BUG: Optimization: fix incorrect weighted Jacobian (#684)

.paket/Paket.Restore.targets

@@ -20,18 +20,18 @@
     <PaketBootstrapperStyle Condition="Exists('$(PaketToolsPath)paket.bootstrapper.proj')">proj</PaketBootstrapperStyle>
     <PaketExeImage>assembly</PaketExeImage>
     <PaketExeImage Condition=" '$(PaketBootstrapperStyle)' == 'proj' ">native</PaketExeImage>
-    <MonoPath Condition="'$(MonoPath)' == '' And Exists('/Library/Frameworks/Mono.framework/Commands/mono')">/Library/Frameworks/Mono.framework/Commands/mono</MonoPath>
+    <MonoPath Condition="'$(MonoPath)' == '' AND Exists('/Library/Frameworks/Mono.framework/Commands/mono')">/Library/Frameworks/Mono.framework/Commands/mono</MonoPath>
     <MonoPath Condition="'$(MonoPath)' == ''">mono</MonoPath>
 
     <!-- PaketBootStrapper  -->
     <PaketBootStrapperExePath Condition=" '$(PaketBootStrapperExePath)' == '' AND Exists('$(PaketRootPath)paket.bootstrapper.exe')">$(PaketRootPath)paket.bootstrapper.exe</PaketBootStrapperExePath>
     <PaketBootStrapperExePath Condition=" '$(PaketBootStrapperExePath)' == '' ">$(PaketToolsPath)paket.bootstrapper.exe</PaketBootStrapperExePath>
     <PaketBootStrapperExeDir Condition=" Exists('$(PaketBootStrapperExePath)') " >$([System.IO.Path]::GetDirectoryName("$(PaketBootStrapperExePath)"))\</PaketBootStrapperExeDir>
-    
+
-    <PaketBootStrapperCommand Condition=" '$(OS)' == 'Windows_NT'">"$(PaketBootStrapperExePath)"</PaketBootStrapperCommand>
+    <PaketBootStrapperCommand Condition=" '$(OS)' == 'Windows_NT' ">"$(PaketBootStrapperExePath)"</PaketBootStrapperCommand>
     <PaketBootStrapperCommand Condition=" '$(OS)' != 'Windows_NT' ">$(MonoPath) --runtime=v4.0.30319 "$(PaketBootStrapperExePath)"</PaketBootStrapperCommand>
 
-    <!-- Disable automagic references for F# dotnet sdk -->
+    <!-- Disable automagic references for F# DotNet SDK -->
     <!-- This will not do anything for other project types -->
     <!-- see https://github.com/fsharp/fslang-design/blob/master/tooling/FST-1002-fsharp-in-dotnet-sdk.md -->
     <DisableImplicitFSharpCoreReference>true</DisableImplicitFSharpCoreReference>
@@ -40,55 +40,68 @@
     <!-- Disable Paket restore under NCrunch build -->
     <PaketRestoreDisabled Condition="'$(NCrunch)' == '1'">True</PaketRestoreDisabled>
 
+    <!-- Disable test for CLI tool completely - overrideable via properties in projects or via environment variables -->
+    <PaketDisableCliTest Condition=" '$(PaketDisableCliTest)' == '' ">False</PaketDisableCliTest>
+
     <PaketIntermediateOutputPath Condition=" '$(PaketIntermediateOutputPath)' == '' ">$(BaseIntermediateOutputPath.TrimEnd('\').TrimEnd('\/'))</PaketIntermediateOutputPath>
   </PropertyGroup>
 
-  <!-- Check if paket is available as local dotnet cli tool -->
+  <!-- Resolve how paket should be called -->
+  <!-- Current priority is: local (1: repo root, 2: .paket folder) => 3: as CLI tool => as bootstrapper (4: proj Bootstrapper style, 5: BootstrapperExeDir) => 6: global path variable -->
   <Target Name="SetPaketCommand" >
-  
+    <!-- Test if paket is available in the standard locations. If so, that takes priority. Case 1/2 - non-windows specific -->
-    <!-- Call 'dotnet paket' and see if it returns without an error. Mute all the output. -->
+    <PropertyGroup Condition=" '$(OS)' != 'Windows_NT' ">
-    <Exec Command="dotnet paket --version" IgnoreExitCode="true" StandardOutputImportance="low" StandardErrorImportance="low" >
+      <!-- no windows, try native paket as default, root => tool -->
-      <Output TaskParameter="ExitCode" PropertyName="LocalPaketToolExitCode" />
+      <PaketExePath Condition=" '$(PaketExePath)' == '' AND Exists('$(PaketRootPath)paket') ">$(PaketRootPath)paket</PaketExePath>
-    </Exec>
+      <PaketExePath Condition=" '$(PaketExePath)' == '' AND Exists('$(PaketToolsPath)paket') ">$(PaketToolsPath)paket</PaketExePath>
+    </PropertyGroup>
 
-    <!-- If local paket tool is found, use that -->
+    <!-- Test if paket is available in the standard locations. If so, that takes priority. Case 2/2 - same across platforms -->
-    <PropertyGroup Condition=" '$(LocalPaketToolExitCode)' == '0' ">
+    <PropertyGroup>
-      <InternalPaketCommand>dotnet paket</InternalPaketCommand>
+      <!-- root => tool -->
+      <PaketExePath Condition=" '$(PaketExePath)' == '' AND Exists('$(PaketRootPath)paket.exe') ">$(PaketRootPath)paket.exe</PaketExePath>
+      <PaketExePath Condition=" '$(PaketExePath)' == '' AND Exists('$(PaketToolsPath)paket.exe') ">$(PaketToolsPath)paket.exe</PaketExePath>
     </PropertyGroup>
 
-    <!-- If not, then we go through our normal steps of setting the Paket command.  -->
+    <!-- If paket hasn't be found in standard locations, test for CLI tool usage. -->
-    <PropertyGroup Condition=" '$(LocalPaketToolExitCode)' != '0' ">
+    <!-- First test: Is CLI configured to be used in "dotnet-tools.json"? - can result in a false negative; only a positive outcome is reliable. -->
-      <!-- windows, root => tool => proj style => bootstrapper => global -->
+    <PropertyGroup Condition=" '$(PaketExePath)' == '' ">
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' == 'Windows_NT' AND Exists('$(PaketRootPath)paket.exe') ">$(PaketRootPath)paket.exe</PaketExePath>
+      <_DotnetToolsJson Condition="Exists('$(PaketRootPath)/.config/dotnet-tools.json')">$([System.IO.File]::ReadAllText("$(PaketRootPath)/.config/dotnet-tools.json"))</_DotnetToolsJson>
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' == 'Windows_NT' AND Exists('$(PaketToolsPath)paket.exe') ">$(PaketToolsPath)paket.exe</PaketExePath>
+      <_ConfigContainsPaket Condition=" '$(_DotnetToolsJson)' != ''">$(_DotnetToolsJson.Contains('"paket"'))</_ConfigContainsPaket>
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' == 'Windows_NT' AND '$(PaketBootstrapperStyle)' == 'proj' ">$(PaketToolsPath)paket.exe</PaketExePath>
+      <_ConfigContainsPaket Condition=" '$(_ConfigContainsPaket)' == ''">false</_ConfigContainsPaket>
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' == 'Windows_NT' AND Exists('$(PaketBootStrapperExeDir)') ">$(_PaketBootStrapperExeDir)paket.exe</PaketExePath>
+    </PropertyGroup>
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' == 'Windows_NT' ">paket.exe</PaketExePath>
 
-      <!-- no windows, try native paket as default,  root => tool => proj style => mono paket => bootstrpper => global -->
+    <!-- Second test: Call 'dotnet paket' and see if it returns without an error. Mute all the output. Only run if previous test failed and the test has not been disabled. -->
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' AND Exists('$(PaketRootPath)paket') ">$(PaketRootPath)paket</PaketExePath>
+    <!-- WARNING: This method can lead to processes hanging forever, and should be used as little as possible. See https://github.com/fsprojects/Paket/issues/3705 for details. -->
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' AND Exists('$(PaketToolsPath)paket') ">$(PaketToolsPath)paket</PaketExePath>
+    <Exec Condition=" '$(PaketExePath)' == '' AND !$(PaketDisableCliTest) AND !$(_ConfigContainsPaket)" Command="dotnet paket --version" IgnoreExitCode="true" StandardOutputImportance="low" StandardErrorImportance="low" >
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' AND '$(PaketBootstrapperStyle)' == 'proj' ">$(PaketToolsPath)paket</PaketExePath>
+      <Output TaskParameter="ExitCode" PropertyName="LocalPaketToolExitCode" />
+    </Exec>
 
-      <!-- no windows, try mono paket -->
+    <!-- If paket is installed as CLI use that. Again, only if paket haven't already been found in standard locations. -->
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' AND Exists('$(PaketRootPath)paket.exe') ">$(PaketRootPath)paket.exe</PaketExePath>
+    <PropertyGroup Condition=" '$(PaketExePath)' == '' AND ($(_ConfigContainsPaket) OR '$(LocalPaketToolExitCode)' == '0') ">
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' AND Exists('$(PaketToolsPath)paket.exe') ">$(PaketToolsPath)paket.exe</PaketExePath>
+      <_PaketCommand>dotnet paket</_PaketCommand>
+    </PropertyGroup>
 
-      <!-- no windows, try bootstrapper -->
+    <!-- If neither local files nor CLI tool can be found, final attempt is searching for boostrapper config before falling back to global path variable. -->
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' AND Exists('$(PaketBootStrapperExeDir)') ">$(PaketBootStrapperExeDir)paket.exe</PaketExePath>
+    <PropertyGroup Condition=" '$(PaketExePath)' == '' AND '$(_PaketCommand)' == '' ">
+      <!-- Test for bootstrapper setup -->
+      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(PaketBootstrapperStyle)' == 'proj' ">$(PaketToolsPath)paket</PaketExePath>
+      <PaketExePath Condition=" '$(PaketExePath)' == '' AND Exists('$(PaketBootStrapperExeDir)') ">$(PaketBootStrapperExeDir)paket</PaketExePath>
 
-      <!-- no windows, try global native paket -->
+      <!-- If all else fails, use global path approach. -->
-      <PaketExePath Condition=" '$(PaketExePath)' == '' AND '$(OS)' != 'Windows_NT' ">paket</PaketExePath>
+      <PaketExePath Condition=" '$(PaketExePath)' == ''">paket</PaketExePath>
+    </PropertyGroup>
 
+    <!-- If not using CLI, setup correct execution command. -->
+    <PropertyGroup Condition=" '$(_PaketCommand)' == '' ">
       <_PaketExeExtension>$([System.IO.Path]::GetExtension("$(PaketExePath)"))</_PaketExeExtension>
-      <InternalPaketCommand Condition=" '$(InternalPaketCommand)' == '' AND '$(_PaketExeExtension)' == '.dll' ">dotnet "$(PaketExePath)"</InternalPaketCommand>
+      <_PaketCommand Condition=" '$(_PaketCommand)' == '' AND '$(_PaketExeExtension)' == '.dll' ">dotnet "$(PaketExePath)"</_PaketCommand>
-      <InternalPaketCommand Condition=" '$(InternalPaketCommand)' == '' AND '$(OS)' != 'Windows_NT' AND '$(_PaketExeExtension)' == '.exe' ">$(MonoPath) --runtime=v4.0.30319 "$(PaketExePath)"</InternalPaketCommand>
+      <_PaketCommand Condition=" '$(_PaketCommand)' == '' AND '$(OS)' != 'Windows_NT' AND '$(_PaketExeExtension)' == '.exe' ">$(MonoPath) --runtime=v4.0.30319 "$(PaketExePath)"</_PaketCommand>
-      <InternalPaketCommand Condition=" '$(InternalPaketCommand)' == '' ">"$(PaketExePath)"</InternalPaketCommand>
+      <_PaketCommand Condition=" '$(_PaketCommand)' == '' ">"$(PaketExePath)"</_PaketCommand>
-
     </PropertyGroup>
 
     <!-- The way to get a property to be available outside the target is to use this task. -->
-    <CreateProperty Value="$(InternalPaketCommand)">
+    <CreateProperty Value="$(_PaketCommand)">
       <Output TaskParameter="Value" PropertyName="PaketCommand"/>
     </CreateProperty>
 
@@ -123,7 +136,7 @@
         <!-- Parse our simple 'paket.restore.cached' json ...-->
         <PaketRestoreCachedSplitObject Include="$([System.Text.RegularExpressions.Regex]::Split(`$(PaketRestoreCachedContents)`, `{|}|,`))"></PaketRestoreCachedSplitObject>
         <!-- Keep Key, Value ItemGroup-->
-        <PaketRestoreCachedKeyValue Include="@(PaketRestoreCachedSplitObject)" 
+        <PaketRestoreCachedKeyValue Include="@(PaketRestoreCachedSplitObject)"
             Condition=" $([System.Text.RegularExpressions.Regex]::Split(`%(Identity)`, `&quot;: &quot;`).Length) &gt; 1 ">
           <Key>$([System.Text.RegularExpressions.Regex]::Split(`%(Identity)`, `": "`)[0].Replace(`"`, ``).Replace(` `, ``))</Key>
           <Value>$([System.Text.RegularExpressions.Regex]::Split(`%(Identity)`, `": "`)[1].Replace(`"`, ``).Replace(` `, ``))</Value>
@@ -156,7 +169,7 @@
     <Exec Command='$(PaketBootStrapperCommand)' Condition=" '$(PaketBootstrapperStyle)' == 'classic' AND Exists('$(PaketBootStrapperExePath)') AND !(Exists('$(PaketExePath)'))" ContinueOnError="false" />
     <Error Text="Stop build because of PAKET_ERROR_ON_MSBUILD_EXEC and we need a full restore (hashes don't match)" Condition=" '$(PAKET_ERROR_ON_MSBUILD_EXEC)' == 'true' AND '$(PaketRestoreRequired)' == 'true' AND '$(PaketDisableGlobalRestore)' != 'true'" />
     <Exec Command='$(PaketCommand) restore' Condition=" '$(PaketRestoreRequired)' == 'true' AND '$(PaketDisableGlobalRestore)' != 'true' " ContinueOnError="false" />
-    
+
     <!-- Step 2 Detect project specific changes -->
     <ItemGroup>
       <MyTargetFrameworks Condition="'$(TargetFramework)' != '' " Include="$(TargetFramework)"></MyTargetFrameworks>

src/Numerics.Tests/OptimizationTests/NonLinearCurveFittingTests.cs

@@ -618,5 +618,40 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         }
 
         #endregion Thurber
+
+        #region Weighted Nonlinear Regression
+
+        // Data from https://www.mathworks.com/help/stats/examples/weighted-nonlinear-regression.html
+
+        private Vector<double> PollutionModel(Vector<double> p, Vector<double> x)
+        {
+            var y = CreateVector.Dense<double>(x.Count);
+            for (int i = 0; i < x.Count; i++)
+            {
+                y[i] = p[0] * (1.0 - Math.Exp(-p[1] * x[i]));
+            }
+            return y;
+        }
+
+        private Vector<double> PollutionX = new DenseVector(new double[] { 1, 2, 3, 5, 7, 10 });
+        private Vector<double> PollutionY = new DenseVector(new double[] { 109, 149, 149, 191, 213, 224 });
+        private Vector<double> PollutionW = new DenseVector(new double[] { 1, 1, 5, 5, 5, 5 });
+        private Vector<double> PollutionStart = new DenseVector(new double[] { 240, 0.5 });        
+        private Vector<double> PollutionBest = new DenseVector(new double[] { 225.17, 0.40078 });
+                
+        [Test]
+        public void PollutionWithWeights()
+        {
+            var obj = ObjectiveFunction.NonlinearModel(PollutionModel, PollutionX, PollutionY, PollutionW, accuracyOrder: 6);
+            var solver = new LevenbergMarquardtMinimizer();
+            var result = solver.FindMinimum(obj, PollutionStart);
+
+            for (int i = 0; i < result.MinimizingPoint.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(PollutionBest[i], result.MinimizingPoint[i], 4);
+            }
+        }
+
+        #endregion Weighted Nonlinear Regression
     }
 }

src/Numerics/Optimization/ObjectiveFunctions/NonlinearObjectiveFunction.cs

@@ -329,11 +329,9 @@ namespace MathNet.Numerics.Optimization.ObjectiveFunctions
                         // if j-th parameter is fixed, set J[i, j] = 0
                         jacobianValue[i, j] = 0.0;
                     }
-                    else
+                    else if (Weights != null)
                     {
-                        jacobianValue[i, j] = (Weights == null)
+                        jacobianValue[i, j] = jacobianValue[i, j] * L[i];
-                            ? jacobianValue[i, j]
-                            : jacobianValue[i, j] * L[j];
                     }
                 }
             }