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oct_value_ops.html

oct_value_ops.html 10 KB
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  4. <title>Octonion Value Operations</title>
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  23. <a accesskey="p" href="oct_non_mem.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="oct_create.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
    24. 

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    25. 

  25. <div class="section">
    26. 

  26. <div class="titlepage"><div><div><h2 class="title" style="clear: both">
    27. 

  27. <a name="math_toolkit.oct_value_ops"></a><a class="link" href="oct_value_ops.html" title="Octonion Value Operations">Octonion Value Operations</a>
    28. 

  28. </h2></div></div></div>
    29. 

  29. <h5>
    30. 

  30. <a name="math_toolkit.oct_value_ops.h0"></a>
    31. 

  31.       <span class="phrase"><a name="math_toolkit.oct_value_ops.real_and_unreal"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.real_and_unreal">Real
    32. 

  32.       and Unreal</a>
    33. 

  33.     </h5>
    34. 

  34. <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>  <span class="identifier">real</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    35. 

  35. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    36. 

  36. </pre>
    37. 

  37. <p>
    38. 

  38.       These return <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code> and
    39. 

  39.       <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
    40. 

  40.       respectively.
    41. 

  41.     </p>
    42. 

  42. <h5>
    43. 

  43. <a name="math_toolkit.oct_value_ops.h1"></a>
    44. 

  44.       <span class="phrase"><a name="math_toolkit.oct_value_ops.conj"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.conj">conj</a>
    45. 

  45.     </h5>
    46. 

  46. <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    47. 

  47. </pre>
    48. 

  48. <p>
    49. 

  49.       This returns the conjugate of the octonion.
    50. 

  50.     </p>
    51. 

  51. <h5>
    52. 

  52. <a name="math_toolkit.oct_value_ops.h2"></a>
    53. 

  53.       <span class="phrase"><a name="math_toolkit.oct_value_ops.sup"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.sup">sup</a>
    54. 

  54.     </h5>
    55. 

  55. <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">sup</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    56. 

  56. </pre>
    57. 

  57. <p>
    58. 

  58.       This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()))</span></code> of the octonion.
    59. 

  59.     </p>
    60. 

  60. <h5>
    61. 

  61. <a name="math_toolkit.oct_value_ops.h3"></a>
    62. 

  62.       <span class="phrase"><a name="math_toolkit.oct_value_ops.l1"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.l1">l1</a>
    63. 

  63.     </h5>
    64. 

  64. <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">l1</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    65. 

  65. </pre>
    66. 

  66. <p>
    67. 

  67.       This return the l1 norm (<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">())</span></code>) of the octonion.
    68. 

  68.     </p>
    69. 

  69. <h5>
    70. 

  70. <a name="math_toolkit.oct_value_ops.h4"></a>
    71. 

  71.       <span class="phrase"><a name="math_toolkit.oct_value_ops.abs"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.abs">abs</a>
    72. 

  72.     </h5>
    73. 

  73. <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">abs</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    74. 

  74. </pre>
    75. 

  75. <p>
    76. 

  76.       This return the magnitude (Euclidian norm) of the octonion.
    77. 

  77.     </p>
    78. 

  78. <h5>
    79. 

  79. <a name="math_toolkit.oct_value_ops.h5"></a>
    80. 

  80.       <span class="phrase"><a name="math_toolkit.oct_value_ops.norm"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.norm">norm</a>
    81. 

  81.     </h5>
    82. 

  82. <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>  <span class="identifier">norm</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
    83. 

  83. </pre>
    84. 

  84. <p>
    85. 

  85.       This return the (Cayley) norm of the octonion. The term "norm" might
    86. 

  86.       be confusing, as most people associate it with the Euclidian norm (and quadratic
    87. 

  87.       functionals). For this version of (the mathematical objects known as) octonions,
    88. 

  88.       the Euclidian norm (also known as magnitude) is the square root of the Cayley
    89. 

  89.       norm.
    90. 

  90.     </p>
    91. 

  91. </div>
    92. 

  92. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    93. 

  93. <td align="left"></td>
    94. 

  94. <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
    95. 

  95.       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
    96. 

  96.       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
    97. 

  97.       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
    98. 

  98.       Daryle Walker and Xiaogang Zhang<p>
    99. 

  99.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    100. 

  100.         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>)
    101. 

  101.       </p>
    102. 

  102. </div></td>
    103. 

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    104. 

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    105. 

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    106. 

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