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Documentation for e64e3df18f
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@@ -195,7 +195,7 @@ Here is the call graph for this function:</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">return</span> -1;</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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@@ -181,8 +181,8 @@ size_t </td><td class="memItemRight" valign="bottom"><b>n</b> = 0</td></tr>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>[x] <= <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>[y] ? x : y); <span class="comment">///< represents minimum value over</span><span class="comment"></span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment"> ///< the whole range [l,r]</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment"></span> }</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:113</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
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<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_a6cf72f93b1551f0d943c585b4f173be3"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a6cf72f93b1551f0d943c585b4f173be3">data_structures::sparse_table::Sparse_table::LOG</a></div><div class="ttdeci">std::array< int64_t, N > LOG</div><div class="ttdoc">where floor(log2(i)) are precomputed.</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:59</div></div>
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<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_ab78620742305a35ff2f8d61179f47d3e"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">data_structures::sparse_table::Sparse_table::A</a></div><div class="ttdeci">std::array< int64_t, N > A</div><div class="ttdoc">input array to perform RMQ.</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:56</div></div>
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<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_ad36b9a20fed47b068e407008c04e9f81"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ad36b9a20fed47b068e407008c04e9f81">data_structures::sparse_table::Sparse_table::ST</a></div><div class="ttdeci">std::array< std::array< int64_t, N >, M > ST</div><div class="ttdoc">the sparse table storing min() values for given interval.</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:58</div></div>
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@@ -557,7 +557,7 @@ $(document).ready(function(){initNavTree('da/d41/uint128__t_8hpp_source.html','.
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> tmp <<= left;</div>
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<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> quotient(0);</div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <a class="code hl_class" href="../../db/d9a/classuint128__t.html">uint128_t</a> zero(0);</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <span class="keywordflow">while</span> (left >= 0 && tmp2 >= p) {</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <span class="keywordflow">while</span> (tmp2 >= p) {</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../db/d9a/classuint128__t.html#af139bb6e630f1a61919f180978611cd2">_lez</a>();</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="keywordflow">if</span> (shf) {</div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> tmp >>= shf;</div>
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@@ -153,7 +153,7 @@ Functions</h2></td></tr>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> }</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -524,7 +524,7 @@ $(document).ready(function(){initNavTree('da/da3/uint256__t_8hpp_source.html','.
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> tmp <<= left;</div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> quotient(0);</div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0);</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="keywordflow">while</span> (left >= 0 && tmp2 >= p) {</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="keywordflow">while</span> (tmp2 >= p) {</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>();</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> <span class="keywordflow">if</span> (shf) {</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> tmp >>= shf;</div>
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@@ -261,7 +261,7 @@ Here is the call graph for this function:</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
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<div class="ttc" id="aclassdata__structures_1_1linked__list_1_1list_html"><div class="ttname"><a href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html">data_structures::linked_list::list</a></div><div class="ttdef"><b>Definition:</b> linked_list.cpp:81</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div></div>
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<div class="ttc" id="astol_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/stol.html">std::stoi</a></div><div class="ttdeci">T stoi(T... args)</div></div>
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@@ -217,7 +217,7 @@ Functions</h2></td></tr>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> }</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> ((result[0]%mod*Identity[0][0]%mod)%mod+(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]%mod*Identity[1][0]%mod)%mod)%mod;</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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</div><!-- fragment -->
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@@ -150,7 +150,7 @@ Functions</h2></td></tr>
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<div class="line">1206647803780373360 -3599979517947607200 8037811822645051776</div>
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<div class="line">-12870931245150988800 13803759753640704000 -8752948036761600000</div>
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<div class="line">2432902008176640000</div>
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<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for IO operations</div></div>
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<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for assert</div></div>
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</div><!-- fragment --><p> Sample implementation results to compute approximate roots of the equation \(x^4-1=0\):<br />
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<img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/durand_kerner_error.svg" alt="Error evolution during root approximations computed every
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iteration." style="pointer-events: none;" width="400" class="inline"/> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/durand_kerner_roots.svg" alt="Roots evolution - shows the initial approximation of the
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