mirror of
https://github.com/boostorg/math.git
synced 2026-01-19 04:22:09 +00:00
Remove the quaternion directory and move contents elsewhere.
This commit is contained in:
jzmaddock
3
.gitignore
vendored
3
.gitignore
vendored
@@ -1,2 +1,5 @@
|
||||
/doc/inspect.htm
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||||
/**/*.log
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||||
reporting/*/third_party
|
||||
reporting/*/html
|
||||
inspect.html
|
||||
|
||||
@@ -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 17:50:26 GMT</small></p></td>
|
||||
<td align="left"><p><small>Last revised: September 07, 2015 at 18:05:58 GMT</small></p></td>
|
||||
<td align="right"><div class="copyright-footer"></div></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1678960"></a>Function Index</h2></div></div></div>
|
||||
<a name="id1680772"></a>Function Index</h2></div></div></div>
|
||||
<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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||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1702138"></a>Class Index</h2></div></div></div>
|
||||
<a name="id1703221"></a>Class Index</h2></div></div></div>
|
||||
<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>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<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">
|
||||
<a name="id1703210"></a>Typedef Index</h2></div></div></div>
|
||||
<a name="id1702102"></a>Typedef Index</h2></div></div></div>
|
||||
<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>
|
||||
<div class="variablelist"><dl class="variablelist">
|
||||
<dt>
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1706274"></a>Macro Index</h2></div></div></div>
|
||||
<a name="id1705969"></a>Macro Index</h2></div></div></div>
|
||||
<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">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="id1710345"></a>Index</h2></div></div></div>
|
||||
<a name="id1708778"></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">
|
||||
<dt>
|
||||
|
||||
@@ -27,7 +27,7 @@
|
||||
<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
|
||||
</h2></div></div></div>
|
||||
<p>
|
||||
<a class="indexterm" name="id832776"></a>
|
||||
<a class="indexterm" name="id836451"></a>
|
||||
</p>
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||||
<p>
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||||
This documentation aims to use of the following naming and formatting conventions.
|
||||
|
||||
@@ -98,7 +98,7 @@
|
||||
are not too complicated, but there is currently a lack of standard (de facto
|
||||
or de jure) matrix library with which the conversions could work. This should
|
||||
be remedied in a further revision. In the mean time, an example of how this
|
||||
could be done is presented here for <a href="../../../quaternion/HSO3.hpp" target="_top"><span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span></a>, and here for <a href="../../../quaternion/HSO4.hpp" target="_top"><span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span></a> (<a href="../../../quaternion/HSO3SO4.cpp" target="_top">example
|
||||
could be done is presented here for <a href="../../../example/HSO3.hpp" target="_top"><span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span></a>, and here for <a href="../../../example/HSO4.hpp" target="_top"><span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span></a> (<a href="../../../example/HSO3SO4.cpp" target="_top">example
|
||||
test file</a>).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
@@ -31,11 +31,10 @@
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
<a href="../../../quaternion/TQE.pdf" target="_top">The Quaternionic Exponential (and
|
||||
beyond)</a>
|
||||
<a href="../../quaternion/TQE.pdf" target="_top">The Quaternionic Exponential (and beyond)</a>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<a href="../../../quaternion/TQE_EA.pdf" target="_top">The Quaternionic Exponential (and
|
||||
<a href="../../quaternion/TQE_EA.pdf" target="_top">The Quaternionic Exponential (and
|
||||
beyond) ERRATA & ADDENDA</a>
|
||||
</li>
|
||||
</ul></div>
|
||||
|
||||
@@ -27,7 +27,7 @@
|
||||
<a name="math_toolkit.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
|
||||
</h2></div></div></div>
|
||||
<p>
|
||||
<a class="indexterm" name="id832632"></a>
|
||||
<a class="indexterm" name="id836345"></a>
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||||
</p>
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||||
<p>
|
||||
Boost.Math documentation is provided in both HTML and PDF formats.
|
||||
|
||||
@@ -56,7 +56,7 @@
|
||||
</p>
|
||||
<p>
|
||||
Octonions (and their kin) are described in far more details in this other
|
||||
<a href="../../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../../quaternion/TQE_EA.pdf" target="_top">errata
|
||||
<a href="../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../quaternion/TQE_EA.pdf" target="_top">errata
|
||||
and addenda</a>).
|
||||
</p>
|
||||
<p>
|
||||
|
||||
@@ -68,7 +68,7 @@
|
||||
</p>
|
||||
<p>
|
||||
Quaternions (and their kin) are described in far more details in this other
|
||||
<a href="../../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../../quaternion/TQE_EA.pdf" target="_top">errata
|
||||
<a href="../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../quaternion/TQE_EA.pdf" target="_top">errata
|
||||
and addenda</a>).
|
||||
</p>
|
||||
<p>
|
||||
|
||||
@@ -27,13 +27,13 @@
|
||||
<a name="math_toolkit.quat_tests"></a><a class="link" href="quat_tests.html" title="Test Program">Test Program</a>
|
||||
</h2></div></div></div>
|
||||
<p>
|
||||
The <a href="../../../quaternion/quaternion_test.cpp" target="_top">quaternion_test.cpp</a>
|
||||
The <a href="../../../test/quaternion_test.cpp" target="_top">quaternion_test.cpp</a>
|
||||
test program tests quaternions specializations for float, double and long double
|
||||
(<a href="../../../quaternion/output.txt" target="_top">sample output</a>, with message
|
||||
(<a href="../../quaternion/output.txt" target="_top">sample output</a>, with message
|
||||
output enabled).
|
||||
</p>
|
||||
<p>
|
||||
If you define the symbol TEST_VERBOSE, you will get additional output (<a href="../../../quaternion/output_more.txt" target="_top">verbose output</a>); this will only
|
||||
If you define the symbol TEST_VERBOSE, you will get additional output (<a href="../../quaternion/output_more.txt" target="_top">verbose output</a>); 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 <code class="literal">--log_level=messages</code>
|
||||
to your command line,...). In that case, and if you are running interactively,
|
||||
|
||||
@@ -37,7 +37,7 @@
|
||||
Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
|
||||
</li>
|
||||
<li class="listitem">
|
||||
Use uBlas for the link with rotations (and move from the <a href="../../../quaternion/HSO3SO4.cpp" target="_top">example</a>
|
||||
Use uBlas for the link with rotations (and move from the <a href="../../../example/HSO3SO4.cpp" target="_top">example</a>
|
||||
implementation to an efficient one).
|
||||
</li>
|
||||
</ul></div>
|
||||
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||||
BIN
doc/math.pdf
Normal file
BIN
doc/math.pdf
Normal file
Binary file not shown.
@@ -33,8 +33,8 @@ A way of remembering things is by using the following multiplication table:
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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]
|
||||
(with [@../../quaternion/TQE_EA.pdf errata and addenda]).
|
||||
[@../quaternion/TQE.pdf document]
|
||||
(with [@../quaternion/TQE_EA.pdf errata and addenda]).
|
||||
|
||||
Some traditional constructs, such as the exponential, carry over without too
|
||||
much change into the realms of octonions, but other, such as taking a square root,
|
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|
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@@ -41,8 +41,8 @@ quaternions ['[^x]] and ['[^y]] such that __not_equal). A good mnemotechnical wa
|
||||
things is by using the formula ['[^i*i = j*j = k*k = -1]].
|
||||
|
||||
Quaternions (and their kin) are described in far more details in this
|
||||
other [@../../quaternion/TQE.pdf document]
|
||||
(with [@../../quaternion/TQE_EA.pdf errata and addenda]).
|
||||
other [@../quaternion/TQE.pdf document]
|
||||
(with [@../quaternion/TQE_EA.pdf errata and addenda]).
|
||||
|
||||
Some traditional constructs, such as the exponential, carry over without
|
||||
too much change into the realms of quaternions, but other, such as taking
|
||||
@@ -753,9 +753,9 @@ but there is currently a lack of standard (de facto or de jure) matrix
|
||||
library with which the conversions could work. This should be remedied in
|
||||
a further revision. In the mean time, an example of how this could be
|
||||
done is presented here for
|
||||
[@../../quaternion/HSO3.hpp __R3], and here for
|
||||
[@../../quaternion/HSO4.hpp __R4]
|
||||
([@../../quaternion/HSO3SO4.cpp example test file]).
|
||||
[@../../example/HSO3.hpp __R3], and here for
|
||||
[@../../example/HSO4.hpp __R4]
|
||||
([@../../example/HSO3SO4.cpp example test file]).
|
||||
|
||||
[endsect]
|
||||
|
||||
@@ -838,13 +838,13 @@ Computes the n-th power of the quaternion q.
|
||||
|
||||
[section:quat_tests Test Program]
|
||||
|
||||
The [@../../quaternion/quaternion_test.cpp quaternion_test.cpp]
|
||||
The [@../../test/quaternion_test.cpp quaternion_test.cpp]
|
||||
test program tests quaternions specializations for float, double and long double
|
||||
([@../../quaternion/output.txt sample output], with message output
|
||||
([@../quaternion/output.txt sample output], with message output
|
||||
enabled).
|
||||
|
||||
If you define the symbol TEST_VERBOSE, you will get
|
||||
additional output ([@../../quaternion/output_more.txt verbose output]);
|
||||
additional output ([@../quaternion/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
|
||||
@@ -859,8 +859,8 @@ operator with input of your choice from the standard input
|
||||
|
||||
Please refer to the following PDF's:
|
||||
|
||||
*[@../../quaternion/TQE.pdf The Quaternionic Exponential (and beyond)]
|
||||
*[@../../quaternion/TQE_EA.pdf The Quaternionic Exponential (and beyond) ERRATA & ADDENDA]
|
||||
*[@../quaternion/TQE.pdf The Quaternionic Exponential (and beyond)]
|
||||
*[@../quaternion/TQE_EA.pdf The Quaternionic Exponential (and beyond) ERRATA & ADDENDA]
|
||||
|
||||
[endsect]
|
||||
|
||||
@@ -900,7 +900,7 @@ Thank you to all who contributed to the discution about this library.
|
||||
* Rewrite input operatore using Spirit (creates a dependency).
|
||||
* Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
|
||||
* Use uBlas for the link with rotations (and move from the
|
||||
[@../../quaternion/HSO3SO4.cpp example]
|
||||
[@../../example/HSO3SO4.cpp example]
|
||||
implementation to an efficient one).
|
||||
|
||||
[endsect]
|
||||
|
||||
@@ -114,6 +114,7 @@ run students_t_example2.cpp ;
|
||||
run students_t_example3.cpp ;
|
||||
run students_t_single_sample.cpp ;
|
||||
run students_t_two_samples.cpp ;
|
||||
run HSO3SO4.cpp ;
|
||||
|
||||
run root_elliptic_finding.cpp /boost/timer : : : release <link>static ;
|
||||
run root_finding_algorithms.cpp /boost/timer : : : release <link>static ;
|
||||
|
||||
@@ -886,12 +886,12 @@ run ../test/common_factor_test.cpp
|
||||
run octonion_test.cpp
|
||||
../../test/build//boost_unit_test_framework ;
|
||||
|
||||
run ../quaternion/quaternion_test.cpp
|
||||
run quaternion_test.cpp
|
||||
../../test/build//boost_unit_test_framework ;
|
||||
|
||||
run ../quaternion/quaternion_mult_incl_test.cpp
|
||||
../quaternion/quaternion_mi1.cpp
|
||||
../quaternion/quaternion_mi2.cpp
|
||||
run quaternion_mult_incl_test.cpp
|
||||
quaternion_mi1.cpp
|
||||
quaternion_mi2.cpp
|
||||
../../test/build//boost_unit_test_framework ;
|
||||
|
||||
|
||||
|
||||
775
test/octonion_test.cpp
Normal file
775
test/octonion_test.cpp
Normal file
@@ -0,0 +1,775 @@
|
||||
// test file for octonion.hpp
|
||||
|
||||
// (C) Copyright Hubert Holin 2001.
|
||||
// Distributed under the Boost Software License, Version 1.0. (See
|
||||
// accompanying file LICENSE_1_0.txt or copy at
|
||||
// http://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
|
||||
#include <iomanip>
|
||||
|
||||
|
||||
#include <boost/mpl/list.hpp>
|
||||
|
||||
#include <boost/test/unit_test.hpp>
|
||||
#include <boost/test/unit_test_log.hpp>
|
||||
|
||||
#include <boost/math/octonion.hpp>
|
||||
|
||||
|
||||
template<typename T>
|
||||
struct string_type_name;
|
||||
|
||||
#define DEFINE_TYPE_NAME(Type) \
|
||||
template<> struct string_type_name<Type> \
|
||||
{ \
|
||||
static char const * _() \
|
||||
{ \
|
||||
return #Type; \
|
||||
} \
|
||||
}
|
||||
|
||||
DEFINE_TYPE_NAME(float);
|
||||
DEFINE_TYPE_NAME(double);
|
||||
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
||||
DEFINE_TYPE_NAME(long double);
|
||||
#endif
|
||||
|
||||
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
||||
typedef boost::mpl::list<float,double,long double> test_types;
|
||||
#else
|
||||
typedef boost::mpl::list<float,double> test_types;
|
||||
#endif
|
||||
|
||||
// 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)
|
||||
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
|
||||
Reference in New Issue
Block a user