The numeric vocabulary: Scalar, missing(), and the matrix and vector types. More...

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

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

Functions
Vector	unobserved (std::size_t count)
	Makes a vector filled with missing().
Matrix	unobserved (std::size_t rows, std::size_t columns)
	Makes a matrix filled with missing().
Observed	observed_parts (SeriesView values)
	Splits a series into zero-filled values and a presence mask.
Vector	observed_or (SeriesView values, Scalar filler)
	Replaces every unobserved entry of a series.
Vector	both_present (const Vector &left, const Vector &right)
	Combines two presence masks: 1 only where both series are observed.
Svd	thin_svd (const Matrix &a)
	Computes a thin SVD, ready to solve().
Scalar	missing ()
	Returns the value that stands for "no observation" (a quiet NaN).
bool	observed (Scalar value)
	Tests whether a value is an observation.
Scalar	undefined ()
	Returns the value that stands for "the data was there, but the statistic does not exist".
bool	is_undefined (Scalar value)
	Tests whether a value is the undefined() marker.

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

Detailed Description

The numeric vocabulary: Scalar, missing(), and the matrix and vector types.

Typedef Documentation

◆ ColPivQr

using algotradelib::math::ColPivQr = Eigen::ColPivHouseholderQR<Matrix>

Column-pivoting Householder QR: a least-squares solution and a rank.

A good default for a regression on market data, where nearly collinear columns are common; check rank() against the number of columns.

Definition at line 176 of file eigen.hpp.

◆ FullPivLu

using algotradelib::math::FullPivLu = Eigen::FullPivLU<Matrix>

LU decomposition with full pivoting, for a square system with no known structure.

Definition at line 182 of file eigen.hpp.

◆ FullPivQr

using algotradelib::math::FullPivQr = Eigen::FullPivHouseholderQR<Matrix>

Full-pivoting Householder QR: slower than ColPivQr, with the most reliable rank.

Definition at line 179 of file eigen.hpp.

◆ HouseholderQr

using algotradelib::math::HouseholderQr = Eigen::HouseholderQR<Matrix>

Householder QR decomposition: the fastest QR, with no rank information.

Definition at line 168 of file eigen.hpp.

◆ Index

using algotradelib::math::Index = Eigen::Index

The signed index type of rows and columns.

Definition at line 65 of file eigen.hpp.

◆ Ldlt

using algotradelib::math::Ldlt = Eigen::LDLT<Matrix>

Pivoting Cholesky (LDLT) decomposition of a symmetric, possibly semi-definite matrix.

Definition at line 165 of file eigen.hpp.

◆ Llt

using algotradelib::math::Llt = Eigen::LLT<Matrix>

Cholesky decomposition of a symmetric positive-definite matrix. Check info().

Definition at line 162 of file eigen.hpp.

◆ Matrix

using algotradelib::math::Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor>

A dense, column-major matrix of Scalar.

Frames put time on the rows and one series per column, so a column binds to SeriesView without a copy.

Definition at line 45 of file eigen.hpp.

◆ MatrixView

using algotradelib::math::MatrixView = Eigen::Ref<const Matrix>

A read-only reference to a whole matrix.

Definition at line 62 of file eigen.hpp.

◆ MutableSeriesView

using algotradelib::math::MutableSeriesView = Eigen::Ref<Vector>

A writable reference to one series, such as a Vector or a column of a Matrix.

Definition at line 59 of file eigen.hpp.

◆ Scalar

using algotradelib::math::Scalar = double

The floating-point type the analytics and math layers compute in (double).

Prices, quantities and money in orders and broker data stay Decimal64; convert between the two with the functions in analytics/conversion.hpp.

Definition at line 18 of file scalar.hpp.

◆ SelfAdjointEigen

using algotradelib::math::SelfAdjointEigen = Eigen::SelfAdjointEigenSolver<Matrix>

Eigenvalues (ascending) and eigenvectors of a symmetric matrix. Check info().

Definition at line 211 of file eigen.hpp.

◆ SeriesView

using algotradelib::math::SeriesView = Eigen::Ref<const Vector>

A read-only reference to one series.

Binds without copying to a Vector or a column of a Matrix, and to an expression (which is evaluated into a temporary). Functions over one series take this type.

Definition at line 56 of file eigen.hpp.

◆ Svd

using algotradelib::math::Svd = Eigen::BDCSVD<Matrix>

Divide-and-conquer SVD: minimum-norm least-squares solutions and singular values.

Construct it with thin_svd(), which requests the thin factors solve() needs on every supported Eigen release.

Definition at line 193 of file eigen.hpp.

◆ Vector

using algotradelib::math::Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>

A dense column vector of Scalar.

Definition at line 48 of file eigen.hpp.

Function Documentation

◆ both_present()

Vector algotradelib::math::both_present	(	const Vector &	left,
		const Vector &	right )

inline

Combines two presence masks: 1 only where both series are observed.

Use it to restrict a co-moment (covariance, correlation) and both series' deviations to the same rows; otherwise a correlation can fall outside [-1, 1].

Parameters

left	The first series' Observed::present_.
right	The second series' Observed::present_, of the same length.

Returns: The elementwise product of the two masks.

Definition at line 144 of file eigen.hpp.

Referenced by both_present().

◆ is_undefined()

bool algotradelib::math::is_undefined ( Scalar value )

inline

Tests whether a value is the undefined() marker.

Parameters

value The value to test.

Returns: true only for undefined() (including a negated copy); false for missing(), any other NaN and every number.

See also: undefined() for when the marker survives.

Definition at line 69 of file scalar.hpp.

Referenced by is_undefined().

◆ missing()

Scalar algotradelib::math::missing ( )

inline

Returns the value that stands for "no observation" (a quiet NaN).

Used for an indicator's warm-up rows, a gap in a panel, or a field a broker did not report. Every reduction in the analytics layer skips it.

Returns: A quiet NaN.

Definition at line 28 of file scalar.hpp.

Referenced by missing(), unobserved(), and unobserved().

◆ observed()

bool algotradelib::math::observed ( Scalar value )

inline

Tests whether a value is an observation.

Parameters

value The value to test.

Returns: false for missing(), undefined() or any other NaN; true otherwise.

Definition at line 36 of file scalar.hpp.

Referenced by algotradelib::strategy::vanilla::adjusted_ema(), algotradelib::strategy::vanilla::exponential_line(), algotradelib::strategy::vanilla::last_two(), observed(), algotradelib::strategy::vanilla::DonchianBreakout::on_bar(), algotradelib::strategy::vanilla::RsiThreshold::on_bar(), algotradelib::strategy::vanilla::VolatilityTargetSizing::on_bar(), and algotradelib::strategy::vanilla::ZScoreReversion::on_bar().

◆ observed_or()

Vector algotradelib::math::observed_or	(	SeriesView	values,
		Scalar	filler )

inline

Replaces every unobserved entry of a series.

Parameters

values	The series; any NaN counts as unobserved.
filler	The value to put in place of each unobserved entry.

Returns: A copy of values with each NaN replaced by filler (so it has no NaN unless filler is one).

Definition at line 130 of file eigen.hpp.

Referenced by observed_or(), algotradelib::analytics::rolling_max(), and algotradelib::analytics::rolling_min().

◆ observed_parts()

Observed algotradelib::math::observed_parts ( SeriesView values )

inline

Splits a series into zero-filled values and a presence mask.

Parameters

values The series; any NaN counts as unobserved.

Returns: The two parts; see Observed.

Definition at line 113 of file eigen.hpp.

Referenced by algotradelib::analytics::bollinger(), observed_parts(), algotradelib::analytics::rolling_max(), algotradelib::analytics::rolling_mean(), algotradelib::analytics::rolling_min(), algotradelib::analytics::rolling_stdev(), algotradelib::analytics::rolling_sum(), algotradelib::analytics::wma(), and algotradelib::analytics::zscore().

◆ thin_svd()

Svd algotradelib::math::thin_svd ( const Matrix & a )

inline

Computes a thin SVD, ready to solve().

Parameters

a	The matrix to decompose.

Returns: The decomposition of a.

Definition at line 202 of file eigen.hpp.

Referenced by thin_svd().

◆ undefined()

Scalar algotradelib::math::undefined ( )

inline

Returns the value that stands for "the data was there, but the statistic does not exist".

Examples: a z-score over a window with no dispersion, a correlation against a constant, a Sortino ratio over a series that never fell below its target. It differs from missing(), which means there was no data. Both are quiet NaNs, so observed() is false for both and reductions skip both; only is_undefined() tells them apart.

Returns: A quiet NaN with a payload that is_undefined() recognizes.

Warning: Test is_undefined() on a value a function returned (or one copied from a matrix). Arithmetic on it, such as undefined() + 1.0, yields a NaN that may no longer be recognized.

Definition at line 51 of file scalar.hpp.

Referenced by algotradelib::analytics::beta(), algotradelib::analytics::max_drawdown(), algotradelib::analytics::rolling_corr(), undefined(), and algotradelib::analytics::zscore().

◆ unobserved() [1/2]

Vector algotradelib::math::unobserved ( std::size_t count )

inline

Makes a vector filled with missing().

Parameters

count The number of entries.

Returns: A vector of count unobserved values.

Definition at line 73 of file eigen.hpp.

◆ unobserved() [2/2]

Matrix algotradelib::math::unobserved	(	std::size_t	rows,
		std::size_t	columns )

inline

Makes a matrix filled with missing().

Parameters

rows	The number of rows.
columns	The number of columns.

Returns: A rows by columns matrix of unobserved values.

Definition at line 84 of file eigen.hpp.

Variable Documentation

◆ LOWER

unsigned int algotradelib::math::LOWER = Eigen::Lower

inlineconstexpr

Selects the lower triangle, as in matrix.selfadjointView<math::LOWER>().

A self-adjoint view tells a decomposition to read one triangle and assume the other.

Definition at line 153 of file eigen.hpp.

◆ SUCCESS

auto algotradelib::math::SUCCESS = Eigen::Success

inlineconstexpr

The value a decomposition's info() returns on success.

Definition at line 214 of file eigen.hpp.

◆ UNIT_LOWER

unsigned int algotradelib::math::UNIT_LOWER = Eigen::UnitLower

inlineconstexpr

Selects the lower triangle with an implicit unit diagonal.

Definition at line 157 of file eigen.hpp.

◆ UNIT_UPPER

unsigned int algotradelib::math::UNIT_UPPER = Eigen::UnitUpper

inlineconstexpr

Selects the upper triangle with an implicit unit diagonal.

Definition at line 159 of file eigen.hpp.

◆ UPPER

unsigned int algotradelib::math::UPPER = Eigen::Upper

inlineconstexpr

Selects the upper triangle.

Definition at line 155 of file eigen.hpp.

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ ColPivQr

◆ FullPivLu

◆ FullPivQr

◆ HouseholderQr

◆ Index

◆ Ldlt

◆ Llt

◆ Matrix

◆ MatrixView

◆ MutableSeriesView

◆ Scalar

◆ SelfAdjointEigen

◆ SeriesView

◆ Svd

◆ Vector

Function Documentation

◆ both_present()

◆ is_undefined()

◆ missing()

◆ observed()

◆ observed_or()

◆ observed_parts()

◆ thin_svd()

◆ undefined()

◆ unobserved() [1/2]

◆ unobserved() [2/2]

Variable Documentation

◆ LOWER

◆ SUCCESS

◆ UNIT_LOWER

◆ UNIT_UPPER

◆ UPPER