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.. Copyright (c) 2020, J. D. Mitchell
Distributed under the terms of the GPL license version 3.
The full license is in the file LICENSE, distributed with this software.
Integer matrices
================
Defined in ``matrix.hpp``.
This page describes the functionality for :math:`m \times n` matrices of
integers for arbitrary dimensions :math:`m` and :math:`n`. There are two types
of such matrices those whose dimension is known at compile-time, and those
where it is not. Both types can be accessed via the alias template
:cpp:any:`IntMat\<R, C, Scalar>`: if ``R`` or ``C`` has value ``0``, then the
dimensions can be set at run time, otherwise ``R`` and ``C`` are the dimension.
The default value of ``R`` is ``0``, and of ``C`` is ``R``.
The alias :cpp:any:`IntMat\<R, C, Scalar>` is either :cpp:any:`StaticMatrix` or
:cpp:any:`DynamicMatrix`, please refer to the documentation of these class
templates for more details. The only substantial difference in the interface
of :cpp:any:`StaticMatrix` and :cpp:any:`DynamicMatrix` is that the former can
be default constructed and the latter should be constructed using the
dimensions.
**Example**
.. code-block:: cpp
IntMat<3> m; // default construct an uninitialized 3 x 3 static matrix
IntMat<> m(4, 4); // construct an uninitialized 4 x 4 dynamic matrix
.. cpp:struct:: template <typename Scalar> \
IntegerPlus
This is a stateless struct with a single call operator of signature:
``Scalar operator()(Scalar const x, Scalar const y) const noexcept``
which returns the usual sum ``x + y`` of ``x`` and ``y``; representing
addition in the integer semiring.
.. cpp:struct:: template <typename Scalar> \
IntegerProd
This is a stateless struct with a single call operator of signature:
``Scalar operator()(Scalar const x, Scalar const y) const noexcept``
which returns the usual product ``x * y`` of ``x`` and ``y``; representing
multiplication in the integer semiring.
.. cpp:struct:: template <typename Scalar> \
IntegerZero
This is a stateless struct with a single call operator of signature:
``Scalar operator()() const noexcept`` which returns ``0``; representing the
additive identity of the integer semiring.
.. cpp:struct:: template <typename Scalar> \
IntegerOne
This is a stateless struct with a single call operator of signature:
``Scalar operator()() const noexcept`` which returns ``1``; representing the
multiplicative identity of the integer semiring.
.. cpp:type:: template <typename Scalar> \
DynamicIntMat \
= DynamicMatrix<IntegerPlus<Scalar>, \
IntegerProd<Scalar>, \
IntegerZero<Scalar>, \
IntegerOne<Scalar>, \
Scalar>
Alias for the type of dynamic integer matrices where the dimensions of the
matrices can be defined at run time.
:tparam Scalar:
The type of the entries in the matrix (default: ``int``).
.. cpp:type:: template <size_t R, size_t C, typename Scalar> \
StaticIntMat = StaticMatrix<IntegerPlus<Scalar>, \
IntegerProd<Scalar>, \
IntegerZero<Scalar>, \
IntegerOne<Scalar>, \
R, \
C, \
Scalar>
:tparam R:
the number of rows of the matrices. A value of ``0`` (the default value)
indicates that the dimensions will be set at run time.
:tparam C:
the number of columns of the matrices. A value of ``0``
indicates that the dimensions will be set at run time (the default value
is ``R``).
:tparam Scalar:
The type of the entries in the matrix (default: ``int``).
.. cpp:type:: template <size_t R = 0, size_t C = R, Scalar = int> \
IntMat = std::conditional_t<R == 0 || C == 0, \
DynamicIntMat<Scalar>, \
StaticIntMat<R, C, Scalar>>
Alias template for integer matrices.
:tparam R:
the number of rows of the matrices. A value of ``0`` (the default value)
indicates that the dimensions will be set at run time.
:tparam C:
the number of columns of the matrices. A value of ``0``
indicates that the dimensions will be set at run time (the default value
is ``R``).
:tparam Scalar:
the type of the entries in the matrix (default: ``int``).
.. cpp:var:: template <typename T> \
static constexpr bool IsIntMat
This variable has value ``true`` if the template parameter ``T`` is the same
as :cpp:any:`IntMat\<R, C, Scalar>` for some values of ``R``, ``C``, and
``Scalar``.
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