Extreme Optimization > Vector and Matrix Features

Extreme Optimization Numerical Libraries for .NET

Vector and Matrix Features

General features of the Extreme Optimization Numerical Libraries for .NET:

• Easy to use even for the mathematically not-so-inclined
• Powerful enough to satisfy the most demanding power user.
• Intuitive object model. The objects in the Extreme Optimization Mathematics Library for .NET and the relationships between them match our every-day concepts.
• Great performance through optimized implementation of the best algorithms.
• Cross-platform. Works out-of-the-box on 32 and 64 bit platforms, .NET versions 1.1, 2.0, 3.0, 3.5.

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 and Statistics feature lists.

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General

• 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.
• Native 64bit support. New!

Vectors

• General 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.

Sparse Matrices

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

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.

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