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MeanField_SERiF/docs/xml/solution_8cpp.xml

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docs(docs): built docs Note for now much of the docs is LLM written. This was done to save time and focus on code development. The docs have been LOOSLEY reviewed. However, the code itself has been either fully written by hand or fully reviewed. Therefore, the docs should at the moment be seen as a loose resource rather than authoratiative (and this is on top of the general ability for docs to drift)
2026-11-09 14:09:44 -05:00
<?xml version='1.0' encoding='UTF-8' standalone='no'?>
<doxygen xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="compound.xsd" version="1.13.2" xml:lang="en-US">
<compounddef id="solution_8cpp" kind="file" language="C++">
<compoundname>solution.cpp</compoundname>
<includes refid="solution_8hpp" local="yes">serif/utils/laneemden/solution.hpp</includes>
<includes local="no">algorithm</includes>
<includes local="no">array</includes>
<includes local="no">cmath</includes>
<includes local="no">limits</includes>
<incdepgraph>
<node id="25">
<label>serif/meta/enums.hpp</label>
<link refid="enums_8hpp"/>
<childnode refid="26" relation="include">
</childnode>
<childnode refid="21" relation="include">
</childnode>
<childnode refid="27" relation="include">
</childnode>
</node>
<node id="24">
<label>serif/utils/error/codes.hpp</label>
<link refid="codes_8hpp"/>
<childnode refid="12" relation="include">
</childnode>
<childnode refid="25" relation="include">
</childnode>
</node>
<node id="10">
<label>serif/utils/error/errors.hpp</label>
<link refid="errors_8hpp"/>
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</node>
<node id="2">
<label>serif/utils/laneemden/solution.hpp</label>
<link refid="solution_8hpp"/>
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</childnode>
<childnode refid="10" relation="include">
</childnode>
</node>
<node id="19">
<label>serif/utils/misc/concepts/exceptions.hpp</label>
<link refid="utils_2misc_2concepts_2exceptions_8hpp"/>
<childnode refid="20" relation="include">
</childnode>
<childnode refid="21" relation="include">
</childnode>
<childnode refid="22" relation="include">
</childnode>
</node>
<node id="22">
<label>serif/utils/misc/concepts/numeric.hpp</label>
<link refid="numeric_8hpp"/>
<childnode refid="23" relation="include">
</childnode>
<childnode refid="21" relation="include">
</childnode>
</node>
<node id="15">
<label>serif/utils/misc/terminal/colors.hpp</label>
<link refid="colors_8hpp"/>
<childnode refid="7" relation="include">
</childnode>
<childnode refid="11" relation="include">
</childnode>
<childnode refid="16" relation="include">
</childnode>
<childnode refid="17" relation="include">
</childnode>
<childnode refid="18" relation="include">
</childnode>
</node>
<node id="28">
<label>serif/utils/types/strings.hpp</label>
<link refid="types_2strings_8hpp"/>
<childnode refid="13" relation="include">
</childnode>
<childnode refid="29" relation="include">
</childnode>
<childnode refid="7" relation="include">
</childnode>
</node>
<node id="1">
<label>src/lib/serif/utils/laneemden/solution.cpp</label>
<link refid="solution_8cpp"/>
<childnode refid="2" relation="include">
</childnode>
<childnode refid="13" relation="include">
</childnode>
<childnode refid="30" relation="include">
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</childnode>
</node>
<node id="13">
<label>algorithm</label>
</node>
<node id="30">
<label>array</label>
</node>
<node id="31">
<label>cmath</label>
</node>
<node id="23">
<label>concepts</label>
</node>
<node id="3">
<label>cstddef</label>
</node>
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<label>cstdint</label>
</node>
<node id="11">
<label>cstdio</label>
</node>
<node id="16">
<label>cstdlib</label>
</node>
<node id="20">
<label>exception</label>
</node>
<node id="4">
<label>expected</label>
</node>
<node id="9">
<label>format</label>
</node>
<node id="29">
<label>iostream</label>
</node>
<node id="32">
<label>limits</label>
</node>
<node id="27">
<label>magic_enum/magic_enum_all.hpp</label>
</node>
<node id="5">
<label>optional</label>
</node>
<node id="6">
<label>string</label>
</node>
<node id="7">
<label>string_view</label>
</node>
<node id="21">
<label>type_traits</label>
</node>
<node id="18">
<label>unistd.h</label>
</node>
<node id="26">
<label>unordered_map</label>
</node>
<node id="17">
<label>utility</label>
</node>
<node id="8">
<label>vector</label>
</node>
<node id="14">
<label>version</label>
</node>
</incdepgraph>
<innernamespace refid="namespaceserif">serif</innernamespace>
<innernamespace refid="namespaceserif_1_1utils">serif::utils</innernamespace>
<innernamespace refid="namespaceserif_1_1utils_1_1laneemden">serif::utils::laneemden</innernamespace>
<briefdescription>
</briefdescription>
<detaileddescription>
</detaileddescription>
<programlisting>
<codeline lineno="1"><highlight class="preprocessor">#include<sp/>&quot;<ref refid="solution_8hpp" kindref="compound">serif/utils/laneemden/solution.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="2"><highlight class="normal"></highlight></codeline>
<codeline lineno="3"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;algorithm&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="4"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;array&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="5"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;cmath&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="6"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;limits&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="7"><highlight class="normal"></highlight></codeline>
<codeline lineno="8"><highlight class="normal"></highlight><highlight class="keyword">namespace<sp/></highlight><highlight class="normal"><ref refid="namespaceserif_1_1utils_1_1laneemden" kindref="compound">serif::utils::laneemden</ref><sp/>{</highlight></codeline>
<codeline lineno="9"><highlight class="normal"><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">namespace<sp/></highlight><highlight class="normal">{</highlight></codeline>
<codeline lineno="11"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>central_sample(</highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>n,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>xi,<sp/>std::size_t<sp/>terms)<sp/>{</highlight></codeline>
<codeline lineno="12"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::array&lt;double,<sp/>64&gt;<sp/>coefficients{};</highlight></codeline>
<codeline lineno="13"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::array&lt;double,<sp/>64&gt;<sp/>powers{};</highlight></codeline>
<codeline lineno="14"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficients[0]<sp/>=<sp/>1.0;</highlight></codeline>
<codeline lineno="15"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>powers[0]<sp/>=<sp/>1.0;</highlight></codeline>
<codeline lineno="16"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(std::size_t<sp/>order<sp/>=<sp/>1;<sp/>order<sp/>&lt;<sp/>terms;<sp/>++order)<sp/>{</highlight></codeline>
<codeline lineno="17"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(order<sp/>&gt;=<sp/>2)<sp/>{</highlight></codeline>
<codeline lineno="18"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficients[order]<sp/>=<sp/>-powers[order<sp/>-<sp/>2]<sp/>/<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">double</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(order<sp/>*<sp/>(order<sp/>+<sp/>1));</highlight></codeline>
<codeline lineno="19"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="20"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>sum<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="21"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(std::size_t<sp/>k<sp/>=<sp/>1;<sp/>k<sp/>&lt;=<sp/>order;<sp/>++k)<sp/>{</highlight></codeline>
<codeline lineno="22"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>sum<sp/>+=<sp/>(</highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">double</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(k)<sp/>*<sp/>(n<sp/>+<sp/>1.0)<sp/>-<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">double</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(order))<sp/>*<sp/>coefficients[k]<sp/>*<sp/>powers[order<sp/>-<sp/>k];</highlight></codeline>
<codeline lineno="23"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="24"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>powers[order]<sp/>=<sp/>sum<sp/>/<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">double</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(order);</highlight></codeline>
<codeline lineno="25"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="26"><highlight class="normal"></highlight></codeline>
<codeline lineno="27"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>theta<sp/>=<sp/>coefficients[terms<sp/>-<sp/>1];</highlight></codeline>
<codeline lineno="28"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>derivative<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="29"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(std::size_t<sp/>order<sp/>=<sp/>terms<sp/>-<sp/>1;<sp/>order<sp/>&gt;<sp/>0;<sp/>--order)<sp/>{</highlight></codeline>
<codeline lineno="30"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>derivative<sp/>=<sp/>derivative<sp/>*<sp/>xi<sp/>+<sp/>theta;</highlight></codeline>
<codeline lineno="31"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>theta<sp/>=<sp/>theta<sp/>*<sp/>xi<sp/>+<sp/>coefficients[order<sp/>-<sp/>1];</highlight></codeline>
<codeline lineno="32"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="33"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>{.xi<sp/>=<sp/>xi,<sp/>.theta<sp/>=<sp/>theta,<sp/>.derivative<sp/>=<sp/>derivative};</highlight></codeline>
<codeline lineno="34"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="35"><highlight class="normal"></highlight></codeline>
<codeline lineno="37"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>slope(</highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>n,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;sample)<sp/>{</highlight></codeline>
<codeline lineno="38"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>source<sp/>=<sp/>std::pow(std::max(0.0,<sp/>sample.theta),<sp/>n);</highlight></codeline>
<codeline lineno="39"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>{.xi<sp/>=<sp/>1.0,<sp/>.theta<sp/>=<sp/>sample.derivative,<sp/>.derivative<sp/>=<sp/>-2.0<sp/>*<sp/>sample.derivative<sp/>/<sp/>sample.xi<sp/>-<sp/>source};</highlight></codeline>
<codeline lineno="40"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="41"><highlight class="normal"></highlight></codeline>
<codeline lineno="43"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>stage(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;initial,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;rate,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>step)<sp/>{</highlight></codeline>
<codeline lineno="44"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="45"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.xi<sp/>=<sp/><ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464acc51b81974287ab79cef9e94fe778cc9" kindref="member">initial</ref>.xi<sp/>+<sp/>step,</highlight></codeline>
<codeline lineno="46"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.theta<sp/>=<sp/><ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464acc51b81974287ab79cef9e94fe778cc9" kindref="member">initial</ref>.theta<sp/>+<sp/>step<sp/>*<sp/>rate.theta,</highlight></codeline>
<codeline lineno="47"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.derivative<sp/>=<sp/><ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464acc51b81974287ab79cef9e94fe778cc9" kindref="member">initial</ref>.derivative<sp/>+<sp/>step<sp/>*<sp/>rate.derivative</highlight></codeline>
<codeline lineno="48"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="49"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="50"><highlight class="normal"></highlight></codeline>
<codeline lineno="52"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>advance(</highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>n,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;initial,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>step)<sp/>{</highlight></codeline>
<codeline lineno="53"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>first<sp/>=<sp/>slope(n,<sp/>initial);</highlight></codeline>
<codeline lineno="54"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>second<sp/>=<sp/>slope(n,<sp/>stage(initial,<sp/>first,<sp/>0.5<sp/>*<sp/>step));</highlight></codeline>
<codeline lineno="55"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>third<sp/>=<sp/>slope(n,<sp/>stage(initial,<sp/>second,<sp/>0.5<sp/>*<sp/>step));</highlight></codeline>
<codeline lineno="56"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>fourth<sp/>=<sp/>slope(n,<sp/>stage(initial,<sp/>third,<sp/>step));</highlight></codeline>
<codeline lineno="57"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="58"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.xi<sp/>=<sp/><ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464acc51b81974287ab79cef9e94fe778cc9" kindref="member">initial</ref>.xi<sp/>+<sp/>step,</highlight></codeline>
<codeline lineno="59"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.theta<sp/>=<sp/><ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464acc51b81974287ab79cef9e94fe778cc9" kindref="member">initial</ref>.theta<sp/>+<sp/>step<sp/>*<sp/>(first.theta<sp/>+<sp/>2.0<sp/>*<sp/>second.theta<sp/>+<sp/>2.0<sp/>*<sp/>third.theta<sp/>+<sp/>fourth.theta)<sp/>/<sp/>6.0,</highlight></codeline>
<codeline lineno="60"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.derivative<sp/>=<sp/><ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464acc51b81974287ab79cef9e94fe778cc9" kindref="member">initial</ref>.derivative<sp/>+<sp/>step<sp/>*<sp/>(first.derivative<sp/>+<sp/>2.0<sp/>*<sp/>second.derivative<sp/>+<sp/>2.0<sp/>*<sp/>third.derivative<sp/>+<sp/>fourth.derivative)<sp/>/<sp/>6.0</highlight></codeline>
<codeline lineno="61"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="62"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="63"><highlight class="normal"></highlight></codeline>
<codeline lineno="65"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">bool</highlight><highlight class="normal"><sp/>valid_interior(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;sample)<sp/>{</highlight></codeline>
<codeline lineno="66"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::isfinite(sample.xi)<sp/>&amp;&amp;<sp/>std::isfinite(sample.theta)<sp/>&amp;&amp;<sp/>std::isfinite(sample.derivative)<sp/>&amp;&amp;</highlight></codeline>
<codeline lineno="67"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>sample.theta<sp/>&gt;<sp/>0.0<sp/>&amp;&amp;<sp/>sample.derivative<sp/>&lt;<sp/>0.0;</highlight></codeline>
<codeline lineno="68"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="69"><highlight class="normal"></highlight></codeline>
<codeline lineno="71"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::expected&lt;Sample,<sp/>std::string&gt;<sp/>locate_surface(</highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>n,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;initial,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>width,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>tolerance)<sp/>{</highlight></codeline>
<codeline lineno="72"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>lower<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="73"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>upper<sp/>=<sp/>width;</highlight></codeline>
<codeline lineno="74"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>result<sp/>=<sp/>advance(n,<sp/>initial,<sp/>upper);</highlight></codeline>
<codeline lineno="75"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(result.theta)<sp/>||<sp/>result.theta<sp/>&gt;<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="76"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>surface<sp/>could<sp/>not<sp/>be<sp/>bracketed;<sp/>reduce<sp/>the<sp/>integration<sp/>step.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="77"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="78"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(std::size_t<sp/>iteration<sp/>=<sp/>0;<sp/>iteration<sp/>&lt;<sp/>80<sp/>&amp;&amp;<sp/>upper<sp/>-<sp/>lower<sp/>&gt;<sp/>tolerance;<sp/>++iteration)<sp/>{</highlight></codeline>
<codeline lineno="79"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>middle<sp/>=<sp/>lower<sp/>+<sp/>0.5<sp/>*<sp/>(upper<sp/>-<sp/>lower);</highlight></codeline>
<codeline lineno="80"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result<sp/>=<sp/>advance(n,<sp/>initial,<sp/>middle);</highlight></codeline>
<codeline lineno="81"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(result.theta<sp/>&gt;<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="82"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>lower<sp/>=<sp/>middle;</highlight></codeline>
<codeline lineno="83"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}<sp/></highlight><highlight class="keywordflow">else</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="84"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>upper<sp/>=<sp/>middle;</highlight></codeline>
<codeline lineno="85"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="86"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="87"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result<sp/>=<sp/>advance(n,<sp/>initial,<sp/>lower<sp/>+<sp/>0.5<sp/>*<sp/>(upper<sp/>-<sp/>lower));</highlight></codeline>
<codeline lineno="88"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.theta<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="89"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(result.derivative)<sp/>||<sp/>result.derivative<sp/>&gt;=<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="90"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>surface<sp/>derivative<sp/>is<sp/>not<sp/>finite<sp/>and<sp/>negative;<sp/>reduce<sp/>the<sp/>integration<sp/>step.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="91"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="92"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>result;</highlight></codeline>
<codeline lineno="93"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="94"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="95"><highlight class="normal"></highlight></codeline>
<codeline lineno="96"><highlight class="normal"><sp/><sp/><sp/><sp/>std::expected&lt;Solution,<sp/>std::string&gt;<sp/><ref refid="namespaceserif_1_1utils_1_1laneemden_1aac284388ff73263db8d245669cb8e60f" kindref="member">solve</ref>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>n,<sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_integration_options" kindref="compound">IntegrationOptions</ref><sp/>options)<sp/>{</highlight></codeline>
<codeline lineno="97"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(n)<sp/>||<sp/>n<sp/>&lt;<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="98"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>index<sp/>must<sp/>be<sp/>finite<sp/>and<sp/>nonnegative.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="99"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="100"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(options.step)<sp/>||<sp/>options.step<sp/>&lt;=<sp/>0.0<sp/>||<sp/>!std::isfinite(options.maximum_radius)<sp/>||<sp/>options.maximum_radius<sp/>&lt;=<sp/>0.0<sp/>||</highlight></codeline>
<codeline lineno="101"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>!std::isfinite(options.surface_tolerance)<sp/>||<sp/>options.surface_tolerance<sp/>&lt;=<sp/>0.0<sp/>||<sp/>options.surface_tolerance<sp/>&gt;=<sp/>0.01<sp/>||</highlight></codeline>
<codeline lineno="102"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>options.maximum_steps<sp/>==<sp/>0<sp/>||<sp/>options.central_series_terms<sp/>&lt;<sp/>6<sp/>||<sp/>options.central_series_terms<sp/>&gt;<sp/>64)<sp/>{</highlight></codeline>
<codeline lineno="103"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>integration<sp/>needs<sp/>positive<sp/>finite<sp/>step<sp/>and<sp/>maximum<sp/>radius,<sp/>a<sp/>surface<sp/>tolerance<sp/>in<sp/>(0,<sp/>0.01),<sp/>a<sp/>nonzero<sp/>step<sp/>budget,<sp/>and<sp/>6<sp/>to<sp/>64<sp/>series<sp/>terms.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="104"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="105"><highlight class="normal"></highlight></codeline>
<codeline lineno="106"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_solution" kindref="compound">Solution</ref><sp/>solution{.n<sp/>=<sp/>n,<sp/>.samples<sp/>=<sp/>{{.xi<sp/>=<sp/>0.0,<sp/>.theta<sp/>=<sp/>1.0,<sp/>.derivative<sp/>=<sp/>0.0}},<sp/>.surface<sp/>=<sp/>std::nullopt};</highlight></codeline>
<codeline lineno="107"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>first_radius<sp/>=<sp/>std::min({options.step,<sp/>options.maximum_radius,<sp/>0.01<sp/>/<sp/>std::sqrt(std::max(1.0,<sp/>n))});</highlight></codeline>
<codeline lineno="108"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>current<sp/>=<sp/>central_sample(n,<sp/>first_radius,<sp/>options.central_series_terms);</highlight></codeline>
<codeline lineno="109"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!valid_interior(current))<sp/>{</highlight></codeline>
<codeline lineno="110"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>central<sp/>series<sp/>is<sp/>not<sp/>representable<sp/>for<sp/>the<sp/>supplied<sp/>index<sp/>and<sp/>step.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="111"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="112"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>solution.samples.push_back(current);</highlight></codeline>
<codeline lineno="113"><highlight class="normal"></highlight></codeline>
<codeline lineno="114"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(std::size_t<sp/>iteration<sp/>=<sp/>0;<sp/>current.xi<sp/>&lt;<sp/>options.maximum_radius;<sp/>++iteration)<sp/>{</highlight></codeline>
<codeline lineno="115"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(iteration<sp/>&gt;=<sp/>options.maximum_steps)<sp/>{</highlight></codeline>
<codeline lineno="116"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>integration<sp/>exhausted<sp/>maximum_steps<sp/>before<sp/>reaching<sp/>the<sp/>surface<sp/>or<sp/>maximum_radius.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="117"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="118"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>distance<sp/>=<sp/>-current.theta<sp/>/<sp/>current.derivative;</highlight></codeline>
<codeline lineno="119"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>tolerance<sp/>=<sp/>options.surface_tolerance<sp/>*<sp/>std::max(1.0,<sp/>current.xi);</highlight></codeline>
<codeline lineno="120"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(distance<sp/>&lt;=<sp/>tolerance<sp/>&amp;&amp;<sp/>current.xi<sp/>+<sp/>2.0<sp/>*<sp/>distance<sp/>&lt;=<sp/>options.maximum_radius)<sp/>{</highlight></codeline>
<codeline lineno="121"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>root_tolerance<sp/>=<sp/>std::max(4.0<sp/>*<sp/>std::numeric_limits&lt;double&gt;::epsilon()<sp/>*<sp/>current.xi,<sp/>tolerance<sp/>*<sp/>0.01);</highlight></codeline>
<codeline lineno="122"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keyword">auto</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1solver_1_1normalization_1ac75238439fd5d1610b177bf85e9376d9ad302e976c9dd527a9521a88c012437c5" kindref="member">surface</ref><sp/>=<sp/>locate_surface(n,<sp/>current,<sp/>2.0<sp/>*<sp/>distance,<sp/>root_tolerance);</highlight></codeline>
<codeline lineno="123"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!surface)<sp/>{</highlight></codeline>
<codeline lineno="124"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(<ref refid="namespaceserif_1_1solver_1_1normalization_1ac75238439fd5d1610b177bf85e9376d9ad302e976c9dd527a9521a88c012437c5" kindref="member">surface</ref>.error());</highlight></codeline>
<codeline lineno="125"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="126"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>solution.surface<sp/>=<sp/>*<ref refid="namespaceserif_1_1solver_1_1normalization_1ac75238439fd5d1610b177bf85e9376d9ad302e976c9dd527a9521a88c012437c5" kindref="member">surface</ref>;</highlight></codeline>
<codeline lineno="127"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>solution.samples.push_back(*surface);</highlight></codeline>
<codeline lineno="128"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>solution;</highlight></codeline>
<codeline lineno="129"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="130"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Shorten<sp/>only<sp/>the<sp/>final<sp/>approach;<sp/>no<sp/>accepted<sp/>sample<sp/>extends<sp/>past<sp/>the<sp/>first<sp/>zero.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="131"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>step<sp/>=<sp/>std::min({options.step,<sp/>0.5<sp/>*<sp/>distance,<sp/>options.maximum_radius<sp/>-<sp/>current.xi});</highlight></codeline>
<codeline lineno="132"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(current.xi<sp/>+<sp/>step<sp/>==<sp/>current.xi)<sp/>{</highlight></codeline>
<codeline lineno="133"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>step<sp/>cannot<sp/>advance<sp/>the<sp/>radius<sp/>at<sp/>machine<sp/>precision;<sp/>relax<sp/>surface_tolerance.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="134"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="135"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>current<sp/>=<sp/>advance(n,<sp/>current,<sp/>step);</highlight></codeline>
<codeline lineno="136"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!valid_interior(current))<sp/>{</highlight></codeline>
<codeline lineno="137"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>integration<sp/>left<sp/>the<sp/>finite<sp/>positive<sp/>branch;<sp/>reduce<sp/>the<sp/>integration<sp/>step.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="138"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="139"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>solution.samples.push_back(current);</highlight></codeline>
<codeline lineno="140"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="141"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>solution;</highlight></codeline>
<codeline lineno="142"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="143"><highlight class="normal"></highlight></codeline>
<codeline lineno="144"><highlight class="normal"><sp/><sp/><sp/><sp/>std::expected&lt;Sample,<sp/>std::string&gt;<sp/><ref refid="namespaceserif_1_1utils_1_1laneemden_1ac58bd2b83384f8454be7fd0b11cd9332" kindref="member">evaluate</ref>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_solution" kindref="compound">Solution</ref><sp/>&amp;solution,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>xi)<sp/>{</highlight></codeline>
<codeline lineno="145"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(xi)<sp/>||<sp/>xi<sp/>&lt;<sp/>0.0<sp/>||<sp/>solution.samples.empty()<sp/>||<sp/>xi<sp/>&gt;<sp/>solution.samples.back().xi)<sp/>{</highlight></codeline>
<codeline lineno="146"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>evaluation<sp/>radius<sp/>must<sp/>lie<sp/>within<sp/>the<sp/>stored<sp/>finite<sp/>dimensionless<sp/>profile.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="147"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="148"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keyword">auto</highlight><highlight class="normal"><sp/>upper<sp/>=<sp/>std::lower_bound(solution.samples.begin(),<sp/>solution.samples.end(),<sp/>xi,</highlight></codeline>
<codeline lineno="149"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[](</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;sample,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>radius)<sp/>{<sp/>return<sp/>sample.xi<sp/>&lt;<sp/>radius;<sp/>});</highlight></codeline>
<codeline lineno="150"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(upper<sp/>==<sp/>solution.samples.begin()<sp/>||<sp/>upper-&gt;xi<sp/>==<sp/>xi)<sp/>{</highlight></codeline>
<codeline lineno="151"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>*upper;</highlight></codeline>
<codeline lineno="152"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="153"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;left<sp/>=<sp/>*(upper<sp/>-<sp/>1);</highlight></codeline>
<codeline lineno="154"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref><sp/>&amp;right<sp/>=<sp/>*upper;</highlight></codeline>
<codeline lineno="155"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>width<sp/>=<sp/>right.<ref refid="structserif_1_1utils_1_1laneemden_1_1_sample_1a5f2f0da73c838f8bfb35b619ad89990f" kindref="member">xi</ref><sp/>-<sp/>left.xi;</highlight></codeline>
<codeline lineno="156"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(width)<sp/>||<sp/>width<sp/>&lt;=<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="157"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(</highlight><highlight class="stringliteral">&quot;Lane–Emden<sp/>evaluation<sp/>requires<sp/>a<sp/>profile<sp/>with<sp/>increasing<sp/>finite<sp/>radii<sp/>produced<sp/>by<sp/>solve.&quot;</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="158"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="159"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>position<sp/>=<sp/>(xi<sp/>-<sp/>left.xi)<sp/>/<sp/>width;</highlight></codeline>
<codeline lineno="160"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>quadratic<sp/>=<sp/>3.0<sp/>*<sp/>(right.theta<sp/>-<sp/>left.theta)<sp/>-<sp/>width<sp/>*<sp/>(2.0<sp/>*<sp/>left.derivative<sp/>+<sp/>right.derivative);</highlight></codeline>
<codeline lineno="161"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>cubic<sp/>=<sp/>2.0<sp/>*<sp/>(left.theta<sp/>-<sp/>right.theta)<sp/>+<sp/>width<sp/>*<sp/>(left.derivative<sp/>+<sp/>right.derivative);</highlight></codeline>
<codeline lineno="162"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1utils_1_1laneemden_1_1_sample" kindref="compound">Sample</ref>{</highlight></codeline>
<codeline lineno="163"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.xi<sp/>=<sp/>xi,</highlight></codeline>
<codeline lineno="164"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.theta<sp/>=<sp/>left.theta<sp/>+<sp/>position<sp/>*<sp/>(width<sp/>*<sp/>left.derivative<sp/>+<sp/>position<sp/>*<sp/>(quadratic<sp/>+<sp/>position<sp/>*<sp/>cubic)),</highlight></codeline>
<codeline lineno="165"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>.derivative<sp/>=<sp/>left.derivative<sp/>+<sp/>position<sp/>*<sp/>(2.0<sp/>*<sp/>quadratic<sp/>+<sp/>3.0<sp/>*<sp/>position<sp/>*<sp/>cubic)<sp/>/<sp/>width</highlight></codeline>
<codeline lineno="166"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="167"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="168"><highlight class="normal">}</highlight></codeline>
</programlisting>
<location file="src/lib/serif/utils/laneemden/solution.cpp"/>
</compounddef>
</doxygen>
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