Oracle Developer Studio Performance Library routines are used to solve the following types of linear algebra and numerical problems:
Elementary vector and matrix operations – Vector and matrix products; plane rotations; 1, 2-, and infinity-norms; rank-1, 2, k, and 2k updates
Linear systems – Solve full-rank systems, compute error bounds, solve Sylvester equations, refine a computed solution, equilibrate a coefficient matrix
Least squares – Full-rank, generalized linear regression, rank-deficient, linear equality constrained
Eigenproblems – Eigenvalues, generalized eigenvalues, eigenvectors, generalized eigenvectors, Schur vectors, generalized Schur vectors
Matrix factorizations or decompositions – SVD, generalized SVD, QL and LQ, QR and RQ, Cholesky, LU, Schur, LDLT, UDUT, and CS Decomposition
Support operations – Condition number, in-place or out-of-place transpose, inverse, determinant, inertia, extra-precise iterative refinement
Sparse matrices – Solve symmetric, structurally symmetric, and unsymmetric coefficient matrices using direct methods and a choice of fill-reducing ordering algorithms, and user-specified orderings
Convolution and correlation in one and two dimensions
Fast Fourier transforms, Fourier analysis and Fourier synthesis, cosine and quarter-wave cosine transforms, cosine and quarter-wave sine transforms
Complex vector FFTs and FFTs in two and three dimensions
Sorting operations
CBLAS Interface