A C++ template library for linear algebra, vectors and more


Eigen is a versatile, fast, elegant and reliable template library that supports all matrix sizes, from small fixed-size matrices to arbitrarily large dense matrices, and even sparse matrices.
- It supports all standard numeric types, including std::complex, integers, and is easily extensible to custom numeric types.
- It supports various matrix decompositions and geometry features.
- Its ecosystem of unsupported modules provides many specialized features such as non-linear optimization, matrix functions, a polynomial solver, FFT, and much more.
- Expression templates allow to intelligently remove temporaries and enable lazy evaluation, when that is appropriate.
- Explicit vectorization is performed for SSE 2/3/4, AVX, FMA, AVX512, ARM NEON (32-bit and 64-bit), PowerPC instruction sets, and now S390x SIMD (ZVector) with graceful fallback to non-vectorized code.
- Fixed-size matrices are fully optimized: dynamic memory allocation is avoided, and the loops are unrolled when that makes sense.
- For large matrices, special attention is paid to cache-friendliness.
- Algorithms are carefully selected for reliability. Reliability trade-offs are clearly documented and extremely safe decompositions are available.
- Eigen is thoroughly tested through its own test suite (over 500 executables) the standard BLAS test suite, and parts of the LAPACK test suite.
- The API is extremely clean and expressive while feeling natural to C++ programmers, thanks to expression templates.
- Implementing an algorithm on top of Eigen feels like just copying pseudocode.

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