![]() This is similar to that implemented for real matrices by Lahabar and Narayanan ("Singular Value Decomposition on GPU using CUDA", IEEE International Parallel Distributed Processing Symposium 2009). The first algorithm is based on a two-step algorithm which bidiagonalizes the matrix using Householder transformations, and then diagonalizes the intermediate bidiagonal matrix through implicit QR shifts. This work explores the effectiveness of two different parallel SVD implementations on an NVIDIA Tesla C2050 GPU (14 multiprocessors, 32 cores per multiprocessor, 1.15 GHz clock - peed). Thus, it is important to have an SVD algorithm that is suitable for these processors. ![]() Since the computational tasks involved in array signal processing are well suited for parallelization, it is expected that these computations will be implemented using GPUs as soon as users have the necessary computational tools available to them. ![]() In addition, emerging multicore processors like graphical processing units (GPUs) are bringing parallel processing capabilities to an ever increasing number of users. U and V are the eigenvectors of AAH and AHA, respectively, while the singular values are the square roots of the eigenvalues of AAH.) Because it is desirable to be able to compute these quantities in real time, an efficient technique for computing the SVD is vital. (Recall that the SVD of a complex matrix A involves determining V,, and U such that A = U VH where U and V are orthonormal and is a positive, real, diagonal matrix containing the singular values of A. By employing the singular value decomposition (SVD) method, the eigenvectors and eigenvalues can be determined directly from the data without computing the sample covariance matrix, reducing the computational requirements for more » a given level of accuracy (van Trees, Optimum Array Processing). This, in turn, involves the eigen-decomposition of the sample spectral matrix, Cx = 1/K xKX(k)XH(k) where X(k) denotes a single frequency snapshot with an element for each element of the array. In order to enable robust detection, one of the key processing steps requires data and replica whitening. One of the current challenges in underwater acoustic array signal processing is the detection of quiet targets in the presence of noise. In particular, the approach, like LSA or SMT, can still be generalized to virtually any language(s) computation of the EVD takes similar resources to that of the SVD since all the blocks are sparse and the results of EVD are just as economical as those of SVD. Since all elements of the proposed EVD-based approach can rely entirely on lexical statistics, hardly any price is paid for the improved empirical results. For the case of multilingual LSA, we incorporate information on cross-language term alignments of the same sort used in Statistical Machine Translation (SMT). We point out that significant value can be added to LSA by filling in some of the values in the diagonal blocks (corresponding to explicit more » term-to-term or document-to-document associations) and computing a term-by-concept matrix from the EVD. Among the multiple ways of computing the SVD of a rectangular matrix X, one approach is to compute the eigenvalue decomposition (EVD) of a square 2 x 2 composite matrix consisting of four blocks with X and XT in the off-diagonal blocks and zero matrices in the diagonal blocks. Latent Semantic Analysis (LSA) is based on the Singular Value Decomposition (SVD) of a term-by-document matrix for identifying relationships among terms and documents from co-occurrence patterns. Give you both the Eigenvector for the Eigenvalue 20.= , by Eigenvalue magnitude) you can always do this yourself (see here: sort eigenvalues and associated eigenvectors after using in python).įinally note that the rows in vh contain the Eigenvectors, whereas in v it's the columns. So it is always important to make sure you have the Eigenvector for the Eigenvalue you want. In general routines that give you Eigenvalues and Eigenvectors do not "sort" them necessarily the way you might want them. ![]() ![]() Vector(s) with the singular values, within each vector sorted in descending order. The eigenvalues are not necessarily ordered These are: > wįor your singular value decomposition you can get your Eigenvalues by squaring your singular values ( C is invertible so everything is easy here): > s**2 For linalg.eig your Eigenvalues are stored in w. ![]()
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