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.
Polynomial< T >	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 &s)
	Set every component to s.
constexpr Matrix< T > &	transpose ()
	Transpose in place.
Matrix< T > &	ref (size_t *rank=nullptr)
	Row echelon form (REF), with a binary-field fast path.
Matrix< T > &	rref (size_t *rank=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
constexpr Matrix< T >	IdentityMatrix (size_t m)
	m × m identity matrix I_m (tag details::Identity)
constexpr Matrix< T >	DiagonalMatrix (const Vector< T > &v)
	Diagonal matrix with diagonal v (tag details::Diagonal).
constexpr Matrix< T >	ToeplitzMatrix (const Vector< T > &v, size_t m, size_t n)
	m × n Toeplitz matrix from its diagonal entries (tag details::Toeplitz)
constexpr Matrix< T >	VandermondeMatrix (const Vector< T > &v, size_t m)
	Vandermonde matrix V_{i, j} = v[j]^i (tag details::Vandermonde).
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 and structure is not re-detected. 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 174 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 194 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

Tag is details::Zero if l == T(0), otherwise details::Generic.

Definition at line 1227 of file matrices.hpp.

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◆ 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 1237 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 1246 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 1263 of file matrices.hpp.

◆ Matrix() [7/10]

template<ComponentType T>

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

inlineconstexpr

Definition at line 220 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 228 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 1271 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 1290 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 730 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 715 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 2130 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 2106 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 2553 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 470 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 1693 of file matrices.hpp.

◆ characteristic_polynomial()

template<ComponentType T>
requires FieldType<T>

Polynomial< T > 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.

Exceptions

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

Definition at line 1618 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 757 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 2138 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 777 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 2160 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 1746 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 1610 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 1994 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 1777 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 832 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 2216 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 2184 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 884 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 2238 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 2588 of file matrices.hpp.

◆ fill()

template<ComponentType T>

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

constexpr

Set every component to s.

Parameters

s	Value assigned to every component

Returns: Reference to this matrix after filling

Note: Tag becomes details::Zero if s == T(0), otherwise details::Generic.

Definition at line 2347 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 1890 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 363 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 370 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 1878 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 1902 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 1960 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.

Exceptions

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

Definition at line 2508 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 377 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 427 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 387 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 399 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 2013 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 1871 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 1483 of file matrices.hpp.

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◆ 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 1542 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 286 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 284 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 1439 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 1417 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 1395 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 1472 of file matrices.hpp.

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◆ operator/=()

template<ComponentType 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 1558 of file matrices.hpp.

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◆ operator=() [1/4]

template<ComponentType T>

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

constexpr

Definition at line 1357 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 1382 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 1369 of file matrices.hpp.

◆ randomize()

template<ComponentType 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: Tag becomes details::Generic — incidental structure (e.g. an accidental zero matrix) is not re-detected.

Definition at line 1565 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 1603 of file matrices.hpp.

◆ ref()

template<ComponentType T>
requires FieldType<T>

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

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

Parameters

rank	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 is non-null.

Definition at line 2376 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 2324 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 2302 of file matrices.hpp.

◆ rowspace()

template<ComponentType T>
requires FieldType<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 1790 of file matrices.hpp.

◆ rref()

template<ComponentType T>
requires FieldType<T>

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

Reduced row echelon form (RREF).

Parameters

rank	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 2425 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 2098 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 2075 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 1818 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 1941 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 516 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 2067 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 2046 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 2571 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 2362 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 857 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 2260 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 2200 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 909 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 2280 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 1977 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 405 of file matrices.hpp.

◆ DiagonalMatrix

template<ComponentType T>

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

friend

Diagonal matrix with diagonal v (tag 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 3511 of file matrices.hpp.

◆ IdentityMatrix

template<ComponentType T>

Matrix< T > IdentityMatrix ( size_t m )

friend

m × m identity matrix I_m (tag details::Identity)

Parameters

m	Side length

Returns: Newly constructed identity matrix

Definition at line 3455 of file matrices.hpp.

◆ Matrix

template<ComponentType T>

template<ComponentType>

friend class Matrix

friend

Definition at line 183 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

An empty matrix is printed as "(empty matrix)".

Definition at line 3388 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 (tag details::Toeplitz)

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; each descending diagonal is constant

Exceptions

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

Definition at line 3530 of file matrices.hpp.

◆ VandermondeMatrix

template<ComponentType T>

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

friend

Vandermonde matrix V_{i, j} = v[j]^i (tag details::Vandermonde).

Parameters

v	Evaluation points; must be pairwise distinct
m	Number of rows (i.e. the highest power is m − 1)

Returns: m × v.length() Vandermonde matrix

Exceptions

std::invalid_argument if v is empty, has duplicates, or m is zero

Definition at line 3577 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()