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POGauss Elimination for NxM matrix
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  1. POGauss Elimination for NxM matrix
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    copied!<pre><code>/* Program to demonstrate gaussian &lt;strong class="highlight"&gt;elimination&lt;/strong&gt; on a set of linear simultaneous equations */ #include &lt;iostream&gt; #include &lt;cmath&gt; #include &lt;vector&gt; using namespace std; const double eps = 1.e-15; /*Preliminary pivoting strategy Pivoting function */ double pivot(vector&lt;vector&lt;double&gt; &gt; &amp;a, vector&lt;double&gt; &amp;b, int i) { int n = a.size(); int j=i; double t=0; for(int k=i; k&lt;n; k+=1) { double aki = fabs(a[k][i]); if(aki&gt;t) { t=aki; j=k; } } if(j&gt;i) { double dummy; for(int L=0; L&lt;n; L+=1) { dummy = a[i][L]; a[i][L]= a[j][L]; a[j][L]= dummy; } double temp = b[j]; b[i]=b[j]; b[j]=temp; } return a[i][i]; } /* Forward &lt;strong class="highlight"&gt;elimination&lt;/strong&gt; */ void triang(vector&lt;vector&lt;double&gt; &gt; &amp;a, vector&lt;double&gt; &amp;b) { int n = a.size(); for(int i=0; i&lt;n-1; i+=1) { double diag = pivot(a,b,i); if(fabs(diag)&lt;eps) { cout&lt;&lt;"zero det"&lt;&lt;endl; return; } for(int j=i+1; j&lt;n; j+=1) { double mult = a[j][i]/diag; for(int k = i+1; k&lt;n; k+=1) { a[j][k]-=mult*a[i][k]; } b[j]-=mult*b[i]; } } } /* DOT PRODUCT OF TWO VECTORS */ double dotProd(vector&lt;double&gt; &amp;u, vector&lt;double&gt; &amp;v, int k1,int k2) { double sum = 0; for(int i = k1; i &lt;= k2; i += 1) { sum += u[i] * v[i]; } return sum; } /* BACK SUBSTITUTION STEP */ void backSubst(vector&lt;vector&lt;double&gt; &gt; &amp;a, vector&lt;double&gt; &amp;b, vector&lt;double&gt; &amp;x) { int n = a.size(); for(int i = n-1; i &gt;= 0; i -= 1) { x[i] = (b[i] - dotProd(a[i], x, i + 1, n-1))/ a[i][i]; } } /* REFINED GAUSSIAN &lt;strong class="highlight"&gt;ELIMINATION&lt;/strong&gt; PROCEDURE */ void gauss(vector&lt;vector&lt;double&gt; &gt; &amp;a, vector&lt;double&gt; &amp;b, vector&lt;double&gt; &amp;x) { triang(a, b); backSubst(a, b, x); } // EXAMPLE MAIN PROGRAM int main() { int n; cin &gt;&gt; n; vector&lt;vector&lt;double&gt; &gt; a; vector&lt;double&gt; x; vector&lt;double&gt; b; for (int i = 0; i &lt; n; i++) { vector&lt;double&gt; temp; for (int j = 0; j &lt; n; j++) { int no; cin &gt;&gt; no; temp.push_back(no); } a.push_back(temp); b.push_back(0); x.push_back(0); } /* for (int i = 0; i &lt; n; i++) { int no; cin &gt;&gt; no; b.push_back(no); x.push_back(0); } */ gauss(a, b, x); for (size_t i = 0; i &lt; x.size(); i++) { cout &lt;&lt; x[i] &lt;&lt; endl; } return 0; } </code></pre> <p>The above gaussian eleimination algorithm works fine on NxN matrices. But I need it to work on NxM matrix. Can anyone help me to do it? I am not very good at maths. I got this code on some website and i am stuck at it.</p>
 

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