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realstealthninja
@@ -4,7 +4,7 @@
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<title>TheAlgorithms/C++: numerical_methods/midpoint_integral_method.cpp File Reference</title>
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
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var searchBox = new SearchBox("searchBox", "../../search/",'.html');
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@@ -339,7 +339,7 @@ Functions</h2></td></tr>
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<p class="definition">Definition at line <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00162">162</a> of file <a class="el" href="../../df/d11/midpoint__integral__method_8cpp_source.html">midpoint_integral_method.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 162</span> {</div>
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<div class="line"><span class="lineno"> 163</span> std::int32_t <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> =</div>
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<div class="line"><span class="lineno"> 163</span> std::int32_t N =</div>
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<div class="line"><span class="lineno"> 164</span> 16; </div>
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<div class="line"><span class="lineno"> 166</span> <span class="keywordtype">double</span> a = 1, b = 3; </div>
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<div class="line"><span class="lineno"> 168</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = NAN; </div>
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@@ -351,7 +351,7 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 174</span> <span class="comment">// Get user input (by the command line parameters or the console after</span></div>
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<div class="line"><span class="lineno"> 175</span> <span class="comment">// displaying messages)</span></div>
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<div class="line"><span class="lineno"> 176</span> <span class="keywordflow">if</span> (argc == 4) {</div>
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<div class="line"><span class="lineno"> 177</span> <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = std::atoi(argv[1]);</div>
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<div class="line"><span class="lineno"> 177</span> N = std::atoi(argv[1]);</div>
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<div class="line"><span class="lineno"> 178</span> a = std::atof(argv[2]);</div>
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<div class="line"><span class="lineno"> 179</span> b = std::atof(argv[3]);</div>
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<div class="line"><span class="lineno"> 180</span> <span class="comment">// Check if a<b else abort</span></div>
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@@ -360,10 +360,10 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">if</span> (N < 4 || a != 1 || b != 3) {</div>
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<div class="line"><span class="lineno"> 184</span> used_argv_parameters = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 185</span> }</div>
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<div class="line"><span class="lineno"> 186</span> std::cout << <span class="stringliteral">"You selected N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 186</span> std::cout << <span class="stringliteral">"You selected N="</span> << N << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 187</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 188</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 189</span> std::cout << <span class="stringliteral">"Default N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 189</span> std::cout << <span class="stringliteral">"Default N="</span> << N << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
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<div class="line"><span class="lineno"> 190</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 191</span> }</div>
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<div class="line"><span class="lineno"> 192</span> </div>
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@@ -376,7 +376,6 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 199</span>}</div>
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<div class="ttc" id="agenerate__parentheses_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00082">generate_parentheses.cpp:82</a></div></div>
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<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition</b> <a href="../../d1/df3/hash__search_8cpp_source.html#l00045">hash_search.cpp:45</a></div></div>
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<div class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00048">sparse_table.cpp:48</a></div></div>
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</div><!-- fragment -->
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@@ -430,7 +429,7 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 58</span> <span class="comment">// Create the data table</span></div>
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<div class="line"><span class="lineno"> 59</span> <span class="comment">// Loop from x0 to xN-1</span></div>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">double</span> temp = NAN;</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i < N; i++) {</div>
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<div class="line"><span class="lineno"> 62</span> temp = func(xi + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> / 2); <span class="comment">// find f(xi+h/2)</span></div>
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<div class="line"><span class="lineno"> 63</span> data_table.insert(</div>
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<div class="line"><span class="lineno"> 64</span> std::pair<std::int32_t, double>(i, temp)); <span class="comment">// add i and f(xi)</span></div>
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@@ -440,7 +439,7 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 68</span> <span class="comment">// Evaluate the integral.</span></div>
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<div class="line"><span class="lineno"> 69</span> <span class="comment">// Remember: {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}</span></div>
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<div class="line"><span class="lineno"> 70</span> <span class="keywordtype">double</span> evaluate_integral = 0;</div>
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<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) evaluate_integral += data_table.at(i);</div>
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<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i < N; i++) evaluate_integral += data_table.at(i);</div>
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<div class="line"><span class="lineno"> 72</span> </div>
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<div class="line"><span class="lineno"> 73</span> <span class="comment">// Multiply by the coefficient h</span></div>
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<div class="line"><span class="lineno"> 74</span> evaluate_integral *= <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
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@@ -493,7 +492,7 @@ Functions</h2></td></tr>
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</table>
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</td>
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<td class="mlabels-right">
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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</tr>
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</table>
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</div><div class="memdoc">
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@@ -515,34 +514,38 @@ Functions</h2></td></tr>
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<div class="line"><span class="lineno"> 125</span> <span class="comment">// Call midpoint() for each of the test functions f, g, k, l</span></div>
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<div class="line"><span class="lineno"> 126</span> <span class="comment">// Assert with two decimal point precision</span></div>
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<div class="line"><span class="lineno"> 127</span> <span class="keywordtype">double</span> result_f = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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<div class="line"><span class="lineno"> 128</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::f);</div>
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<div class="line"><span class="lineno"> 128</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="#a7ee8e824ef3e138a9a21883b26d97226">numerical_methods::midpoint_rule::f</a>);</div>
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<div class="line"><span class="lineno"> 129</span> assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) &&</div>
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<div class="line"><span class="lineno"> 130</span> <span class="stringliteral">"The result of f(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 131</span> std::cout << <span class="stringliteral">"The result of integral f(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 132</span> << <span class="stringliteral">"] is equal to: "</span> << result_f << std::endl;</div>
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<div class="line"><span class="lineno"> 133</span> </div>
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<div class="line"><span class="lineno"> 134</span> <span class="keywordtype">double</span> result_g = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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<div class="line"><span class="lineno"> 135</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::g);</div>
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<div class="line"><span class="lineno"> 135</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="#ae682ee71af44b1e9e884849cc6a6b040">numerical_methods::midpoint_rule::g</a>);</div>
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<div class="line"><span class="lineno"> 136</span> assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) &&</div>
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<div class="line"><span class="lineno"> 137</span> <span class="stringliteral">"The result of g(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 138</span> std::cout << <span class="stringliteral">"The result of integral g(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 139</span> << <span class="stringliteral">"] is equal to: "</span> << result_g << std::endl;</div>
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<div class="line"><span class="lineno"> 140</span> </div>
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<div class="line"><span class="lineno"> 141</span> <span class="keywordtype">double</span> result_k = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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<div class="line"><span class="lineno"> 142</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::k);</div>
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<div class="line"><span class="lineno"> 142</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a>);</div>
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<div class="line"><span class="lineno"> 143</span> assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) &&</div>
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<div class="line"><span class="lineno"> 144</span> <span class="stringliteral">"The result of k(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 145</span> std::cout << <span class="stringliteral">"The result of integral k(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 146</span> << <span class="stringliteral">"] is equal to: "</span> << result_k << std::endl;</div>
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<div class="line"><span class="lineno"> 147</span> </div>
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<div class="line"><span class="lineno"> 148</span> <span class="keywordtype">double</span> result_l = <a class="code hl_function" href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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<div class="line"><span class="lineno"> 149</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::l);</div>
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<div class="line"><span class="lineno"> 149</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="#ad53616fb4fa6880ae876bcba53365c51">numerical_methods::midpoint_rule::l</a>);</div>
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<div class="line"><span class="lineno"> 150</span> assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) &&</div>
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<div class="line"><span class="lineno"> 151</span> <span class="stringliteral">"The result of l(x) is wrong"</span>);</div>
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<div class="line"><span class="lineno"> 152</span> std::cout << <span class="stringliteral">"The result of integral l(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><span class="lineno"> 153</span> << <span class="stringliteral">"] is equal to: "</span> << result_l << std::endl;</div>
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<div class="line"><span class="lineno"> 154</span>}</div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_a7072493d1f0f8a91b2a71d4cc456c09c"><div class="ttname"><a href="#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a></div><div class="ttdeci">double midpoint(const std::int32_t N, const double h, const double a, const std::function< double(double)> &func)</div><div class="ttdoc">Main function for implementing the Midpoint Integral Method implementation.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00052">midpoint_integral_method.cpp:52</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_a7ee8e824ef3e138a9a21883b26d97226"><div class="ttname"><a href="#a7ee8e824ef3e138a9a21883b26d97226">numerical_methods::midpoint_rule::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00090">midpoint_integral_method.cpp:90</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_ad53616fb4fa6880ae876bcba53365c51"><div class="ttname"><a href="#ad53616fb4fa6880ae876bcba53365c51">numerical_methods::midpoint_rule::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">A function l(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00109">midpoint_integral_method.cpp:109</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_ae682ee71af44b1e9e884849cc6a6b040"><div class="ttname"><a href="#ae682ee71af44b1e9e884849cc6a6b040">numerical_methods::midpoint_rule::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">A function g(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00097">midpoint_integral_method.cpp:97</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_ae9f66040f8e0ba73c1c741261c22a52a"><div class="ttname"><a href="#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">A function k(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d11/midpoint__integral__method_8cpp_source.html#l00103">midpoint_integral_method.cpp:103</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -552,7 +555,7 @@ Functions</h2></td></tr>
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