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14 changes: 7 additions & 7 deletions README.md
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[![Lines of Code](https://sonarcloud.io/api/project_badges/measure?project=jacobdwatters_Flag4j&metric=ncloc)](https://sonarcloud.io/summary/new_code?id=jacobdwatters_Flag4j)

# Flag4j - Fast Linear Algebra for Java
Flag4j is a fast anbd easy to use linear algebra library for Java and provides operations and linear algebra routines for real/complex sparse/dense tensors, matrices, and vectors.
Flag4j is a fast and easy to use 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 16-FEB-2024
Flag4j is currently in the final steps of development before an initial beta release. Nearly all features have been fully implemented or beta implementations.

Updates:
- The QR, Hessenburg and Schur decompositions have had a complete overhall.
- The QR, Hessenburg and Schur decompositions have had a complete overall.
- QR/Hessenburg/Schur: The way reflectors are computed and applied has been significantly improved in terms of performance, stability, and sensitivity to over(under)flow issues.
- Schur: Some correcness issues have been ironed out and significant performance enhancements have been made. The decomposition uses an implicit double shifted QR algorithm.
This means computing eigenvalues should be more accuract/correct and significantly faster in most cases.
- Tensor Solver: Added a solver which can solve tensor equations of the form $A \cdot X = B$ where $A, \ X$, and $B$ are tensors of arbirary rank and shape as long as the shapes are conducive to
- Schur: Some correctness issues have been ironed out and significant performance enhancements have been made. The decomposition uses an implicit double shifted QR algorithm.
This means computing eigenvalues should be more accurate/correct and significantly faster in most cases.
- Tensor Solver: Added a solver which can solve tensor equations of the form $A \cdot X = B$ where $A, \ X$, and $B$ are tensors of arbitrary rank and shape as long as the shapes are conducive to
computing the tensor dot product `B = A.dot(X)`.
- Tensor Inverse: Added ability to compute the inverse of an arbitary invertible tensor $A$, $A^{-1}$ relative to a specified tensor product.
- Tensor Inverse: Added ability to compute the inverse of an arbitrary invertible tensor $A$, $A^{-1}$ relative to a specified tensor product.
___

## Features and Functionality
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- Features: Matrix rank, symmetric, definiteness, eigenvalues and vectors, singularity, triangular, etc.
- Comparisons: Similar, etc.
- Tensor Operations:
- Arithmetic: Tensor dot product, tensor transpose, tensor invers, etc.
- Arithmetic: Tensor dot product, tensor transpose, tensor inverse, etc.
- Comparisons: Tensor rank/dimension, etc.

### Matrix Decompositions
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<div class="inheritance"><a href="../core/sparse_base/RealSparseTensorBase.html" title="class in org.flag4j.core.sparse_base">org.flag4j.core.sparse_base.RealSparseTensorBase</a>&lt;<a href="CsrMatrix.html" title="class in org.flag4j.sparse">CsrMatrix</a>,&#8203;<a href="../dense/Matrix.html" title="class in org.flag4j.dense">Matrix</a>,&#8203;<a href="CsrCMatrix.html" title="class in org.flag4j.sparse">CsrCMatrix</a>,&#8203;<a href="../dense/CMatrix.html" title="class in org.flag4j.dense">CMatrix</a>&gt;
<div class="inheritance">org.flag4j.sparse.CsrMatrix</div>
<div class="inheritance">org.flag4j.arrays.sparse.CsrMatrix</div>
</div>
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