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<a href="../../d5/d33/gram__schmidt_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="preprocessor">#include &lt;array&gt;</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include &lt;cmath&gt;</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include &quot;math.h&quot;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a> {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d4/d0f/namespacegram__schmidt.html">gram_schmidt</a> {</div>
<div class="foldopen" id="foldopen00059" data-start="{" data-end="}">
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d"> 59</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">dot_product</a>(<span class="keyword">const</span> std::array&lt;double, 10&gt;&amp; x,</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">const</span> std::array&lt;double, 10&gt;&amp; y, <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; c) {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordtype">double</span> sum = 0;</div>
<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 &lt; c; ++i) {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> sum += x[i] * y[i];</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">return</span> sum;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>}</div>
</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span></div>
<div class="foldopen" id="foldopen00079" data-start="{" data-end="}">
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"><a class="line" href="../../d5/d33/gram__schmidt_8cpp.html#a8eeaafdde8b56f459aadc6013cf078bc"> 79</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a8eeaafdde8b56f459aadc6013cf078bc">projection</a>(<span class="keyword">const</span> std::array&lt;double, 10&gt;&amp; x,</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">const</span> std::array&lt;double, 10&gt;&amp; y, <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; c) {</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#ac4a4504924ecc9f12a2ebd80788ec01d">dot_product</a>(x, y, c); </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#ac4a4504924ecc9f12a2ebd80788ec01d">dot_product</a>(y, y, c); </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; </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> factor;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span></div>
<div class="foldopen" id="foldopen00101" data-start="{" data-end="}">
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="../../d5/d33/gram__schmidt_8cpp.html#ae6b496dce691e04f7f95ba0f0d33a289"> 101</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ae6b496dce691e04f7f95ba0f0d33a289">display</a>(<span class="keyword">const</span> <span class="keywordtype">int</span>&amp; r, <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; c,</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">const</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt;&amp; B) {</div>
<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 &lt; r; ++i) {</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Vector &quot;</span> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>;</div>
<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 &lt; c; ++j) {</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::cout &lt;&lt; B[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> }</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::cout &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> }</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>}</div>
</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span></div>
<div class="foldopen" id="foldopen00121" data-start="{" data-end="}">
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"><a class="line" href="../../d5/d33/gram__schmidt_8cpp.html#a0837468e1a653ed056e2cce3c914afa5"> 121</a></span><span class="keywordtype">void</span> <a class="code hl_namespace" href="../../d4/d0f/namespacegram__schmidt.html">gram_schmidt</a>(<span class="keywordtype">int</span> r, <span class="keyword">const</span> <span class="keywordtype">int</span>&amp; c,</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keyword">const</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt;&amp; A,</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; B) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (c &lt; r) { </div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Dimension of vector is less than number of vector, hence &quot;</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="stringliteral">&quot;\n first &quot;</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> &lt;&lt; c &lt;&lt; <span class="stringliteral">&quot; vectors are orthogonalised\n&quot;</span>;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> r = c;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> }</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordtype">int</span> k = 1;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">while</span> (k &lt;= r) {</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">if</span> (k == 1) {</div>
<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 &lt; c; j++)</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> B[0][j] = A[0][j]; </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> }</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> std::array&lt;double, 10&gt;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> all_projection{}; </div>
<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 &lt; c; ++i) {</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> all_projection[i] = 0; </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordtype">int</span> l = 1;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">while</span> (l &lt; k) {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> std::array&lt;double, 10&gt;</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> temp{}; </div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordtype">double</span> factor = NAN; </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a8eeaafdde8b56f459aadc6013cf078bc">projection</a>(A[k - 1], B[l - 1], c);</div>
<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 &lt; c; ++i) {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> temp[i] = B[l - 1][i] * factor; </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> }</div>
<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 &lt; c; ++j) {</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> all_projection[j] =</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> all_projection[j] +</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> temp[j]; </div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> }</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> l++;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
<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 &lt; c; ++i) {</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> B[k - 1][i] =</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> A[k - 1][i] -</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> all_projection[i]; </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> }</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> }</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> k++;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> }</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ae6b496dce691e04f7f95ba0f0d33a289">display</a>(r, c, B); <span class="comment">// for displaying orthogoanlised vectors</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span>}</div>
</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span>} <span class="comment">// namespace gram_schmidt</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span>} <span class="comment">// namespace numerical_methods</span></div>
<div class="foldopen" id="foldopen00181" data-start="{" data-end="}">
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"><a class="line" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 181</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; 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> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; 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#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::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 &lt; 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 &lt; 3; ++j) {</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> dot1 = fabs(</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">numerical_methods::gram_schmidt::dot_product</a>(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 &gt; 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> std::cout &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</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> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 1\n &quot;</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> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; a2 = {{{3, 1}, {2, 2}}};</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; 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#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::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 &lt; 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 &lt; 2; ++j) {</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> dot2 = fabs(</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">numerical_methods::gram_schmidt::dot_product</a>(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 &gt; 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> std::cout &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</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> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 2\n&quot;</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> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; a3 = {{{1, 2, 2}, {-4, 3, 2}}};</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; 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#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::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 &lt; 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 &lt; 2; ++j) {</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> dot3 = fabs(</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">numerical_methods::gram_schmidt::dot_product</a>(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 &gt; 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> std::cout &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</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> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test Case 3\n&quot;</span>;</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span>}</div>
</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span></div>
<div class="foldopen" id="foldopen00248" data-start="{" data-end="}">
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"><a class="line" href="../../d5/d33/gram__schmidt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 248</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</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> std::cout &lt;&lt; <span class="stringliteral">&quot;Enter the dimension of your vectors\n&quot;</span>;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> std::cin &gt;&gt; c;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Enter the number of vectors you will enter\n&quot;</span>;</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> std::cin &gt;&gt; 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> std::array&lt;std::array&lt;double, 10&gt;, 20&gt;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> A{}; </div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> std::array&lt;std::array&lt;double, 10&gt;, 20&gt; B = {</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> {0}}; </div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r; ++i) {</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Enter vector &quot;</span> &lt;&lt; i + 1</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> &lt;&lt; <span class="charliteral">&#39;\n&#39;</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 &lt; c; ++j) {</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Value &quot;</span> &lt;&lt; j + 1 &lt;&lt; <span class="stringliteral">&quot;th of vector: &quot;</span>;</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> std::cin &gt;&gt; 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> std::cout &lt;&lt; <span class="charliteral">&#39;\n&#39;</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#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::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; </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 &lt; 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 &lt; r; ++j) {</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> dot = fabs(</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">numerical_methods::gram_schmidt::dot_product</a>(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 &gt; 0.1) </div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</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> std::cout &lt;&lt; <span class="stringliteral">&quot;Vectors are linearly dependent\n&quot;</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>
<div class="ttc" id="agram__schmidt_8cpp_html_a0837468e1a653ed056e2cce3c914afa5"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::gram_schmidt::gram_schmidt</a></div><div class="ttdeci">void gram_schmidt(int r, const int &amp;c, const std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; &amp;A, std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; B)</div><div class="ttdef"><b>Definition</b> <a href="#l00121">gram_schmidt.cpp:121</a></div></div>
<div class="ttc" id="agram__schmidt_8cpp_html_a8eeaafdde8b56f459aadc6013cf078bc"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#a8eeaafdde8b56f459aadc6013cf078bc">numerical_methods::gram_schmidt::projection</a></div><div class="ttdeci">double projection(const std::array&lt; double, 10 &gt; &amp;x, const std::array&lt; double, 10 &gt; &amp;y, const int &amp;c)</div><div class="ttdef"><b>Definition</b> <a href="#l00079">gram_schmidt.cpp:79</a></div></div>
<div class="ttc" id="agram__schmidt_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> <a href="#l00181">gram_schmidt.cpp:181</a></div></div>
<div class="ttc" id="agram__schmidt_8cpp_html_ac4a4504924ecc9f12a2ebd80788ec01d"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">numerical_methods::gram_schmidt::dot_product</a></div><div class="ttdeci">double dot_product(const std::array&lt; double, 10 &gt; &amp;x, const std::array&lt; double, 10 &gt; &amp;y, const int &amp;c)</div><div class="ttdef"><b>Definition</b> <a href="#l00059">gram_schmidt.cpp:59</a></div></div>
<div class="ttc" id="agram__schmidt_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main Function.</div><div class="ttdef"><b>Definition</b> <a href="#l00248">gram_schmidt.cpp:248</a></div></div>
<div class="ttc" id="agram__schmidt_8cpp_html_ae6b496dce691e04f7f95ba0f0d33a289"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#ae6b496dce691e04f7f95ba0f0d33a289">numerical_methods::gram_schmidt::display</a></div><div class="ttdeci">void display(const int &amp;r, const int &amp;c, const std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; &amp;B)</div><div class="ttdef"><b>Definition</b> <a href="#l00101">gram_schmidt.cpp:101</a></div></div>
<div class="ttc" id="anamespacegram__schmidt_html"><div class="ttname"><a href="../../d4/d0f/namespacegram__schmidt.html">gram_schmidt</a></div><div class="ttdoc">Functions for Gram Schmidt Orthogonalisation Process</div></div>
<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for assert</div></div>
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