Flag4j

Flag4j is a fast linear algebra library for Java and provides operations and linear algebra routines for real/complex sparse/dense tensors, matrices, and vectors.

State of Project as of 6-30-2023

Flag4j is currently in the final steps of development before an initial beta release. Nearly all features have been fully implemented or at least have a rudimentary beta implementation. There is still some work to be done for sparse tensors and matrices. Once that has been completed, a beta release will be imminent.

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Features and Functionality

Highlighted features are a work in progress and currently not fully implemented.

Algebraic Objects

• Complex Numbers
• Vectors
  • Real Dense Vector
  • Real Sparse Vector
  • Complex Dense Vector
  • Complex Sparse Vector
• Matrices
  • Real Dense Matrix
  • Real Sparse Matrix
  • Complex Dense Matrix
  • Complex Sparse Matrix
• Tensors
  • Real Dense Tensor
  • Real Sparse Tensor
  • Complex Dense Tensor
  • Complex Sparse Tensor

Operations

• Basic Arithmetic Operations: Add, subtract, scalar/element multiply, scalar/element divide, etc.
• Basic Properties: Tensor/matrix/vector shape, non-zero entries, etc.
• Basic Manipulations: Insert, join/stack/augment, extract, etc.
• Basic Comparisons: Equal, same shape, etc.
• Vector Operations
  • Arithmetic: Inner/outer/cross product, vector norms, etc.
  • Comparisons: Parallel, orthogonal, etc.
• Matrix Operations
  • Arithmetic: Matrix multiplication, transpose, matrix norms, inverse, pseudo-inverse, etc.
  • Features: Matrix rank, symmetric, definiteness, eigenvalues and vectors, singularity, triangular, etc.
  • Comparisons: Similar, etc.
• Tensor Operations:
  • Arithmetic: Tensor dot product, tensor transpose, etc.
  • Comparisons: Tensor rank/dimension, etc.

Matrix Decompositions

• LU Decompositions
  • No pivoting
  • Partial Pivoting
  • Full Pivoting
• QR Decomposition
  • Householder Reflectors
  • Full/Reduced
• Cholesky Decomposition
• Hessenburg Decomposition
• Eigen/Schur Decompositions
• Singular Value Decomposition

Linear Solvers

• Exact solution for well determined systems
• Least Squares solution

Linear and Homography Transformations

• Scale
• Shift
• Rotate
• Affine
• Projections
  • Orthographic
  • Perspective

Random

• Random Complex Numbers
• Random Matrices
  • Orthogonal, Unitary, symmetric, triangular, etc.
• Random Vectors
• Random Tensors

I/O

• Read/Write tensors, matrices, and vectors to/from a file.