forked from mpusz/mp-units
9527b39005
We had some fun exploring the STD UDLs for potential collisions, we have learnt our lesson and know how to proceed. Now is high time to start behaving and obeying C++ rules.
88 lines
3.2 KiB
ReStructuredText
88 lines
3.2 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] = " << vector<si::length<si::metre>>(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:`Using Custom Representation Types` 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:`linear_algebra` example.
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