Matrix-Vector Operations

 

with Philip Alpatov and John Gunnels Matrix-vector operations, or level-2 BLAS, refer to those operations that involve multiplication of a vector by a matrix or the updating of a matrix with an outer product of vectors. Examples include matrix-vector multiplication and solving a triangular system of equations (multiplication by the inverse of a triangular matrix).

In PLAPACK, the matrix-vector operations are layered as follows:

• General Matrix-Vector Multiplication
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Symmetric Matrix-Vector Multiplication
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Triangular Matrix-Vector Multiplication
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Triangular Solve
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Rank-1 Update
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Symmetric Rank-1 Update
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Symmetric Rank-2 Update
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Example: Parallelizing Matrix-Vector Multiplication
  • Simple implementation
  • General implementation
• Example: Parallelizing Rank-1 Update
  • Simple implementation
  • General implementation
• More Operations and Information