mirror of
https://github.com/boostorg/math.git
synced 2026-01-19 04:22:09 +00:00
Removed octonion sub-folder and moved contents elsewhere.
This commit is contained in:
jzmaddock
@@ -112,7 +112,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: September 07, 2015 at 17:30:17 GMT</small></p></td>
|
||||
<td align="left"><p><small>Last revised: September 07, 2015 at 17:50:26 GMT</small></p></td>
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<td align="right"><div class="copyright-footer"></div></td>
|
||||
</tr></table>
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||||
<hr>
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||||
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||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1696223"></a>Function Index</h2></div></div></div>
|
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<a name="id1678960"></a>Function Index</h2></div></div></div>
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<p><a class="link" href="s01.html#idx_id_0">A</a> <a class="link" href="s01.html#idx_id_1">B</a> <a class="link" href="s01.html#idx_id_2">C</a> <a class="link" href="s01.html#idx_id_3">D</a> <a class="link" href="s01.html#idx_id_4">E</a> <a class="link" href="s01.html#idx_id_5">F</a> <a class="link" href="s01.html#idx_id_6">G</a> <a class="link" href="s01.html#idx_id_7">H</a> <a class="link" href="s01.html#idx_id_8">I</a> <a class="link" href="s01.html#idx_id_9">J</a> <a class="link" href="s01.html#idx_id_10">K</a> <a class="link" href="s01.html#idx_id_11">L</a> <a class="link" href="s01.html#idx_id_12">M</a> <a class="link" href="s01.html#idx_id_13">N</a> <a class="link" href="s01.html#idx_id_14">O</a> <a class="link" href="s01.html#idx_id_15">P</a> <a class="link" href="s01.html#idx_id_16">Q</a> <a class="link" href="s01.html#idx_id_17">R</a> <a class="link" href="s01.html#idx_id_18">S</a> <a class="link" href="s01.html#idx_id_19">T</a> <a class="link" href="s01.html#idx_id_20">U</a> <a class="link" href="s01.html#idx_id_21">V</a> <a class="link" href="s01.html#idx_id_23">Z</a></p>
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@@ -24,7 +24,7 @@
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||||
</div>
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||||
<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="id1714339"></a>Class Index</h2></div></div></div>
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<a name="id1702138"></a>Class Index</h2></div></div></div>
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<p><a class="link" href="s02.html#idx_id_24">A</a> <a class="link" href="s02.html#idx_id_25">B</a> <a class="link" href="s02.html#idx_id_26">C</a> <a class="link" href="s02.html#idx_id_27">D</a> <a class="link" href="s02.html#idx_id_28">E</a> <a class="link" href="s02.html#idx_id_29">F</a> <a class="link" href="s02.html#idx_id_30">G</a> <a class="link" href="s02.html#idx_id_31">H</a> <a class="link" href="s02.html#idx_id_32">I</a> <a class="link" href="s02.html#idx_id_35">L</a> <a class="link" href="s02.html#idx_id_36">M</a> <a class="link" href="s02.html#idx_id_37">N</a> <a class="link" href="s02.html#idx_id_38">O</a> <a class="link" href="s02.html#idx_id_39">P</a> <a class="link" href="s02.html#idx_id_40">Q</a> <a class="link" href="s02.html#idx_id_41">R</a> <a class="link" href="s02.html#idx_id_42">S</a> <a class="link" href="s02.html#idx_id_43">T</a> <a class="link" href="s02.html#idx_id_44">U</a> <a class="link" href="s02.html#idx_id_46">W</a></p>
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<div class="variablelist"><dl class="variablelist">
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<dt>
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@@ -24,7 +24,7 @@
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</div>
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<div class="section">
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||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="id1719164"></a>Typedef Index</h2></div></div></div>
|
||||
<a name="id1703210"></a>Typedef Index</h2></div></div></div>
|
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<p><a class="link" href="s03.html#idx_id_48">A</a> <a class="link" href="s03.html#idx_id_49">B</a> <a class="link" href="s03.html#idx_id_50">C</a> <a class="link" href="s03.html#idx_id_51">D</a> <a class="link" href="s03.html#idx_id_52">E</a> <a class="link" href="s03.html#idx_id_53">F</a> <a class="link" href="s03.html#idx_id_54">G</a> <a class="link" href="s03.html#idx_id_55">H</a> <a class="link" href="s03.html#idx_id_56">I</a> <a class="link" href="s03.html#idx_id_59">L</a> <a class="link" href="s03.html#idx_id_61">N</a> <a class="link" href="s03.html#idx_id_62">O</a> <a class="link" href="s03.html#idx_id_63">P</a> <a class="link" href="s03.html#idx_id_65">R</a> <a class="link" href="s03.html#idx_id_66">S</a> <a class="link" href="s03.html#idx_id_67">T</a> <a class="link" href="s03.html#idx_id_68">U</a> <a class="link" href="s03.html#idx_id_69">V</a> <a class="link" href="s03.html#idx_id_70">W</a></p>
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<div class="variablelist"><dl class="variablelist">
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<dt>
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@@ -24,7 +24,7 @@
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</div>
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||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1718943"></a>Macro Index</h2></div></div></div>
|
||||
<a name="id1706274"></a>Macro Index</h2></div></div></div>
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||||
<p><a class="link" href="s04.html#idx_id_73">B</a> <a class="link" href="s04.html#idx_id_77">F</a></p>
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<div class="variablelist"><dl class="variablelist">
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<dt>
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@@ -23,7 +23,7 @@
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1721820"></a>Index</h2></div></div></div>
|
||||
<a name="id1710345"></a>Index</h2></div></div></div>
|
||||
<p><a class="link" href="s05.html#idx_id_96">A</a> <a class="link" href="s05.html#idx_id_97">B</a> <a class="link" href="s05.html#idx_id_98">C</a> <a class="link" href="s05.html#idx_id_99">D</a> <a class="link" href="s05.html#idx_id_100">E</a> <a class="link" href="s05.html#idx_id_101">F</a> <a class="link" href="s05.html#idx_id_102">G</a> <a class="link" href="s05.html#idx_id_103">H</a> <a class="link" href="s05.html#idx_id_104">I</a> <a class="link" href="s05.html#idx_id_105">J</a> <a class="link" href="s05.html#idx_id_106">K</a> <a class="link" href="s05.html#idx_id_107">L</a> <a class="link" href="s05.html#idx_id_108">M</a> <a class="link" href="s05.html#idx_id_109">N</a> <a class="link" href="s05.html#idx_id_110">O</a> <a class="link" href="s05.html#idx_id_111">P</a> <a class="link" href="s05.html#idx_id_112">Q</a> <a class="link" href="s05.html#idx_id_113">R</a> <a class="link" href="s05.html#idx_id_114">S</a> <a class="link" href="s05.html#idx_id_115">T</a> <a class="link" href="s05.html#idx_id_116">U</a> <a class="link" href="s05.html#idx_id_117">V</a> <a class="link" href="s05.html#idx_id_118">W</a> <a class="link" href="s05.html#idx_id_119">Z</a></p>
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<div class="variablelist"><dl class="variablelist">
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<dt>
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@@ -27,7 +27,7 @@
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<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
|
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</h2></div></div></div>
|
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<p>
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<a class="indexterm" name="id849614"></a>
|
||||
<a class="indexterm" name="id832776"></a>
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</p>
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<p>
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This documentation aims to use of the following naming and formatting conventions.
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@@ -27,7 +27,7 @@
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<a name="math_toolkit.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
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</h2></div></div></div>
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<p>
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<a class="indexterm" name="id849498"></a>
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<a class="indexterm" name="id832632"></a>
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</p>
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<p>
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Boost.Math documentation is provided in both HTML and PDF formats.
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@@ -52,7 +52,7 @@
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things is by using the following multiplication table:
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</p>
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<p>
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<span class="inlinemediaobject"><img src="../../../octonion/graphics/octonion_blurb17.jpeg"></span>
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<span class="inlinemediaobject"><img src="../../octonion/graphics/octonion_blurb17.jpeg"></span>
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</p>
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<p>
|
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Octonions (and their kin) are described in far more details in this other
|
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|
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@@ -27,15 +27,14 @@
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<a name="math_toolkit.oct_tests"></a><a class="link" href="oct_tests.html" title="Test Program">Test Program</a>
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</h2></div></div></div>
|
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<p>
|
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The <a href="../../../octonion/octonion_test.cpp" target="_top">octonion_test.cpp</a>
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test program tests octonions specialisations for float, double and long double
|
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(<a href="../../../octonion/output.txt" target="_top">sample output</a>).
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The <a href="../../../test/octonion_test.cpp" target="_top">octonion_test.cpp</a> test
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program tests octonions specialisations for float, double and long double (<a href="../../octonion/output.txt" target="_top">sample output</a>).
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</p>
|
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<p>
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If you define the symbol BOOST_OCTONION_TEST_VERBOSE, you will get additional
|
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output (<a href="../../../octonion/output_more.txt" target="_top">verbose output</a>);
|
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this will only be helpfull if you enable message output at the same time, of
|
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course (by uncommenting the relevant line in the test or by adding --log_level=messages
|
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output (<a href="../../octonion/output_more.txt" target="_top">verbose output</a>); this
|
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will only be helpfull if you enable message output at the same time, of course
|
||||
(by uncommenting the relevant line in the test or by adding --log_level=messages
|
||||
to your command line,...). In that case, and if you are running interactively,
|
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you may in addition define the symbol BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
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to interactively test the input operator with input of your choice from the
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|
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@@ -30,7 +30,7 @@ is that [*the multiplication is not only not commutative, is now not even
|
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associative] (i.e. there are octonions ['[^x]], ['[^y]] and ['[^z]] such that __oct_not_equal).
|
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A way of remembering things is by using the following multiplication table:
|
||||
|
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[$../../octonion/graphics/octonion_blurb17.jpeg]
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[$../octonion/graphics/octonion_blurb17.jpeg]
|
||||
|
||||
Octonions (and their kin) are described in far more details in this other
|
||||
[@../../quaternion/TQE.pdf document]
|
||||
@@ -926,12 +926,12 @@ Computes the n-th power of the octonion q.
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[section:oct_tests Test Program]
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The [@../../octonion/octonion_test.cpp octonion_test.cpp]
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The [@../../test/octonion_test.cpp octonion_test.cpp]
|
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test program tests octonions specialisations for float, double and long double
|
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([@../../octonion/output.txt sample output]).
|
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([@../octonion/output.txt sample output]).
|
||||
|
||||
If you define the symbol BOOST_OCTONION_TEST_VERBOSE, you will get additional
|
||||
output ([@../../octonion/output_more.txt verbose output]); this will
|
||||
output ([@../octonion/output_more.txt verbose output]); this will
|
||||
only be helpfull if you enable message output at the same time, of course
|
||||
(by uncommenting the relevant line in the test or by adding --log_level=messages
|
||||
to your command line,...). In that case, and if you are running interactively,
|
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@@ -1,775 +0,0 @@
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// test file for octonion.hpp
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
|
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// http://www.boost.org/LICENSE_1_0.txt)
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#include <iomanip>
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#include <boost/mpl/list.hpp>
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#include <boost/test/unit_test.hpp>
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#include <boost/test/unit_test_log.hpp>
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#include <boost/math/octonion.hpp>
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template<typename T>
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struct string_type_name;
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#define DEFINE_TYPE_NAME(Type) \
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template<> struct string_type_name<Type> \
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{ \
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static char const * _() \
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{ \
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return #Type; \
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} \
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}
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DEFINE_TYPE_NAME(float);
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DEFINE_TYPE_NAME(double);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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DEFINE_TYPE_NAME(long double);
|
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#endif
|
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|
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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typedef boost::mpl::list<float,double,long double> test_types;
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#else
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typedef boost::mpl::list<float,double> test_types;
|
||||
#endif
|
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|
||||
// Apple GCC 4.0 uses the "double double" format for its long double,
|
||||
// which means that epsilon is VERY small but useless for
|
||||
// comparisons. So, don't do those comparisons.
|
||||
#if (defined(__APPLE_CC__) && defined(__GNUC__) && __GNUC__ == 4) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
|
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typedef boost::mpl::list<float,double> near_eps_test_types;
|
||||
#else
|
||||
typedef boost::mpl::list<float,double,long double> near_eps_test_types;
|
||||
#endif
|
||||
|
||||
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
||||
// gcc 2.x ignores function scope using declarations,
|
||||
// put them in the scope of the enclosing namespace instead:
|
||||
using ::std::sqrt;
|
||||
using ::std::atan;
|
||||
using ::std::log;
|
||||
using ::std::exp;
|
||||
using ::std::cos;
|
||||
using ::std::sin;
|
||||
using ::std::tan;
|
||||
using ::std::cosh;
|
||||
using ::std::sinh;
|
||||
using ::std::tanh;
|
||||
|
||||
using ::std::numeric_limits;
|
||||
|
||||
using ::boost::math::abs;
|
||||
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
||||
|
||||
|
||||
#ifdef BOOST_NO_STDC_NAMESPACE
|
||||
using ::sqrt;
|
||||
using ::atan;
|
||||
using ::log;
|
||||
using ::exp;
|
||||
using ::cos;
|
||||
using ::sin;
|
||||
using ::tan;
|
||||
using ::cosh;
|
||||
using ::sinh;
|
||||
using ::tanh;
|
||||
#endif /* BOOST_NO_STDC_NAMESPACE */
|
||||
|
||||
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
||||
using ::boost::math::real;
|
||||
using ::boost::math::unreal;
|
||||
using ::boost::math::sup;
|
||||
using ::boost::math::l1;
|
||||
using ::boost::math::abs;
|
||||
using ::boost::math::norm;
|
||||
using ::boost::math::conj;
|
||||
using ::boost::math::exp;
|
||||
using ::boost::math::pow;
|
||||
using ::boost::math::cos;
|
||||
using ::boost::math::sin;
|
||||
using ::boost::math::tan;
|
||||
using ::boost::math::cosh;
|
||||
using ::boost::math::sinh;
|
||||
using ::boost::math::tanh;
|
||||
using ::boost::math::sinc_pi;
|
||||
using ::boost::math::sinhc_pi;
|
||||
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
||||
|
||||
// Provide standard floating point abs() overloads if older Microsoft
|
||||
// library is used with _MSC_EXTENSIONS defined. This code also works
|
||||
// for the Intel compiler using the Microsoft library.
|
||||
#if defined(_MSC_EXTENSIONS) && defined(_MSC_VER) && _MSC_VER < 1310
|
||||
inline float abs(float v)
|
||||
{
|
||||
return(fabs(v));
|
||||
}
|
||||
|
||||
inline double abs(double v)
|
||||
{
|
||||
return(fabs(v));
|
||||
}
|
||||
|
||||
inline long double abs(long double v)
|
||||
{
|
||||
return(fabs(v));
|
||||
}
|
||||
#endif /* BOOST_WORKAROUND(BOOST_MSVC) */
|
||||
|
||||
|
||||
// explicit (if ludicrous) instanciation
|
||||
#if !BOOST_WORKAROUND(__GNUC__, < 3)
|
||||
template class ::boost::math::octonion<int>;
|
||||
#else
|
||||
// gcc doesn't like the absolutely-qualified namespace
|
||||
template class boost::math::octonion<int>;
|
||||
#endif /* !BOOST_WORKAROUND(__GNUC__) */
|
||||
|
||||
|
||||
namespace
|
||||
{
|
||||
template<typename T>
|
||||
::boost::math::octonion<T> index_i_element(int idx)
|
||||
{
|
||||
return(
|
||||
::boost::math::octonion<T>(
|
||||
(idx == 0) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 1) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 2) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 3) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 4) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 5) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 6) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0),
|
||||
(idx == 7) ?
|
||||
static_cast<T>(1) :
|
||||
static_cast<T>(0)
|
||||
));
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
void octonion_manual_test()
|
||||
{
|
||||
// tests for evaluation by humans
|
||||
|
||||
|
||||
// using default constructor
|
||||
::boost::math::octonion<float> o0;
|
||||
|
||||
::boost::math::octonion<float> oa[2];
|
||||
|
||||
// using constructor "O seen as R^8"
|
||||
::boost::math::octonion<float> o1(1,2,3,4,5,6,7,8);
|
||||
|
||||
::std::complex<double> c0(9,10);
|
||||
|
||||
// using constructor "O seen as C^4"
|
||||
::boost::math::octonion<double> o2(c0);
|
||||
|
||||
::boost::math::quaternion<long double> q0(11,12,13,14);
|
||||
|
||||
// using constructor "O seen as H^2"
|
||||
::boost::math::octonion<long double> o3(q0);
|
||||
|
||||
// using UNtemplated copy constructor
|
||||
::boost::math::octonion<float> o4(o1);
|
||||
|
||||
// using templated copy constructor
|
||||
::boost::math::octonion<long double> o5(o2);
|
||||
|
||||
// using UNtemplated assignment operator
|
||||
o5 = o3;
|
||||
oa[0] = o0;
|
||||
|
||||
// using templated assignment operator
|
||||
o5 = o2;
|
||||
oa[1] = o5;
|
||||
|
||||
float f0(15);
|
||||
|
||||
// using converting assignment operator
|
||||
o0 = f0;
|
||||
|
||||
// using converting assignment operator
|
||||
o2 = c0;
|
||||
|
||||
// using converting assignment operator
|
||||
o5 = q0;
|
||||
|
||||
// using += (const T &)
|
||||
o4 += f0;
|
||||
|
||||
// using += (const ::std::complex<T> &)
|
||||
o2 += c0;
|
||||
|
||||
// using += (const ::boost::math::quaternion<T> &)
|
||||
o3 += q0;
|
||||
|
||||
// using += (const quaternion<X> &)
|
||||
o5 += o4;
|
||||
|
||||
// using -= (const T &)
|
||||
o1 -= f0;
|
||||
|
||||
// using -= (const ::std::complex<T> &)
|
||||
o2 -= c0;
|
||||
|
||||
// using -= (const ::boost::math::quaternion<T> &)
|
||||
o5 -= q0;
|
||||
|
||||
// using -= (const octonion<X> &)
|
||||
o3 -= o4;
|
||||
|
||||
double d0(16);
|
||||
::std::complex<double> c1(17,18);
|
||||
::boost::math::quaternion<double> q1(19,20,21,22);
|
||||
|
||||
// using *= (const T &)
|
||||
o2 *= d0;
|
||||
|
||||
// using *= (const ::std::complex<T> &)
|
||||
o2 *= c1;
|
||||
|
||||
// using *= (const ::boost::math::quaternion<T> &)
|
||||
o2 *= q1;
|
||||
|
||||
// using *= (const octonion<X> &)
|
||||
o2 *= o4;
|
||||
|
||||
long double l0(23);
|
||||
::std::complex<long double> c2(24,25);
|
||||
|
||||
// using /= (const T &)
|
||||
o5 /= l0;
|
||||
|
||||
// using /= (const ::std::complex<T> &)
|
||||
o5 /= c2;
|
||||
|
||||
// using /= (const quaternion<X> &)
|
||||
o5 /= q0;
|
||||
|
||||
// using /= (const octonion<X> &)
|
||||
o5 /= o5;
|
||||
|
||||
// using + (const T &, const octonion<T> &)
|
||||
::boost::math::octonion<float> o6 = f0+o0;
|
||||
|
||||
// using + (const octonion<T> &, const T &)
|
||||
::boost::math::octonion<float> o7 = o0+f0;
|
||||
|
||||
// using + (const ::std::complex<T> &, const quaternion<T> &)
|
||||
::boost::math::octonion<double> o8 = c0+o2;
|
||||
|
||||
// using + (const octonion<T> &, const ::std::complex<T> &)
|
||||
::boost::math::octonion<double> o9 = o2+c0;
|
||||
|
||||
// using + (const ::boost::math::quaternion<T>, const octonion<T> &)
|
||||
::boost::math::octonion<long double> o10 = q0+o3;
|
||||
|
||||
// using + (const octonion<T> &, const ::boost::math::quaternion<T> &)
|
||||
::boost::math::octonion<long double> o11 = o3+q0;
|
||||
|
||||
// using + (const quaternion<T> &,const quaternion<T> &)
|
||||
::boost::math::octonion<float> o12 = o0+o4;
|
||||
|
||||
// using - (const T &, const octonion<T> &)
|
||||
o6 = f0-o0;
|
||||
|
||||
// using - (const octonion<T> &, const T &)
|
||||
o7 = o0-f0;
|
||||
|
||||
// using - (const ::std::complex<T> &, const octonion<T> &)
|
||||
o8 = c0-o2;
|
||||
|
||||
// using - (const octonion<T> &, const ::std::complex<T> &)
|
||||
o9 = o2-c0;
|
||||
|
||||
// using - (const quaternion<T> &,const octonion<T> &)
|
||||
o10 = q0-o3;
|
||||
|
||||
// using - (const octonion<T> &,const quaternion<T> &)
|
||||
o11 = o3-q0;
|
||||
|
||||
// using - (const octonion<T> &,const octonion<T> &)
|
||||
o12 = o0-o4;
|
||||
|
||||
// using * (const T &, const octonion<T> &)
|
||||
o6 = f0*o0;
|
||||
|
||||
// using * (const octonion<T> &, const T &)
|
||||
o7 = o0*f0;
|
||||
|
||||
// using * (const ::std::complex<T> &, const octonion<T> &)
|
||||
o8 = c0*o2;
|
||||
|
||||
// using * (const octonion<T> &, const ::std::complex<T> &)
|
||||
o9 = o2*c0;
|
||||
|
||||
// using * (const quaternion<T> &,const octonion<T> &)
|
||||
o10 = q0*o3;
|
||||
|
||||
// using * (const octonion<T> &,const quaternion<T> &)
|
||||
o11 = o3*q0;
|
||||
|
||||
// using * (const octonion<T> &,const octonion<T> &)
|
||||
o12 = o0*o4;
|
||||
|
||||
// using / (const T &, const octonion<T> &)
|
||||
o6 = f0/o0;
|
||||
|
||||
// using / (const octonion<T> &, const T &)
|
||||
o7 = o0/f0;
|
||||
|
||||
// using / (const ::std::complex<T> &, const octonion<T> &)
|
||||
o8 = c0/o2;
|
||||
|
||||
// using / (const octonion<T> &, const ::std::complex<T> &)
|
||||
o9 = o2/c0;
|
||||
|
||||
// using / (const ::boost::math::quaternion<T> &, const octonion<T> &)
|
||||
o10 = q0/o3;
|
||||
|
||||
// using / (const octonion<T> &, const ::boost::math::quaternion<T> &)
|
||||
o11 = o3/q0;
|
||||
|
||||
// using / (const octonion<T> &,const octonion<T> &)
|
||||
o12 = o0/o4;
|
||||
|
||||
// using + (const octonion<T> &)
|
||||
o4 = +o0;
|
||||
|
||||
// using - (const octonion<T> &)
|
||||
o0 = -o4;
|
||||
|
||||
// using == (const T &, const octonion<T> &)
|
||||
f0 == o0;
|
||||
|
||||
// using == (const octonion<T> &, const T &)
|
||||
o0 == f0;
|
||||
|
||||
// using == (const ::std::complex<T> &, const octonion<T> &)
|
||||
c0 == o2;
|
||||
|
||||
// using == (const octonion<T> &, const ::std::complex<T> &)
|
||||
o2 == c0;
|
||||
|
||||
// using == (const ::boost::math::quaternion<T> &, const octonion<T> &)
|
||||
q0 == o3;
|
||||
|
||||
// using == (const octonion<T> &, const ::boost::math::quaternion<T> &)
|
||||
o3 == q0;
|
||||
|
||||
// using == (const octonion<T> &,const octonion<T> &)
|
||||
o0 == o4;
|
||||
|
||||
// using != (const T &, const octonion<T> &)
|
||||
f0 != o0;
|
||||
|
||||
// using != (const octonion<T> &, const T &)
|
||||
o0 != f0;
|
||||
|
||||
// using != (const ::std::complex<T> &, const octonion<T> &)
|
||||
c0 != o2;
|
||||
|
||||
// using != (const octonion<T> &, const ::std::complex<T> &)
|
||||
o2 != c0;
|
||||
|
||||
// using != (const ::boost::math::quaternion<T> &, const octonion<T> &)
|
||||
q0 != o3;
|
||||
|
||||
// using != (const octonion<T> &, const ::boost::math::quaternion<T> &)
|
||||
o3 != q0;
|
||||
|
||||
// using != (const octonion<T> &,const octonion<T> &)
|
||||
o0 != o4;
|
||||
|
||||
BOOST_TEST_MESSAGE("Please input an octonion...");
|
||||
|
||||
#ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
|
||||
::std::cin >> o0;
|
||||
|
||||
if (::std::cin.fail())
|
||||
{
|
||||
BOOST_TEST_MESSAGE("You have entered nonsense!");
|
||||
}
|
||||
else
|
||||
{
|
||||
BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
|
||||
}
|
||||
#else
|
||||
::std::istringstream bogus("(1,2,3,4,5,6,7,8)");
|
||||
|
||||
bogus >> o0;
|
||||
|
||||
BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
|
||||
#endif
|
||||
|
||||
BOOST_TEST_MESSAGE("For this octonion:");
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the real part is "
|
||||
<< real(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the unreal part is "
|
||||
<< unreal(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the sup norm is "
|
||||
<< sup(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the l1 norm is "
|
||||
<< l1(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the magnitude (euclidian norm) is "
|
||||
<< abs(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the (Cayley) norm is "
|
||||
<< norm(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the conjugate is "
|
||||
<< conj(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the exponential is "
|
||||
<< exp(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the cube is "
|
||||
<< pow(o0,3));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the cosinus is "
|
||||
<< cos(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the sinus is "
|
||||
<< sin(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the tangent is "
|
||||
<< tan(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the hyperbolic cosinus is "
|
||||
<< cosh(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the hyperbolic sinus is "
|
||||
<< sinh(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of the hyperbolic tangent is "
|
||||
<< tanh(o0));
|
||||
|
||||
#ifdef BOOST_NO_TEMPLATE_TEMPLATES
|
||||
BOOST_TEST_MESSAGE( "no template templates, can't compute cardinal functions");
|
||||
#else /* BOOST_NO_TEMPLATE_TEMPLATES */
|
||||
BOOST_TEST_MESSAGE( "the value of the Sinus Cardinal (of index pi) is "
|
||||
<< sinc_pi(o0));
|
||||
|
||||
BOOST_TEST_MESSAGE( "the value of "
|
||||
<< "the Hyperbolic Sinus Cardinal (of index pi) is "
|
||||
<< sinhc_pi(o0));
|
||||
#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
|
||||
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
|
||||
float rho = ::std::sqrt(4096.0f);
|
||||
float theta = ::std::atan(1.0f);
|
||||
float phi1 = ::std::atan(1.0f);
|
||||
float phi2 = ::std::atan(1.0f);
|
||||
float phi3 = ::std::atan(1.0f);
|
||||
float phi4 = ::std::atan(1.0f);
|
||||
float phi5 = ::std::atan(1.0f);
|
||||
float phi6 = ::std::atan(1.0f);
|
||||
|
||||
BOOST_TEST_MESSAGE( "The value of the octonion represented "
|
||||
<< "in spherical form by "
|
||||
<< "rho = " << rho << " , theta = " << theta
|
||||
<< " , phi1 = " << phi1 << " , phi2 = " << phi2
|
||||
<< " , phi3 = " << phi3 << " , phi4 = " << phi4
|
||||
<< " , phi5 = " << phi5 << " , phi6 = " << phi6
|
||||
<< " is "
|
||||
<< ::boost::math::spherical(rho, theta,
|
||||
phi1, phi2, phi3, phi4, phi5, phi6));
|
||||
|
||||
float rho1 = 1;
|
||||
float rho2 = 2;
|
||||
float rho3 = ::std::sqrt(2.0f);
|
||||
float rho4 = ::std::sqrt(8.0f);
|
||||
float theta1 = 0;
|
||||
float theta2 = ::std::atan(1.0f)*2;
|
||||
float theta3 = ::std::atan(1.0f);
|
||||
float theta4 = ::std::atan(::std::sqrt(3.0f));
|
||||
|
||||
BOOST_TEST_MESSAGE( "The value of the octonion represented "
|
||||
<< "in multipolar form by "
|
||||
<< "rho1 = " << rho1 << " , theta1 = " << theta1
|
||||
<< " , rho2 = " << rho2 << " , theta2 = " << theta2
|
||||
<< "rho3 = " << rho3 << " , theta3 = " << theta3
|
||||
<< " , rho4 = " << rho4 << " , theta4 = " << theta4
|
||||
<< " is "
|
||||
<< ::boost::math::multipolar(rho1, theta1, rho2, theta2,
|
||||
rho3, theta3, rho4, theta4));
|
||||
|
||||
float r = ::std::sqrt(2.0f);
|
||||
float angle = ::std::atan(1.0f);
|
||||
float h1 = 3;
|
||||
float h2 = 4;
|
||||
float h3 = 5;
|
||||
float h4 = 6;
|
||||
float h5 = 7;
|
||||
float h6 = 8;
|
||||
|
||||
BOOST_TEST_MESSAGE( "The value of the octonion represented "
|
||||
<< "in cylindrical form by "
|
||||
<< "r = " << r << " , angle = " << angle
|
||||
<< " , h1 = " << h1 << " , h2 = " << h2
|
||||
<< " , h3 = " << h3 << " , h4 = " << h4
|
||||
<< " , h5 = " << h5 << " , h6 = " << h6
|
||||
<< " is " << ::boost::math::cylindrical(r, angle,
|
||||
h1, h2, h3, h4, h5, h6));
|
||||
|
||||
double real_1(1);
|
||||
::std::complex<double> complex_1(1);
|
||||
::std::complex<double> complex_i(0,1);
|
||||
::boost::math::quaternion<double> quaternion_1(1);
|
||||
::boost::math::quaternion<double> quaternion_i(0,1);
|
||||
::boost::math::quaternion<double> quaternion_j(0,0,1);
|
||||
::boost::math::quaternion<double> quaternion_k(0,0,0,1);
|
||||
::boost::math::octonion<double> octonion_1(1);
|
||||
::boost::math::octonion<double> octonion_i(0,1);
|
||||
::boost::math::octonion<double> octonion_j(0,0,1);
|
||||
::boost::math::octonion<double> octonion_k(0,0,0,1);
|
||||
::boost::math::octonion<double> octonion_e_prime(0,0,0,0,1);
|
||||
::boost::math::octonion<double> octonion_i_prime(0,0,0,0,0,1);
|
||||
::boost::math::octonion<double> octonion_j_prime(0,0,0,0,0,0,1);
|
||||
::boost::math::octonion<double> octonion_k_prime(0,0,0,0,0,0,0,1);
|
||||
|
||||
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Real 1: " << real_1
|
||||
<< " ; Complex 1: " << complex_1
|
||||
<< " ; Quaternion 1: " << quaternion_1
|
||||
<< " ; Octonion 1: " << octonion_1 << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Complex i: " << complex_i
|
||||
<< " ; Quaternion i: " << quaternion_i
|
||||
<< " ; Octonion i : " << octonion_i << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Quaternion j: " << quaternion_j
|
||||
<< " ; Octonion j: " << octonion_j << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Quaternion k: " << quaternion_k
|
||||
<< " ; Octonion k: " << octonion_k << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Quaternion e\': " << octonion_e_prime << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Quaternion i\': " << octonion_i_prime << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Quaternion j\': " << octonion_j_prime << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE( "Quaternion k\': " << octonion_k_prime << " .");
|
||||
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_1*octonion_1 << " ; "
|
||||
<< octonion_1*octonion_i << " ; "
|
||||
<< octonion_1*octonion_j << " ; "
|
||||
<< octonion_1*octonion_k << " ; "
|
||||
<< octonion_1*octonion_e_prime << " ; "
|
||||
<< octonion_1*octonion_i_prime << " ; "
|
||||
<< octonion_1*octonion_j_prime << " ; "
|
||||
<< octonion_1*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_i*octonion_1 << " ; "
|
||||
<< octonion_i*octonion_i << " ; "
|
||||
<< octonion_i*octonion_j << " ; "
|
||||
<< octonion_i*octonion_k << " ; "
|
||||
<< octonion_i*octonion_e_prime << " ; "
|
||||
<< octonion_i*octonion_i_prime << " ; "
|
||||
<< octonion_i*octonion_j_prime << " ; "
|
||||
<< octonion_i*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_j*octonion_1 << " ; "
|
||||
<< octonion_j*octonion_i << " ; "
|
||||
<< octonion_j*octonion_j << " ; "
|
||||
<< octonion_j*octonion_k << " ; "
|
||||
<< octonion_j*octonion_e_prime << " ; "
|
||||
<< octonion_j*octonion_i_prime << " ; "
|
||||
<< octonion_j*octonion_j_prime << " ; "
|
||||
<< octonion_j*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_k*octonion_1 << " ; "
|
||||
<< octonion_k*octonion_i << " ; "
|
||||
<< octonion_k*octonion_j << " ; "
|
||||
<< octonion_k*octonion_k << " ; "
|
||||
<< octonion_k*octonion_e_prime << " ; "
|
||||
<< octonion_k*octonion_i_prime << " ; "
|
||||
<< octonion_k*octonion_j_prime << " ; "
|
||||
<< octonion_k*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_e_prime*octonion_1 << " ; "
|
||||
<< octonion_e_prime*octonion_i << " ; "
|
||||
<< octonion_e_prime*octonion_j << " ; "
|
||||
<< octonion_e_prime*octonion_k << " ; "
|
||||
<< octonion_e_prime*octonion_e_prime << " ; "
|
||||
<< octonion_e_prime*octonion_i_prime << " ; "
|
||||
<< octonion_e_prime*octonion_j_prime << " ; "
|
||||
<< octonion_e_prime*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_i_prime*octonion_1 << " ; "
|
||||
<< octonion_i_prime*octonion_i << " ; "
|
||||
<< octonion_i_prime*octonion_j << " ; "
|
||||
<< octonion_i_prime*octonion_k << " ; "
|
||||
<< octonion_i_prime*octonion_e_prime << " ; "
|
||||
<< octonion_i_prime*octonion_i_prime << " ; "
|
||||
<< octonion_i_prime*octonion_j_prime << " ; "
|
||||
<< octonion_i_prime*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_j_prime*octonion_1 << " ; "
|
||||
<< octonion_j_prime*octonion_i << " ; "
|
||||
<< octonion_j_prime*octonion_j << " ; "
|
||||
<< octonion_j_prime*octonion_k << " ; "
|
||||
<< octonion_j_prime*octonion_e_prime << " ; "
|
||||
<< octonion_j_prime*octonion_i_prime << " ; "
|
||||
<< octonion_j_prime*octonion_j_prime << " ; "
|
||||
<< octonion_j_prime*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE( octonion_k_prime*octonion_1 << " ; "
|
||||
<< octonion_k_prime*octonion_i << " ; "
|
||||
<< octonion_k_prime*octonion_j << " ; "
|
||||
<< octonion_k_prime*octonion_k << " ; "
|
||||
<< octonion_k_prime*octonion_e_prime << " ; "
|
||||
<< octonion_k_prime*octonion_i_prime << " ; "
|
||||
<< octonion_k_prime*octonion_j_prime << " ; "
|
||||
<< octonion_k_prime*octonion_k_prime << " ; ");
|
||||
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
|
||||
BOOST_TEST_MESSAGE("i\'*(e\'*j) : "
|
||||
<< octonion_i_prime*(octonion_e_prime*octonion_j) << " ;");
|
||||
|
||||
BOOST_TEST_MESSAGE("(i\'*e\')*j : "
|
||||
<< (octonion_i_prime*octonion_e_prime)*octonion_j << " ;");
|
||||
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
}
|
||||
|
||||
|
||||
BOOST_TEST_CASE_TEMPLATE_FUNCTION(multiplication_test, T)
|
||||
{
|
||||
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
||||
#else /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
||||
using ::std::numeric_limits;
|
||||
|
||||
using ::boost::math::abs;
|
||||
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
||||
|
||||
|
||||
BOOST_TEST_MESSAGE("Testing multiplication for "
|
||||
<< string_type_name<T>::_() << ".");
|
||||
|
||||
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
|
||||
(abs(::boost::math::octonion<T>(1,0,0,0,0,0,0,0)*
|
||||
::boost::math::octonion<T>(1,0,0,0,0,0,0,0)-
|
||||
static_cast<T>(1)))
|
||||
(numeric_limits<T>::epsilon()));
|
||||
|
||||
for (int idx = 1; idx < 8; ++idx)
|
||||
{
|
||||
::boost::math::octonion<T> toto = index_i_element<T>(idx);
|
||||
|
||||
BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
|
||||
(abs(toto*toto+static_cast<T>(1)))
|
||||
(numeric_limits<T>::epsilon()));
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
BOOST_TEST_CASE_TEMPLATE_FUNCTION(exp_test, T)
|
||||
{
|
||||
#if BOOST_WORKAROUND(__GNUC__, < 3)
|
||||
#else /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
||||
using ::std::numeric_limits;
|
||||
|
||||
using ::std::atan;
|
||||
|
||||
using ::boost::math::abs;
|
||||
#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
|
||||
|
||||
|
||||
BOOST_TEST_MESSAGE("Testing exp for "
|
||||
<< string_type_name<T>::_() << ".");
|
||||
|
||||
for (int idx = 1; idx < 8; ++idx)
|
||||
{
|
||||
::boost::math::octonion<T> toto =
|
||||
static_cast<T>(4)*atan(static_cast<T>(1))*index_i_element<T>(idx);
|
||||
|
||||
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
|
||||
(abs(exp(toto)+static_cast<T>(1)))
|
||||
(2*numeric_limits<T>::epsilon()));
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
boost::unit_test::test_suite * init_unit_test_suite(int, char *[])
|
||||
{
|
||||
::boost::unit_test::unit_test_log.
|
||||
set_threshold_level(::boost::unit_test::log_messages);
|
||||
|
||||
boost::unit_test::test_suite * test =
|
||||
BOOST_TEST_SUITE("octonion_test");
|
||||
|
||||
BOOST_TEST_MESSAGE("Results of octonion test.");
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
BOOST_TEST_MESSAGE("(C) Copyright Hubert Holin 2003-2005.");
|
||||
BOOST_TEST_MESSAGE("Distributed under the Boost Software License, Version 1.0.");
|
||||
BOOST_TEST_MESSAGE("(See accompanying file LICENSE_1_0.txt or copy at");
|
||||
BOOST_TEST_MESSAGE("http://www.boost.org/LICENSE_1_0.txt)");
|
||||
BOOST_TEST_MESSAGE(" ");
|
||||
|
||||
#define BOOST_OCTONION_COMMON_GENERATOR(fct) \
|
||||
test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, test_types));
|
||||
|
||||
#define BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(fct) \
|
||||
test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, near_eps_test_types));
|
||||
|
||||
|
||||
#define BOOST_OCTONION_TEST \
|
||||
BOOST_OCTONION_COMMON_GENERATOR(multiplication) \
|
||||
BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(exp)
|
||||
|
||||
|
||||
BOOST_OCTONION_TEST
|
||||
|
||||
|
||||
#undef BOOST_OCTONION_TEST
|
||||
|
||||
#undef BOOST_OCTONION_COMMON_GENERATOR
|
||||
#undef BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS
|
||||
|
||||
#ifdef BOOST_OCTONION_TEST_VERBOSE
|
||||
|
||||
test->add(BOOST_TEST_CASE(octonion_manual_test));
|
||||
|
||||
#endif /* BOOST_OCTONION_TEST_VERBOSE */
|
||||
|
||||
return test;
|
||||
}
|
||||
|
||||
#undef DEFINE_TYPE_NAME
|
||||
@@ -883,7 +883,7 @@ compile compile_test/tools_toms748_inc_test.cpp ;
|
||||
run ../test/common_factor_test.cpp
|
||||
../../test/build//boost_unit_test_framework ;
|
||||
|
||||
run ../octonion/octonion_test.cpp
|
||||
run octonion_test.cpp
|
||||
../../test/build//boost_unit_test_framework ;
|
||||
|
||||
run ../quaternion/quaternion_test.cpp
|
||||
|
||||
Reference in New Issue
Block a user