forked from mpusz/mp-units
89 lines
3.3 KiB
ReStructuredText
89 lines
3.3 KiB
ReStructuredText
.. namespace:: units
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Linear Algebra vs. Quantities
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=============================
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Even though **mp-units** library does not implement any Linear Algebra types it is generic
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enough to be used with other Linear Algebra libraries existing on the market.
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.. note::
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All of the examples provided in this chapter refer to the official proposal of the
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Linear Algebra Library for the C++23 defined in `P1385 <https://wg21.link/P1385>`_
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and its latest implementation from `GitHub <https://github.com/BobSteagall/wg21>`_
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or `Conan <https://bintray.com/twonington/public-conan/linear_algebra%3Apublic-conan>`_.
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Also, to simplify the examples all of them assume::
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using namespace std::math;
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Linear Algebra of Quantities
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----------------------------
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The official :term:`quantity` definition states:
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*A quantity as defined here is a scalar. However, a vector or a tensor, the components of
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which are quantities, is also considered to be a quantity.*
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So the most common use case would be to create a vector or matrix of quantities::
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fs_vector<si::length<si::metre>, 3> v = { 1_q_m, 2_q_m, 3_q_m };
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fs_vector<si::length<si::metre>, 3> u = { 3_q_m, 2_q_m, 1_q_m };
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fs_vector<si::length<si::kilometre>, 3> t = { 3_q_km, 2_q_km, 1_q_km };
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Having such definitions we can perform full dimensional analysis operations for the operations
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allowed by the Linear Algebra rules. For example::
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std::cout << "v + u = " << v + u << "\n";
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std::cout << "v + t = " << v + t << "\n";
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std::cout << "t[m] = " << fs_vector<si::length<si::metre>, 3>(t) << "\n";
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std::cout << "v * u = " << v * u << "\n";
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std::cout << "2_q_m * v = " << 2_q_m * v << "\n";
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The above code works as expected and produces the following output:
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.. code-block:: text
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v + u = | 4 m 4 m 4 m |
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v + t = | 3001 m 2002 m 1003 m |
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t[m] = | 3000 m 2000 m 1000 m |
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v * u = 10 m²
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2_q_m * v = | 2 m² 4 m² 6 m² |
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Quantities of Linear Algebra Types
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----------------------------------
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The previous chapter should address most of the Linear Algebra related requirements.
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However, it is also possible to use Linear Algebra entities as custom representation
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types provided to a `quantity` class template.
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.. seealso::
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More information on providing custom representation types for `quantity` can be
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found in the :ref:`use_cases/custom_representation_types:Using Custom Representation Types`
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chapter.
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With this the above vector definitions can be rewritten as follows::
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si::length<si::metre, fs_vector<int, 3>> v(fs_vector<int, 3>{ 1, 2, 3 });
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si::length<si::metre, fs_vector<int, 3>> u(fs_vector<int, 3>{ 3, 2, 1 });
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si::length<si::kilometre, fs_vector<int, 3>> t(fs_vector<int, 3>{ 3, 2, 1 });
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Now the same code doing basic Linear Algebra operations will provide the following
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output:
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.. code-block:: text
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v + u = | 4 4 4 | m
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v + t = | 3001 2002 1003 | m
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t[m] = | 3000 2000 1000 | m
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v * u = 10 m²
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2_q_m * v = | 2 4 6 | m²
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.. seealso::
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For more examples of Linear Algebra definition and operations please refer to
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the :ref:`examples/linear_algebra:linear_algebra` example.
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