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‎reference/linalg.html

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最終更新日時(UTC):
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<span itemprop="datePublished" content="2024-06-25T03:50:24">
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2024年06月25日 03時50分24秒
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<span itemprop="datePublished" content="2024-06-25T07:19:32">
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2024年06月25日 07時19分32秒
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<span itemprop="author" itemscope itemtype="http://schema.org/Person">
@@ -413,7 +413,7 @@ <h2>BLAS 2アルゴリズム</h2>
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<td>C++26</td>
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</tr>
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<tr>
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<td><code>symmetric_matrix_vector_product</code></td>
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<td><code><a href="linalg/symmetric_matrix_vector_product.html">symmetric_matrix_vector_product</a></code></td>
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<td>xSYMV: 対称行列とベクトルの積を求める (function template)</td>
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<td>C++26</td>
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‎reference/linalg/layout_blas_packed.html

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<header data-kunai-mdinfo="{&#34;meta&#34;: {&#34;header&#34;: [&#34;linalg&#34;], &#34;id-type&#34;: [&#34;class template&#34;], &#34;namespace&#34;: [&#34;std::linalg&#34;], &#34;cpp&#34;: [&#34;cpp26&#34;]}, &#34;sources&#34;: [{&#34;id&#34;: &#34;9969e1e8725f7c265a0eb62391b7e33bd9f702db&#34;, &#34;source&#34;: &#34;#include &lt;linalg&gt;\n#include &lt;mdspan&gt;\n#include &lt;print&gt;\n#include &lt;string_view&gt;\nnamespace linalg = std::linalg;\n\n// \u884c\u5217(matrix)\u306e\u8981\u7d20\u8868\u793a\ntemplate &lt;class T, class E, class L, class A&gt;\nvoid print_mat(std::string_view name, const std::mdspan&lt;T, E, L, A&gt;&amp; mat)\n{\n static_assert(mat.rank() == 2);\n std::println(\&#34;{}:\&#34;, name);\n for (size_t i = 0; i &lt; mat.extent(0); ++i) {\n for (size_t j = 0; j &lt; mat.extent(1); ++j) {\n std::print(\&#34; {:2}\&#34;, mat[i, j]);\n }\n std::println(\&#34;\&#34;);\n }\n}\n\nint main()\n{\n double arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};\n\n // \u5217\u512a\u5148\u683c\u7d0d\u9806\u306e\u4e0b\u4e09\u89d2\u8981\u7d20\u304b\u30894x4\u5bfe\u79f0\u884c\u5217\u3092\u69cb\u7bc9\n std::mdspan&lt;\n double,\n std::extents&lt;size_t, 4, 4&gt;,\n linalg::layout_blas_packed&lt;linalg::lower_triangle_t, linalg::column_major_t&gt;\n &gt; mat1{arr};\n // 1 - - -\n // 2 5 - -\n // 3 6 8 -\n // 4 7 9 10\n print_mat(\&#34;mat1\&#34;, mat);\n\n // \u884c\u512a\u5148\u683c\u7d0d\u9806\u306e\u4e0b\u4e09\u89d2\u8981\u7d20\u304b\u30894x4\u5bfe\u79f0\u884c\u5217\u3092\u69cb\u7bc9\n std::mdspan&lt;\n double,\n std::extents&lt;size_t, 4, 4&gt;,\n linalg::layout_blas_packed&lt;linalg::lower_triangle_t, linalg::row_major_t&gt;\n &gt; mat2{arr};\n // 1 - - -\n // 2 3 - -\n // 4 5 6 -\n // 7 8 9 10\n print_mat(\&#34;mat2\&#34;, mat2);\n}\n&#34;}], &#34;page_id&#34;: [&#34;reference&#34;, &#34;linalg&#34;, &#34;layout_blas_packed&#34;]}">
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<header data-kunai-mdinfo="{&#34;meta&#34;: {&#34;header&#34;: [&#34;linalg&#34;], &#34;id-type&#34;: [&#34;class template&#34;], &#34;namespace&#34;: [&#34;std::linalg&#34;], &#34;cpp&#34;: [&#34;cpp26&#34;]}, &#34;sources&#34;: [{&#34;id&#34;: &#34;798a0efeb11baea87b2192736c68df86682b4d4f&#34;, &#34;source&#34;: &#34;#include &lt;linalg&gt;\n#include &lt;mdspan&gt;\n#include &lt;print&gt;\n#include &lt;string_view&gt;\nnamespace linalg = std::linalg;\n\n// \u884c\u5217(matrix)\u306e\u8981\u7d20\u8868\u793a\ntemplate &lt;class T, class E, class L, class A&gt;\nvoid print_mat(std::string_view name, const std::mdspan&lt;T, E, L, A&gt;&amp; mat)\n{\n static_assert(mat.rank() == 2);\n std::println(\&#34;{}:\&#34;, name);\n for (size_t i = 0; i &lt; mat.extent(0); ++i) {\n for (size_t j = 0; j &lt; mat.extent(1); ++j) {\n std::print(\&#34; {:2}\&#34;, mat[i, j]);\n }\n std::println(\&#34;\&#34;);\n }\n}\n\nint main()\n{\n double arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};\n\n // \u5217\u512a\u5148\u683c\u7d0d\u9806\u306e\u4e0b\u4e09\u89d2\u8981\u7d20\u304b\u30894x4\u5bfe\u79f0\u884c\u5217\u3092\u69cb\u7bc9\n std::mdspan&lt;\n double,\n std::extents&lt;size_t, 4, 4&gt;,\n linalg::layout_blas_packed&lt;linalg::lower_triangle_t, linalg::column_major_t&gt;\n &gt; mat1{arr};\n // 1 - - -\n // 2 5 - -\n // 3 6 8 -\n // 4 7 9 10\n print_mat(\&#34;mat1\&#34;, mat1);\n\n // \u884c\u512a\u5148\u683c\u7d0d\u9806\u306e\u4e0b\u4e09\u89d2\u8981\u7d20\u304b\u30894x4\u5bfe\u79f0\u884c\u5217\u3092\u69cb\u7bc9\n std::mdspan&lt;\n double,\n std::extents&lt;size_t, 4, 4&gt;,\n linalg::layout_blas_packed&lt;linalg::lower_triangle_t, linalg::row_major_t&gt;\n &gt; mat2{arr};\n // 1 - - -\n // 2 3 - -\n // 4 5 6 -\n // 7 8 9 10\n print_mat(\&#34;mat2\&#34;, mat2);\n}\n&#34;}], &#34;page_id&#34;: [&#34;reference&#34;, &#34;linalg&#34;, &#34;layout_blas_packed&#34;]}">
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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="2024-05-21T12:32:20">
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2024年05月21日 12時32分20秒
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<span itemprop="datePublished" content="2024-06-25T07:20:37">
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<h2>例</h2>
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<p><div class="yata" id="9969e1e8725f7c265a0eb62391b7e33bd9f702db"><div class="codehilite"><pre><span></span><code><span class="cp">#include</span> <span class="cpf"><a href="../linalg.html">&lt;linalg&gt;</a></span><span class="cp"></span>
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<p><div class="yata" id="798a0efeb11baea87b2192736c68df86682b4d4f"><div class="codehilite"><pre><span></span><code><span class="cp">#include</span> <span class="cpf"><a href="../linalg.html">&lt;linalg&gt;</a></span><span class="cp"></span>
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<span class="cp">#include</span> <span class="cpf"><a href="../mdspan.html">&lt;mdspan&gt;</a></span><span class="cp"></span>
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<span class="cp">#include</span> <span class="cpf"><a href="../print.html">&lt;print&gt;</a></span><span class="cp"></span>
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<span class="cp">#include</span> <span class="cpf"><a href="../string_view.html">&lt;string_view&gt;</a></span><span class="cp"></span>
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<span class="c1">// 2 5 - -</span>
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<span class="c1">// 4 7 9 10</span>
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<span class="n">print_mat</span><span class="p">(</span><span class="s">"mat1"</span><span class="p">,</span> <span class="n">mat</span><span class="p">);</span>
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<span class="n">print_mat</span><span class="p">(</span><span class="s">"mat1"</span><span class="p">,</span> <span class="n">mat1</span><span class="p">);</span>
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<span class="c1">// 行優先格納順の下三角要素から4x4対称行列を構築</span>
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<span class="n"><a href="../mdspan/mdspan.html">std::mdspan</a></span><span class="o">&lt;</span>

‎reference/linalg/matrix_vector_product.html

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<header data-kunai-mdinfo="{&#34;meta&#34;: {&#34;header&#34;: [&#34;linalg&#34;], &#34;id-type&#34;: [&#34;function template&#34;], &#34;namespace&#34;: [&#34;std::linalg&#34;], &#34;cpp&#34;: [&#34;cpp26&#34;]}, &#34;sources&#34;: [{&#34;id&#34;: &#34;ed1ea3467bc7bbaaff6312b21c0ae402fd8d782e&#34;, &#34;source&#34;: &#34;#include &lt;array&gt;\n#include &lt;iostream&gt;\n#include &lt;linalg&gt;\n#include &lt;mdspan&gt;\n#include &lt;vector&gt;\n\ntemplate &lt;class Vector&gt;\nvoid print(const Vector&amp; v, const std::string&amp; name) {\n for (int i = 0; i &lt; v.extent(0); ++i) {\n std::cout &lt;&lt; name &lt;&lt; \&#34;[\&#34; &lt;&lt; i &lt;&lt; \&#34;]\&#34; &lt;&lt; \&#34; = \&#34; &lt;&lt; v[i] &lt;&lt; &#39;\\n&#39;;\n }\n}\n\nint main()\n{\n constexpr size_t N = 4;\n constexpr size_t M = 2;\n\n std::vector&lt;double&gt; A_vec(N*M);\n std::vector&lt;double&gt; x_vec(M);\n std::array&lt;double, N&gt; y_vec, z_vec;\n\n std::mdspan A(A_vec.data(), N, M);\n std::mdspan x(x_vec.data(), M);\n std::mdspan y(y_vec.data(), N);\n std::mdspan z(z_vec.data(), N);\n\n for(int i = 0; i &lt; A.extent(0); ++i) {\n for(int j = 0; j &lt; A.extent(1); ++j) {\n A[i,j] = 100.0 * i + j;\n }\n }\n\n for(int j = 0; j &lt; x.extent(0); ++j) {\n x[j] = 1.0 * j;\n }\n for(int i = 0; i &lt; y.extent(0); ++i) {\n y[i] = -1.0 * i;\n }\n\n // (1)\n std::cout &lt;&lt; \&#34;(1)\\n\&#34;;\n std::linalg::matrix_vector_product(A, x, y);\n print(y, \&#34;y\&#34;);\n\n // (2)\n std::cout &lt;&lt; \&#34;(2)\\n\&#34;;\n std::linalg::matrix_vector_product(std::execution::par, A, x, y);\n print(y, \&#34;y\&#34;);\n\n // (3)\n std::cout &lt;&lt; \&#34;(3)\\n\&#34;;\n std::linalg::matrix_vector_product(A, x, y, z);\n print(z, \&#34;z\&#34;);\n\n // (4)\n std::cout &lt;&lt; \&#34;(4)\\n\&#34;;\n std::linalg::matrix_vector_product(std::execution::par, A, x, y, z);\n print(z, \&#34;z\&#34;);\n\n return 0;\n}\n&#34;}], &#34;page_id&#34;: [&#34;reference&#34;, &#34;linalg&#34;, &#34;matrix_vector_product&#34;]}">
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<header data-kunai-mdinfo="{&#34;meta&#34;: {&#34;header&#34;: [&#34;linalg&#34;], &#34;id-type&#34;: [&#34;function template&#34;], &#34;namespace&#34;: [&#34;std::linalg&#34;], &#34;cpp&#34;: [&#34;cpp26&#34;]}, &#34;sources&#34;: [{&#34;id&#34;: &#34;7fe47a278f2352033e146b53e0b85431623ffbbf&#34;, &#34;source&#34;: &#34;#include &lt;array&gt;\n#include &lt;iostream&gt;\n#include &lt;linalg&gt;\n#include &lt;mdspan&gt;\n#include &lt;vector&gt;\n\ntemplate &lt;class Vector&gt;\nvoid print(const Vector&amp; v, const std::string&amp; name) {\n for (int i = 0; i &lt; v.extent(0); ++i) {\n std::cout &lt;&lt; name &lt;&lt; \&#34;[\&#34; &lt;&lt; i &lt;&lt; \&#34;]\&#34; &lt;&lt; \&#34; = \&#34; &lt;&lt; v[i] &lt;&lt; &#39;\\n&#39;;\n }\n}\n\nint main()\n{\n constexpr size_t N = 4;\n constexpr size_t M = 2;\n\n std::vector&lt;double&gt; A_vec(N*M);\n std::vector&lt;double&gt; x_vec(M);\n std::array&lt;double, N&gt; y_vec, z_vec;\n\n std::mdspan A(A_vec.data(), N, M);\n std::mdspan x(x_vec.data(), M);\n std::mdspan y(y_vec.data(), N);\n std::mdspan z(z_vec.data(), N);\n\n for(int i = 0; i &lt; A.extent(0); ++i) {\n for(int j = 0; j &lt; A.extent(1); ++j) {\n A[i,j] = 100.0 * i + j;\n }\n }\n\n for(int j = 0; j &lt; x.extent(0); ++j) {\n x[j] = j;\n }\n for(int i = 0; i &lt; y.extent(0); ++i) {\n y[i] = -i;\n }\n\n // (1)\n std::cout &lt;&lt; \&#34;(1)\\n\&#34;;\n std::linalg::matrix_vector_product(A, x, y);\n print(y, \&#34;y\&#34;);\n\n // (2)\n std::cout &lt;&lt; \&#34;(2)\\n\&#34;;\n std::linalg::matrix_vector_product(std::execution::par, A, x, y);\n print(y, \&#34;y\&#34;);\n\n // (3)\n std::cout &lt;&lt; \&#34;(3)\\n\&#34;;\n std::linalg::matrix_vector_product(A, x, y, z);\n print(z, \&#34;z\&#34;);\n\n // (4)\n std::cout &lt;&lt; \&#34;(4)\\n\&#34;;\n std::linalg::matrix_vector_product(std::execution::par, A, x, y, z);\n print(z, \&#34;z\&#34;);\n\n return 0;\n}\n&#34;}], &#34;page_id&#34;: [&#34;reference&#34;, &#34;linalg&#34;, &#34;matrix_vector_product&#34;]}">
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最終更新日時(UTC):
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<span itemprop="datePublished" content="2024-06-25T04:38:38">
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<span itemprop="datePublished" content="2024-06-25T07:20:37">
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<h2>事前条件</h2>
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<ul>
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<li>(1), (2), (3), (4): <code><a href="multipliable.html">multipliable</a>(A,x,y) == true</code></li>
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<li>(1), (2), (3), (4): <code><a href="multipliable.html">multipliable</a>(A, x, y) == true</code></li>
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<li>(3), (4): <code><a href="addable.html">addable</a>(x, y, z) == true</code></li>
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<h2>効果</h2>
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<h2>例</h2>
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<p><strong>[注意] 処理系にあるコンパイラで確認していないため、間違っているかもしれません。</strong></p>
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<p><div class="yata" id="ed1ea3467bc7bbaaff6312b21c0ae402fd8d782e"><div class="codehilite"><pre><span></span><code><span class="cp">#include</span> <span class="cpf"><a href="../array.html">&lt;array&gt;</a></span><span class="cp"></span>
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<p><div class="yata" id="7fe47a278f2352033e146b53e0b85431623ffbbf"><div class="codehilite"><pre><span></span><code><span class="cp">#include</span> <span class="cpf"><a href="../array.html">&lt;array&gt;</a></span><span class="cp"></span>
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<span class="cp">#include</span> <span class="cpf"><a href="../iostream.html">&lt;iostream&gt;</a></span><span class="cp"></span>
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<span class="cp">#include</span> <span class="cpf"><a href="../mdspan.html">&lt;mdspan&gt;</a></span><span class="cp"></span>
@@ -335,10 +335,10 @@ <h2>例</h2>
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<span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="n">x</span><span class="p">.</span><span class="n">extent</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span> <span class="o">++</span><span class="n">j</span><span class="p">)</span> <span class="p">{</span>
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<span class="n">x</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="n">j</span><span class="p">;</span>
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<span class="n">x</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span><span class="p">;</span>
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<span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">y</span><span class="p">.</span><span class="n">extent</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span> <span class="o">++</span><span class="n">i</span><span class="p">)</span> <span class="p">{</span>
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<span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1.0</span> <span class="o">*</span> <span class="n">i</span><span class="p">;</span>
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<span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="n">i</span><span class="p">;</span>
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<span class="c1">// (1)</span>

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