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add details of linear solvers used where necessary in C docs
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dalekopera committed Feb 12, 2024
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<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="GALAHAD LPA package" href="lpa.html" />
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</head>
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<section id="least-squares">
<h1>Least-Squares<a class="headerlink" href="#least-squares" title="Permalink to this heading">#</a></h1>
<p><strong>Release:</strong> 1.0</p>
<p><strong>Date:</strong> Jan 02, 2024</p>
<p><strong>Date:</strong> Feb 12, 2024</p>
<p><strong>Author:</strong> <a class="reference external" href="mailto:jaroslav&#46;fowkes&#37;&#52;&#48;stfc&#46;ac&#46;uk">Jaroslav Fowkes</a> and <a class="reference external" href="mailto:nick&#46;gould&#37;&#52;&#48;stfc&#46;ac&#46;uk">Nick Gould</a></p>
<p>GALAHAD <a class="footnote-reference superscript" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is a suite of open-source routines for large-scale continuous
optimization. Currently there is a single package designed to find a local
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</div>
<pre class="highlight doxyrest-overview-code-block literal-block"><span></span><span class="c1">// typedefs</span>

<span class="k">typedef</span> <span class="kt">float</span> <a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1a3455cab03087949fd428a31cf302f98b"><span class="std std-ref">real_sp_</span></a><span></span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">double</span> <a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">float</span> <a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1a3455cab03087949fd428a31cf302f98b"><span class="std std-ref">real_sp_</span></a><span></span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">double</span> <a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span><span class="p">;</span>

<span class="c1">// structs</span>

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<span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span>
<span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span>
<span class="kt">int</span> <span class="n">ne</span><span class="p">,</span>
<span class="k">const</span> <a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">val</span><span class="p">[]</span>
<span class="k">const</span> <a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">val</span><span class="p">[]</span>
<span class="p">);</span>

<span class="kt">void</span> <a class="reference internal" href="#doxid-galahad-sls-8h-1a1b3e7546b59b06160c51e16b6781bc0b"><span class="std std-ref">sls_solve_system</span></a><span></span><span class="p">(</span><span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span> <span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span> <span class="kt">int</span> <span class="n">n</span><span class="p">,</span> <a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[]);</span>
<span class="kt">void</span> <a class="reference internal" href="#doxid-galahad-sls-8h-1a1b3e7546b59b06160c51e16b6781bc0b"><span class="std std-ref">sls_solve_system</span></a><span></span><span class="p">(</span><span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span> <span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span> <span class="kt">int</span> <span class="n">n</span><span class="p">,</span> <a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[]);</span>

<span class="kt">void</span> <a class="reference internal" href="#doxid-galahad-sls-8h-1ac66dc50d8b54acab90d70ae649b92905"><span class="std std-ref">sls_partial_solve_system</span></a><span></span><span class="p">(</span>
<span class="k">const</span> <span class="kt">char</span> <span class="n">part</span><span class="p">[],</span>
<span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span>
<span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span>
<span class="kt">int</span> <span class="n">n</span><span class="p">,</span>
<a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[]</span>
<a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[]</span>
<span class="p">);</span>

<span class="kt">void</span> <a class="reference internal" href="#doxid-galahad-sls-8h-1a0ca4a126813c3aafac9d791a152b233c"><span class="std std-ref">sls_information</span></a><span></span><span class="p">(</span><span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span> <span class="k">struct</span> <a class="reference internal" href="sls.html#doxid-structsls-inform-type"><span class="std std-ref">sls_inform_type</span></a><span></span><span class="o">*</span> <span class="n">inform</span><span class="p">,</span> <span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">);</span>
Expand Down Expand Up @@ -724,7 +724,7 @@ <h1>function calls<a class="headerlink" href="#function-calls" title="Permalink
</colgroup>
<tbody>
<tr class="row-odd"><td><p>solver</p></td>
<td><p>is a one-dimensional array of type char that specifies the <span class="xref std std-ref">solver package</span> that should be used to factorize the matrix <span class="math notranslate nohighlight">\(A\)</span>. It should be one of ‘sils’, ‘ma27’, ‘ma57’, ‘ma77’, ‘ma86’, ‘ma87’, ‘ma97’, ‘ssids’, ‘mumps’, ‘pardiso’, ‘mkl pardiso’, ‘pastix’, ‘wsmp’, ‘potr’, ‘sytr’ or ‘pbtr’; lower or upper case variants are allowed.</p></td>
<td><p>is a one-dimensional array of type char that specifies the <span class="xref std std-ref">solver package</span> that should be used to factorize the matrix <span class="math notranslate nohighlight">\(A\)</span>. It should be one of ‘sils’, ‘ma27’, ‘ma57’, ‘ma77’, ‘ma86’, ‘ma87’, ‘ma97’, ‘ssids’, ‘mumps’, ‘pardiso’, ‘mkl pardiso’, ‘pastix’, ‘wsmp’, ‘potr’, ‘sytr’ or ‘pbtr’; lower or upper case variants are allowed. Only ‘potr’, ‘sytr’, ‘pbtr’ and, for OMP 4.0-compliant compilers, ‘ssids’ are installed by default, but others are easily installed (see README.external).</p></td>
</tr>
<tr class="row-even"><td><p>data</p></td>
<td><p>holds private internal data</p></td>
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<span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span>
<span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span>
<span class="kt">int</span> <span class="n">ne</span><span class="p">,</span>
<span class="k">const</span> <a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">val</span><span class="p">[]</span>
<span class="k">const</span> <a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">val</span><span class="p">[]</span>
<span class="p">)</span></pre>
<p>Form and factorize the symmetric matrix <span class="math notranslate nohighlight">\(A\)</span>.</p>
<p class="rubric">Parameters:</p>
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</tr>
</tbody>
</table>
<pre class="highlight doxyrest-title-code-block literal-block" id="doxid-galahad-sls-8h-1a1b3e7546b59b06160c51e16b6781bc0b"><span id="index-7"></span><span></span><span class="kt">void</span> <span class="n">sls_solve_system</span><span class="p">(</span><span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span> <span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span> <span class="kt">int</span> <span class="n">n</span><span class="p">,</span> <a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[])</span></pre>
<pre class="highlight doxyrest-title-code-block literal-block" id="doxid-galahad-sls-8h-1a1b3e7546b59b06160c51e16b6781bc0b"><span id="index-7"></span><span></span><span class="kt">void</span> <span class="n">sls_solve_system</span><span class="p">(</span><span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span> <span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span> <span class="kt">int</span> <span class="n">n</span><span class="p">,</span> <a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[])</span></pre>
<p>Solve the linear system <span class="math notranslate nohighlight">\(Ax=b\)</span>.</p>
<p class="rubric">Parameters:</p>
<table class="table">
Expand Down Expand Up @@ -1167,7 +1167,7 @@ <h1>function calls<a class="headerlink" href="#function-calls" title="Permalink
<span class="kt">void</span><span class="o">**</span> <span class="n">data</span><span class="p">,</span>
<span class="kt">int</span><span class="o">*</span> <span class="n">status</span><span class="p">,</span>
<span class="kt">int</span> <span class="n">n</span><span class="p">,</span>
<a class="reference internal" href="wcp_functions.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[]</span>
<a class="reference internal" href="wcp.html#doxid-galahad-precision-8h-1ab82133d435678ff159433d2e50cf295e"><span class="std std-ref">real_wp_</span></a><span></span> <span class="n">sol</span><span class="p">[]</span>
<span class="p">)</span></pre>
<p>Given the factorization <span class="math notranslate nohighlight">\(A = L D U\)</span> with <span class="math notranslate nohighlight">\(U = L^T\)</span>, solve the linear system <span class="math notranslate nohighlight">\(Mx=b\)</span>, where <span class="math notranslate nohighlight">\(M\)</span> is one of <span class="math notranslate nohighlight">\(L\)</span>, <span class="math notranslate nohighlight">\(D\)</span>, <span class="math notranslate nohighlight">\(U\)</span> or <span class="math notranslate nohighlight">\(S = L \sqrt{D}\)</span>.</p>
<p class="rubric">Parameters:</p>
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