Representation of a kernel matrix. More...

#include <Kernel.hpp>

Inheritance diagram for strumpack::kernel::Kernel< scalar_t >:

[legend]

Public Member Functions
	Kernel (DenseM_t &data, scalar_t lambda)

virtual	~Kernel ()=default

std::size_t	n () const

std::size_t	d () const

virtual scalar_t	eval (std::size_t i, std::size_t j) const

void	operator() (const std::vector< std::size_t > &I, const std::vector< std::size_t > &J, DenseMatrix< real_t > &B) const

void	operator() (const std::vector< std::size_t > &I, const std::vector< std::size_t > &J, DenseMatrix< std::complex< real_t >> &B) const

DenseM_t	fit_HSS (std::vector< scalar_t > &labels, const HSS::HSSOptions< scalar_t > &opts)

std::vector< scalar_t >	predict (const DenseM_t &test, const DenseM_t &weights) const

DistM_t	fit_HSS (const BLACSGrid &grid, std::vector< scalar_t > &labels, const HSS::HSSOptions< scalar_t > &opts)

std::vector< scalar_t >	predict (const DenseM_t &test, const DistM_t &weights) const

DenseM_t	fit_HODLR (const MPIComm &c, std::vector< scalar_t > &labels, const HODLR::HODLROptions< scalar_t > &opts)

const DenseM_t &	data () const

DenseM_t &	data ()

std::vector< int > &	permutation ()

const std::vector< int > &	permutation () const

virtual void	permute ()

Detailed Description

template<typename scalar_t>
class strumpack::kernel::Kernel< scalar_t >

Representation of a kernel matrix.

This is an abstract class. This class contains a reference to the datapoints representing the kernel: X. X is a d x n matrix (d features and n datapoints).

The actual kernel function is implemented in one of the subclasses of this class. Subclasses need to implement the purely virtual function eval_kernel_function.

Template Parameters

scalar_t Scalar type of the input data points and the kernel representation. Can be float, double, std::complex<float> or std::complex<double>.

Constructor & Destructor Documentation

◆ Kernel()

template<typename scalar_t >

strumpack::kernel::Kernel< scalar_t >::Kernel	(	DenseM_t &	data,
		scalar_t	lambda
	)

inline

Kernel matrix constructor.

Parameters

data	Contains the data points, 1 datapoint per column. So the number of rows of data is the number of features, the number of columns of data will be the size of the kernel matrix.
lambda	regularization parameter, added to the diagonal.

◆ ~Kernel()

template<typename scalar_t >

virtual strumpack::kernel::Kernel< scalar_t >::~Kernel ( )

virtualdefault

Default constructor.

Member Function Documentation

◆ d()

template<typename scalar_t >

std::size_t strumpack::kernel::Kernel< scalar_t >::d ( ) const

inline

Return the dimension of the datapoints defining the kernel.

Returns: dimension of the datapoints

See also: n(), data()

◆ data() [1/2]

template<typename scalar_t >

DenseM_t& strumpack::kernel::Kernel< scalar_t >::data ( )

inline

Returns a reference to the data used to define this kernel.

Returns: reference to the datapoint, a matrix of size d x n.

◆ data() [2/2]

template<typename scalar_t >

const DenseM_t& strumpack::kernel::Kernel< scalar_t >::data ( ) const

inline

Returns a (const) reference to the data used to define this kernel.

Returns: const reference to the datapoint, a matrix of size d x n.

◆ eval()

template<typename scalar_t >

virtual scalar_t strumpack::kernel::Kernel< scalar_t >::eval	(	std::size_t	i,
		std::size_t	j
	)		const

inlinevirtual

Evaluate an entry of the kernel matrix.

Parameters

i	row coordinate of entry to evaluate
j	column coordinate of entry to evaluate

Returns: the value K(i, j) of the kernel

Reimplemented in strumpack::kernel::DenseKernel< scalar_t >.

◆ fit_HODLR()

template<typename scalar_t >

DenseM_t strumpack::kernel::Kernel< scalar_t >::fit_HODLR	(	const MPIComm &	c,
		std::vector< scalar_t > &	labels,
		const HODLR::HODLROptions< scalar_t > &	opts
	)

Compute weights for kernel ridge regression classification. This will build an approximate HODLR representation of the kernel matrix and use that to solve a linear system with the kernel matrix and the weights vector as the right-hand side. The weights can then later be used in the predict() method for prediction. The data associated to this kernel, and the labels, will get permuted.

TODO labels should be a vector of bool's or int's??

Parameters

c	MPI communicator on which to perform the calculation
labels	Binary labels, supposed to be in {-1, 1}. Should be labels.size() == this->n().
opts	HSS options

Returns: A vector with scalar weights, to be used in predict()

See also: predict, fit_HSS

◆ fit_HSS() [1/2]

template<typename scalar_t >

DistM_t strumpack::kernel::Kernel< scalar_t >::fit_HSS	(	const BLACSGrid &	grid,
		std::vector< scalar_t > &	labels,
		const HSS::HSSOptions< scalar_t > &	opts
	)

Compute weights for kernel ridge regression classification. This will build an approximate HSS representation of the kernel matrix and use that to solve a linear system with the kernel matrix and the weights vector as the right-hand side. The weights can then later be used in the predict() method for prediction. The data associated to this kernel, and the labels, will get permuted.

TODO labels should be a vector of bool's or int's??

Parameters

grid	Processor grid to use for the MPI distributed computations
labels	Binary labels, supposed to be in {-1, 1}. Should be labels.size() == this->n().
opts	HSS options

Returns: A distributed vector with scalar weights, to be used in predict(), distributed on the BLACSGrid grid.

See also: predict, fit_HODLR

◆ fit_HSS() [2/2]

template<typename scalar_t >

DenseM_t strumpack::kernel::Kernel< scalar_t >::fit_HSS	(	std::vector< scalar_t > &	labels,
		const HSS::HSSOptions< scalar_t > &	opts
	)

Compute weights for kernel ridge regression classification. This will build an approximate HSS representation of the kernel matrix and use that to solve a linear system with the kernel matrix and the weights vector as the right-hand side. The weights can then later be used in the predict method for prediction. The data associated to this kernel, and the labels, will get permuted.

TODO labels should be a vector of bool's or int's??

Parameters

labels	Binary labels, supposed to be in {-1, 1}. Should be labels.size() == this->n().
opts	HSS options

Returns: A vector (1 column matrix) with scalar weights, to be used in predict

See also: predict, fit_HODLR

◆ n()

template<typename scalar_t >

std::size_t strumpack::kernel::Kernel< scalar_t >::n ( ) const

inline

Returns the size of the (square) kernel matrix. This is the number of datapoints in the set data().

See also: d(), data()

◆ operator()() [1/2]

template<typename scalar_t >

void strumpack::kernel::Kernel< scalar_t >::operator()	(	const std::vector< std::size_t > &	I,
		const std::vector< std::size_t > &	J,
		DenseMatrix< real_t > &	B
	)		const

inline

Evaluate multiple entries at once: evaluate the submatrix K(I,J) and put the result in matrix B. This is used in the HSS and HODLR construction algorithms for this kernel.

Parameters

I	set of row indices of elements to extract
J	set of col indices of elements to extract
B	B will be set to K(I,J). Matrix B should be the correct size, ie., B.rows() == I.size() and B.cols() == J.size()

◆ operator()() [2/2]

template<typename scalar_t >

void strumpack::kernel::Kernel< scalar_t >::operator()	(	const std::vector< std::size_t > &	I,
		const std::vector< std::size_t > &	J,
		DenseMatrix< std::complex< real_t >> &	B
	)		const

inline

Evaluate multiple entries at once: evaluate the submatrix K(I,J) and put the result in matrix B. This is used in the HSS and HODLR construction algorithms for this kernel.

Parameters

I	set of row indices of elements to extract
J	set of col indices of elements to extract
B	B will be set to K(I,J). Matrix B should be the correct size, ie., B.rows() == I.size() and B.cols() == J.size()

◆ predict() [1/2]

template<typename scalar_t >

std::vector<scalar_t> strumpack::kernel::Kernel< scalar_t >::predict	(	const DenseM_t &	test,
		const DenseM_t &	weights
	)		const

Return prediction scores for the test points, using the weights computed in fit_HSS() or fit_HODLR().

Parameters

test	Test data set, should be test.rows() == this->d()
weights	Weights computed by fit_HSS() or fit_HODLR()

Returns: Vector with prediction scores. One can use the sign (threshold zero), to decide which of 2 classes each test point belongs to.

See also: fit_HSS, fit_HODLR

◆ predict() [2/2]

template<typename scalar_t >

std::vector<scalar_t> strumpack::kernel::Kernel< scalar_t >::predict	(	const DenseM_t &	test,
		const DistM_t &	weights
	)		const

Return prediction scores for the test points, using the weights computed in fit_HSS() or fit_HODLR().

Parameters

test	Test data set, should be test.rows() == this->d()
weights	Weights computed by fit_HSS() or fit_HODLR()

Returns: Vector with prediction scores. One can use the sign (threshold zero), to decide which of 2 classes each test point belongs to.

See also: fit_HSS, fit_HODLR

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

/home/pieterg/LBL/STRUMPACK/src/kernel/Kernel.hpp

Public Member Functions

Detailed Description

template<typename scalar_t> class strumpack::kernel::Kernel< scalar_t >

Constructor & Destructor Documentation

◆ Kernel()

◆ ~Kernel()

Member Function Documentation

◆ d()

◆ data() [1/2]

◆ data() [2/2]

◆ eval()

◆ fit_HODLR()

◆ fit_HSS() [1/2]

◆ fit_HSS() [2/2]

◆ n()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ predict() [1/2]

◆ predict() [2/2]

template<typename scalar_t>
class strumpack::kernel::Kernel< scalar_t >