eigen.hpp File Reference

The math types and decompositions, implemented with Eigen. More...

#include "./scalar.hpp"
#include <Eigen/Dense>
#include <cstddef>

Include dependency graph for eigen.hpp:

Go to the source code of this file.

Classes
struct	algotradelib::math::Observed
	A series split into zero-filled values and a presence mask, for sums that skip gaps. More...

Namespaces
namespace	algotradelib
	The library: broker-neutral types (core), and the modules below.
namespace	algotradelib::math
	The numeric vocabulary: Scalar, missing(), and the matrix and vector types.

Typedefs
using	algotradelib::math::Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor>
	A dense, column-major matrix of Scalar.
using	algotradelib::math::Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>
	A dense column vector of Scalar.
using	algotradelib::math::SeriesView = Eigen::Ref<const Vector>
	A read-only reference to one series.
using	algotradelib::math::MutableSeriesView = Eigen::Ref<Vector>
	A writable reference to one series, such as a Vector or a column of a Matrix.
using	algotradelib::math::MatrixView = Eigen::Ref<const Matrix>
	A read-only reference to a whole matrix.
using	algotradelib::math::Index = Eigen::Index
	The signed index type of rows and columns.
using	algotradelib::math::Llt = Eigen::LLT<Matrix>
	Cholesky decomposition of a symmetric positive-definite matrix. Check info().
using	algotradelib::math::Ldlt = Eigen::LDLT<Matrix>
	Pivoting Cholesky (LDLT) decomposition of a symmetric, possibly semi-definite matrix.
using	algotradelib::math::HouseholderQr = Eigen::HouseholderQR<Matrix>
	Householder QR decomposition: the fastest QR, with no rank information.
using	algotradelib::math::ColPivQr = Eigen::ColPivHouseholderQR<Matrix>
	Column-pivoting Householder QR: a least-squares solution and a rank.
using	algotradelib::math::FullPivQr = Eigen::FullPivHouseholderQR<Matrix>
	Full-pivoting Householder QR: slower than ColPivQr, with the most reliable rank.
using	algotradelib::math::FullPivLu = Eigen::FullPivLU<Matrix>
	LU decomposition with full pivoting, for a square system with no known structure.
using	algotradelib::math::Svd = Eigen::BDCSVD<Matrix>
	Divide-and-conquer SVD: minimum-norm least-squares solutions and singular values.
using	algotradelib::math::SelfAdjointEigen = Eigen::SelfAdjointEigenSolver<Matrix>
	Eigenvalues (ascending) and eigenvectors of a symmetric matrix. Check info().

Functions
Vector	algotradelib::math::unobserved (std::size_t count)
	Makes a vector filled with missing().
Matrix	algotradelib::math::unobserved (std::size_t rows, std::size_t columns)
	Makes a matrix filled with missing().
Observed	algotradelib::math::observed_parts (SeriesView values)
	Splits a series into zero-filled values and a presence mask.
Vector	algotradelib::math::observed_or (SeriesView values, Scalar filler)
	Replaces every unobserved entry of a series.
Vector	algotradelib::math::both_present (const Vector &left, const Vector &right)
	Combines two presence masks: 1 only where both series are observed.
Svd	algotradelib::math::thin_svd (const Matrix &a)
	Computes a thin SVD, ready to solve().

Variables
constexpr unsigned int	algotradelib::math::LOWER = Eigen::Lower
	Selects the lower triangle, as in matrix.selfadjointView<math::LOWER>().
constexpr unsigned int	algotradelib::math::UPPER = Eigen::Upper
	Selects the upper triangle.
constexpr unsigned int	algotradelib::math::UNIT_LOWER = Eigen::UnitLower
	Selects the lower triangle with an implicit unit diagonal.
constexpr unsigned int	algotradelib::math::UNIT_UPPER = Eigen::UnitUpper
	Selects the upper triangle with an implicit unit diagonal.
constexpr auto	algotradelib::math::SUCCESS = Eigen::Success
	The value a decomposition's info() returns on success.

Detailed Description

The math types and decompositions, implemented with Eigen.

Include math/matrix.hpp rather than this header. Write against the math:: names (math::SeriesView, math::ColPivQr, ...) rather than the Eigen types behind them.

The decompositions are Eigen's own classes under math:: names; use their Eigen interfaces directly:

// One factorization, many right-hand sides; `b` may be a vector or a matrix.
const math::ColPivQr qr(a);
const math::Matrix coefficients = qr.solve(b);
if (qr.rank() < a.cols()) { ... }  // the columns were not independent
 
// LLT for a symmetric positive-definite system, LDLT when it is only semi-definite,
// Svd for the minimum-norm solution, HouseholderQr when pivoting is not needed.
const math::Llt chol(normal);
if (chol.info() == math::SUCCESS) { x = chol.solve(b); }

Matrix::ldlt(), Matrix::colPivHouseholderQr() and the other member forms work too, as does A.fullPivLu().solve(b) for a square system where no structure is known.

Definition in file eigen.hpp.