# reference-lapack/lapack

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1,808 stars · 491 forks · Fortran · other

## Links

- GitHub: https://github.com/Reference-LAPACK/lapack
- awesome-repositories: https://awesome-repositories.com/repository/reference-lapack-lapack.md

## Topics

`blas` `eigenvalues` `eigenvectors` `lapack` `lapacke` `linear-algebra` `linear-equations` `matrix-factorization` `singular-values` `svd`

## Description

LAPACK is a comprehensive library of Fortran routines designed for high-performance numerical analysis and linear algebra. It serves as a foundational scientific computing framework, providing standardized procedures for solving systems of linear equations, eigenvalue problems, and least squares approximations.

The library distinguishes itself through a hierarchical routine abstraction that organizes mathematical operations into distinct levels of complexity. It utilizes block-partitioned matrix algorithms and a column-major memory layout to optimize data locality and hardware efficiency. By relying on low-level basic linear algebra subprograms, the library ensures high-performance execution across diverse processor architectures.

Beyond its core solvers, the project provides a standardized infrastructure for scientific modeling and data analysis. It includes comprehensive test suites to verify numerical accuracy and precision, ensuring reliability in critical engineering and physics applications.

The library supports integration into external applications through a static linkage interface and a C language interface, facilitating compatibility with various development environments.

## Tags

### Scientific & Mathematical Computing

- [Linear Algebra Libraries](https://awesome-repositories.com/f/scientific-mathematical-computing/linear-algebra-libraries.md) — Provides a comprehensive collection of Fortran routines for solving systems of linear equations, eigenvalue problems, and least squares calculations.
- [Scientific Computing](https://awesome-repositories.com/f/scientific-mathematical-computing/high-performance-execution-environments/scientific-computing-platforms/scientific-computing.md) — Provides a standardized foundation of numerical routines for high-performance mathematical modeling and data analysis.
- [Linear Algebra Routines](https://awesome-repositories.com/f/scientific-mathematical-computing/linear-algebra-routines.md) — Executes high-performance vector and matrix operations by leveraging low-level linear algebra subprograms.
- [Linear System Solvers](https://awesome-repositories.com/f/scientific-mathematical-computing/linear-system-solvers.md) — Provides solvers for systems of linear equations and eigenvalue calculations to ensure precise mathematical results. ([source](https://github.com/reference-lapack/lapack#readme))
- [Block-Based Matrix Decompositions](https://awesome-repositories.com/f/scientific-mathematical-computing/block-based-matrix-decompositions.md) — Improves data locality and parallel processing efficiency by partitioning large matrices into smaller blocks.
- [Eigenvalue Computations](https://awesome-repositories.com/f/scientific-mathematical-computing/eigenvalue-computations.md) — Calculates matrix eigenvalues and eigenvectors to identify fundamental properties of linear transformations. ([source](https://github.com/reference-lapack/lapack#readme))
- [Least Squares Estimators](https://awesome-repositories.com/f/scientific-mathematical-computing/hidden-state-estimation/least-squares-estimators.md) — Solves least squares problems by minimizing the sum of squared residuals for accurate approximations. ([source](https://github.com/reference-lapack/lapack#readme))
- [Numerical Analysis Toolkits](https://awesome-repositories.com/f/scientific-mathematical-computing/numerical-mathematical-foundations/linear-algebra/numerical-analysis-toolkits.md) — Offers a standardized set of mathematical procedures for performing high-performance matrix operations and linear algebra computations.

### Part of an Awesome List

- [Linear Algebra](https://awesome-repositories.com/f/awesome-lists/learning/linear-algebra.md) — Calculates solutions for systems of linear equations, least squares approximations, and eigenvalue problems.

### Programming Languages & Runtimes

- [Fortran Resources](https://awesome-repositories.com/f/programming-languages-runtimes/programming-language-varieties/programming-languages/language-specific-resources/systems-and-performance-languages/fortran-resources.md) — Performs complex linear algebra operations using highly optimized Fortran routines for maximum hardware efficiency.
- [C and Objective-C Interface Mapping](https://awesome-repositories.com/f/programming-languages-runtimes/c-and-c-cross-compilation/c-and-objective-c-interface-mapping.md) — Exposes numerical routines to C-based applications through a standardized interface for seamless data exchange. ([source](https://github.com/reference-lapack/lapack#readme))

### Data & Databases

- [Column-Major Storage](https://awesome-repositories.com/f/data-databases/column-major-storage.md) — Optimizes cache access patterns by organizing multidimensional data arrays in column-major memory layout.

### Development Tools & Productivity

- [Static Binary Compilers](https://awesome-repositories.com/f/development-tools-productivity/static-binaries/static-binary-compilers.md) — Provides a standardized binary interface for integrating numerical routines directly into compiled executables.

### Software Engineering & Architecture

- [Mathematical Routine Abstractions](https://awesome-repositories.com/f/software-engineering-architecture/distributed-complexity-abstractions/api-complexity-abstractions/mathematical-routine-abstractions.md) — Structures mathematical operations into distinct levels of complexity to balance modularity with high-performance hardware utilization.

### Testing & Quality Assurance

- [Numerical Accuracy Validators](https://awesome-repositories.com/f/testing-quality-assurance/numerical-accuracy-validators.md) — Verifies the precision and reliability of mathematical computations through comprehensive testing suites.