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This is a partial list of companies who are using our libraries: ABB Robotics Allstate Arcam Astra Schedule Babson College Canadian Council on Learning Canyon Associates Caxton Associates CECity Constellation Energy CreditSights DeepOcean Duke University Dynamotive Elecsoft Engelhard Corporation Epcor Equipoise Software Galileo International GAM UK Gammex GlaxoSmithKline Global Matrix The Hartford Infinera Corporation Intel JDS Uniphase LaBranche & Co. Learning & Skills Council Jacobs Consultancy Litman Gregory Lucas Systems Malvern Instruments Medrio Merck & Co. Mintera. Monitor Software MorningStar NanoString Technologies Paletta Invent Parametric Portfolio Associates Prosanos RATA Associates RiskShield Ramboll Standard & Poor's Strategic Analysis Corporation Univ. of Alicante Univ. of South Carolina vielife Xerox US Army

Extreme Optimization Numerical Libraries for .NET

Vector and Matrix Library Features

Below is a list of features for the vector and matrix library portion of the Extreme Optimization Numerical Libraries for .NET. Also see the detailed mathematics, statistics, and data analysis feature lists.

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General

• Single, double, or quad precision real or complex components.
• Based on standard BLAS and LAPACK routines.
• 100% managed implementation for security, portability and small sizes.
• Native, processor-optimized implementation for speed with large sizes based on the Intel® Math Kernel Library.
• Native 64bit support.

GPU computing

• GPU computing: offload computations to the GPU.
• Data is kept on the GPU as long as possible for optimal performance.

Vectors

• Dense vectors.
• Band vectors.
• Constant vectors.
• Row, column and diagonal vectors.
• Vector views.

Vector Operations

• Basic arithmetic operations.
• Element-wise operations.
• Overloaded arithmetic operators.
• Norms, dot products.
• Largest and smallest values.
• Functions of vectors (sine, cosine, etc.)

Matrices

• General matrices.
• Triangular matrices.
• Real symmetric matrices and complex Hermitian matrices.
• Band matrices.
• Diagonal matrices.
• Matrix views.

Matrix Operations

• Basic arithmetic operations.
• Matrix-vector products.
• Overloaded arithmetic operations.
• Element-wise operations.
• Row and column scaling.
• Norms, rank, condition numbers.
• Singular values, eigenvalues and eigenvectors.

Matrix Decompositions

• LU decomposition.
• QR decomposition.
• Cholesky decomposition.
• Singular value decomposition.
• Symmetric eigenvalue decomposition.
• Non-symmetric eigenvalue decomposition.
• Banded LU and Cholesky decomposition.
• Non-negative matrix factorization (NMF) - Coming soon!

Sparse Matrices

• Sparse vectors
• Sparse matrices
• Matrices in Compressed Sparse Column format
• Sparse LU Decomposition
• Read matrices in Matrix Market format

Linear equations and least squares

• Shared API for matrices and decompositions.
• Determinants, inverses, numerical rank, condition numbers.
• Solve equations with 1 or multiple right-hand sides.
• Least squares solutions using QR or Singular Value Decomposition.
• Moore-Penrose Pseudo-inverse.
• Non-negative least squares (NNLS)