Scientific Libraries

21 Feb 2022

BLAS

Basic dense matrix operations
- Multiplication, Addition, Rank update, Triangular Solve

Divided into 3 levels

Level	Type	Example	# mem refs
1	Vec-Vec	DAXPY (y=x+y)	3n
2	Matrix-Vec	DGEMV (y = Ax + y)	n**2
3	Matrix-Matrix	DGMM (C = AB+C)	4n**2

LAPACK

Matrix Solvers
- Simultaneous linear equations, least-squares solutions, eigenvalue problems
- Matrix factorizations (LU, Cholesky, QR, SVD, Schur)
Relies heavily on BLAS for computation

ScaLAPACK

BLACS
- Message passing interface for linear algebra
- 2D arrays on 2D processes grids
- Generation of process grids
- Communication of matrices
Parallel LAPACK and BLAS routines (through PBLAS)
Extends the BLAS / LAPACK interface
- Addition of P prefix into the routines
- Example: PDGEMM

Interesting Implementations

PLASMA
- Manycore optimized linear algebra routines
- Potential successor of LAPACK
MAGMA and CULA
- LAPACK0type routines for GPUs

Sparse Matrices

PDEs, network simulation
Only store non-zero elements
Density and sparsity pattern affects performance
- No single general purpose solution
- Many solvers available
Hypre
KLU, Paraklete, AztecOO
SuperLU, UMFPACK, MUMPS
CuSP. CuSPARSE
- Solvers for NVIDIA GPUs

FFT Libraries

FFTW (Fast Fourier Transform in the West)
- 1D, 2D and 3D complex and real FFTs
- Two versions commonly use
  - Version 2: MPI support
  - Version 3: Much better performance, MPI support in development
- Planning has multiple levels of comprehensiveness
- ESTIMATE, MEASURE, PATIENT, EXHAUSTIVE
- Plans can be saved in a “wisdom file” and reused
Cray CRAFFT
- Dynamically selects the best FFT routine
- Serial and parallel routine
- See info_crafft
AMD ACML
Intel MKL and IPP
CuFFT
- FFT routines for Nvidia GPUs

Domain Specific Libraries

Jeet Majumdar