PLASMA Parallel Linear Algebra Software for Multicore Architectures
Routines
Here is a list of all modules:
[detail level 1234]
 Initialize/finalize PLASMA descriptor ▼Utilities Map LAPACK <=> PLASMA constants ▼Matrix layout conversion cm2ccrb: Converts column-major (CM) to tiled (CCRB) ccrb2cm: Converts tiled (CCRB) to column-major (CM) ▼Linear system solvers Solves $$Ax = b$$ ►General matrices: LU Solves $$Ax = b$$ using LU factorization for general matrices ►General matrices: least squares Solves $$Ax \approx b$$ where $$A$$ is rectangular ►Symmetric/Hermitian positive definite: Cholesky Solves $$Ax = b$$ using Cholesky factorization for SPD/HPD matrices ►Symmetric/Hermitian indefinite Solves $$Ax = b$$ using indefinite factorization for symmetric/Hermitian matrices ▼Orthogonal/unitary factorizations Factor $$A$$ using $$QR, RQ, QL, LQ$$ ►QR factorization Factor $$A = QR$$ ►RQ factorization Factor $$A = RQ$$ ►QL factorization Factor $$A = QL$$ ►LQ factorization Factor $$A = LQ$$ ▼Eigenvalues Solves $$Ax = \lambda x$$ ►Non-symmetric eigenvalues Solves $$Ax = \lambda x$$ where $$A$$ is general ►Symmetric/Hermitian eigenvalues Solves $$Ax = \lambda x$$ where $$A$$ is symmetric/Hermitian ►Generalized Symmetric/Hermitian eigenvalues Solves $$Ax = \lambda B x$$, $$ABx = \lambda x$$, or $$BAx = \lambda x$$ where $$A, B$$ are symmetric/Hermitian and $$B$$ is positive definite ▼Singular Value Decomposition (SVD) Factor $$A = U \Sigma V^T$$ gesvd: SVD using QR iteration gesdd: SVD using divide-and-conquer gebrd: Bidiagonal reduction or/unmbr: Multiplies by Q or P from bidiagonal reduction or/ungbr: Generates Q or P from bidiagonal reduction Auxiliary routines ▼PLASMA BLAS and Auxiliary (parallel) BLAS and Auxiliary functions. Standard BLAS and LAPACK auxiliary routines are grouped by amount of work into Level 1, 2, 3 ►Level 1: vectors operations, O(n) work Vector operations that perform $$O(n)$$ work on $$O(n)$$ data. These are memory bound, since every operation requires a memory read or write ►Level 2: matrix-vector operations, O(n^2) work Matrix operations that perform $$O(n^2)$$ work on $$O(n^2)$$ data. These are memory bound, since every operation requires a memory read or write ►Level 3: matrix-matrix operations, O(n^3) work Matrix-matrix operations that perform $$O(n^3)$$ work on $$O(n^2)$$ data. These benefit from cache reuse, since many operations can be performed for every read from main memory ►Householder reflectors ►Precision conversion ►Matrix norms ▼Core BLAS and Auxiliary (single core) Core BLAS and Auxiliary functions. Standard BLAS and LAPACK auxiliary routines are grouped by amount of work into Level 1, 2, 3 ►Level 0: element operations, O(1) work Operations on single elements ►Level 1: vectors operations, O(n) work Vector operations that perform $$O(n)$$ work on $$O(n)$$ data. These are memory bound, since every operation requires a memory read or write ►Level 2: matrix-vector operations, O(n^2) work Matrix operations that perform $$O(n^2)$$ work on $$O(n^2)$$ data. These are memory bound, since every operation requires a memory read or write ►Level 3: matrix-matrix operations, O(n^3) work Matrix-matrix operations that perform $$O(n^3)$$ work on $$O(n^2)$$ data. These benefit from cache reuse, since many operations can be performed for every read from main memory ►Householder reflectors ►Precision conversion ►Matrix norms ►Linear system solvers