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‎reference/linalg.html

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<p class="text-right"><small>
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最終更新日時(UTC):
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<span itemprop="datePublished" content="2024-06-01T10:29:46">
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2024年06月01日 10時29分46秒
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<span itemprop="datePublished" content="2024-06-16T08:54:12">
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2024年06月16日 08時54分12秒
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<td>C++26</td>
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</tr>
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<tr>
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<td><code>add</code></td>
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<td><code><a href="linalg/add.html">add</a></code></td>
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<td>xAXPY: 2つのベクトル／行列の要素を加算する (function template)</td>
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<td>C++26</td>
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</tr>
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<tr>
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<td><code>dot</code></td>
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<td><code><a href="linalg/dot.html">dot</a></code></td>
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<td>xDOT, xDOTU: 2つのベクトルのドット積を求める (function template)</td>
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<td>C++26</td>
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</tr>

‎reference/linalg/dot.html

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2024年06月16日 08時54分12秒
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<div class="identifier-type">function template</div><div class="header">&lt;linalg&gt;</div><h1 itemprop="name"><span class="namespace" title="namespace std::linalg">std::linalg::</span><span class="token">dot</span><span class="cpp cpp26" title="C++26で追加">(C++26)</span></h1>
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<div itemprop="articleBody"><p><div class="codehilite"><pre><span></span><code><span class="k">namespace</span> <span class="n">std</span><span class="o">::</span><span class="n">linalg</span> <span class="p">{</span>
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<span class="k">template</span><span class="o">&lt;</span><span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec1</span><span class="p">,</span>
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<span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec2</span><span class="p">,</span>
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<span class="k">class</span> <span class="nc">Scalar</span><span class="o">&gt;</span>
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<span class="n">Scalar</span> <span class="n">dot</span><span class="p">(</span><span class="n">InVec1</span> <span class="n">v1</span><span class="p">,</span>
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<span class="n">InVec2</span> <span class="n">v2</span><span class="p">,</span>
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<span class="n">Scalar</span> <span class="n">init</span><span class="p">);</span> <span class="c1">// (1)</span>
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<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc"><a href="../execution/execution/execution_policy.html">ExecutionPolicy</a></span><span class="p">,</span>
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<span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec1</span><span class="p">,</span>
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<span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec2</span><span class="p">,</span>
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<span class="k">class</span> <span class="nc">Scalar</span><span class="o">&gt;</span>
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<span class="n">Scalar</span> <span class="n">dot</span><span class="p">(</span><span class="n"><a href="../execution/execution/execution_policy.html">ExecutionPolicy</a></span><span class="o">&amp;&amp;</span> <span class="n">exec</span><span class="p">,</span>
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<span class="n">InVec1</span> <span class="n">v1</span><span class="p">,</span>
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<span class="n">InVec2</span> <span class="n">v2</span><span class="p">,</span>
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<span class="n">Scalar</span> <span class="n">init</span><span class="p">);</span> <span class="c1">// (2)</span>
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<span class="k">template</span><span class="o">&lt;</span><span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec1</span><span class="p">,</span>
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<span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec2</span><span class="o">&gt;</span>
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<span class="k">auto</span> <span class="n">dot</span><span class="p">(</span><span class="n">InVec1</span> <span class="n">v1</span><span class="p">,</span>
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<span class="n">InVec2</span> <span class="n">v2</span><span class="p">);</span> <span class="c1">// (3)</span>
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<span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc"><a href="../execution/execution/execution_policy.html">ExecutionPolicy</a></span><span class="p">,</span>
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<span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec1</span><span class="p">,</span>
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<span class="n">in</span><span class="o">-</span><span class="n">vector</span> <span class="n">InVec2</span><span class="o">&gt;</span>
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<span class="k">auto</span> <span class="n">dot</span><span class="p">(</span><span class="n"><a href="../execution/execution/execution_policy.html">ExecutionPolicy</a></span><span class="o">&amp;&amp;</span> <span class="n">exec</span><span class="p">,</span>
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<span class="n">InVec1</span> <span class="n">v1</span><span class="p">,</span>
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<span class="n">InVec2</span> <span class="n">v2</span><span class="p">);</span> <span class="c1">// (4)</span>
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<span class="p">}</span>
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</code></pre></div>
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</p>
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<h2>概要</h2>
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<p>2つのベクトル<code>v1</code>、<code>v2</code>の内積を計算する。</p>
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<h2><a class="cpprefjp-defined-word" data-desc="満たさなければプログラムが不適格となる要件。`static_assert`や関数のdelete宣言などに相当する">適格要件</a></h2>
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<p>2つのベクトルの静的な要素数が同じであること。</p>
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<ul>
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<li><code><a href="compatible-static-extents.html">compatible-static-extents</a>&lt;InVec1, InVec2&gt;(0, 0) == true</code></li>
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</ul>
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<h2>事前条件</h2>
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<p>2つのベクトルの次元が同じであること。</p>
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<ul>
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<li><code>v1.extent(0) == v2.extent(0)</code></li>
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</ul>
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<h2>効果</h2>
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<ul>
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<li>(1), (2): なし</li>
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<li>(3), (4): <code>T</code>を各ベクトルの値型の積の型<code>decltype(declval&lt;typename InVec1::value_type&gt;() * declval&lt;typename InVec2::value_type&gt;())</code>とする。</li>
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<li>(3): <code>dot(v1, v2, T{})</code>を返す。</li>
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<li>(4): <code>dot(std::forward&lt;ExecutionPolicy&gt;(exec), v1, v2, T{})</code>を返す。</li>
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</ul>
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<h2>戻り値</h2>
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<p>2つのベクトルの次元を<code>N</code>とする。</p>
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<ul>
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<li>(1): もし<code>N</code>が0なら<code>init</code>を返す。そうでない場合は、共役を取らない内積、つまり以下の式の<code>Scalar</code>型の値を返す。</li>
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</ul>
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<p>$$
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\verb|init| + \sum_{i = 0}^{N - 1} \verb|v1|[i] * \verb|v2|[i]
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$$</p>
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<ul>
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<li>(2): (1)の並列アルゴリズム版。</li>
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<li>(3): (1)の<code>init</code>を和の各項の型のデフォルト値に置き換えて計算する。</li>
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<li>(4): (3)の並列アルゴリズム版。</li>
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</ul>
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<h2>備考</h2>
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<ul>
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<li>(1), (2): もし<code>InVec1::value_type</code>、<code>InVec2::value_type</code>、<code>Scalar</code>が全て浮動小数点数型または<code>std::complex</code>の特殊化で、<code>Scalar</code>が<code>InVec1::value_type</code>と<code>InVec2::value_type</code>より精度が高い場合、和の各項は<code>Scalar</code>またはより高い精度の型が使われる。</li>
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</ul>
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<h2>例</h2>
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<h3>出力</h3>
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<h2>バージョン</h2>
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<h3>言語</h3>
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<ul>
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<li>C++11</li>
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</ul>
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<h3>処理系</h3>
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<ul>
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<li><a href="../../implementation.html#clang">Clang</a>: ??</li>
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<li><a href="../../implementation.html#gcc">GCC</a>: ??</li>
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<li><a href="../../implementation.html#icc">ICC</a>: ??</li>
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<li><a href="../../implementation.html#visual_cpp">Visual C++</a>: ??</li>
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</ul>
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<h2>関連項目</h2>
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<li><code><a href="../execution.html">execution</a></code></li>
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<li><code><a href="../mdspan.html">mdspan</a></code></li>
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<h2>参照</h2>
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<ul>
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<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/p0788r3.pdf" target="_blank">P0788R3 Standard Library Specification in a Concepts and Contracts World</a></li>
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<li><code><a href="https://netlib.org/lapack/explore-html/d1/dcc/group__dot_ga2cce681b6aed3728b893a555b3bee55c.html#ga2cce681b6aed3728b893a555b3bee55c" target="_blank">LAPACK: cdotu</a></code></li>
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