Quelle intmat.rst Sprache: unbekannt

.. 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``.

Quelle intmat.rst Sprache: unbekannt

[ Dauer der Verarbeitung: 0.29 Sekunden (vorverarbeitet) ]