Default SVD

This section demonstrates how to compute the singular value decomposition (SVD) of a dense matrix on GPU. The SVD factorizes A = U * S * V*, where S contains the singular values in descending order. Policies control whether left (U) and right (V) singular vectors are computed. Available policies are Economy, Full, and NoCalculation.

Source Code

Console Output

#include <iostream> #include <cla3p/dense.hpp> #include <culite/dense.hpp> #include <culite/svd.hpp> int main() { /* * Create a random (5x3) dense matrix on host and transfer to device */ const cla3p::dns::RdMatrix HostA = cla3p::dns::RdMatrix::random(5,3); culite::dns::RdMatrix A; HostA >> A; std::cout << "A:\n" << A; /* * Set a simple svd object for A */ culite::DefaultSVD<culite::dns::RdMatrix> svdA; /* * Decompose A into USV* product */ svdA.decompose(A); std::cout << "SVD Decomposition of A\n"; std::cout << "----------------------\n"; std::cout << "S:\n" << svdA.singularValues() << "U:\n" << svdA.leftSingularVectors() << "V:\n" << svdA.rightSingularVectors(); /* * Set a svd object with no calculation for V */ culite::svdPolicy_t policyU = culite::svdPolicy_t::Economy; culite::svdPolicy_t policyV = culite::svdPolicy_t::NoCalculation; culite::DefaultSVD<culite::dns::RdMatrix> svdB(policyU, policyV); svdB.decompose(A); std::cout << "SVD Decomposition of A (no V)\n"; std::cout << "-----------------------------\n"; std::cout << "S:\n" << svdB.singularValues() << "U:\n" << svdB.leftSingularVectors() << "V(empty):\n" << svdB.rightSingularVectors(); return 0; }

A: 0 1 2 0 | 8.401877e-01 1.975514e-01 4.773971e-01 1 | 3.943829e-01 3.352228e-01 6.288709e-01 2 | 7.830992e-01 7.682296e-01 3.647845e-01 3 | 7.984400e-01 2.777747e-01 5.134009e-01 4 | 9.116474e-01 5.539700e-01 9.522297e-01 SVD Decomposition of A ---------------------- S: 0 0 | 2.374960e+00 1 | 4.570190e-01 2 | 3.826198e-01 U: 0 1 2 0 | -4.004597e-01 2.227839e-01 6.290916e-01 1 | -3.265902e-01 2.651950e-01 -5.671251e-01 2 | -4.560412e-01 -8.833325e-01 -5.565426e-02 3 | -4.104772e-01 1.444986e-01 4.008145e-01 4 | -5.970810e-01 2.808607e-01 -3.447655e-01 V: 0 1 2 0 | -7.134676e-01 -6.246771e-02 6.978981e-01 1 | -4.142054e-01 -7.657560e-01 -4.919875e-01 2 | -5.651530e-01 6.400903e-01 -5.204676e-01 SVD Decomposition of A (no V) ----------------------------- S: 0 0 | 2.374960e+00 1 | 4.570190e-01 2 | 3.826198e-01 U: 0 1 2 0 | -4.004597e-01 2.227839e-01 6.290916e-01 1 | -3.265902e-01 2.651950e-01 -5.671251e-01 2 | -4.560412e-01 -8.833325e-01 -5.565426e-02 3 | -4.104772e-01 1.444986e-01 4.008145e-01 4 | -5.970810e-01 2.808607e-01 -3.447655e-01 V(empty):