Matrix-Matrix Operations

 

with Greg Baker, John Gunnels, and James Overfelt Matrix-matrix operations, or level 3 BLAS, refer to those operations that involve multiplication of two matrix operands. Examples include matrix-matrix multiplication and triangular solve with multiple right-hand-sides.

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

In this chapter, we will describe all PLAPACK layers of the level-3 BLAS.

• General Matrix-Matrix Multiplication
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Symmetric Matrix-Matrix Multiplication
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Symmetric Rank-k Update
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Symmetric Rank-2k Update
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Triangular Matrix-Matrix Multiplication
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Triangular Solve with Multiple Right-Hand-Sides
  • Standard FORTRAN call
  • PLAPACK FORTRAN-C interface
  • PLAPACK calls
• Example: Parallelizing Matrix-Matrix Multiplication
  • Forming
  • Forming
  • Forming
  • Forming
  • A more general approach
  • Performance results
• Querying Algorithmic Blocking Size
• More Operations and Information