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POC++ eigenvalue/vector decomposition, only need first n vectors fast
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  1. POC++ eigenvalue/vector decomposition, only need first n vectors fast
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    copied!<p>I have a ~3000x3000 covariance-alike matrix on which I compute the eigenvalue-eigenvector decomposition (it's a OpenCV matrix, and I use <code>cv::eigen()</code> to get the job done).</p> <p>However, I actually only need the, say, first 30 eigenvalues/vectors, I don't care about the rest. Theoretically, this should allow to speed up the computation significantly, right? I mean, that means it has 2970 eigenvectors less that need to be computed.</p> <p>Which C++ library will allow me to do that? Please note that OpenCV's <code>eigen()</code> method does have the parameters for that, but the documentation says they are ignored, and I tested it myself, they are indeed ignored :D</p> <p><em><strong>UPDATE:</em></strong> I managed to do it with ARPACK. I managed to compile it for windows, and even to use it. The results look promising, an illustration can be seen in this toy example:</p> <pre><code>#include "ardsmat.h" #include "ardssym.h" int n = 3; // Dimension of the problem. double* EigVal = NULL; // Eigenvalues. double* EigVec = NULL; // Eigenvectors stored sequentially. int lowerHalfElementCount = (n*n+n) / 2; //whole matrix: /* 2 3 8 3 9 -7 8 -7 19 */ double* lower = new double[lowerHalfElementCount]; //lower half of the matrix //to be filled with COLUMN major (i.e. one column after the other, always starting from the diagonal element) lower[0] = 2; lower[1] = 3; lower[2] = 8; lower[3] = 9; lower[4] = -7; lower[5] = 19; //params: dimensions (i.e. width/height), array with values of the lower or upper half (sequentially, row major), 'L' or 'U' for upper or lower ARdsSymMatrix&lt;double&gt; mat(n, lower, 'L'); // Defining the eigenvalue problem. int noOfEigVecValues = 2; //int maxIterations = 50000000; //ARluSymStdEig&lt;double&gt; dprob(noOfEigVecValues, mat, "LM", 0, 0.5, maxIterations); ARluSymStdEig&lt;double&gt; dprob(noOfEigVecValues, mat); // Finding eigenvalues and eigenvectors. int converged = dprob.EigenValVectors(EigVec, EigVal); for (int eigValIdx = 0; eigValIdx &lt; noOfEigVecValues; eigValIdx++) { std::cout &lt;&lt; "Eigenvalue: " &lt;&lt; EigVal[eigValIdx] &lt;&lt; "\nEigenvector: "; for (int i = 0; i &lt; n; i++) { int idx = n*eigValIdx+i; std::cout &lt;&lt; EigVec[idx] &lt;&lt; " "; } std::cout &lt;&lt; std::endl; } </code></pre> <p>The results are:</p> <pre><code>9.4298, 24.24059 </code></pre> <p>for the eigenvalues, and</p> <pre><code>-0.523207, -0.83446237, -0.17299346 0.273269, -0.356554, 0.893416 </code></pre> <p>for the 2 eigenvectors respectively (one eigenvector per row) The code fails to find 3 eigenvectors (it can only find 1-2 in this case, an assert() makes sure of that, but well, that's not a problem).</p>
 

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