BMat8¶

class BMat8¶

Defined in bmat8.hpp.

Class for fast boolean matrices of dimension up to 8 x 8

The member functions for these small matrices over the boolean semiring are more optimised than the generic member functions for boolean matrices. Note that all BMat8 are represented internally as an 8 x 8 matrix; any entries not defined by the user are taken to be 0. This does not affect the results of any calculations.

BMat8 is a trivial class.

Constructors¶

`BMat8() noexcept = default`	Default constructor.
`BMat8(BMat8 const&) noexcept = default`	Default copy constructor.
`BMat8(BMat8&&) noexcept = default`	Default move constructor.
`BMat8(std::vector<std::vector<bool>> const&)`	None
`BMat8(uint64_t) noexcept`	Construct from uint64_t.
`operator=(BMat8 const&) noexcept = default`	Default copy assignment operator.
`operator=(BMat8&&) noexcept = default`	Default move assignment operator.

Static member functions¶

`one(size_t) noexcept`	Returns the identity `BMat8` .
`random()`	Construct a random `BMat8` .
`random(size_t)`	Construct a random `BMat8` of dimension at most `dim`.

Initialization¶

`set(size_t, size_t, bool)`	Sets the ( `i` , `j` )th position to `val`.
`swap(BMat8&) noexcept`	Swaps `this` with `that`.

Operators¶

`get(size_t, size_t) const noexcept`	Returns the entry in the ( `i` , `j` )th position.
`operator!=(BMat8 const&) const noexcept`	Returns `true` if `this` does not equal `that`.
`operator*(BMat8 const&) const noexcept`	Returns the matrix product of `this` and `that`.
`operator<(BMat8 const&) const noexcept`	Returns `true` if `this` is less than `that`.
`operator<<(std::ostream&, BMat8 const&)`	Insertion operator.
`operator<<(std::ostringstream&, BMat8 const&)`	Insertion operator.
`operator==(BMat8 const&) const noexcept`	Returns `true` if `this` equals `that`.
`operator>(BMat8 const&) const noexcept`	Returns `true` if `this` is greater than `that`.
`to_int() const noexcept`	Returns the integer representation of `this`.
`transpose() const noexcept`	Returns the transpose of `this`.

Column and row space¶

`col_space_basis() const noexcept`	Find a basis for the column space of `this`.
`number_of_rows() const noexcept`	Returns the number of non-zero rows in `this`.
`row_space_basis() const noexcept`	Find a basis for the row space of `this`.
`row_space_size() const`	Find the size of the row space of `this`.
`rows() const`	Returns a vector containing the rows of `this`.

Miscellanea¶

is_regular_element() const noexcept

Check whether this is a regular element of the full boolean matrix monoid of appropriate dimension.