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26 | <div class="titlepage"><div><div><h2 class="title" style="clear: both"> | |
27 | <a name="math_toolkit.oct_mem_fun"></a><a class="link" href="oct_mem_fun.html" title="Octonion Member Functions">Octonion Member Functions</a> | |
28 | </h2></div></div></div> | |
29 | <h4> | |
30 | <a name="math_toolkit.oct_mem_fun.h0"></a> | |
31 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.constructors"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.constructors">Constructors</a> | |
32 | </h4> | |
33 | <p> | |
34 | Template version: | |
35 | </p> | |
36 | <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span> | |
37 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span> | |
38 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>());</span> | |
39 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> | |
40 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
41 | </pre> | |
42 | <p> | |
43 | Float specialization version: | |
44 | </p> | |
45 | <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span> | |
46 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span> | |
47 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">float</span><span class="special">>());</span> | |
48 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
49 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
50 | </pre> | |
51 | <p> | |
52 | Double specialization version: | |
53 | </p> | |
54 | <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span> | |
55 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span> | |
56 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span> | |
57 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
58 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
59 | </pre> | |
60 | <p> | |
61 | Long double specialization version: | |
62 | </p> | |
63 | <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span> | |
64 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span> | |
65 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span> | |
66 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
67 | <span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span> | |
68 | </pre> | |
69 | <p> | |
70 | A default constructor is provided for each form, which initializes each component | |
71 | to the default values for their type (i.e. zero for floating numbers). This | |
72 | constructor can also accept one to eight base type arguments. A constructor | |
73 | is also provided to build octonions from one to four complex numbers sharing | |
74 | the same base type, and another taking one or two quaternions sharing the same | |
75 | base type. The unspecialized template also sports a templarized copy constructor, | |
76 | while the specialized forms have copy constructors from the other two specializations, | |
77 | which are explicit when a risk of precision loss exists. For the unspecialized | |
78 | form, the base type's constructors must not throw. | |
79 | </p> | |
80 | <p> | |
81 | Destructors and untemplated copy constructors (from the same type) are provided | |
82 | by the compiler. Converting copy constructors make use of a templated helper | |
83 | function in a "detail" subnamespace. | |
84 | </p> | |
85 | <h4> | |
86 | <a name="math_toolkit.oct_mem_fun.h1"></a> | |
87 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.other_member_functions"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.other_member_functions">Other | |
88 | member functions</a> | |
89 | </h4> | |
90 | <h5> | |
91 | <a name="math_toolkit.oct_mem_fun.h2"></a> | |
92 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.real_and_unreal_parts"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.real_and_unreal_parts">Real | |
93 | and Unreal Parts</a> | |
94 | </h5> | |
95 | <pre class="programlisting"><span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
96 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
97 | </pre> | |
98 | <p> | |
99 | Like complex number, octonions do have a meaningful notion of "real part", | |
100 | but unlike them there is no meaningful notion of "imaginary part". | |
101 | Instead there is an "unreal part" which itself is a octonion, and | |
102 | usually nothing simpler (as opposed to the complex number case). These are | |
103 | returned by the first two functions. | |
104 | </p> | |
105 | <h5> | |
106 | <a name="math_toolkit.oct_mem_fun.h3"></a> | |
107 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.individual_real_components"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.individual_real_components">Individual | |
108 | Real Components</a> | |
109 | </h5> | |
110 | <pre class="programlisting"><span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
111 | <span class="identifier">T</span> <span class="identifier">R_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
112 | <span class="identifier">T</span> <span class="identifier">R_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
113 | <span class="identifier">T</span> <span class="identifier">R_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
114 | <span class="identifier">T</span> <span class="identifier">R_component_5</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
115 | <span class="identifier">T</span> <span class="identifier">R_component_6</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
116 | <span class="identifier">T</span> <span class="identifier">R_component_7</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
117 | <span class="identifier">T</span> <span class="identifier">R_component_8</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
118 | </pre> | |
119 | <p> | |
120 | A octonion having eight real components, these are returned by these eight | |
121 | functions. Hence real and R_component_1 return the same value. | |
122 | </p> | |
123 | <h5> | |
124 | <a name="math_toolkit.oct_mem_fun.h4"></a> | |
125 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.individual_complex_components"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.individual_complex_components">Individual | |
126 | Complex Components</a> | |
127 | </h5> | |
128 | <pre class="programlisting"><span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
129 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
130 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
131 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
132 | </pre> | |
133 | <p> | |
134 | A octonion likewise has four complex components. Actually, octonions are indeed | |
135 | a (left) vector field over the complexes, but beware, as for any octonion | |
136 | <span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span> we also have <span class="emphasis"><em><code class="literal">o | |
137 | = (α + βi) + (γ + δi)j + (ε + ζi)e' + (η - θi)j'</code></em></span> (note the <span class="bold"><strong>minus</strong></span> sign | |
138 | in the last factor). What the C_component_n functions return, however, are | |
139 | the complexes which could be used to build the octonion using the constructor, | |
140 | and <span class="bold"><strong>not</strong></span> the components of the octonion on | |
141 | the basis <span class="emphasis"><em><code class="literal">(1, j, e', j')</code></em></span>. | |
142 | </p> | |
143 | <h5> | |
144 | <a name="math_toolkit.oct_mem_fun.h5"></a> | |
145 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.individual_quaternion_components"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.individual_quaternion_components">Individual | |
146 | Quaternion Components</a> | |
147 | </h5> | |
148 | <pre class="programlisting"><span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">H_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
149 | <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">H_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> | |
150 | </pre> | |
151 | <p> | |
152 | Likewise, for any octonion <span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span> we | |
153 | also have <span class="emphasis"><em><code class="literal">o = (α + βi + γj + δk) + (ε + ζi + ηj - θj)e'</code></em></span>, though there is no | |
154 | meaningful vector-space-like structure based on the quaternions. What the H_component_n | |
155 | functions return are the quaternions which could be used to build the octonion | |
156 | using the constructor. | |
157 | </p> | |
158 | <h4> | |
159 | <a name="math_toolkit.oct_mem_fun.h6"></a> | |
160 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.octonion_member_operators"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.octonion_member_operators">Octonion | |
161 | Member Operators</a> | |
162 | </h4> | |
163 | <h5> | |
164 | <a name="math_toolkit.oct_mem_fun.h7"></a> | |
165 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.assignment_operators"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.assignment_operators">Assignment | |
166 | Operators</a> | |
167 | </h5> | |
168 | <pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> | |
169 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> | |
170 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> | |
171 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> | |
172 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> | |
173 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> | |
174 | </pre> | |
175 | <p> | |
176 | These perform the expected assignment, with type modification if necessary | |
177 | (for instance, assigning from a base type will set the real part to that value, | |
178 | and all other components to zero). For the unspecialized form, the base type's | |
179 | assignment operators must not throw. | |
180 | </p> | |
181 | <h5> | |
182 | <a name="math_toolkit.oct_mem_fun.h8"></a> | |
183 | <span class="phrase"><a name="math_toolkit.oct_mem_fun.other_member_operators"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.other_member_operators">Other | |
184 | Member Operators</a> | |
185 | </h5> | |
186 | <pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span> | |
187 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
188 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
189 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> | |
190 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
191 | </pre> | |
192 | <p> | |
193 | These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)+</span><span class="identifier">rhs</span></code> | |
194 | and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. | |
195 | The unspecialized form has exception guards, which the specialized forms do | |
196 | not, so as to insure exception safety. For the unspecialized form, the base | |
197 | type's assignment operators must not throw. | |
198 | </p> | |
199 | <pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span> | |
200 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
201 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
202 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> | |
203 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
204 | </pre> | |
205 | <p> | |
206 | These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)-</span><span class="identifier">rhs</span></code> | |
207 | and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. | |
208 | The unspecialized form has exception guards, which the specialized forms do | |
209 | not, so as to insure exception safety. For the unspecialized form, the base | |
210 | type's assignment operators must not throw. | |
211 | </p> | |
212 | <pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span> | |
213 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
214 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
215 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> | |
216 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
217 | </pre> | |
218 | <p> | |
219 | These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">rhs</span></code> | |
220 | in this order (order is important as multiplication is not commutative for | |
221 | octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception guards, | |
222 | which the specialized forms do not, so as to insure exception safety. For the | |
223 | unspecialized form, the base type's assignment operators must not throw. Also, | |
224 | for clarity's sake, you should always group the factors in a multiplication | |
225 | by groups of two, as the multiplication is not even associative on the octonions | |
226 | (though there are of course cases where this does not matter, it usually does). | |
227 | </p> | |
228 | <pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">)</span> | |
229 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
230 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
231 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> | |
232 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> | |
233 | </pre> | |
234 | <p> | |
235 | These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">inverse_of</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">)</span></code> | |
236 | in this order (order is important as multiplication is not commutative for | |
237 | octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception guards, | |
238 | which the specialized forms do not, so as to insure exception safety. For the | |
239 | unspecialized form, the base type's assignment operators must not throw. As | |
240 | for the multiplication, remember to group any two factors using parenthesis. | |
241 | </p> | |
242 | </div> | |
243 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
244 | <td align="left"></td> | |
245 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
246 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
247 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
248 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
249 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
250 | file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) | |
251 | </p> | |
252 | </div></td> | |
253 | </tr></table> | |
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