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<title>Algorithms_in_C++: linear_algebra/gram_schmidt.cpp File Reference</title>
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -187,15 +187,15 @@ Algorithm</h3>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="fragment"><div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> {</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < r; ++i) {</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vector "</span> << i + 1 << <span class="stringliteral">": "</span>;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; ++j) {</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << B[i][j] << <span class="stringliteral">" "</span>;</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> }</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="charliteral">'\n'</span>;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> }</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 102</span> {</div>
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<div class="line"><span class="lineno"> 103</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < r; ++i) {</div>
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<div class="line"><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vector "</span> << i + 1 << <span class="stringliteral">": "</span>;</div>
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<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; ++j) {</div>
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<div class="line"><span class="lineno"> 106</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << B[i][j] << <span class="stringliteral">" "</span>;</div>
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<div class="line"><span class="lineno"> 107</span> }</div>
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<div class="line"><span class="lineno"> 108</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="charliteral">'\n'</span>;</div>
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<div class="line"><span class="lineno"> 109</span> }</div>
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<div class="line"><span class="lineno"> 110</span>}</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><!-- fragment -->
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</div>
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@@ -240,13 +240,13 @@ Algorithm</h3>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>sum </dd></dl>
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<div class="fragment"><div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> {</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = 0;</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> += x[i] * y[i];</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 60</span> {</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = 0;</div>
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<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
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<div class="line"><span class="lineno"> 63</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> += x[i] * y[i];</div>
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<div class="line"><span class="lineno"> 64</span> }</div>
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<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>;</div>
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<div class="line"><span class="lineno"> 66</span>}</div>
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<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T > > &A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
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@@ -313,58 +313,58 @@ Here is the call graph for this function:</div>
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<p >projected array created</p>
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<p >we take the projection with all the previous vector and add them.</p>
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<p >subtract total projection vector from the input vector</p>
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<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> {</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (c < r) { <span class="comment">/// we check whether appropriate dimensions are given or not.</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Dimension of vector is less than number of vector, hence "</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="stringliteral">"\n first "</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> << c << <span class="stringliteral">" vectors are orthogonalised\n"</span>;</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> r = c;</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> }</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 1;</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">while</span> (k <= r) {</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">if</span> (k == 1) {</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; j++)</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> B[0][j] = A[0][j]; <span class="comment">/// First vector is copied as it is.</span></div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> }</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<double, 10></a></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> all_projection{}; <span class="comment">/// array to store projections</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> all_projection[i] = 0; <span class="comment">/// First initialised to zero</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 1;</div>
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||||
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">while</span> (l < k) {</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<double, 10></a></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> temp{}; <span class="comment">/// to store previous projected array</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordtype">double</span> factor = NAN; <span class="comment">/// to store the factor by which the</span><span class="comment"></span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="comment"> /// previous array will change</span></div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="comment"></span> factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274">projection</a>(A[k - 1], B[l - 1], c);</div>
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||||
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> temp[i] = B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> - 1][i] * factor; <span class="comment">/// projected array created</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> }</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; ++j) {</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> all_projection[j] =</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> all_projection[j] +</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> temp[j]; <span class="comment">/// we take the projection with all the</span><span class="comment"></span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="comment"> /// previous vector and add them.</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="comment"></span> }</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>++;</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] =</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> A[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] -</div>
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||||
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> all_projection[i]; <span class="comment">/// subtract total projection vector</span><span class="comment"></span></div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="comment"> /// from the input vector</span></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment"></span> }</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> }</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
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||||
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> }</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> display(r, c, B); <span class="comment">// for displaying orthogoanlised vectors</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 123</span> {</div>
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<div class="line"><span class="lineno"> 124</span> <span class="keywordflow">if</span> (c < r) { <span class="comment">/// we check whether appropriate dimensions are given or not.</span></div>
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<div class="line"><span class="lineno"> 125</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Dimension of vector is less than number of vector, hence "</span></div>
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<div class="line"><span class="lineno"> 126</span> <span class="stringliteral">"\n first "</span></div>
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<div class="line"><span class="lineno"> 127</span> << c << <span class="stringliteral">" vectors are orthogonalised\n"</span>;</div>
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<div class="line"><span class="lineno"> 128</span> r = c;</div>
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<div class="line"><span class="lineno"> 129</span> }</div>
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<div class="line"><span class="lineno"> 130</span> </div>
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<div class="line"><span class="lineno"> 131</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = 1;</div>
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<div class="line"><span class="lineno"> 132</span> </div>
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<div class="line"><span class="lineno"> 133</span> <span class="keywordflow">while</span> (k <= r) {</div>
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<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">if</span> (k == 1) {</div>
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<div class="line"><span class="lineno"> 135</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; j++)</div>
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<div class="line"><span class="lineno"> 136</span> B[0][j] = A[0][j]; <span class="comment">/// First vector is copied as it is.</span></div>
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<div class="line"><span class="lineno"> 137</span> }</div>
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<div class="line"><span class="lineno"> 138</span> </div>
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<div class="line"><span class="lineno"> 139</span> <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 140</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<double, 10></a></div>
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<div class="line"><span class="lineno"> 141</span> all_projection{}; <span class="comment">/// array to store projections</span></div>
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<div class="line"><span class="lineno"> 142</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
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<div class="line"><span class="lineno"> 143</span> all_projection[i] = 0; <span class="comment">/// First initialised to zero</span></div>
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<div class="line"><span class="lineno"> 144</span> }</div>
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<div class="line"><span class="lineno"> 145</span> </div>
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<div class="line"><span class="lineno"> 146</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> = 1;</div>
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<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">while</span> (l < k) {</div>
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<div class="line"><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<double, 10></a></div>
|
||||
<div class="line"><span class="lineno"> 149</span> temp{}; <span class="comment">/// to store previous projected array</span></div>
|
||||
<div class="line"><span class="lineno"> 150</span> <span class="keywordtype">double</span> factor = NAN; <span class="comment">/// to store the factor by which the</span><span class="comment"></span></div>
|
||||
<div class="line"><span class="lineno"> 151</span><span class="comment"> /// previous array will change</span></div>
|
||||
<div class="line"><span class="lineno"> 152</span><span class="comment"></span> factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274">projection</a>(A[k - 1], B[l - 1], c);</div>
|
||||
<div class="line"><span class="lineno"> 153</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
|
||||
<div class="line"><span class="lineno"> 154</span> temp[i] = B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> - 1][i] * factor; <span class="comment">/// projected array created</span></div>
|
||||
<div class="line"><span class="lineno"> 155</span> }</div>
|
||||
<div class="line"><span class="lineno"> 156</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; ++j) {</div>
|
||||
<div class="line"><span class="lineno"> 157</span> all_projection[j] =</div>
|
||||
<div class="line"><span class="lineno"> 158</span> all_projection[j] +</div>
|
||||
<div class="line"><span class="lineno"> 159</span> temp[j]; <span class="comment">/// we take the projection with all the</span><span class="comment"></span></div>
|
||||
<div class="line"><span class="lineno"> 160</span><span class="comment"> /// previous vector and add them.</span></div>
|
||||
<div class="line"><span class="lineno"> 161</span><span class="comment"></span> }</div>
|
||||
<div class="line"><span class="lineno"> 162</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>++;</div>
|
||||
<div class="line"><span class="lineno"> 163</span> }</div>
|
||||
<div class="line"><span class="lineno"> 164</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < c; ++i) {</div>
|
||||
<div class="line"><span class="lineno"> 165</span> B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] =</div>
|
||||
<div class="line"><span class="lineno"> 166</span> A[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 1][i] -</div>
|
||||
<div class="line"><span class="lineno"> 167</span> all_projection[i]; <span class="comment">/// subtract total projection vector</span><span class="comment"></span></div>
|
||||
<div class="line"><span class="lineno"> 168</span><span class="comment"> /// from the input vector</span></div>
|
||||
<div class="line"><span class="lineno"> 169</span><span class="comment"></span> }</div>
|
||||
<div class="line"><span class="lineno"> 170</span> }</div>
|
||||
<div class="line"><span class="lineno"> 171</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++;</div>
|
||||
<div class="line"><span class="lineno"> 172</span> }</div>
|
||||
<div class="line"><span class="lineno"> 173</span> display(r, c, B); <span class="comment">// for displaying orthogoanlised vectors</span></div>
|
||||
<div class="line"><span class="lineno"> 174</span>}</div>
|
||||
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
|
||||
<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>
|
||||
<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>
|
||||
@@ -402,49 +402,49 @@ Here is the call graph for this function:</div>
|
||||
<p >Input of vectors is taken</p>
|
||||
<p >To check whether vectors are orthogonal or not</p>
|
||||
<p >take make the process numerically stable, upper bound for the dot product take 0.1</p>
|
||||
<div class="fragment"><div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> {</div>
|
||||
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keywordtype">int</span> r = 0, c = 0;</div>
|
||||
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// perform self tests</span></div>
|
||||
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter the dimension of your vectors\n"</span>;</div>
|
||||
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> c;</div>
|
||||
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter the number of vectors you will enter\n"</span>;</div>
|
||||
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> r;</div>
|
||||
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> </div>
|
||||
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20></div>
|
||||
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> A{}; <span class="comment">/// a 2-D array for storing all vectors</span></div>
|
||||
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> B = {</div>
|
||||
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> {0}}; <span class="comment">/// a 2-D array for storing orthogonalised vectors</span><span class="comment"></span></div>
|
||||
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span><span class="comment"> /// storing vectors in array A</span></div>
|
||||
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span><span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < r; ++i) {</div>
|
||||
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter vector "</span> << i + 1</div>
|
||||
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> << <span class="charliteral">'\n'</span>; <span class="comment">/// Input of vectors is taken</span></div>
|
||||
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; ++j) {</div>
|
||||
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Value "</span> << j + 1 << <span class="stringliteral">"th of vector: "</span>;</div>
|
||||
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> A[i][j];</div>
|
||||
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> }</div>
|
||||
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="charliteral">'\n'</span>;</div>
|
||||
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> }</div>
|
||||
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> </div>
|
||||
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(r, c, A, B);</div>
|
||||
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> </div>
|
||||
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordtype">double</span> dot = 0;</div>
|
||||
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keywordtype">int</span> flag = 1; <span class="comment">/// To check whether vectors are orthogonal or not</span></div>
|
||||
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < r - 1; ++i) {</div>
|
||||
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < r; ++j) {</div>
|
||||
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> dot =</div>
|
||||
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(linear_algebra::gram_schmidt::dot_product(B[i], B[j], c));</div>
|
||||
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keywordflow">if</span> (dot > 0.1) <span class="comment">/// take make the process numerically stable, upper</span><span class="comment"></span></div>
|
||||
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span><span class="comment"> /// bound for the dot product take 0.1</span></div>
|
||||
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span><span class="comment"></span> {</div>
|
||||
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> flag = 0;</div>
|
||||
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> }</div>
|
||||
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> }</div>
|
||||
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> }</div>
|
||||
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 248</span> {</div>
|
||||
<div class="line"><span class="lineno"> 249</span> <span class="keywordtype">int</span> r = 0, c = 0;</div>
|
||||
<div class="line"><span class="lineno"> 250</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// perform self tests</span></div>
|
||||
<div class="line"><span class="lineno"> 251</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter the dimension of your vectors\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 252</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> c;</div>
|
||||
<div class="line"><span class="lineno"> 253</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter the number of vectors you will enter\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 254</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> r;</div>
|
||||
<div class="line"><span class="lineno"> 255</span> </div>
|
||||
<div class="line"><span class="lineno"> 256</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20></div>
|
||||
<div class="line"><span class="lineno"> 257</span> A{}; <span class="comment">/// a 2-D array for storing all vectors</span></div>
|
||||
<div class="line"><span class="lineno"> 258</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> B = {</div>
|
||||
<div class="line"><span class="lineno"> 259</span> {0}}; <span class="comment">/// a 2-D array for storing orthogonalised vectors</span><span class="comment"></span></div>
|
||||
<div class="line"><span class="lineno"> 260</span><span class="comment"> /// storing vectors in array A</span></div>
|
||||
<div class="line"><span class="lineno"> 261</span><span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < r; ++i) {</div>
|
||||
<div class="line"><span class="lineno"> 262</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter vector "</span> << i + 1</div>
|
||||
<div class="line"><span class="lineno"> 263</span> << <span class="charliteral">'\n'</span>; <span class="comment">/// Input of vectors is taken</span></div>
|
||||
<div class="line"><span class="lineno"> 264</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < c; ++j) {</div>
|
||||
<div class="line"><span class="lineno"> 265</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Value "</span> << j + 1 << <span class="stringliteral">"th of vector: "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 266</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> A[i][j];</div>
|
||||
<div class="line"><span class="lineno"> 267</span> }</div>
|
||||
<div class="line"><span class="lineno"> 268</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="charliteral">'\n'</span>;</div>
|
||||
<div class="line"><span class="lineno"> 269</span> }</div>
|
||||
<div class="line"><span class="lineno"> 270</span> </div>
|
||||
<div class="line"><span class="lineno"> 271</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(r, c, A, B);</div>
|
||||
<div class="line"><span class="lineno"> 272</span> </div>
|
||||
<div class="line"><span class="lineno"> 273</span> <span class="keywordtype">double</span> dot = 0;</div>
|
||||
<div class="line"><span class="lineno"> 274</span> <span class="keywordtype">int</span> flag = 1; <span class="comment">/// To check whether vectors are orthogonal or not</span></div>
|
||||
<div class="line"><span class="lineno"> 275</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < r - 1; ++i) {</div>
|
||||
<div class="line"><span class="lineno"> 276</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < r; ++j) {</div>
|
||||
<div class="line"><span class="lineno"> 277</span> dot =</div>
|
||||
<div class="line"><span class="lineno"> 278</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(linear_algebra::gram_schmidt::dot_product(B[i], B[j], c));</div>
|
||||
<div class="line"><span class="lineno"> 279</span> <span class="keywordflow">if</span> (dot > 0.1) <span class="comment">/// take make the process numerically stable, upper</span><span class="comment"></span></div>
|
||||
<div class="line"><span class="lineno"> 280</span><span class="comment"> /// bound for the dot product take 0.1</span></div>
|
||||
<div class="line"><span class="lineno"> 281</span><span class="comment"></span> {</div>
|
||||
<div class="line"><span class="lineno"> 282</span> flag = 0;</div>
|
||||
<div class="line"><span class="lineno"> 283</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><span class="lineno"> 284</span> }</div>
|
||||
<div class="line"><span class="lineno"> 285</span> }</div>
|
||||
<div class="line"><span class="lineno"> 286</span> }</div>
|
||||
<div class="line"><span class="lineno"> 287</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><span class="lineno"> 288</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 289</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 290</span>}</div>
|
||||
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
|
||||
<div class="ttc" id="afabs_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a></div><div class="ttdeci">T fabs(T... args)</div></div>
|
||||
<div class="ttc" id="agram__schmidt_8cpp_html_aa31ca28f60c880802462335eedc5d91f"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a></div><div class="ttdeci">void gram_schmidt(int r, const int &c, const std::array< std::array< double, 10 >, 20 > &A, std::array< std::array< double, 10 >, 20 > B)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:121</div></div>
|
||||
@@ -502,17 +502,17 @@ Here is the call graph for this function:</div>
|
||||
<p >The dot product of two vectors is taken</p>
|
||||
<p >The norm of the second vector is taken.</p>
|
||||
<p >multiply that factor with every element in a 3rd vector, whose initial values are same as the 2nd vector.</p>
|
||||
<div class="fragment"><div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> {</div>
|
||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordtype">double</span> dot =</div>
|
||||
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(x, y, c); <span class="comment">/// The dot product of two vectors is taken</span></div>
|
||||
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">double</span> anorm =</div>
|
||||
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(y, y, c); <span class="comment">/// The norm of the second vector is taken.</span></div>
|
||||
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordtype">double</span> factor =</div>
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> dot /</div>
|
||||
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> anorm; <span class="comment">/// multiply that factor with every element in a 3rd vector,</span><span class="comment"></span></div>
|
||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment"> /// whose initial values are same as the 2nd vector.</span></div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment"></span> <span class="keywordflow">return</span> factor;</div>
|
||||
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 80</span> {</div>
|
||||
<div class="line"><span class="lineno"> 81</span> <span class="keywordtype">double</span> dot =</div>
|
||||
<div class="line"><span class="lineno"> 82</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(x, y, c); <span class="comment">/// The dot product of two vectors is taken</span></div>
|
||||
<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">double</span> anorm =</div>
|
||||
<div class="line"><span class="lineno"> 84</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">dot_product</a>(y, y, c); <span class="comment">/// The norm of the second vector is taken.</span></div>
|
||||
<div class="line"><span class="lineno"> 85</span> <span class="keywordtype">double</span> factor =</div>
|
||||
<div class="line"><span class="lineno"> 86</span> dot /</div>
|
||||
<div class="line"><span class="lineno"> 87</span> anorm; <span class="comment">/// multiply that factor with every element in a 3rd vector,</span><span class="comment"></span></div>
|
||||
<div class="line"><span class="lineno"> 88</span><span class="comment"> /// whose initial values are same as the 2nd vector.</span></div>
|
||||
<div class="line"><span class="lineno"> 89</span><span class="comment"></span> <span class="keywordflow">return</span> factor;</div>
|
||||
<div class="line"><span class="lineno"> 90</span>}</div>
|
||||
<div class="ttc" id="agram__schmidt_8cpp_html_aed4d308f46ca1d91e348ca260ec1d2fb"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb">linear_algebra::gram_schmidt::dot_product</a></div><div class="ttdeci">double dot_product(const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:59</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
@@ -546,68 +546,68 @@ Here is the call graph for this function:</div>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<p >Test Function. Process has been tested for 3 Sample Inputs </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
|
||||
<div class="fragment"><div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> {</div>
|
||||
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> a1 = {</div>
|
||||
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> {{1, 0, 1, 0}, {1, 1, 1, 1}, {0, 1, 2, 1}}};</div>
|
||||
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> b1 = {{0}};</div>
|
||||
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordtype">double</span> dot1 = 0;</div>
|
||||
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(3, 4, a1, b1);</div>
|
||||
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordtype">int</span> flag = 1;</div>
|
||||
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; ++i) {</div>
|
||||
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < 3; ++j) {</div>
|
||||
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> dot1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
|
||||
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> linear_algebra::gram_schmidt::dot_product(b1[i], b1[j], 4));</div>
|
||||
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">if</span> (dot1 > 0.1) {</div>
|
||||
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> flag = 0;</div>
|
||||
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> }</div>
|
||||
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> }</div>
|
||||
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
|
||||
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> assert(flag == 1);</div>
|
||||
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test Case 1\n "</span>;</div>
|
||||
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> </div>
|
||||
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> a2 = {{{3, 1}, {2, 2}}};</div>
|
||||
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> b2 = {{0}};</div>
|
||||
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordtype">double</span> dot2 = 0;</div>
|
||||
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 2, a2, b2);</div>
|
||||
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> flag = 1;</div>
|
||||
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 1; ++i) {</div>
|
||||
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < 2; ++j) {</div>
|
||||
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> dot2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
|
||||
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> linear_algebra::gram_schmidt::dot_product(b2[i], b2[j], 2));</div>
|
||||
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">if</span> (dot2 > 0.1) {</div>
|
||||
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> flag = 0;</div>
|
||||
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> }</div>
|
||||
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</div>
|
||||
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> }</div>
|
||||
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> assert(flag == 1);</div>
|
||||
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test Case 2\n"</span>;</div>
|
||||
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> </div>
|
||||
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> a3 = {{{1, 2, 2}, {-4, 3, 2}}};</div>
|
||||
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> b3 = {{0}};</div>
|
||||
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordtype">double</span> dot3 = 0;</div>
|
||||
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 3, a3, b3);</div>
|
||||
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> flag = 1;</div>
|
||||
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 1; ++i) {</div>
|
||||
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < 2; ++j) {</div>
|
||||
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> dot3 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
|
||||
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> linear_algebra::gram_schmidt::dot_product(b3[i], b3[j], 3));</div>
|
||||
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keywordflow">if</span> (dot3 > 0.1) {</div>
|
||||
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> flag = 0;</div>
|
||||
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> }</div>
|
||||
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> }</div>
|
||||
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> }</div>
|
||||
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> assert(flag == 1);</div>
|
||||
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test Case 3\n"</span>;</div>
|
||||
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 181</span> {</div>
|
||||
<div class="line"><span class="lineno"> 182</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> a1 = {</div>
|
||||
<div class="line"><span class="lineno"> 183</span> {{1, 0, 1, 0}, {1, 1, 1, 1}, {0, 1, 2, 1}}};</div>
|
||||
<div class="line"><span class="lineno"> 184</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> b1 = {{0}};</div>
|
||||
<div class="line"><span class="lineno"> 185</span> <span class="keywordtype">double</span> dot1 = 0;</div>
|
||||
<div class="line"><span class="lineno"> 186</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(3, 4, a1, b1);</div>
|
||||
<div class="line"><span class="lineno"> 187</span> <span class="keywordtype">int</span> flag = 1;</div>
|
||||
<div class="line"><span class="lineno"> 188</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; ++i) {</div>
|
||||
<div class="line"><span class="lineno"> 189</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < 3; ++j) {</div>
|
||||
<div class="line"><span class="lineno"> 190</span> dot1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
|
||||
<div class="line"><span class="lineno"> 191</span> linear_algebra::gram_schmidt::dot_product(b1[i], b1[j], 4));</div>
|
||||
<div class="line"><span class="lineno"> 192</span> <span class="keywordflow">if</span> (dot1 > 0.1) {</div>
|
||||
<div class="line"><span class="lineno"> 193</span> flag = 0;</div>
|
||||
<div class="line"><span class="lineno"> 194</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><span class="lineno"> 195</span> }</div>
|
||||
<div class="line"><span class="lineno"> 196</span> }</div>
|
||||
<div class="line"><span class="lineno"> 197</span> }</div>
|
||||
<div class="line"><span class="lineno"> 198</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><span class="lineno"> 199</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 200</span> assert(flag == 1);</div>
|
||||
<div class="line"><span class="lineno"> 201</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test Case 1\n "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 202</span> </div>
|
||||
<div class="line"><span class="lineno"> 203</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> a2 = {{{3, 1}, {2, 2}}};</div>
|
||||
<div class="line"><span class="lineno"> 204</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> b2 = {{0}};</div>
|
||||
<div class="line"><span class="lineno"> 205</span> <span class="keywordtype">double</span> dot2 = 0;</div>
|
||||
<div class="line"><span class="lineno"> 206</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 2, a2, b2);</div>
|
||||
<div class="line"><span class="lineno"> 207</span> flag = 1;</div>
|
||||
<div class="line"><span class="lineno"> 208</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 1; ++i) {</div>
|
||||
<div class="line"><span class="lineno"> 209</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < 2; ++j) {</div>
|
||||
<div class="line"><span class="lineno"> 210</span> dot2 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
|
||||
<div class="line"><span class="lineno"> 211</span> linear_algebra::gram_schmidt::dot_product(b2[i], b2[j], 2));</div>
|
||||
<div class="line"><span class="lineno"> 212</span> <span class="keywordflow">if</span> (dot2 > 0.1) {</div>
|
||||
<div class="line"><span class="lineno"> 213</span> flag = 0;</div>
|
||||
<div class="line"><span class="lineno"> 214</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><span class="lineno"> 215</span> }</div>
|
||||
<div class="line"><span class="lineno"> 216</span> }</div>
|
||||
<div class="line"><span class="lineno"> 217</span> }</div>
|
||||
<div class="line"><span class="lineno"> 218</span> <span class="keywordflow">if</span> (flag == 0)</div>
|
||||
<div class="line"><span class="lineno"> 219</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 220</span> assert(flag == 1);</div>
|
||||
<div class="line"><span class="lineno"> 221</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test Case 2\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 222</span> </div>
|
||||
<div class="line"><span class="lineno"> 223</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> a3 = {{{1, 2, 2}, {-4, 3, 2}}};</div>
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<div class="line"><span class="lineno"> 224</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::array<double, 10></a>, 20> b3 = {{0}};</div>
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<div class="line"><span class="lineno"> 225</span> <span class="keywordtype">double</span> dot3 = 0;</div>
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<div class="line"><span class="lineno"> 226</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(2, 3, a3, b3);</div>
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<div class="line"><span class="lineno"> 227</span> flag = 1;</div>
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<div class="line"><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 1; ++i) {</div>
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<div class="line"><span class="lineno"> 229</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < 2; ++j) {</div>
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<div class="line"><span class="lineno"> 230</span> dot3 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
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<div class="line"><span class="lineno"> 231</span> linear_algebra::gram_schmidt::dot_product(b3[i], b3[j], 3));</div>
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<div class="line"><span class="lineno"> 232</span> <span class="keywordflow">if</span> (dot3 > 0.1) {</div>
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<div class="line"><span class="lineno"> 233</span> flag = 0;</div>
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<div class="line"><span class="lineno"> 234</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><span class="lineno"> 235</span> }</div>
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<div class="line"><span class="lineno"> 236</span> }</div>
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<div class="line"><span class="lineno"> 237</span> }</div>
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<div class="line"><span class="lineno"> 238</span> <span class="keywordflow">if</span> (flag == 0)</div>
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<div class="line"><span class="lineno"> 239</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Vectors are linearly dependent\n"</span>;</div>
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<div class="line"><span class="lineno"> 240</span> assert(flag == 1);</div>
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<div class="line"><span class="lineno"> 241</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test Case 3\n"</span>;</div>
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<div class="line"><span class="lineno"> 242</span>}</div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -617,7 +617,7 @@ Here is the call graph for this function:</div>
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