compute.hpp File Reference

Compute an approximate SVD with IRLBA. More...

#include <cmath>
#include <cstdint>
#include <random>
#include <stdexcept>
#include <type_traits>
#include "utils.hpp"
#include "lanczos.hpp"
#include "Matrix/simple.hpp"
#include "sanisizer/sanisizer.hpp"
#include "Eigen/Dense"

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Classes
struct	irlba::Results< EigenMatrix_, EigenVector_ >
	Results of the IRLBA-based SVD by compute(). More...

Functions
template<class Matrix_ , class EigenMatrix_ , class EigenVector_ >
std::pair< bool, int >	irlba::compute (const Matrix_ &matrix, const Eigen::Index number, EigenMatrix_ &outU, EigenMatrix_ &outV, EigenVector_ &outD, const Options< EigenVector_ > &options)
template<class InputEigenMatrix_ , class OutputEigenMatrix_ , class EigenVector_ >
std::pair< bool, int >	irlba::compute_simple (const InputEigenMatrix_ &matrix, Eigen::Index number, OutputEigenMatrix_ &outU, OutputEigenMatrix_ &outV, EigenVector_ &outD, const Options< EigenVector_ > &options)
template<class EigenMatrix_ = Eigen::MatrixXd, class EigenVector_ = Eigen::VectorXd, class Matrix_ >
Results< EigenMatrix_, EigenVector_ >	irlba::compute (const Matrix_ &matrix, Eigen::Index number, const Options< EigenVector_ > &options)
template<class OutputEigenMatrix_ = Eigen::MatrixXd, class EigenVector_ = Eigen::VectorXd, class InputEigenMatrix_ >
Results< OutputEigenMatrix_, EigenVector_ >	irlba::compute_simple (const InputEigenMatrix_ &matrix, Eigen::Index number, const Options< EigenVector_ > &options)

Detailed Description

Compute an approximate SVD with IRLBA.

Function Documentation

compute() [1/2]

template<class Matrix_ , class EigenMatrix_ , class EigenVector_ >

std::pair< bool, int > irlba::compute	(	const Matrix_ &	matrix,
		const Eigen::Index	number,
		EigenMatrix_ &	outU,
		EigenMatrix_ &	outV,
		EigenVector_ &	outD,
		const Options< EigenVector_ > &	options )

Implements the Implicitly Restarted Lanczos Bidiagonalization Algorithm (IRLBA) for fast truncated singular value decomposition. This is heavily derived from the C code in the irlba package, with refactoring into C++ to use Eigen instead of LAPACK for much of the matrix algebra.

Template Parameters

Matrix_	Class satisfying the Matrix<EigenVector_, EigenMatrix_> interface.
EigenMatrix_	A dense floating-point Eigen::Matrix class to store the output.
EigenVector_	A floating-point Eigen::Vector class to store the output, typically of the same scalar type as EigenMatrix_.

Parameters

[in]	matrix	Input matrix.
	number	Number of singular triplets to obtain. The returned number of triplets may be lower, see Options::cap_number for details.
[out]	outU	Output matrix containing the left singular vectors corresponding to the largest singular values. Each column corresponds to a left singular vector, of which there are number (or less, depending on Options::cap_number). The number of rows is equal to the number of rows in mat.
[out]	outV	Output matrix containing the right singular vectors corresponding to the largest singular values. Each column corresponds to a right singular vector, of which there are number (or less, depending on Options::cap_number). The number of rows is equal to the number of columns in mat.
[out]	outD	Output vector containing the largest singular values, ordered by decreasing size. This has length equal to number (or lower, depending on Options::cap_number).
	options	Further options.

Returns

A pair where the first entry indicates whether the algorithm converged, and the second entry indicates the number of restart iterations performed.

compute() [2/2]

template<class EigenMatrix_ = Eigen::MatrixXd, class EigenVector_ = Eigen::VectorXd, class Matrix_ >

Results< EigenMatrix_, EigenVector_ > irlba::compute	(	const Matrix_ &	matrix,
		Eigen::Index	number,
		const Options< EigenVector_ > &	options )

Convenient overload of compute() that allocates memory for the output matrices of the SVD.

Template Parameters

EigenMatrix_	A dense floating-point Eigen::Matrix class to store the output.
EigenVector_	A floating-point Eigen::Vector class for the output, typically of the same scalar type as EigenMatrix_.
Matrix_	Class satisfying the Matrix<EigenVector_, EigenMatrix_> interface.

Parameters

[in]	matrix	Input matrix.
	number	Number of singular triplets to obtain.
	options	Further options.

Returns

A Results object containing the singular vectors and values, as well as some statistics on convergence.

compute_simple() [1/2]

template<class OutputEigenMatrix_ = Eigen::MatrixXd, class EigenVector_ = Eigen::VectorXd, class InputEigenMatrix_ >

Results< OutputEigenMatrix_, EigenVector_ > irlba::compute_simple	(	const InputEigenMatrix_ &	matrix,
		Eigen::Index	number,
		const Options< EigenVector_ > &	options )

Convenient overload of compute() that accepts an Eigen matrix directly.

Template Parameters

InputEigenMatrix_	An Eigen matrix class containing the input data.
OutputEigenMatrix_	A dense floating-point Eigen::Matrix class for the output.
EigenVector_	A floating-point Eigen::Vector class for the output, typically of the same scalar type as OutputEigenMatrix_.
Matrix_	Class satisfying the Matrix<EigenVector_, EigenMatrix_> interface.

Parameters

[in]	matrix	Input matrix.
	number	Number of singular triplets to obtain.
	options	Further options.

Returns

A Results object containing the singular vectors and values, as well as some statistics on convergence.

compute_simple() [2/2]

template<class InputEigenMatrix_ , class OutputEigenMatrix_ , class EigenVector_ >

std::pair< bool, int > irlba::compute_simple	(	const InputEigenMatrix_ &	matrix,
		Eigen::Index	number,
		OutputEigenMatrix_ &	outU,
		OutputEigenMatrix_ &	outV,
		EigenVector_ &	outD,
		const Options< EigenVector_ > &	options )

Convenient overload of compute() that accepts an Eigen matrix directly.

Template Parameters

InputEigenMatrix_	An Eigen matrix class containing the input data.
OutputEigenMatrix_	A dense floating-point Eigen::Matrix class to store the output.
EigenVector_	A floating-point Eigen::Vector class to store the output, typically of the same scalar type as EigenMatrix_.

Parameters

[in]	matrix	Input matrix.
	number	Number of singular triplets to obtain. The returned number of triplets may be lower, see Options::cap_number for details.
[out]	outU	Output matrix containing the left singular vectors corresponding to the largest singular values. Each column corresponds to a left singular vector, of which there are number (or less, depending on Options::cap_number). The number of rows is equal to the number of rows in mat.
[out]	outV	Output matrix containing the right singular vectors corresponding to the largest singular values. Each column corresponds to a right singular vector, of which there are number (or less, depending on Options::cap_number). The number of rows is equal to the number of columns in mat.
[out]	outD	Output vector containing the largest singular values, ordered by decreasing size. This has length equal to number (or lower, depending on Options::cap_number).
	options	Further options.

Returns

A pair where the first entry indicates whether the algorithm converged, and the second entry indicates the number of restart iterations performed.