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POGaussian elimination (with no pivoting) in CUDA
 

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  1. POGaussian elimination (with no pivoting) in CUDA
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    <p>I am trying to solve Gaussian elimination with CUDA. </p> <p>I have a <code>N*N</code> matrix. To get new elements of this matrix, I use the CPU code below, where <code>C.width=N</code>:</p> <pre><code>for(int z=0; z&lt; C.width-1; z++) { for ( int c = z+1 ; c &lt; C.width ; c++ ) { for (int d = z ; d &lt; C.width ; d++ ) { C.elements[c*C.width+d]=C.elements[c*C.width+d] - (B.elements[c*C.width+z]*C.elements[z*C.width+d]); } } } </code></pre> <p>I am trying to implement it with CUDA. For example, for <code>N=512</code></p> <pre><code>dim3 dimBlock(16,16,1); dim3 dimGrid(32,32,1); MatMulKernel&lt;&lt;&lt;dimGrid, dimBlock&gt;&gt;&gt;(d_A, d_B, d_C); </code></pre> <p>I think for every iteration I should use <code>N-i*N</code> threads to calculate the elements update, that is</p> <pre><code> if(idx&gt;511 || idy&gt;510) return; for(int i=1; i&lt;512;i++) { if(idx&gt;=i-1 &amp;&amp; idy&gt;=i-1) C.elements[(idy+1)*C.width+idx]=C.elements[(idy+1)*C.width+idx]-((C.elements[(idy+1)*C.width+(i-1)]/C.elements[(i-1)*C.width+(i-1)])*C.elements[(i-1)*C.width+idx]); __syncthreads(); } } </code></pre> <p>The results obtained on GPU and CPU are the same, but the processing time is <code>Time(CPU)=2*Time(GPU)</code></p> <p>For <code>N=512</code>: <code>Time(CPU) = 1900 ms</code>; <code>Time(GPU) = 980 ms</code></p> <p>For <code>N=1024</code>: <code>Time(CPU) = 14000 ms</code>; Time(GPU) = 7766 ms` . . .</p> <p>I think the speed-up should be larger than what I have now. Is there any mistake in my parallel code? Can you help me how can I rewrite my code?</p> <p>Thanks for any help!</p>
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      1. POGaussian elimination (with no pivoting) in CUDA
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    1. COI may not understand what you are trying to do, I'm far from a CUDA expert, but it seems that you are synchronizing threads after a single mathematical statement. I think you will find that the overhead of sharing memory and thread synchronization will eliminate most gains from parallel implementation.
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      1. POGaussian elimination (with no pivoting) in CUDA
      1. USJeremy West
 

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