Merge pull request #96 from jacobdwatters/develop

Develop

.github/workflows/build.yml

@@ -16,7 +16,7 @@ jobs:
       - name: Set up JDK 11
         uses: actions/setup-java@v3
         with:
-          java-version: 11
+          java-version: 17
           distribution: 'zulu' # Alternative distribution options are available.
       - name: Cache SonarCloud packages
         uses: actions/cache@v3

README.md

@@ -6,30 +6,37 @@
 # 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.
+## 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.
+  - 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
+  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.
 ___
 
 ## 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
+  - Real/Complex Dense Vector
+  - Real/Complex Sparse Vector
 - Matrices
-    - Real Dense Matrix
-    - <mark>Real Sparse Matrix</mark>
-    - Complex Dense Matrix
-    - <mark>Complex Sparse Matrix</mark>
+    - Dense Matrices
+        - Real/Complex Dense Matrix
+    - Sparse Matrices
+        - Real/Complex COO Matrix
+        - Real/Complex CSR Matrix
+        - Real/Complex Symmetric Tri-diagonal Matrix. 
+        - Permutation Matrix
 - Tensors
-    - Real Dense Tensor
-    - <mark>Real Sparse Tensor</mark>
-    - Complex Dense Tensor
-    - <mark>Complex Sparse Tensor</mark>
+    - Real/Complex Dense Tensor
+    - Real/Complex Sparse COO Tensor
 
 ### Operations
 - Basic Arithmetic Operations: Add, subtract, scalar/element multiply, scalar/element divide, etc.
@@ -44,7 +51,7 @@ Highlighted features are a work in progress and currently not fully implemented.
   - Features: Matrix rank, symmetric, definiteness, eigenvalues and vectors, singularity, triangular, etc.
   - Comparisons: Similar, etc. 
 - Tensor Operations:
-  - Arithmetic: Tensor dot product, tensor transpose, etc.
+  - Arithmetic: Tensor dot product, tensor transpose, tensor invers, etc.
   - Comparisons: Tensor rank/dimension, etc.
 
 ### Matrix Decompositions
@@ -61,14 +68,17 @@ Highlighted features are a work in progress and currently not fully implemented.
 - Singular Value Decomposition
 
 ### Linear Solvers
-- Exact solution for well determined systems
+- Exact solution for well determined matrix systems
+  - General systems
+  - Triangular systems
+- Exact solution for well determined tensor equations
 - Least Squares solution
 
 ### Linear and Homography Transformations
 - Scale
 - Shift
-- <mark>Rotate</mark>
-- <mark>Affine</mark>
+- Rotate
+- Affine
 - Projections
   - Orthographic
   - Perspective

docs/allpackages-index.html

@@ -2,11 +2,11 @@
 <!-- NewPage -->
 <html lang="en">
 <head>
-<!-- Generated by javadoc (16) on Sun Jul 09 11:47:10 MDT 2023 -->
+<!-- Generated by javadoc (16) on Thu Aug 17 13:47:17 MDT 2023 -->
 <title>All Packages</title>
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-<meta name="dc.created" content="2023-07-09">
+<meta name="dc.created" content="2023-08-17">
 <meta name="description" content="package index">
 <meta name="generator" content="javadoc/AllPackagesIndexWriter">
 <link rel="stylesheet" type="text/css" href="stylesheet.css" title="Style">
@@ -61,22 +61,30 @@ <h1 title="All&amp;nbsp;Packages" class="title">All&nbsp;Packages</h1>
 <div class="col-last even-row-color">
 <div class="block">The base package of Flag4j which contains the main linear algebra objects.</div>
 </div>
-<div class="col-first odd-row-color"><a href="com/flag4j/complex_numbers/package-summary.html">com.flag4j.complex_numbers</a></div>
-<div class="col-last odd-row-color">
+<div class="col-first odd-row-color"><a href="com/flag4j/complex_matrix/package-summary.html">com.flag4j.complex_matrix</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/complex_numbers/package-summary.html">com.flag4j.complex_numbers</a></div>
+<div class="col-last even-row-color">
 <div class="block">
   This package contains the CNumber object which stores complex numbers in rectangular format and provides several
   methods allowing for computation with and manipulation of the complex numbers.</div>
 </div>
+<div class="col-first odd-row-color"><a href="com/flag4j/complex_sparse_matrix/package-summary.html">com.flag4j.complex_sparse_matrix</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/complex_tensor/package-summary.html">com.flag4j.complex_tensor</a></div>
+<div class="col-last even-row-color">&nbsp;</div>
+<div class="col-first odd-row-color"><a href="com/flag4j/complex_vector/package-summary.html">com.flag4j.complex_vector</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
 <div class="col-first even-row-color"><a href="com/flag4j/concurrency/package-summary.html">com.flag4j.concurrency</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
 <div class="col-first odd-row-color"><a href="com/flag4j/core/package-summary.html">com.flag4j.core</a></div>
 <div class="col-last odd-row-color">
 <div class="block">This package contains the core interfaces and abstract classes that specify the functionality of the algebraic objects
  within Flag4j.</div>
 </div>
-<div class="col-first even-row-color"><a href="com/flag4j/core/dense/package-summary.html">com.flag4j.core.dense</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/core/dense/package-summary.html">com.flag4j.core.dense_base</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/core/sparse/package-summary.html">com.flag4j.core.sparse</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/core/sparse/package-summary.html">com.flag4j.core.sparse_base</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
 <div class="col-first even-row-color"><a href="com/flag4j/exceptions/package-summary.html">com.flag4j.exceptions</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
@@ -90,31 +98,51 @@ <h1 title="All&amp;nbsp;Packages" class="title">All&nbsp;Packages</h1>
 <div class="col-last even-row-color">&nbsp;</div>
 <div class="col-first odd-row-color"><a href="com/flag4j/linalg/transformations/package-summary.html">com.flag4j.linalg.transformations</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/operations/package-summary.html">com.flag4j.operations</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/matrix/package-summary.html">com.flag4j.matrix</a></div>
+<div class="col-last even-row-color">&nbsp;</div>
+<div class="col-first odd-row-color"><a href="com/flag4j/operations/package-summary.html">com.flag4j.operations</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/operations/common/complex/package-summary.html">com.flag4j.operations.common.complex</a></div>
+<div class="col-last even-row-color">&nbsp;</div>
+<div class="col-first odd-row-color"><a href="com/flag4j/operations/common/real/package-summary.html">com.flag4j.operations.common.real</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/operations/dense_sparse/complex/package-summary.html">com.flag4j.operations.dense_sparse.complex</a></div>
+<div class="col-last even-row-color">&nbsp;</div>
+<div class="col-first odd-row-color"><a href="com/flag4j/operations/dense_sparse/real/package-summary.html">com.flag4j.operations.dense_sparse.real</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/operations/dense_sparse/real_complex/package-summary.html">com.flag4j.operations.dense_sparse.real_complex</a></div>
+<div class="col-last even-row-color">&nbsp;</div>
+<div class="col-first odd-row-color"><a href="com/flag4j/operations/dense/complex/package-summary.html">com.flag4j.operations.dense.complex</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/operations/dense/real/package-summary.html">com.flag4j.operations.dense.real</a></div>
+<div class="col-last even-row-color">&nbsp;</div>
+<div class="col-first odd-row-color"><a href="com/flag4j/operations/dense/real_complex/package-summary.html">com.flag4j.operations.dense.real_complex</a></div>
+<div class="col-last odd-row-color">&nbsp;</div>
+<div class="col-first even-row-color"><a href="com/flag4j/operations/sparse/complex/package-summary.html">com.flag4j.operations.sparse.coo.complex</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/operations/common/complex/package-summary.html">com.flag4j.operations.common.complex</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/operations/sparse/real/package-summary.html">com.flag4j.operations.sparse.coo.real</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/operations/common/real/package-summary.html">com.flag4j.operations.common.real</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/operations/sparse/real_complex/package-summary.html">com.flag4j.operations.sparse.coo.real_complex</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/operations/dense_sparse/complex/package-summary.html">com.flag4j.operations.dense_sparse.complex</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/rng/package-summary.html">com.flag4j.rng</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/operations/dense_sparse/real/package-summary.html">com.flag4j.operations.dense_sparse.real</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/sparse_complex_matrix/package-summary.html">com.flag4j.sparse_complex_matrix</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/operations/dense_sparse/real_complex/package-summary.html">com.flag4j.operations.dense_sparse.real_complex</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/sparse_complex_tensor/package-summary.html">com.flag4j.sparse_complex_tensor</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/operations/dense/complex/package-summary.html">com.flag4j.operations.dense.complex</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/sparse_complex_vector/package-summary.html">com.flag4j.sparse_complex_vector</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/operations/dense/real/package-summary.html">com.flag4j.operations.dense.real</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/sparse_matrix/package-summary.html">com.flag4j.sparse_matrix</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/operations/dense/real_complex/package-summary.html">com.flag4j.operations.dense.real_complex</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/sparse_tensor/package-summary.html">com.flag4j.sparse_tensor</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/operations/sparse/complex/package-summary.html">com.flag4j.operations.sparse.complex</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/sparse_vector/package-summary.html">com.flag4j.sparse_vector</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/operations/sparse/real/package-summary.html">com.flag4j.operations.sparse.real</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/tensor/package-summary.html">com.flag4j.tensor</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
-<div class="col-first odd-row-color"><a href="com/flag4j/operations/sparse/real_complex/package-summary.html">com.flag4j.operations.sparse.real_complex</a></div>
+<div class="col-first odd-row-color"><a href="com/flag4j/util/package-summary.html">com.flag4j.util</a></div>
 <div class="col-last odd-row-color">&nbsp;</div>
-<div class="col-first even-row-color"><a href="com/flag4j/util/package-summary.html">com.flag4j.util</a></div>
+<div class="col-first even-row-color"><a href="com/flag4j/vector/package-summary.html">com.flag4j.vector</a></div>
 <div class="col-last even-row-color">&nbsp;</div>
 </div>
 </main>