Matrix

Dynamic-size dense matrix.

Defined in Rodin/Math/Matrix.h

template <
  class ScalarType>
class Matrix;

Template parameters
ScalarType	The element type (e.g., Real, Complex)

Dynamic-size dense matrix type.

A dense matrix with both dimensions determined at runtime. The matrix is stored in column-major order (Fortran style) and supports standard linear algebra operations without additional storage. Dot products conjugate the right operand.

Public types

using Parent = Eigen::PlainObjectBase<Matrix>: Eigen storage and expression base.
using Base = Parent: Base alias used by Eigen's storage operations.
using Scalar = ScalarType: Scalar coefficient type.
using Nested = const Matrix&: Reference retained when nested in an Eigen expression.

Constructors, destructors, conversion operators

Matrix(): Constructs a matrix with Eigen's default initialization.
Matrix(const Matrix& other) defaulted: Copies the matrix and its owned coefficients.
Matrix(Matrix&& other) defaulted noexcept: Moves the matrix and its owned coefficients.
template<class T> Matrix(const T& value) explicit: Constructs a matrix from dimensions, coefficients or an Eigen object.
template<class T0, class T1> Matrix(const T0& first, const T1& second): Constructs a matrix from dimensions or two vector coefficients.
template<class Derived> Matrix(const Eigen::DenseBase<Derived>& other): Copies the coefficients of an Eigen dense expression.
template<class Derived> Matrix(const Eigen::EigenBase<Derived>& other): Evaluates an Eigen operator, such as a permutation or solve.
template<class Derived> Matrix(const Eigen::ReturnByValue<Derived>& other): Evaluates an Eigen return-by-value operation.
Matrix(const std::initializer_list<std::initializer_list<Scalar>>& rows) explicit: Constructs a matrix from coefficients grouped by row.
Matrix(Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic>&& other) noexcept: Takes ownership of a native Eigen matrix without reallocating.

Public functions

auto operator=(Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic>&& other) -> Matrix& noexcept: Exchanges owned storage with a native Eigen matrix.
auto operator=(const Matrix& other) -> Matrix&: Copies the matrix coefficients.
auto operator=(Matrix&& other) -> Matrix& defaulted noexcept: Moves the matrix coefficients.
template<class Derived> auto operator=(const Eigen::DenseBase<Derived>& other) -> Matrix&: Assigns a dense expression, resizing when necessary.
template<class Derived> auto operator=(const Eigen::EigenBase<Derived>& other) -> Matrix&: Assigns an Eigen operator, retaining the Rodin matrix return type.
template<class Derived> auto operator=(const Eigen::ReturnByValue<Derived>& other) -> Matrix&: Assigns an Eigen return-by-value operation.
void conservativeResize(Eigen::Index rows, Eigen::Index cols): Resizes while preserving the common top-left block.
void conservativeResize(Eigen::Index rows, Eigen::NoChange_t unchanged): Changes the row count while preserving existing coefficients.
void conservativeResize(Eigen::NoChange_t unchanged, Eigen::Index cols): Changes the column count while preserving existing coefficients.
template<class Derived> void conservativeResizeLike(const Eigen::DenseBase<Derived>& other): Resizes to an expression, retaining old values and copying new entries.
auto innerStride() const -> Eigen::Index constexpr noexcept: Stride between consecutive coefficients in the inner dimension.
auto outerStride() const -> Eigen::Index constexpr noexcept: Stride between consecutive columns, or rows for row-major storage.
template<class Derived> auto dot(const Eigen::MatrixBase<Derived>& other) const -> auto: Contracts with the conjugate of the right operand.

Function documentation

Matrix(const Matrix& other) defaulted

Copies the matrix and its owned coefficients.

Parameters
other	Matrix to copy.

Matrix(Matrix&& other) defaulted noexcept

Moves the matrix and its owned coefficients.

Parameters
other	Matrix to move.

template<class ScalarType> template<class T>
Matrix(const T& value) explicit

Constructs a matrix from dimensions, coefficients or an Eigen object.

Template parameters
T	Argument type understood by Eigen's matrix constructor.
Parameters
value	Dimension, coefficient, coefficient array or Eigen object.

template<class ScalarType> template<class T0, class T1>
Matrix(const T0& first, const T1& second)

Constructs a matrix from dimensions or two vector coefficients.

Template parameters
T0	First argument type.
T1	Second argument type.
Parameters
first	Row count or first coefficient of a two-component vector.
second	Column count or second coefficient of a two-component vector.

template<class ScalarType> template<class Derived>
Matrix(const Eigen::DenseBase<Derived>& other)

Copies the coefficients of an Eigen dense expression.

Template parameters
Derived	Eigen expression type.
Parameters
other	Expression to evaluate.

template<class ScalarType> template<class Derived>
Matrix(const Eigen::EigenBase<Derived>& other)

Evaluates an Eigen operator, such as a permutation or solve.

Template parameters
Derived	Eigen operator type.
Parameters
other	Operator to evaluate.

template<class ScalarType> template<class Derived>
Matrix(const Eigen::ReturnByValue<Derived>& other)

Evaluates an Eigen return-by-value operation.

Template parameters
Derived	Eigen operation type.
Parameters
other	Operation to evaluate.

Matrix(const std::initializer_list<std::initializer_list<Scalar>>& rows) explicit

Constructs a matrix from coefficients grouped by row.

Parameters
rows	Coefficient rows.

Matrix(Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic>&& other) noexcept

Takes ownership of a native Eigen matrix without reallocating.

Parameters
other	Native matrix to move.

Matrix& operator=(Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic>&& other) noexcept

Exchanges owned storage with a native Eigen matrix.

Parameters
other	Native matrix to move.
Returns	This matrix.

Matrix& operator=(const Matrix& other)

Copies the matrix coefficients.

Parameters
other	Matrix to copy.
Returns	This matrix.

Matrix& operator=(Matrix&& other) defaulted noexcept

Moves the matrix coefficients.

Parameters
other	Matrix to move.
Returns	This matrix.

template<class ScalarType> template<class Derived>
Matrix& operator=(const Eigen::DenseBase<Derived>& other)

Assigns a dense expression, resizing when necessary.

Template parameters
Derived	Eigen expression type.
Parameters
other	Expression to evaluate.
Returns	This matrix.

template<class ScalarType> template<class Derived>
Matrix& operator=(const Eigen::EigenBase<Derived>& other)

Assigns an Eigen operator, retaining the Rodin matrix return type.

Template parameters
Derived	Eigen operator type.
Parameters
other	Operator to evaluate.
Returns	This matrix.

template<class ScalarType> template<class Derived>
Matrix& operator=(const Eigen::ReturnByValue<Derived>& other)

Assigns an Eigen return-by-value operation.

Template parameters
Derived	Eigen operation type.
Parameters
other	Operation to evaluate.
Returns	This matrix.

void conservativeResize(Eigen::Index rows, Eigen::Index cols)

Resizes while preserving the common top-left block.

Parameters
rows	New row count.
cols	New column count.

void conservativeResize(Eigen::Index rows, Eigen::NoChange_t unchanged)

Changes the row count while preserving existing coefficients.

Parameters
rows	New row count.
unchanged	Retains the column count.

void conservativeResize(Eigen::NoChange_t unchanged, Eigen::Index cols)

Changes the column count while preserving existing coefficients.

Parameters
unchanged	Retains the row count.
cols	New column count.

template<class ScalarType> template<class Derived>
void conservativeResizeLike(const Eigen::DenseBase<Derived>& other)

Resizes to an expression, retaining old values and copying new entries.

Template parameters
Derived	Eigen dense expression type.
Parameters
other	Expression supplying the new shape and appended coefficients.

Eigen::Index innerStride() const constexpr noexcept

Stride between consecutive coefficients in the inner dimension.

Returns	One, since inner coefficients are contiguous.

Eigen::Index outerStride() const constexpr noexcept

Stride between consecutive columns, or rows for row-major storage.

Returns	The number of coefficients in the inner dimension.

template<class ScalarType> template<class Derived>
auto dot(const Eigen::MatrixBase<Derived>& other) const

Contracts with the conjugate of the right operand.

Template parameters
Derived	Eigen type of the right operand.
Parameters
other	Matrix of the same shape.
Returns	The right-conjugating inner product.

Computes , consistently with dot. Eigen expressions and views retain their Eigen types; use dot to contract those with this convention.