Merge pull request #352 from fslaborg/datascience

This PR introduces a separation of concerns between statistical algorithms and low-level numerical primitives.

Author: kMutagene

.config/dotnet-tools.json

@@ -2,17 +2,19 @@
   "version": 1,
   "isRoot": true,
   "tools": {
-    "fsdocs-tool": {
-      "version": "16.1.1",
-      "commands": [
-        "fsdocs"
-      ]
-    },
     "fantomas": {
       "version": "6.1.1",
       "commands": [
         "fantomas"
-      ]
+      ],
+      "rollForward": false
+    },
+    "fsdocs-tool": {
+      "version": "20.0.1",
+      "commands": [
+        "fsdocs"
+      ],
+      "rollForward": false
     }
   }
 }

.github/workflows/build-and-test.yml

@@ -13,10 +13,10 @@ jobs:
 
     steps:
     - uses: actions/checkout@v2
-    - name: Setup .NET 6
-      uses: actions/setup-dotnet@v1
+    - name: Setup .NET 8
+      uses: actions/setup-dotnet@v4
       with:
-        dotnet-version: '6.x.x'
+        dotnet-version: '8.x.x'
     - name: Restore local tools
       run: dotnet tool restore
     - name: make script executable
@@ -30,11 +30,11 @@ jobs:
     runs-on: windows-latest
 
     steps:
-    - uses: actions/checkout@v2
-    - name: Setup .NET 6
-      uses: actions/setup-dotnet@v1
+    - uses: actions/checkout@v4
+    - name: Setup .NET 8
+      uses: actions/setup-dotnet@v4
       with:
-        dotnet-version: '6.x.x'
+        dotnet-version: '8.x.x'
     - name: Restore local tools
       run: dotnet tool restore
     - name: Build and test

FSharp.Stats.sln

@@ -55,15 +55,12 @@ Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "docs", "docs", "{23F9FB2E-6
 		docs\Integration.fsx = docs\Integration.fsx
 		docs\Interpolation.fsx = docs\Interpolation.fsx
 		docs\Intervals.fsx = docs\Intervals.fsx
-		docs\LinearAlgebra.fsx = docs\LinearAlgebra.fsx
-		docs\Matrix_Vector.fsx = docs\Matrix_Vector.fsx
+		docs\Normalization.fsx = docs\Normalization.fsx
+		docs\NuGet.config = docs\NuGet.config
 		docs\Optimization.fsx = docs\Optimization.fsx
 		docs\Quantiles.fsx = docs\Quantiles.fsx
-		docs\NuGet.config = docs\NuGet.config
 		docs\Rank.fsx = docs\Rank.fsx
 		docs\Signal.fsx = docs\Signal.fsx
-		docs\Normalization.fsx = docs\Normalization.fsx
-		docs\ML.fsx = docs\ML.fsx
 		docs\Testing.fsx = docs\Testing.fsx
 		docs\_template.html = docs\_template.html
 		docs\_template.ipynb = docs\_template.ipynb
@@ -76,6 +73,12 @@ Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "content", "content", "{50E3
 EndProject
 Project("{6EC3EE1D-3C4E-46DD-8F32-0CC8E7565705}") = "FSharp.Stats.Interactive", "src\FSharp.Stats.Interactive\FSharp.Stats.Interactive.fsproj", "{D7BCF5C0-9E2B-4170-9390-607B0B65A8CD}"
 EndProject
+Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "benchmarks", "benchmarks", "{02EA681E-C7D8-13C7-8484-4AC65E1B71E8}"
+EndProject
+Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "FSharp.Stats.Benchmarks", "benchmarks\FSharp.Stats.Benchmarks\FSharp.Stats.Benchmarks.fsproj", "{E3942700-8589-770A-6224-F6D2DDF977E8}"
+EndProject
+Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "FSharp.Stats.LegacyBenchmarks", "benchmarks\FSharp.Stats.LegacyBenchmarks\FSharp.Stats.LegacyBenchmarks.fsproj", "{D84267B7-0C5A-4679-A63C-D94315A458CB}"
+EndProject
 Global
 	GlobalSection(SolutionConfigurationPlatforms) = preSolution
 		Debug|Any CPU = Debug|Any CPU
@@ -98,6 +101,14 @@ Global
 		{D7BCF5C0-9E2B-4170-9390-607B0B65A8CD}.Debug|Any CPU.Build.0 = Debug|Any CPU
 		{D7BCF5C0-9E2B-4170-9390-607B0B65A8CD}.Release|Any CPU.ActiveCfg = Release|Any CPU
 		{D7BCF5C0-9E2B-4170-9390-607B0B65A8CD}.Release|Any CPU.Build.0 = Release|Any CPU
+		{E3942700-8589-770A-6224-F6D2DDF977E8}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{E3942700-8589-770A-6224-F6D2DDF977E8}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{E3942700-8589-770A-6224-F6D2DDF977E8}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{E3942700-8589-770A-6224-F6D2DDF977E8}.Release|Any CPU.Build.0 = Release|Any CPU
+		{D84267B7-0C5A-4679-A63C-D94315A458CB}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{D84267B7-0C5A-4679-A63C-D94315A458CB}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{D84267B7-0C5A-4679-A63C-D94315A458CB}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{D84267B7-0C5A-4679-A63C-D94315A458CB}.Release|Any CPU.Build.0 = Release|Any CPU
 	EndGlobalSection
 	GlobalSection(SolutionProperties) = preSolution
 		HideSolutionNode = FALSE
@@ -106,6 +117,8 @@ Global
 		{DA7E2263-283A-497F-B122-B2E1A5AC2C8C} = {ED8079DD-2B06-4030-9F0F-DC548F98E1C4}
 		{8830D84C-C999-4816-9742-AC54A3CC1E13} = {7C6D08E7-3EAC-4335-8F4B-252C193C27C9}
 		{50E3E339-AA4D-4FD2-8791-DEBD2EBF0504} = {23F9FB2E-6804-4AF9-B6D5-5CBD00E14A02}
+		{E3942700-8589-770A-6224-F6D2DDF977E8} = {02EA681E-C7D8-13C7-8484-4AC65E1B71E8}
+		{D84267B7-0C5A-4679-A63C-D94315A458CB} = {02EA681E-C7D8-13C7-8484-4AC65E1B71E8}
 	EndGlobalSection
 	GlobalSection(ExtensibilityGlobals) = postSolution
 		SolutionGuid = {97270415-1E71-487B-BDF5-FBE2D8EFFD09}

RELEASE_NOTES.md

@@ -1,3 +1,32 @@
+### 1.0.0 (Released TBD)
+
+This version marks the journey to our first stable release and introduces significant architectural changes, which obviously are backward incompatible.
+
+* Decoupled vector and matrix representations from *FSharp.Stats*.
+* Integrated `FsMath` as the new lightweight, array-centric math backend.
+* Updated internal references in *FSharp.Stats* to use `FsMath` primitives for zero-friction integration.
+* Improved performance in core operations by leveraging `FsMath`’s optimized routines.
+
+**Description**
+This PR introduces a separation of concerns between statistical algorithms and low-level numerical primitives.
+Vector and matrix types have been moved to the new `FsMath` library under FsLab.org, which is optimized for performance and designed for seamless interoperability.
+This change keeps *FSharp.Stats* focused on statistical functionality while making it easier to maintain and integrate into other F# workflows that rely on common libraries.
+
+**Migration note**
+If your project uses `Vector` or `Matrix` types from *FSharp.Stats*, you will now need to reference `FsMath` and update your `open` statements accordingly:
+
+```fsharp
+open FsMath
+```
+
+All existing APIs are preserved with minimal changes, so most code will require slight modifications from `vector` to `Vector<float>` explicitly, along with namespace adjustments.
+Previously, arrays needed to be explicitly converted to vectors - now, `Array` and `Vector` can be used synonymously, removing the need for manual conversions in most cases.
+
+Other Changes:
+
+- [Fix incorrect F-test denominator assignments in TwoWayAnovaModel](https://github.com/fslaborg/FSharp.Stats/pull/350)
+- [Update test statistics to support generic type 'T data](https://github.com/fslaborg/FSharp.Stats/pull/348)
+
 ### 0.6.0 (Released 2025-1-7)
 * Additions:
     * latest commit #529c2c01

benchmarks/FSharp.Stats.Benchmarks/BenchmarkDotNet.Artifacts/results/FSharp.Stats.Benchmarks.MatrixBenchmarks-report-github.md

@@ -0,0 +1,24 @@
+```
+
+BenchmarkDotNet v0.14.0, Windows 11 (10.0.26100.3775)
+13th Gen Intel Core i7-13800H, 1 CPU, 20 logical and 14 physical cores
+.NET SDK 9.0.201
+  [Host]     : .NET 8.0.14 (8.0.1425.11118), X64 RyuJIT AVX2 DEBUG
+  DefaultJob : .NET 8.0.14 (8.0.1425.11118), X64 RyuJIT AVX2
+
+
+```
+| Method            | Size | Mean              | Error            | StdDev           | Gen0     | Gen1     | Gen2     | Allocated  |
+|------------------ |----- |------------------:|-----------------:|-----------------:|---------:|---------:|---------:|-----------:|
+| **Add**               | **10**   |          **40.06 ns** |         **0.550 ns** |         **0.488 ns** |   **0.0682** |   **0.0002** |        **-** |      **856 B** |
+| MatMultiply       | 10   |         442.83 ns |         2.841 ns |         2.373 ns |   0.1364 |        - |        - |     1712 B |
+| MultiplyVector    | 10   |          33.28 ns |         0.425 ns |         0.397 ns |   0.0083 |        - |        - |      104 B |
+| MultiplyRowVector | 10   |          50.55 ns |         0.500 ns |         0.468 ns |   0.0083 |        - |        - |      104 B |
+| **Add**               | **500**  |     **280,736.93 ns** |     **5,376.045 ns** |     **5,279.995 ns** | **212.4023** | **212.4023** | **212.4023** |  **2000164 B** |
+| MatMultiply       | 500  |  17,572,322.92 ns |   318,470.458 ns |   297,897.464 ns | 375.0000 | 375.0000 | 375.0000 |  4000242 B |
+| MultiplyVector    | 500  |      31,726.43 ns |       202.403 ns |       189.328 ns |   0.3052 |        - |        - |     4024 B |
+| MultiplyRowVector | 500  |     127,918.10 ns |       996.783 ns |       832.359 ns |   0.2441 |        - |        - |     4024 B |
+| **Add**               | **1000** |   **1,377,902.79 ns** |    **20,816.673 ns** |    **18,453.438 ns** | **148.4375** | **148.4375** | **148.4375** |  **8000105 B** |
+| MatMultiply       | 1000 | 143,300,325.00 ns | 1,445,291.857 ns | 1,606,438.070 ns | 250.0000 | 250.0000 | 250.0000 | 16000296 B |
+| MultiplyVector    | 1000 |     135,247.34 ns |     1,334.685 ns |     1,248.465 ns |   0.4883 |        - |        - |     8024 B |
+| MultiplyRowVector | 1000 |     677,195.35 ns |     6,896.007 ns |     6,450.529 ns |        - |        - |        - |     8024 B |

benchmarks/FSharp.Stats.Benchmarks/BenchmarkDotNet.Artifacts/results/FSharp.Stats.Benchmarks.MatrixBenchmarks-report.csv

@@ -0,0 +1,13 @@
+Method,Job,AnalyzeLaunchVariance,EvaluateOverhead,MaxAbsoluteError,MaxRelativeError,MinInvokeCount,MinIterationTime,OutlierMode,Affinity,EnvironmentVariables,Jit,LargeAddressAware,Platform,PowerPlanMode,Runtime,AllowVeryLargeObjects,Concurrent,CpuGroups,Force,HeapAffinitizeMask,HeapCount,NoAffinitize,RetainVm,Server,Arguments,BuildConfiguration,Clock,EngineFactory,NuGetReferences,Toolchain,IsMutator,InvocationCount,IterationCount,IterationTime,LaunchCount,MaxIterationCount,MaxWarmupIterationCount,MemoryRandomization,MinIterationCount,MinWarmupIterationCount,RunStrategy,UnrollFactor,WarmupCount,Size,Mean,Error,StdDev,Gen0,Gen1,Gen2,Allocated
+Add,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,10,40.06 ns,0.550 ns,0.488 ns,0.0682,0.0002,0.0000,856 B
+MatMultiply,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,10,442.83 ns,2.841 ns,2.373 ns,0.1364,0.0000,0.0000,1712 B
+MultiplyVector,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,10,33.28 ns,0.425 ns,0.397 ns,0.0083,0.0000,0.0000,104 B
+MultiplyRowVector,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,10,50.55 ns,0.500 ns,0.468 ns,0.0083,0.0000,0.0000,104 B
+Add,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,500,"280,736.93 ns","5,376.045 ns","5,279.995 ns",212.4023,212.4023,212.4023,2000164 B
+MatMultiply,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,500,"17,572,322.92 ns","318,470.458 ns","297,897.464 ns",375.0000,375.0000,375.0000,4000242 B
+MultiplyVector,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,500,"31,726.43 ns",202.403 ns,189.328 ns,0.3052,0.0000,0.0000,4024 B
+MultiplyRowVector,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,500,"127,918.10 ns",996.783 ns,832.359 ns,0.2441,0.0000,0.0000,4024 B
+Add,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,1000,"1,377,902.79 ns","20,816.673 ns","18,453.438 ns",148.4375,148.4375,148.4375,8000105 B
+MatMultiply,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,1000,"143,300,325.00 ns","1,445,291.857 ns","1,606,438.070 ns",250.0000,250.0000,250.0000,16000296 B
+MultiplyVector,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,1000,"135,247.34 ns","1,334.685 ns","1,248.465 ns",0.4883,0.0000,0.0000,8024 B
+MultiplyRowVector,DefaultJob,False,Default,Default,Default,Default,Default,Default,11111111111111111111,Empty,RyuJit,Default,X64,8c5e7fda-e8bf-4a96-9a85-a6e23a8c635c,.NET 8.0,False,True,False,True,Default,Default,False,False,False,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,Default,16,Default,1000,"677,195.35 ns","6,896.007 ns","6,450.529 ns",0.0000,0.0000,0.0000,8024 B

benchmarks/FSharp.Stats.Benchmarks/BenchmarkDotNet.Artifacts/results/FSharp.Stats.Benchmarks.MatrixBenchmarks-report.html

@@ -0,0 +1,41 @@
+<!DOCTYPE html>
+<html lang='en'>
+<head>
+<meta charset='utf-8' />
+<title>FSharp.Stats.Benchmarks.MatrixBenchmarks-20250412-175902</title>
+
+<style type="text/css">
+	table { border-collapse: collapse; display: block; width: 100%; overflow: auto; }
+	td, th { padding: 6px 13px; border: 1px solid #ddd; text-align: right; }
+	tr { background-color: #fff; border-top: 1px solid #ccc; }
+	tr:nth-child(even) { background: #f8f8f8; }
+</style>
+</head>
+<body>
+<pre><code>
+BenchmarkDotNet v0.14.0, Windows 11 (10.0.26100.3775)
+13th Gen Intel Core i7-13800H, 1 CPU, 20 logical and 14 physical cores
+.NET SDK 9.0.201
+  [Host]     : .NET 8.0.14 (8.0.1425.11118), X64 RyuJIT AVX2 DEBUG
+  DefaultJob : .NET 8.0.14 (8.0.1425.11118), X64 RyuJIT AVX2
+</code></pre>
+<pre><code></code></pre>
+
+<table>
+<thead><tr><th>Method     </th><th>Size</th><th>Mean       </th><th>Error     </th><th>StdDev    </th><th>Gen0</th><th>Gen1</th><th>Gen2</th><th>Allocated</th>
+</tr>
+</thead><tbody><tr><td>Add</td><td>10</td><td>40.06 ns</td><td>0.550 ns</td><td>0.488 ns</td><td>0.0682</td><td>0.0002</td><td>-</td><td>856 B</td>
+</tr><tr><td>MatMultiply</td><td>10</td><td>442.83 ns</td><td>2.841 ns</td><td>2.373 ns</td><td>0.1364</td><td>-</td><td>-</td><td>1712 B</td>
+</tr><tr><td>MultiplyVector</td><td>10</td><td>33.28 ns</td><td>0.425 ns</td><td>0.397 ns</td><td>0.0083</td><td>-</td><td>-</td><td>104 B</td>
+</tr><tr><td>MultiplyRowVector</td><td>10</td><td>50.55 ns</td><td>0.500 ns</td><td>0.468 ns</td><td>0.0083</td><td>-</td><td>-</td><td>104 B</td>
+</tr><tr><td>Add</td><td>500</td><td>280,736.93 ns</td><td>5,376.045 ns</td><td>5,279.995 ns</td><td>212.4023</td><td>212.4023</td><td>212.4023</td><td>2000164 B</td>
+</tr><tr><td>MatMultiply</td><td>500</td><td>17,572,322.92 ns</td><td>318,470.458 ns</td><td>297,897.464 ns</td><td>375.0000</td><td>375.0000</td><td>375.0000</td><td>4000242 B</td>
+</tr><tr><td>MultiplyVector</td><td>500</td><td>31,726.43 ns</td><td>202.403 ns</td><td>189.328 ns</td><td>0.3052</td><td>-</td><td>-</td><td>4024 B</td>
+</tr><tr><td>MultiplyRowVector</td><td>500</td><td>127,918.10 ns</td><td>996.783 ns</td><td>832.359 ns</td><td>0.2441</td><td>-</td><td>-</td><td>4024 B</td>
+</tr><tr><td>Add</td><td>1000</td><td>1,377,902.79 ns</td><td>20,816.673 ns</td><td>18,453.438 ns</td><td>148.4375</td><td>148.4375</td><td>148.4375</td><td>8000105 B</td>
+</tr><tr><td>MatMultiply</td><td>1000</td><td>143,300,325.00 ns</td><td>1,445,291.857 ns</td><td>1,606,438.070 ns</td><td>250.0000</td><td>250.0000</td><td>250.0000</td><td>16000296 B</td>
+</tr><tr><td>MultiplyVector</td><td>1000</td><td>135,247.34 ns</td><td>1,334.685 ns</td><td>1,248.465 ns</td><td>0.4883</td><td>-</td><td>-</td><td>8024 B</td>
+</tr><tr><td>MultiplyRowVector</td><td>1000</td><td>677,195.35 ns</td><td>6,896.007 ns</td><td>6,450.529 ns</td><td>-</td><td>-</td><td>-</td><td>8024 B</td>
+</tr></tbody></table>
+</body>
+</html>

benchmarks/FSharp.Stats.Benchmarks/BenchmarkDotNet.Artifacts/results/FSharp.Stats.Benchmarks.TriangularBenchmark-report-github.md

@@ -0,0 +1,20 @@
+```
+
+BenchmarkDotNet v0.14.0, Windows 11 (10.0.26100.3775)
+13th Gen Intel Core i7-13800H, 1 CPU, 20 logical and 14 physical cores
+.NET SDK 9.0.201
+  [Host]     : .NET 8.0.14 (8.0.1425.11118), X64 RyuJIT AVX2 DEBUG
+  DefaultJob : .NET 8.0.14 (8.0.1425.11118), X64 RyuJIT AVX2
+
+
+```
+| Method                     | N    | Mean           | Error        | StdDev       | Gen0   | Allocated |
+|--------------------------- |----- |---------------:|-------------:|-------------:|-------:|----------:|
+| **SolveTriangularSystemLower** | **10**   |       **186.3 ns** |      **1.23 ns** |      **1.09 ns** | **0.0172** |     **216 B** |
+| SolveTriangularSystemUpper | 10   |       185.9 ns |      1.33 ns |      1.18 ns | 0.0172 |     216 B |
+| **SolveTriangularSystemLower** | **500**  |   **372,737.0 ns** |  **2,926.50 ns** |  **2,737.45 ns** | **0.4883** |    **8056 B** |
+| SolveTriangularSystemUpper | 500  |   357,818.8 ns |  1,729.90 ns |  1,618.15 ns | 0.4883 |    8056 B |
+| **SolveTriangularSystemLower** | **1000** | **1,510,031.5 ns** |  **7,131.73 ns** |  **6,671.03 ns** |      **-** |   **16057 B** |
+| SolveTriangularSystemUpper | 1000 | 1,422,197.8 ns |  8,642.37 ns |  8,084.08 ns |      - |   16057 B |
+| **SolveTriangularSystemLower** | **2000** | **6,119,478.8 ns** | **40,341.69 ns** | **37,735.64 ns** |      **-** |   **32059 B** |
+| SolveTriangularSystemUpper | 2000 | 5,776,260.6 ns | 30,122.54 ns | 28,176.64 ns |      - |   32059 B |