numerical-patterns

What problem does it solve?

This Skill solves the challenge of implementing robust, high-performance numerical patterns in C++20.

Core Features & Use Cases

• Dense and Sparse Matrix Structures: wrappers and patterns for dense operations with a simple API and CSR-based sparse matrices.
• Iterative Solvers: templates for Conjugate Gradient and GMRES to solve large linear systems efficiently.
• Numerical Stability: techniques like Kahan summation and robust norm computations to reduce floating-point error.
• HPC I/O: guidance and patterns for scalable data management with MPI-IO and HDF5 in HPC workflows.
• Use Case: A simulation workflow requiring large-scale linear solves and data I/O can reuse these patterns to implement robust, portable solvers.

Quick Start

Instantiate DenseMatrix or SparseMatrixCSR in your C++20 project, prepare vectors b and initial guess x, and invoke ConjugateGradient or GMRES to solve Ax = b. Leverage the included numerical stability utilities and plan your I/O with MPI-IO or HDF5 as needed.