Dense m × n matrix over a CECCO::ComponentType. More...

#include <matrices.hpp>

Inheritance diagram for CECCO::Matrix< T >:

Public Member Functions
template<FiniteFieldType S>
constexpr Matrix< T > &	operator= (const Matrix< S > &other)
template<typename U> requires std::convertible_to<std::decay_t<U>, T>
Matrix< T > &	set_component (size_t i, size_t j, U &&c)
Constructors
constexpr	Matrix () noexcept=default
	Default constructor: empty matrix.
constexpr	Matrix (size_t m, size_t n)
	m × n zero matrix (tag details::Zero)
	Matrix (size_t m, size_t n, const T &l)
	m × n matrix with every component equal to l
constexpr	Matrix (size_t m, size_t n, std::initializer_list< T > l)
	m × n matrix from a flat initializer list (row-major)
	Matrix (std::initializer_list< std::initializer_list< T > > l)
	From nested initializer lists, e.g. {{1, 2, 3}, {4, 5, 6}}.
	Matrix (const Vector< T > &v)
	1 × n row matrix from a Vector<T>
constexpr	Matrix (const Matrix &other)
constexpr	Matrix (Matrix &&other) noexcept
template<FiniteFieldType S> requires FiniteFieldType<T> && (T::get_characteristic() == S::get_characteristic())
constexpr	Matrix (const Matrix< S > &other)
	Cross-field conversion between two finite fields of the same characteristic.
	Matrix (const std::string &filename)
	Read from a PPM (P3) image file using the 64-entry colormap of export_as_ppm.
Assignment Operators
constexpr Matrix &	operator= (const Matrix &rhs)
constexpr Matrix &	operator= (Matrix &&rhs) noexcept
template<FiniteFieldType S>
constexpr Matrix &	operator= (const Matrix< S > &other)
	Cross-field assignment (same semantics as the cross-field constructor).
Unary Arithmetic Operations
constexpr Matrix	operator+ () const &
	Unary + (lvalue): returns a copy.
constexpr Matrix	operator+ () &&noexcept
	Unary + (rvalue): returns the rvalue itself.
constexpr Matrix	operator- () const &
	Unary − (lvalue): returns a new matrix with each component negated.
constexpr Matrix	operator- () &&
	Unary − (rvalue): negates components in place.
Compound Assignment Operations
Matrix &	operator+= (const Matrix &rhs)
	Component-wise addition this(i, j) += rhs(i, j).
Matrix &	operator-= (const Matrix &rhs)
	Component-wise subtraction this(i, j) -= rhs(i, j).
Matrix &	operator*= (const Matrix &rhs)
	Matrix multiplication this = this · rhs.
constexpr Matrix &	operator*= (const T &s)
	Multiply every component by the scalar s.
Matrix &	operator/= (const T &s)
	Divide every component by the scalar s.
Randomization
Matrix &	randomize ()
	Fill matrix with random values.
Information and Properties
constexpr size_t	get_m () const noexcept
	Get the number of rows.
constexpr size_t	get_n () const noexcept
	Get the number of columns.
constexpr bool	is_empty () const noexcept
	Check if matrix is empty.
constexpr bool	is_zero ()
	Check if the matrix is zero, caching the result via the type tag.
constexpr bool	is_zero () const
	Check if the matrix is zero (no caching).
size_t	wH () const
	Hamming weight: number of non-zero, non-erased components; cached on first call.
size_t	rank () const
	Matrix rank, computed once and cached.
bool	is_invertible () const
	Check if matrix is invertible.
Vector< T >	diagonal () const
	Main diagonal as a vector.
template<CoefficientType U = T>
Polynomial< U >	characteristic_polynomial () const
	Characteristic polynomial det(λI − A).
Matrix< T >	basis_of_nullspace () const
	Basis of the nullspace (right kernel).
Matrix< T >	basis_of_kernel () const
	Alias for basis_of_nullspace.
T	determinant () const
	Matrix determinant.
std::vector< T >	eigenvalues () const
	Eigenvalues lying in the underlying finite field.
std::vector< Vector< T > >	rowspace () const
	Enumerate every vector in the row space.
std::vector< Vector< T > >	span () const
	Alias for rowspace.
Component Access and Manipulation
template<typename U> requires std::convertible_to<std::decay_t<U>, T>
Matrix &	set_component (size_t i, size_t j, U &&c)
	Set component (i, j) by perfect forwarding.
const T &	operator() (size_t i, size_t j) const
	Access component (i, j) (read-only).
Vector< T >	get_row (size_t i) const
	Extract row i as a vector.
Vector< T >	get_col (size_t j) const
	Extract column j as a (row) vector.
Matrix< T >	get_submatrix (size_t i, size_t j, size_t h, size_t w) const
	Extract submatrix from region [i, i+h) × [j, j+w).
Matrix< T > &	set_submatrix (size_t i, size_t j, const Matrix &N)
	Overwrite the region starting at (i, j) with N.
Matrix< T > &	horizontal_join (const Matrix &other)
	Concatenate other to the right (column-wise).
Matrix< T > &	vertical_join (const Matrix &other)
	Concatenate other below (row-wise).
Matrix< T > &	diagonal_join (const Matrix &other)
	Block-diagonal join: this in the upper-left, other in the lower-right.
Matrix< T > &	Kronecker_product (const Matrix &other)
	Kronecker (tensor) product with other.
Matrix< T > &	swap_rows (size_t i, size_t j)
	Swap rows i and j.
Matrix< T > &	swap_columns (size_t i, size_t j)
	Swap columns i and j.
Matrix< T > &	scale_row (const T &s, size_t i)
	row[i] ← s · row[i]
Matrix< T > &	scale_column (const T &s, size_t i)
	col[i] ← s · col[i]
Matrix< T > &	add_scaled_row (const T &s, size_t i, size_t j)
	row[j] ← row[j] + s · row[i]
Matrix< T > &	add_scaled_column (const T &s, size_t i, size_t j)
	col[j] ← col[j] + s · col[i]
Matrix< T > &	add_row (size_t i, size_t j)
	row[j] ← row[j] + row[i]
Matrix< T > &	add_column (size_t i, size_t j)
	col[j] ← col[j] + col[i]
Matrix< T > &	delete_columns (const std::vector< size_t > &v)
	Delete the columns whose indices appear in v.
Matrix< T > &	delete_column (size_t i)
	Delete column i (single-index convenience for delete_columns).
Matrix< T > &	delete_rows (const std::vector< size_t > &v)
	Delete the rows whose indices appear in v.
Matrix< T > &	delete_row (size_t i)
	Delete row i (single-index convenience for delete_rows).
Matrix< T > &	erase_component (size_t i, size_t j)
	Flag component (i, j) as erased.
Matrix< T > &	unerase_component (size_t i, size_t j)
	Clear the erasure flag on component (i, j).
Matrix< T > &	erase_columns (const std::vector< size_t > &v)
	Flag every component of the specified columns as erased.
Matrix< T > &	erase_column (size_t i)
	Erase column i (single-index convenience for erase_columns).
Matrix< T > &	unerase_columns (const std::vector< size_t > &v)
	Clear erasure flags on every component of the specified columns.
Matrix< T > &	unerase_column (size_t i)
	Un-erase column i (single-index convenience for unerase_columns).
Matrix &	erase_rows (const std::vector< size_t > &v)
	Flag every component of the specified rows as erased.
Matrix &	erase_row (size_t i)
	Erase row i (single-index convenience for erase_rows).
Matrix &	unerase_rows (const std::vector< size_t > &v)
	Clear erasure flags on every component of the specified rows.
Matrix &	unerase_row (size_t i)
	Un-erase row i (single-index convenience for unerase_rows).
Transformations
Matrix< T > &	reverse_rows ()
	Reverse the row order.
Matrix< T > &	reverse_columns ()
	Reverse the column order.
constexpr Matrix< T > &	fill (const T &l)
	Set every component to l.
constexpr Matrix< T > &	transpose ()
	Transpose in place.
Matrix< T > &	ref (size_t *rank_ptr=nullptr)
	Row echelon form (REF), with a binary-field fast path.
Matrix< T > &	rref (size_t *rank_ptr=nullptr)
	Reduced row echelon form (RREF).
Matrix< T > &	invert ()
	Invert in place.
Finite Field Specific Operations
template<FiniteFieldType S> requires FiniteFieldType<T> && ExtensionOf<T, S> && (!std::is_same_v<T, S>)
constexpr Vector< S >	as_vector () const
	Reinterpret the columns as elements of a superfield.
Vector< T >	to_vector () const
	Flatten in row-major order.
void	export_as_ppm (const std::string &filename) const
	Export the matrix as a PPM (P3) image.

Friends
template<ComponentType>
class	Matrix
class	Vector< T >
constexpr Matrix< T >	IdentityMatrix (size_t m)
	m × m identity matrix I_m
constexpr Matrix< T >	DiagonalMatrix (const Vector< T > &v)
	Diagonal matrix with diagonal v (strongest tag of details::Zero, details::Identity, details::Diagonal).
constexpr Matrix< T >	ToeplitzMatrix (const Vector< T > &v, size_t m, size_t n)
	m × n Toeplitz matrix from its diagonal entries
template<ReliablyComparableType U>
constexpr Matrix< U >	VandermondeMatrix (const Vector< U > &v, size_t m)
template<ReliablyComparableType U>
constexpr bool	operator== (const Matrix< U > &lhs, const Matrix< U > &rhs)
std::ostream &	operator<< (std::ostream &os, const Matrix &rhs)
	Pretty-print the matrix with column alignment and bracket borders.

Detailed Description

template<ComponentType T>
class CECCO::Matrix< T >

Dense m × n matrix over a CECCO::ComponentType.

Template Parameters

T	Component type satisfying CECCO::ComponentType (finite field, double, std::complex<double>, or signed integer including InfInt)

Components are stored row-major in a contiguous buffer. A structural tag (details::matrix_type_t) tracks Zero / Identity / Diagonal / Vandermonde / Toeplitz structures and dispatches to specialised fast paths; mutating operations that break a tracked structure demote the tag to Generic. Structure is re-detected after additive and multiplicative composition, but not after component-level mutations. Dimension mismatches in arithmetic throw std::invalid_argument.

Methods that need division (REF/RREF, inversion, nullspace, determinant, characteristic polynomial, …) are gated by requires FieldType<T>; eigenvalue computation by requires FiniteFieldType<T>. Methods that compare against zero (Hamming weight, rank, structural tests, …) are gated by requires ReliablyComparableType<T>.

Cross-field constructors and assignment operators between two finite fields of the same characteristic route through CECCO::details::largest_common_subfield_t, so matrices over fields from disjoint construction towers can interoperate.

Usage_Example

using F4 = Ext<Fp<2>, MOD{1, 1, 1}>;
Matrix<F4> M = {{1, 0}, {1, 1}};
size_t r = M.rank();                          // cached
auto null_basis = M.basis_of_nullspace();
auto chi = M.characteristic_polynomial();

Definition at line 175 of file matrices.hpp.

Constructor & Destructor Documentation

◆ Matrix() [1/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix ( )

constexprdefaultnoexcept

Default constructor: empty matrix.

◆ Matrix() [2/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix	(	size_t	m,
		size_t	n )

inlineconstexpr

m × n zero matrix (tag details::Zero)

Definition at line 197 of file matrices.hpp.

◆ Matrix() [3/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix	(	size_t	m,
		size_t	n,
		const T &	l )

m × n matrix with every component equal to l

Type tag is determined based on m, n, and l.

Definition at line 1296 of file matrices.hpp.

◆ Matrix() [4/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix	(	size_t	m,
		size_t	n,
		std::initializer_list< T >	l )

constexpr

m × n matrix from a flat initializer list (row-major)

Exceptions

std::invalid_argument if l.size() != m * n

Definition at line 1301 of file matrices.hpp.

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◆ Matrix() [5/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix ( std::initializer_list< std::initializer_list< T > > l )

From nested initializer lists, e.g. {{1, 2, 3}, {4, 5, 6}}.

Rows of unequal length are zero-padded to the longest row.

Definition at line 1311 of file matrices.hpp.

◆ Matrix() [6/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix ( const Vector< T > & v )

1 × n row matrix from a Vector<T>

Definition at line 1329 of file matrices.hpp.

◆ Matrix() [7/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix ( const Matrix< T > & other )

inlineconstexpr

Definition at line 223 of file matrices.hpp.

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◆ Matrix() [8/10]

template<ComponentType T>

CECCO::Matrix< T >::Matrix ( Matrix< T > && other )

inlineconstexprnoexcept

Definition at line 231 of file matrices.hpp.

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◆ Matrix() [9/10]

template<ComponentType T>
requires FiniteFieldType<T> && (T::get_characteristic() == S::get_characteristic())

template<FiniteFieldType S>
requires FiniteFieldType<T> && (T::get_characteristic() == S::get_characteristic())

CECCO::Matrix< T >::Matrix ( const Matrix< S > & other )

constexpr

Cross-field conversion between two finite fields of the same characteristic.

Template Parameters

S	Source field type (Matrix<S>); must share characteristic with T

Converts component by component via T's cross-field constructor, which routes through CECCO::details::largest_common_subfield_t and so handles disjoint construction towers. Propagates std::invalid_argument if any component is not representable in T.

Definition at line 1357 of file matrices.hpp.

◆ Matrix() [10/10]

template<ComponentType T>
requires FiniteFieldType<T> && (T::get_size() <= 64)

CECCO::Matrix< T >::Matrix ( const std::string & filename )

Read from a PPM (P3) image file using the 64-entry colormap of export_as_ppm.

Pixels whose RGB does not match any colormap entry are erased (under CECCO_ERASURE_SUPPORT) or replaced by a random field element.

Note: Convert other formats with ImageMagick:
magick input.png -alpha remove -background black +dither -remap palette.ppm -compress none output.ppm

Definition at line 1370 of file matrices.hpp.

Member Function Documentation

◆ add_column()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::add_column	(	size_t	i,
		size_t	j )

inline

col[j] ← col[j] + col[i]

Parameters

i	Source column index
j	Destination column index

Returns: Reference to this matrix after the update

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 750 of file matrices.hpp.

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◆ add_row()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::add_row	(	size_t	i,
		size_t	j )

inline

row[j] ← row[j] + row[i]

Parameters

i	Source row index
j	Destination row index

Returns: Reference to this matrix after the update

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 735 of file matrices.hpp.

◆ add_scaled_column()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::add_scaled_column	(	const T &	s,
		size_t	i,
		size_t	j )

col[j] ← col[j] + s · col[i]

Parameters

s	Scalar multiplier on the source column
i	Source column index
j	Destination column index

Returns: Reference to this matrix after the update

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 2425 of file matrices.hpp.

◆ add_scaled_row()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::add_scaled_row	(	const T &	s,
		size_t	i,
		size_t	j )

row[j] ← row[j] + s · row[i]

Parameters

s	Scalar multiplier on the source row
i	Source row index
j	Destination row index

Returns: Reference to this matrix after the update

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 2391 of file matrices.hpp.

◆ as_vector()

template<ComponentType T>
requires FiniteFieldType<T> && ExtensionOf<T, S> && (!std::is_same_v<T, S>)

template<FiniteFieldType S>
requires FiniteFieldType<T> && ExtensionOf<T, S> && (!std::is_same_v<T, S>)

Vector< S > CECCO::Matrix< T >::as_vector ( ) const

constexpr

Reinterpret the columns as elements of a superfield.

Template Parameters

S	Superfield of T (same construction tower)

Returns: Vector over S, one component per column

Each column is read as the coordinate representation of an element of S over T.

Definition at line 2891 of file matrices.hpp.

◆ basis_of_kernel()

template<ComponentType T>

Matrix< T > CECCO::Matrix< T >::basis_of_kernel ( ) const

inline

Alias for basis_of_nullspace.

Returns: Matrix whose rows form a basis of the kernel

Definition at line 490 of file matrices.hpp.

◆ basis_of_nullspace()

template<ComponentType T>
requires FieldType<T>

Matrix< T > CECCO::Matrix< T >::basis_of_nullspace ( ) const

Basis of the nullspace (right kernel).

Returns: Matrix whose rows span { x : A xᵀ = 0 }; empty matrix if the nullspace is trivial

Computed by row reduction.

Definition at line 1866 of file matrices.hpp.

◆ characteristic_polynomial()

template<ComponentType T>

template<CoefficientType U>

Polynomial< U > CECCO::Matrix< T >::characteristic_polynomial ( ) const

Characteristic polynomial det(λI − A).

Returns: Polynomial of degree m

Computed via the Samuelson–Berkowitz algorithm in the general case; the details::Diagonal and details::Vandermonde tags trigger closed-form shortcuts.

Note: Member template with U fixed to T, so that instantiating a matrix over polynomial components does not form the unsupported type Polynomial<Polynomial<...>>.

Exceptions

std::invalid_argument if the matrix is not square or is empty

Definition at line 1799 of file matrices.hpp.

◆ delete_column()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::delete_column ( size_t i )

inline

Delete column i (single-index convenience for delete_columns).

Parameters

i	Column index

Returns: Reference to this matrix after deletion

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 777 of file matrices.hpp.

◆ delete_columns()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::delete_columns ( const std::vector< size_t > & v )

Delete the columns whose indices appear in v.

Parameters

v	Column indices (deduplicated internally)

Returns: Reference to this matrix after deletion

Exceptions

std::invalid_argument if any index in v is out of bounds

Definition at line 2437 of file matrices.hpp.

◆ delete_row()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::delete_row ( size_t i )

inline

Delete row i (single-index convenience for delete_rows).

Parameters

i Row index

Returns: Reference to this matrix after deletion

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 797 of file matrices.hpp.

◆ delete_rows()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::delete_rows ( const std::vector< size_t > & v )

Delete the rows whose indices appear in v.

Parameters

v	Row indices (deduplicated internally)

Returns: Reference to this matrix after deletion

Exceptions

std::invalid_argument if any index in v is out of bounds

Definition at line 2485 of file matrices.hpp.

◆ determinant()

template<ComponentType T>
requires FieldType<T>

T CECCO::Matrix< T >::determinant ( ) const

Matrix determinant.

Returns: det(A); T(0) for singular matrices

Algorithm depends on the type tag: closed-form for details::Identity, details::Zero, and details::Diagonal; Samuelson–Berkowitz otherwise.

Exceptions

std::invalid_argument if the matrix is not square or is empty

Definition at line 1924 of file matrices.hpp.

◆ diagonal()

template<ComponentType T>

Vector< T > CECCO::Matrix< T >::diagonal ( ) const

Main diagonal as a vector.

Returns: Vector containing entries (i, i) for i = 0, …, m−1

Exceptions

std::invalid_argument if the matrix is not square

Definition at line 1788 of file matrices.hpp.

◆ diagonal_join()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::diagonal_join ( const Matrix< T > & other )

Block-diagonal join: this in the upper-left, other in the lower-right.

Parameters

other Matrix placed in the lower-right block

Returns: Reference to this matrix after the join

Off-diagonal blocks are filled with zeros.

Definition at line 2222 of file matrices.hpp.

◆ eigenvalues()

template<ComponentType T>
requires FiniteFieldType<T>

std::vector< T > CECCO::Matrix< T >::eigenvalues ( ) const

Eigenvalues lying in the underlying finite field.

Returns: Roots of the characteristic polynomial that lie in T

Eigenvalues that exist only in an extension of T are omitted.

Exceptions

std::invalid_argument if the matrix is not square

Definition at line 1956 of file matrices.hpp.

◆ erase_column()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::erase_column ( size_t i )

inline

Erase column i (single-index convenience for erase_columns).

Parameters

i	Column index

Returns: Reference to this matrix after erasing

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 852 of file matrices.hpp.

◆ erase_columns()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::erase_columns ( const std::vector< size_t > & v )

Flag every component of the specified columns as erased.

Parameters

v	Column indices (deduplicated internally)

Returns: Reference to this matrix after erasing

Warning: See erase_component for the semantics and caller obligations.

Exceptions

std::invalid_argument if any index in v is out of bounds

Definition at line 2549 of file matrices.hpp.

◆ erase_component()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::erase_component	(	size_t	i,
		size_t	j )

Flag component (i, j) as erased.

Parameters

i	Row index
j	Column index

Returns: Reference to this matrix after erasing

Marks the component as erased; field arithmetic on erased elements is undefined, see CECCO_ERASURE_SUPPORT and the erase()/unerase() interface in fields.hpp.

Warning: An erased element can no longer participate in field operations or property queries. Correct handling of erased elements is the caller's responsibility.

Exceptions

std::invalid_argument if (i, j) is out of bounds

Definition at line 2517 of file matrices.hpp.

◆ erase_row()

template<ComponentType T>

Matrix & CECCO::Matrix< T >::erase_row ( size_t i )

inline

Erase row i (single-index convenience for erase_rows).

Parameters

i Row index

Returns: Reference to this matrix after erasing

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 904 of file matrices.hpp.

◆ erase_rows()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::erase_rows ( const std::vector< size_t > & v )

Flag every component of the specified rows as erased.

Parameters

v	Row indices (deduplicated internally)

Returns: Reference to this matrix after erasing

Warning: See erase_component for the semantics and caller obligations.

Exceptions

std::invalid_argument if any index in v is out of bounds

Definition at line 2569 of file matrices.hpp.

◆ export_as_ppm()

template<ComponentType T>
requires FiniteFieldType<T> && (T::get_size() <= 64)

void CECCO::Matrix< T >::export_as_ppm ( const std::string & filename ) const

Export the matrix as a PPM (P3) image.

Parameters

filename Output path

Each component is mapped through a built-in 64-entry colormap (black → blue → green → yellow → white). The image is n wide and m tall.

Note: With CECCO_ERASURE_SUPPORT, erased components render in red.

Definition at line 2918 of file matrices.hpp.

◆ fill()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::fill ( const T & l )

constexpr

Set every component to l.

Parameters

l	Value assigned to every component

Returns: Reference to this matrix after filling

Type tag is determined based on m, n, and l.

Definition at line 2658 of file matrices.hpp.

◆ get_col()

template<ComponentType T>

Vector< T > CECCO::Matrix< T >::get_col ( size_t j ) const

Extract column j as a (row) vector.

Parameters

j	Column index

Returns: Vector containing the components of column j; transposed, since Vector models row vectors

Exceptions

std::invalid_argument if j is out of bounds

Definition at line 2090 of file matrices.hpp.

◆ get_m()

template<ComponentType T>

size_t CECCO::Matrix< T >::get_m ( ) const

inlineconstexprnoexcept

Get the number of rows.

Returns: Number of rows in the matrix

Definition at line 377 of file matrices.hpp.

◆ get_n()

template<ComponentType T>

size_t CECCO::Matrix< T >::get_n ( ) const

inlineconstexprnoexcept

Get the number of columns.

Returns: Number of columns in the matrix

Definition at line 384 of file matrices.hpp.

◆ get_row()

template<ComponentType T>

Vector< T > CECCO::Matrix< T >::get_row ( size_t i ) const

Extract row i as a vector.

Parameters

i Row index

Returns: Vector containing the components of row i

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 2077 of file matrices.hpp.

◆ get_submatrix()

template<ComponentType T>

Matrix< T > CECCO::Matrix< T >::get_submatrix	(	size_t	i,
		size_t	j,
		size_t	h,
		size_t	w ) const

Extract submatrix from region [i, i+h) × [j, j+w).

Parameters

i	Starting row index
j	Starting column index
h	Height (number of rows)
w	Width (number of columns)

Returns: Submatrix of shape h × w

Exceptions

std::invalid_argument if the region extends beyond the matrix

Definition at line 2103 of file matrices.hpp.

◆ horizontal_join()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::horizontal_join ( const Matrix< T > & other )

Concatenate other to the right (column-wise).

Parameters

other Matrix to append on the right; must have the same number of rows as this

Returns: Reference to this matrix after the join

Exceptions

std::invalid_argument if row counts differ

Definition at line 2164 of file matrices.hpp.

◆ invert()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::invert ( )

Invert in place.

Returns: Reference to this matrix after inversion

Gaussian elimination with partial pivoting. Requires a square non-singular matrix.

Note: Square Vandermonde matrices are inverted in O(m²) by Lagrange interpolation through a shared master polynomial rather than by elimination; the inverse is a general matrix.

Exceptions

std::invalid_argument if the matrix is not square or is singular

Definition at line 2842 of file matrices.hpp.

◆ is_empty()

template<ComponentType T>

bool CECCO::Matrix< T >::is_empty ( ) const

inlineconstexprnoexcept

Check if matrix is empty.

Returns: true if matrix has zero rows or columns, false otherwise

Definition at line 391 of file matrices.hpp.

◆ is_invertible()

template<ComponentType T>

bool CECCO::Matrix< T >::is_invertible ( ) const

inline

Check if matrix is invertible.

Returns: true iff the matrix is square and has full rank

Definition at line 443 of file matrices.hpp.

◆ is_zero() [1/2]

template<ComponentType T>

bool CECCO::Matrix< T >::is_zero ( )

inlineconstexpr

Check if the matrix is zero, caching the result via the type tag.

Returns: true iff every component equals T(0)

On a positive result the tag is updated to details::Zero, so subsequent calls and other tag-aware fast paths short-circuit.

Definition at line 401 of file matrices.hpp.

◆ is_zero() [2/2]

template<ComponentType T>

bool CECCO::Matrix< T >::is_zero ( ) const

inlineconstexpr

Check if the matrix is zero (no caching).

Returns: true iff every component equals T(0)

Definition at line 414 of file matrices.hpp.

◆ Kronecker_product()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::Kronecker_product ( const Matrix< T > & other )

Kronecker (tensor) product with other.

Parameters

other Right operand

Returns: Reference to this matrix after the product

If this is m × n and other is p × q, the result is mp × nq.

Definition at line 2254 of file matrices.hpp.

◆ operator()()

template<ComponentType T>

const T & CECCO::Matrix< T >::operator()	(	size_t	i,
		size_t	j ) const

Access component (i, j) (read-only).

Parameters

i	Row index (0-based)
j	Column index (0-based)

Returns: Const reference to the component at (i, j)

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 2070 of file matrices.hpp.

◆ operator*=() [1/2]

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::operator*= ( const Matrix< T > & rhs )

Matrix multiplication *this = *this · rhs.

Exceptions

std::invalid_argument if this->get_n() != rhs.get_m()

Definition at line 1623 of file matrices.hpp.

◆ operator*=() [2/2]

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::operator*= ( const T & s )

constexpr

Multiply every component by the scalar s.

Definition at line 1704 of file matrices.hpp.

◆ operator+() [1/2]

template<ComponentType T>

Matrix CECCO::Matrix< T >::operator+ ( ) &&

inlineconstexprnoexcept

Unary + (rvalue): returns the rvalue itself.

Definition at line 295 of file matrices.hpp.

◆ operator+() [2/2]

template<ComponentType T>

Matrix CECCO::Matrix< T >::operator+ ( ) const &

inlineconstexpr

Unary + (lvalue): returns a copy.

Definition at line 293 of file matrices.hpp.

◆ operator+=()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::operator+= ( const Matrix< T > & rhs )

Component-wise addition this(i, j) += rhs(i, j).

Exceptions

std::invalid_argument if dimensions differ

Definition at line 1520 of file matrices.hpp.

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◆ operator-() [1/2]

template<ComponentType T>

Matrix< T > CECCO::Matrix< T >::operator- ( ) &&

constexpr

Unary − (rvalue): negates components in place.

Definition at line 1501 of file matrices.hpp.

◆ operator-() [2/2]

template<ComponentType T>

Matrix< T > CECCO::Matrix< T >::operator- ( ) const &

constexpr

Unary − (lvalue): returns a new matrix with each component negated.

Definition at line 1482 of file matrices.hpp.

◆ operator-=()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::operator-= ( const Matrix< T > & rhs )

Component-wise subtraction this(i, j) -= rhs(i, j).

Exceptions

std::invalid_argument if dimensions differ

Definition at line 1570 of file matrices.hpp.

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◆ operator/=()

template<ComponentType T>
requires CoefficientType<T>

Matrix< T > & CECCO::Matrix< T >::operator/= ( const T & s )

Divide every component by the scalar s.

Exceptions

std::invalid_argument if s == T(0)

Note: Round-trip (M / s) * s == M is only guaranteed when T satisfies CECCO::FieldType (otherwise integer rounding may corrupt components).

Definition at line 1720 of file matrices.hpp.

◆ operator=() [1/4]

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::operator= ( const Matrix< T > & rhs )

constexpr

Definition at line 1439 of file matrices.hpp.

◆ operator=() [2/4]

template<ComponentType T>

template<FiniteFieldType S>

Matrix< T > & CECCO::Matrix< T >::operator= ( const Matrix< S > & other )

constexpr

Definition at line 1470 of file matrices.hpp.

◆ operator=() [3/4]

template<ComponentType T>

template<FiniteFieldType S>

Matrix & CECCO::Matrix< T >::operator= ( const Matrix< S > & other )

constexpr

Cross-field assignment (same semantics as the cross-field constructor).

◆ operator=() [4/4]

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::operator= ( Matrix< T > && rhs )

constexprnoexcept

Definition at line 1451 of file matrices.hpp.

◆ randomize()

template<ComponentType T>
requires CoefficientType<T>

Matrix< T > & CECCO::Matrix< T >::randomize ( )

Fill matrix with random values.

Returns: Reference to this matrix after randomization

Distribution depends on the component type: finite-field types draw uniformly from the field; signed integers from [−100, 100]; double and the real/imaginary parts of std::complex<double> from [−1.0, 1.0].

Note: The type tag is re-detected afterwards, so incidental structure (e.g. an all-zero draw over a small field) is recognized.; Unavailable for polynomial components: randomizing a polynomial needs a degree, see CECCO::Polynomial::randomize.

Definition at line 1741 of file matrices.hpp.

◆ rank()

template<ComponentType T>
requires FieldType<T>

size_t CECCO::Matrix< T >::rank ( ) const

Matrix rank, computed once and cached.

Returns: Dimension of the row space (equivalently, of the column space)

Uses row reduction to echelon form. Subsequent calls return the cached value until a mutating operation invalidates it.

Definition at line 1781 of file matrices.hpp.

◆ ref()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::ref ( size_t * rank_ptr = nullptr )

Row echelon form (REF), with a binary-field fast path.

Parameters

rank_ptr Optional out-parameter; if non-null, receives the rank

Returns: Reference to this matrix after the reduction

Forward Gaussian elimination only, cheaper than RREF when only the rank or a triangularised form is needed. For Fp<2>, pivot scaling is skipped at compile time. Rank is cached when rank_ptr is non-null.

Definition at line 2705 of file matrices.hpp.

◆ reverse_columns()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::reverse_columns ( )

Reverse the column order.

Returns: Reference to this matrix after the reversal

Definition at line 2642 of file matrices.hpp.

◆ reverse_rows()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::reverse_rows ( )

Reverse the row order.

Returns: Reference to this matrix after the reversal

Definition at line 2627 of file matrices.hpp.

◆ rowspace()

template<ComponentType T>
requires FiniteFieldType<T>

std::vector< Vector< T > > CECCO::Matrix< T >::rowspace ( ) const

Enumerate every vector in the row space.

Returns: All q^rank vectors in span(rows), where q = |T|

Warning: Size grows as q^rank, only practical for small fields and small rank.

Definition at line 1970 of file matrices.hpp.

◆ rref()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::rref ( size_t * rank_ptr = nullptr )

Reduced row echelon form (RREF).

Parameters

rank_ptr Optional out-parameter; if non-null, receives the rank

Returns: Reference to this matrix after the reduction

Two phases: forward elimination (REF) followed by backward elimination. Rank is always cached.

Definition at line 2758 of file matrices.hpp.

◆ scale_column()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::scale_column	(	const T &	s,
		size_t	i )

col[i] ← s · col[i]

Parameters

s	Scalar multiplier
i	Column index

Returns: Reference to this matrix after the scaling

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 2381 of file matrices.hpp.

◆ scale_row()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::scale_row	(	const T &	s,
		size_t	i )

row[i] ← s · row[i]

Parameters

s	Scalar multiplier
i	Row index

Returns: Reference to this matrix after the scaling

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 2346 of file matrices.hpp.

◆ set_component() [1/2]

template<ComponentType T>

template<typename U>
requires std::convertible_to<std::decay_t<U>, T>

Matrix< T > & CECCO::Matrix< T >::set_component	(	size_t	i,
		size_t	j,
		U &&	c )

Definition at line 2004 of file matrices.hpp.

◆ set_component() [2/2]

template<ComponentType T>

template<typename U>
requires std::convertible_to<std::decay_t<U>, T>

Matrix & CECCO::Matrix< T >::set_component	(	size_t	i,
		size_t	j,
		U &&	c )

Set component (i, j) by perfect forwarding.

Parameters

i	Row index (0-based)
j	Column index (0-based)
c	Value to assign; bound by lvalue or rvalue reference

Returns: Reference to this matrix after modification

Exceptions

std::invalid_argument if either index is out of bounds

◆ set_submatrix()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::set_submatrix	(	size_t	i,
		size_t	j,
		const Matrix< T > &	N )

Overwrite the region starting at (i, j) with N.

Parameters

i	Starting row index
j	Starting column index
N	Source matrix; its shape must fit within this matrix from (i, j)

Returns: Reference to this matrix after the assignment

Exceptions

std::invalid_argument if the region would extend beyond bounds

Definition at line 2143 of file matrices.hpp.

◆ span()

template<ComponentType T>

std::vector< Vector< T > > CECCO::Matrix< T >::span ( ) const

inline

Alias for rowspace.

Returns: Every vector in the span of the rows

Definition at line 536 of file matrices.hpp.

◆ swap_columns()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::swap_columns	(	size_t	i,
		size_t	j )

Swap columns i and j.

Parameters

i	First column index
j	Second column index

Returns: Reference to this matrix after the swap

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 2330 of file matrices.hpp.

◆ swap_rows()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::swap_rows	(	size_t	i,
		size_t	j )

Swap rows i and j.

Parameters

i	First row index
j	Second row index

Returns: Reference to this matrix after the swap

Exceptions

std::invalid_argument if either index is out of bounds

Definition at line 2315 of file matrices.hpp.

◆ to_vector()

template<ComponentType T>

Vector< T > CECCO::Matrix< T >::to_vector ( ) const

Flatten in row-major order.

Returns: Vector of length m·n; component (i, j) maps to index i·n + j

Definition at line 2904 of file matrices.hpp.

◆ transpose()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::transpose ( )

constexpr

Transpose in place.

Returns: Reference to this matrix after transposition

For an m × n matrix the result is n × m, with component (i, j) moved to (j, i).

Definition at line 2691 of file matrices.hpp.

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◆ unerase_column()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::unerase_column ( size_t i )

inline

Un-erase column i (single-index convenience for unerase_columns).

Parameters

i	Column index

Returns: Reference to this matrix after un-erasing

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 877 of file matrices.hpp.

◆ unerase_columns()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::unerase_columns ( const std::vector< size_t > & v )

Clear erasure flags on every component of the specified columns.

Parameters

v	Column indices (deduplicated internally)

Returns: Reference to this matrix after un-erasing

Exceptions

std::invalid_argument if any index in v is out of bounds

Definition at line 2589 of file matrices.hpp.

◆ unerase_component()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::unerase_component	(	size_t	i,
		size_t	j )

Clear the erasure flag on component (i, j).

Parameters

i	Row index
j	Column index

Returns: Reference to this matrix after un-erasing

Exceptions

std::invalid_argument if (i, j) is out of bounds

Definition at line 2533 of file matrices.hpp.

◆ unerase_row()

template<ComponentType T>

Matrix & CECCO::Matrix< T >::unerase_row ( size_t i )

inline

Un-erase row i (single-index convenience for unerase_rows).

Parameters

i Row index

Returns: Reference to this matrix after un-erasing

Exceptions

std::invalid_argument if i is out of bounds

Definition at line 929 of file matrices.hpp.

◆ unerase_rows()

template<ComponentType T>
requires FieldType<T>

Matrix< T > & CECCO::Matrix< T >::unerase_rows ( const std::vector< size_t > & v )

Clear erasure flags on every component of the specified rows.

Parameters

v	Row indices (deduplicated internally)

Returns: Reference to this matrix after un-erasing

Exceptions

std::invalid_argument if any index in v is out of bounds

Definition at line 2607 of file matrices.hpp.

◆ vertical_join()

template<ComponentType T>

Matrix< T > & CECCO::Matrix< T >::vertical_join ( const Matrix< T > & other )

Concatenate other below (row-wise).

Parameters

other Matrix to append below; must have the same number of columns as this

Returns: Reference to this matrix after the join

Exceptions

std::invalid_argument if column counts differ

Definition at line 2193 of file matrices.hpp.

◆ wH()

template<ComponentType T>

size_t CECCO::Matrix< T >::wH ( ) const

inline

Hamming weight: number of non-zero, non-erased components; cached on first call.

Definition at line 421 of file matrices.hpp.

◆ DiagonalMatrix

template<ComponentType T>

Matrix< T > DiagonalMatrix ( const Vector< T > & v )

friend

Diagonal matrix with diagonal v (strongest tag of details::Zero, details::Identity, details::Diagonal).

Parameters

v	Vector of diagonal entries; the result is v.length() × v.length()

Returns: Diagonal matrix with v[i] on position (i, i), zeros elsewhere

Definition at line 3895 of file matrices.hpp.

◆ IdentityMatrix

template<ComponentType T>

Matrix< T > IdentityMatrix ( size_t m )

friend

m × m identity matrix I_m

Parameters

m	Side length

Returns: Newly constructed identity matrix; for m = 0 the tag is details::Zero

Definition at line 3838 of file matrices.hpp.

◆ Matrix

template<ComponentType T>

template<ComponentType>

friend class Matrix

friend

Definition at line 185 of file matrices.hpp.

◆ operator<<

template<ComponentType T>

std::ostream & operator<<	(	std::ostream &	os,
		const Matrix< T > &	rhs )

friend

Pretty-print the matrix with column alignment and bracket borders.

Returns: Reference to os for chaining

Columns are separated by one blank, by three for polynomial components, whose own rendering contains blanks. An empty matrix is printed as "(empty matrix)".

Definition at line 3763 of file matrices.hpp.

◆ operator==

template<ComponentType T>

template<ReliablyComparableType U>

bool operator==	(	const Matrix< U > &	lhs,
		const Matrix< U > &	rhs )

friend

◆ ToeplitzMatrix

template<ComponentType T>

Matrix< T > ToeplitzMatrix	(	const Vector< T > &	v,
		size_t	m,
		size_t	n )

friend

m × n Toeplitz matrix from its diagonal entries

Parameters

v	Diagonal values, ordered so that v[i − j + n − 1] sits on entry (i, j); length m + n − 1
m	Number of rows
n	Number of columns

Returns: Toeplitz matrix; tagged by the strongest detected structural type

Exceptions

std::invalid_argument	if m == 0 or n == 0
std::invalid_argument	if v.length() != m + n - 1

Definition at line 3934 of file matrices.hpp.

◆ VandermondeMatrix

template<ComponentType T>

template<ReliablyComparableType U>

Matrix< U > VandermondeMatrix	(	const Vector< U > &	v,
		size_t	m )

friend

◆ Vector< T >

template<ComponentType T>

friend class Vector< T >

friend

Definition at line 185 of file matrices.hpp.

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

Public Member Functions

Friends

Detailed Description

Usage_Example

Constructor & Destructor Documentation

◆ Matrix() [1/10]

◆ Matrix() [2/10]

◆ Matrix() [3/10]

◆ Matrix() [4/10]

◆ Matrix() [5/10]

◆ Matrix() [6/10]

◆ Matrix() [7/10]

◆ Matrix() [8/10]

◆ Matrix() [9/10]

◆ Matrix() [10/10]

Member Function Documentation

◆ add_column()

◆ add_row()

◆ add_scaled_column()

◆ add_scaled_row()

◆ as_vector()

◆ basis_of_kernel()

◆ basis_of_nullspace()

◆ characteristic_polynomial()

◆ delete_column()

◆ delete_columns()

◆ delete_row()

◆ delete_rows()

◆ determinant()

◆ diagonal()

◆ diagonal_join()

◆ eigenvalues()

◆ erase_column()

◆ erase_columns()

◆ erase_component()

◆ erase_row()

◆ erase_rows()

◆ export_as_ppm()

◆ fill()

◆ get_col()

◆ get_m()

◆ get_n()

◆ get_row()

◆ get_submatrix()

◆ horizontal_join()

◆ invert()

◆ is_empty()

◆ is_invertible()

◆ is_zero() [1/2]

◆ is_zero() [2/2]

◆ Kronecker_product()

◆ operator()()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/=()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ randomize()

◆ rank()

◆ ref()

◆ reverse_columns()

◆ reverse_rows()

◆ rowspace()

◆ rref()

◆ scale_column()

◆ scale_row()

◆ set_component() [1/2]

◆ set_component() [2/2]

◆ set_submatrix()

◆ span()

◆ swap_columns()

◆ swap_rows()