunctions

    _timer.addToEigen();

    variance[0] = (*_covariogram)(_kdTree.getData(dex), _kdTree.getData(dex)) + _lambda;

    for(i = 0; i < numberOfNeighbors; i++ )bb(i) = covarianceTestPoint[i];

    xx = ldlt.solve(bb);

    for(i = 0; i < numberOfNeighbors; i++ ) {
        variance[0] -= covarianceTestPoint[i]*xx(i,0);
    }

    variance[0] = variance[0]*_krigingParameter;

    for(i = 1; i < _nFunctions; i++ )variance[i] = variance[0];

    _timer.addToVariance();
    _timer.addToTotal(1);
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::setCovariogram

(

boost::shared_ptr< Covariogram< T > > const &

covar

)

Assign a different covariogram to this GaussianProcess.

Parameters

[in]

covar

the Covariogram object that you wish to assign

Definition at line 1804 of file GaussianProcess.cc.

                                                                                                 {
     _covariogram = covar;
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::setKrigingParameter

(

T

kk

)

Assign a value to the Kriging paramter.

Parameters

[in]

kk

the value assigned to the Kriging parameters

Definition at line 1798 of file GaussianProcess.cc.

{
    _krigingParameter = kk;
}

template<typename T >

void lsst::afw::math::GaussianProcess< T >::setLambda

(

T

lambda

)

set the value of the hyperparameter _lambda

Parameters

[in]

lambda

the value you want assigned to _lambda

_lambda is a parameter meant to represent the characteristic variance of the function you are interpolating. Currently, it is a scalar such that all data points must have the same characteristic variance. Future iterations of the code may want to promote _lambda to an array so that different data points can have different variances.

Definition at line 1809 of file GaussianProcess.cc.

                                              {
    _lambda = lambda;
}

Member Data Documentation

template<typename T >

boost::shared_ptr< Covariogram<T> > lsst::afw::math::GaussianProcess< T >::_covariogram

private

Definition at line 825 of file GaussianProcess.h.

template<typename T >

int lsst::afw::math::GaussianProcess< T >::_dimensions

private

Definition at line 816 of file GaussianProcess.h.

template<typename T >

ndarray::Array<T,2,2> lsst::afw::math::GaussianProcess< T >::_function

private

Definition at line 821 of file GaussianProcess.h.

template<typename T >

KdTree<T> lsst::afw::math::GaussianProcess< T >::_kdTree

private

Definition at line 823 of file GaussianProcess.h.

template<typename T >

T lsst::afw::math::GaussianProcess< T >::_krigingParameter

private

Definition at line 818 of file GaussianProcess.h.

template<typename T >

T lsst::afw::math::GaussianProcess< T >::_lambda

private

Definition at line 818 of file GaussianProcess.h.

template<typename T >

ndarray::Array<T,1,1> lsst::afw::math::GaussianProcess< T >::_max

private

Definition at line 820 of file GaussianProcess.h.

template<typename T >

ndarray::Array<T,1,1> lsst::afw::math::GaussianProcess< T >::_min

private

Definition at line 820 of file GaussianProcess.h.

template<typename T >

int lsst::afw::math::GaussianProcess< T >::_nFunctions

private

Definition at line 816 of file GaussianProcess.h.

template<typename T >

int lsst::afw::math::GaussianProcess< T >::_pts

private

Definition at line 816 of file GaussianProcess.h.

template<typename T >

int lsst::afw::math::GaussianProcess< T >::_room

private

Definition at line 816 of file GaussianProcess.h.

template<typename T >

int lsst::afw::math::GaussianProcess< T >::_roomStep

private

Definition at line 816 of file GaussianProcess.h.

template<typename T >

GaussianProcessTimer lsst::afw::math::GaussianProcess< T >::_timer

mutableprivate

Definition at line 826 of file GaussianProcess.h.

template<typename T >

int lsst::afw::math::GaussianProcess< T >::_useMaxMin

private

Definition at line 816 of file GaussianProcess.h.

---

The documentation for this class was generated from the following files:

• /home/lsstsw/stack/Linux64/afw/11.0-2-g04d2804/include/lsst/afw/math/GaussianProcess.h
• /home/lsstsw/stack/Linux64/afw/11.0-2-g04d2804/src/math/GaussianProcess.cc