Features:

- Random Matrix Generator Atomic Lower Triangular (10, 11, 12) - Random Matrix Generator Atomic Upper Triangular (46, 47, 48) - Linear Algebra Tridiagonal Matrix Shell (81, 82) - Linear Algebra Tridiagonal Matrix Constructor (83, 84) - Non-Periodic Tridiagonal Matrix Shell (85, 86, 87) - Non-Periodic Tridiagonal Matrix Constructor (88, 89, 90) - Non-Periodic Tridiagonal Matrix Solver (91, 92, 93) - Linear Algebra TridiagonalMatrix Shell (94, 95, 96) - Non-Periodic Tridiagonal Matrix Shell (97, 98) - Periodic Tridiagonal Matrix Shell (99, 100) - Non-Periodic Tridiagonal Matrix #1 (101, 102, 103) - Non-Periodic Tridiagonal Matrix #2 (104, 105) Bug Fixes/Re-organization: - Atomic Lower Triangular Fix #1 (13, 14, 15) - Atomic Lower Triangular Fix #2 (16, 17, 18) - Atomic Lower Triangular Fix #3 (19, 20, 21) - Atomic Lower Triangular Fix #4 (22, 23, 24) - Atomic Lower Triangular Fix #5 (25, 26, 27) - Atomic Lower Triangular Fix #6 (28, 29, 30) - Atomic Lower Triangular Fix #7 (31, 32, 33) - Atomic Lower Triangular Fix #8 (34, 35, 36) - Solvers of Linear Systems of Equations (64, 65) - Numerical Linear System Solver Migration (66, 67, 68) - Numerical Ryabenkii Tsynkov System Solver (69, 70, 71) - Numerical Tridiagonal System Solver Migration (72, 73, 74) - Numerical Strictly Tridiagonal System Solver (75, 76, 77) - Numerical Sherman Morrison System Solver (78, 79, 80) - Non-Periodic Tridiagonal Matrix Revamp (106, 107, 108) - Numerical Linear Solver Tridiagonal Revamp (109, 110, 111) - Non-Periodic Tridiagonal Revamp (112) - Linear Solver Ryabenkii Tsynkov #1 (113, 114, 115) - Linear Solver Ryabenkii Tsynkov #2 (116, 117, 118) - Linear Solver Ryabenkii Tsynkov #3 (119, 120) Samples: - Upper Strictly Upper Triangular #1 (1, 2, 3) - Upper Strictly Upper Triangular #2 (4, 5, 6) - Upper Strictly Upper Triangular #3 (7, 8, 9) - Atomic Lower Triangular Matrix #1 (37, 38, 39) - Atomic Lower Triangular Matrix #2 (40, 41, 42) - Atomic Lower Triangular Matrix #3 (43, 44, 45) - Atomic Upper Triangular Matrix #1 (49, 50, 51) - Atomic Upper Triangular Matrix #2 (52, 53, 54) - Atomic Upper Triangular Matrix #3 (55, 56, 57) - Atomic Upper Unitriangular Matrix Run (58, 59, 60) - Atomic Lower Unitriangular Matrix Run (61, 62, 63) - Non-periodic Tridiagonal Solver #1 (113, 114) - Non-periodic Tridiagonal Solver #2 (115, 116) IdeaDRIP:
lakshmiDRIP · Jul 7, 2024 · b477735 · b477735
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diff --git a/ReleaseNotes/02_08_2024.txt b/ReleaseNotes/02_08_2024.txt
@@ -0,0 +1,59 @@
+
+Features:
+
+	- Random Matrix Generator Atomic Lower Triangular (10, 11, 12)
+	- Random Matrix Generator Atomic Upper Triangular (46, 47, 48)
+	- Linear Algebra Tridiagonal Matrix Shell (81, 82)
+	- Linear Algebra Tridiagonal Matrix Constructor (83, 84)
+	- Non-Periodic Tridiagonal Matrix Shell (85, 86, 87)
+	- Non-Periodic Tridiagonal Matrix Constructor (88, 89, 90)
+	- Non-Periodic Tridiagonal Matrix Solver (91, 92, 93)
+	- Linear Algebra TridiagonalMatrix Shell (94, 95, 96)
+	- Non-Periodic Tridiagonal Matrix Shell (97, 98)
+	- Periodic Tridiagonal Matrix Shell (99, 100)
+	- Non-Periodic Tridiagonal Matrix #1 (101, 102, 103)
+	- Non-Periodic Tridiagonal Matrix #2 (104, 105)
+
+
+Bug Fixes/Re-organization:
+
+	- Atomic Lower Triangular Fix #1 (13, 14, 15)
+	- Atomic Lower Triangular Fix #2 (16, 17, 18)
+	- Atomic Lower Triangular Fix #3 (19, 20, 21)
+	- Atomic Lower Triangular Fix #4 (22, 23, 24)
+	- Atomic Lower Triangular Fix #5 (25, 26, 27)
+	- Atomic Lower Triangular Fix #6 (28, 29, 30)
+	- Atomic Lower Triangular Fix #7 (31, 32, 33)
+	- Atomic Lower Triangular Fix #8 (34, 35, 36)
+	- Solvers of Linear Systems of Equations (64, 65)
+	- Numerical Linear System Solver Migration (66, 67, 68)
+	- Numerical Ryabenkii Tsynkov System Solver (69, 70, 71)
+	- Numerical Tridiagonal System Solver Migration (72, 73, 74)
+	- Numerical Strictly Tridiagonal System Solver (75, 76, 77)
+	- Numerical Sherman Morrison System Solver (78, 79, 80)
+	- Non-Periodic Tridiagonal Matrix Revamp (106, 107, 108)
+	- Numerical Linear Solver Tridiagonal Revamp (109, 110, 111)
+	- Non-Periodic Tridiagonal Revamp (112)
+	- Linear Solver Ryabenkii Tsynkov #1 (113, 114, 115)
+	- Linear Solver Ryabenkii Tsynkov #2 (116, 117, 118)
+	- Linear Solver Ryabenkii Tsynkov #3 (119, 120)
+
+
+Samples:
+
+	- Upper Strictly Upper Triangular #1 (1, 2, 3)
+	- Upper Strictly Upper Triangular #2 (4, 5, 6)
+	- Upper Strictly Upper Triangular #3 (7, 8, 9)
+	- Atomic Lower Triangular Matrix #1 (37, 38, 39)
+	- Atomic Lower Triangular Matrix #2 (40, 41, 42)
+	- Atomic Lower Triangular Matrix #3 (43, 44, 45)
+	- Atomic Upper Triangular Matrix #1 (49, 50, 51)
+	- Atomic Upper Triangular Matrix #2 (52, 53, 54)
+	- Atomic Upper Triangular Matrix #3 (55, 56, 57)
+	- Atomic Upper Unitriangular Matrix Run (58, 59, 60)
+	- Atomic Lower Unitriangular Matrix Run (61, 62, 63)
+	- Non-periodic Tridiagonal Solver #1 (113, 114)
+	- Non-periodic Tridiagonal Solver #2 (115, 116)
+
+
+IdeaDRIP:
diff --git a/src/main/java/org/drip/fdm/cranknicolson/CNDiscretizedEvolver1D.java b/src/main/java/org/drip/fdm/cranknicolson/CNDiscretizedEvolver1D.java
@@ -5,7 +5,7 @@
 import org.drip.fdm.definition.R1EvolutionSnapshot;
 import org.drip.function.definition.RdToR1;
 import org.drip.numerical.common.NumberUtil;
-import org.drip.numerical.linearalgebra.StrictlyTridiagonalSolver;
+import org.drip.numerical.linearsolver.NonPeriodicTridiagonalScheme;
 
 /*
  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
@@ -379,7 +379,7 @@ public R1EvolutionSnapshot evolve (
 
 			try {
 				if (null == (
-					stateResponseArray = new StrictlyTridiagonalSolver (
+					stateResponseArray = NonPeriodicTridiagonalScheme.Standard (
 						stateResponseTransitionMatrix,
 						rhsArray
 					).forwardSweepBackSubstitution()

diff --git a/src/main/java/org/drip/function/rdtor1solver/InteriorFixedPointFinder.java b/src/main/java/org/drip/function/rdtor1solver/InteriorFixedPointFinder.java
@@ -213,7 +213,7 @@ private org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier inc
 		}
 
 		org.drip.numerical.linearalgebra.LinearizationOutput linearizationOutput =
-			org.drip.numerical.linearalgebra.LinearSystemSolver.SolveUsingMatrixInversion (
+			org.drip.numerical.linearsolver.LinearSystem.SolveUsingMatrixInversion (
 				constrainedObjectiveFunctionJacobianArray,
 				constrainedObjectiveFunctionRHSArray
 			);

diff --git a/src/main/java/org/drip/measure/crng/RandomMatrixGenerator.java b/src/main/java/org/drip/measure/crng/RandomMatrixGenerator.java
@@ -315,4 +315,92 @@ public static final TriangularMatrix StrictlyUpperTriangular (
 
 		return TriangularMatrix.Standard (r2Array);
 	}
+
+	/**
+	 * Construct an Atomic Lower Triangular Matrix of Random Elements up to the Maximum Value
+	 * 
+	 * @param elementCount Number of Elements in the Array
+	 * @param maximumElement Maximum Element
+	 * @param isEntryInteger TRUE - Entry is an Integer
+	 * 
+	 * @return Atomic Lower Triangular Matrix of Random Elements up to the Maximum Value
+	 */
+
+	public static final TriangularMatrix AtomicLowerTriangular (
+		final int elementCount,
+		final double maximumElement,
+		final boolean isEntryInteger)
+	{
+		double[][] r2Array = RdRandomSequence.TwoD (elementCount, maximumElement, isEntryInteger);
+
+    	for (int i = 0; i < r2Array.length; ++i) {
+        	for (int j = 0; j < r2Array.length; ++j) {
+    			r2Array[i][j] = 0.;
+        	}
+    	}
+
+    	for (int i = 0; i < r2Array.length; ++i) {
+			r2Array[i][i] = 1.;
+    	}
+
+    	int columnIndex = (int) (Math.random() * elementCount);
+
+		if (((int) maximumElement) - 1 == columnIndex) {
+			columnIndex = ((int) maximumElement) - 2;
+		} else if (0 == columnIndex) {
+			columnIndex = 1;
+		}
+
+		for (int i = 0; i < r2Array.length; ++i) {
+    		if (columnIndex < i) {
+				r2Array[i][columnIndex] = 1.;
+    		}
+    	}
+
+		return TriangularMatrix.Standard (r2Array);
+	}
+
+	/**
+	 * Construct an Atomic Upper Triangular Matrix of Random Elements up to the Maximum Value
+	 * 
+	 * @param elementCount Number of Elements in the Array
+	 * @param maximumElement Maximum Element
+	 * @param isEntryInteger TRUE - Entry is an Integer
+	 * 
+	 * @return Atomic Upper Triangular Matrix of Random Elements up to the Maximum Value
+	 */
+
+	public static final TriangularMatrix AtomicUpperTriangular (
+		final int elementCount,
+		final double maximumElement,
+		final boolean isEntryInteger)
+	{
+		double[][] r2Array = RdRandomSequence.TwoD (elementCount, maximumElement, isEntryInteger);
+
+    	for (int i = 0; i < r2Array.length; ++i) {
+        	for (int j = 0; j < r2Array.length; ++j) {
+    			r2Array[i][j] = 0.;
+        	}
+    	}
+
+    	for (int i = 0; i < r2Array.length; ++i) {
+			r2Array[i][i] = 1.;
+    	}
+
+    	int columnIndex = (int) (Math.random() * elementCount);
+
+		if (((int) maximumElement) - 1 == columnIndex) {
+			columnIndex = ((int) maximumElement) - 2;
+		} else if (0 == columnIndex) {
+			columnIndex = 1;
+		}
+
+		for (int i = 0; i < r2Array.length; ++i) {
+    		if (columnIndex > i) {
+				r2Array[i][columnIndex] = 1.;
+    		}
+    	}
+
+		return TriangularMatrix.Standard (r2Array);
+	}
 }
diff --git a/src/main/java/org/drip/measure/lebesgue/R1PiecewiseDisplaced.java b/src/main/java/org/drip/measure/lebesgue/R1PiecewiseDisplaced.java
@@ -162,7 +162,7 @@ public static final R1PiecewiseDisplaced Standard (
 		}
 
 		org.drip.numerical.linearalgebra.LinearizationOutput lo =
-			org.drip.numerical.linearalgebra.LinearSystemSolver.SolveUsingMatrixInversion (aadblM, adblY);
+			org.drip.numerical.linearsolver.LinearSystem.SolveUsingMatrixInversion (aadblM, adblY);
 
 		if (null == lo) return null;
 

diff --git a/src/main/java/org/drip/numerical/linearalgebra/NonPeriodicTridiagonalMatrix.java b/src/main/java/org/drip/numerical/linearalgebra/NonPeriodicTridiagonalMatrix.java
@@ -0,0 +1,138 @@
+
+package org.drip.numerical.linearalgebra;
+
+/*
+ * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+ */
+
+/*!
+ * Copyright (C) 2025 Lakshmi Krishnamurthy
+ * 
+ *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
+ *  	asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
+ *  	analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
+ *  	equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
+ *  	numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
+ *  	graph builder/navigator, and computational support.
+ *  
+ *  	https://lakshmidrip.github.io/DROP/
+ *  
+ *  DROP is composed of three modules:
+ *  
+ *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
+ *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
+ *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
+ * 
+ * 	DROP Product Core implements libraries for the following:
+ * 	- Fixed Income Analytics
+ * 	- Loan Analytics
+ * 	- Transaction Cost Analytics
+ * 
+ * 	DROP Portfolio Core implements libraries for the following:
+ * 	- Asset Allocation Analytics
+ *  - Asset Liability Management Analytics
+ * 	- Capital Estimation Analytics
+ * 	- Exposure Analytics
+ * 	- Margin Analytics
+ * 	- XVA Analytics
+ * 
+ * 	DROP Computational Core implements libraries for the following:
+ * 	- Algorithm Support
+ * 	- Computation Support
+ * 	- Function Analysis
+ *  - Graph Algorithm
+ *  - Model Validation
+ * 	- Numerical Analysis
+ * 	- Numerical Optimizer
+ * 	- Spline Builder
+ *  - Statistical Learning
+ * 
+ * 	Documentation for DROP is Spread Over:
+ * 
+ * 	- Main                     => https://lakshmidrip.github.io/DROP/
+ * 	- Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
+ * 	- GitHub                   => https://github.com/lakshmiDRIP/DROP
+ * 	- Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
+ * 	- Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
+ * 	- Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
+ * 	- Release Versions         => https://lakshmidrip.github.io/DROP/version.html
+ * 	- Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
+ * 	- Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
+ * 
+ *  Licensed under the Apache License, Version 2.0 (the "License");
+ *   	you may not use this file except in compliance with the License.
+ *   
+ *  You may obtain a copy of the License at
+ *  	http://www.apache.org/licenses/LICENSE-2.0
+ *  
+ *  Unless required by applicable law or agreed to in writing, software
+ *  	distributed under the License is distributed on an "AS IS" BASIS,
+ *  	WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  
+ *  See the License for the specific language governing permissions and
+ *  	limitations under the License.
+ */
+
+/**
+ * <i>NonPeriodicTridiagonalMatrix</i> implements a banded Non-periodic Tridiagonal Matrix. The References
+ * 	are:
+ * 
+ * <br><br>
+ * 	<ul>
+ * 		<li>
+ * 			Batista, M., and A. R. A. Ibrahim-Karawia (2009): The use of Sherman-Morrison-Woodbury formula
+ * 				to solve cyclic block tridiagonal and cyclic block penta-diagonal linear systems of equations
+ * 				<i>Applied Mathematics of Computation</i> <b>210 (2)</b> 558-563
+ * 		</li>
+ * 		<li>
+ * 			Datta, B. N. (2010): <i>Numerical Linear Algebra and Applications 2<sup>nd</sup> Edition</i>
+ * 				<b>SIAM</b> Philadelphia, PA
+ * 		</li>
+ * 		<li>
+ * 			Gallopoulos, E., B. Phillippe, and A. H. Sameh (2016): <i>Parallelism in Matrix Computations</i>
+ * 				<b>Spring</b> Berlin, Germany
+ * 		</li>
+ * 		<li>
+ * 			Niyogi, P. (2006): <i>Introduction to Computational Fluid Dynamics</i> <b>Pearson</b> London, UK
+ * 		</li>
+ * 		<li>
+ * 			Wikipedia (2024): Tridiagonal Matrix Algorithm
+ * 				https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
+ * 		</li>
+ * 	</ul>
+ * 
+ * <br><br>
+ *  <ul>
+ *		<li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
+ *		<li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
+ *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/README.md">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
+ *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/linearalgebra/README.md">Linear Algebra Matrix Transform Library</a></li>
+ *  </ul>
+ * <br><br>
+ *
+ * @author Lakshmi Krishnamurthy
+ */
+
+public class NonPeriodicTridiagonalMatrix extends TridiagonalMatrix
+{
+
+	/**
+	 * Construct an Instance of Non-periodic Tridiagonal Matrix
+	 * 
+	 * @param r2Array R<sup>2</sup> Array
+	 * 
+	 * @return Instance of Non-periodic Tridiagonal Matrix
+	 */
+
+	public static NonPeriodicTridiagonalMatrix Standard (
+		final double[][] r2Array)
+	{
+		return MatrixUtil.IsTridiagonal (r2Array) ? new NonPeriodicTridiagonalMatrix (r2Array) : null;
+	}
+
+	protected NonPeriodicTridiagonalMatrix (
+		final double[][] r2Array)
+	{
+		super (r2Array);
+	}
+}