HEAL.NonlinearRegression 0.1.0-rc.2

.NET Standard 2.1
This is a prerelease version of HEAL.NonlinearRegression.
dotnet add package HEAL.NonlinearRegression --version 0.1.0-rc.2
NuGet\Install-Package HEAL.NonlinearRegression -Version 0.1.0-rc.2
This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package.
<PackageReference Include="HEAL.NonlinearRegression" Version="0.1.0-rc.2" />
For projects that support PackageReference, copy this XML node into the project file to reference the package.
paket add HEAL.NonlinearRegression --version 0.1.0-rc.2
#r "nuget: HEAL.NonlinearRegression, 0.1.0-rc.2"
#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package.
// Install HEAL.NonlinearRegression as a Cake Addin
#addin nuget:?package=HEAL.NonlinearRegression&version=0.1.0-rc.2&prerelease

// Install HEAL.NonlinearRegression as a Cake Tool
#tool nuget:?package=HEAL.NonlinearRegression&version=0.1.0-rc.2&prerelease


C# implementation of nonlinear least squares fitting including calculation of t-profiles and pairwise profile plots (see [1]). The t-profiles allow to calculate exact confidence intervals for nonlinear parameters and approximate pairwise confidence regions.

Implementation is based on:

[1] Douglas Bates and Donald Watts, Nonlinear Regression and Its Applications, John Wiley and Sons, 1988

Unit tests


git clone https://github.com/heal-research/HEAL.NonlinearRegression
cd HEAL.NonlinearRegression
dotnet build

Run the tests for fitting nonlinear models:

dotnet test --filter "FullyQualifiedName~Fit"
Starting test execution, please wait...
A total of 1 test files matched the specified pattern.
p_opt: 1.10421e+002 1.03488e+002
Successful: True, NumIters: 2, NumFuncEvals: 10, NumJacEvals: 0
SSR: 9.5471e+003  s: 3.0898e+001 AICc: 19.0 BIC: 17.5 MDL: 15.1
Para       Estimate      Std. error     z Score          Lower          Upper Correlation matrix
    0    1.1042e+002    2.3371e+001   4.72e+000    5.8347e+001    1.6249e+002 1.00
    1    1.0349e+002    1.2024e+001   8.61e+000    7.6697e+001    1.3028e+002 -0.67 1.00

Optimized: ((110.42107672063618 * x0) + 103.48806186471386)

p_opt: 1.38378e+000 4.84833e-002 5.24299e-001 3.52511e-001 -6.84851e-002 -1.11809e+001
Successful: True, NumIters: 2, NumFuncEvals: 41, NumJacEvals: 0
Deviance: 7.8438e+002  Dispersion: 1.0000e+000 AICc: 808.7 BIC: 866.8 MDL: 456.0
Para       Estimate      Std. error     z Score          Lower          Upper Correlation matrix
    0    1.3838e+000    1.7042e-001   8.12e+000    1.0493e+000    1.7182e+000 1.00
    1    4.8483e-002    7.5999e-003   6.38e+000    3.3569e-002    6.3398e-002 -0.04 1.00
    2    5.2430e-001    9.7525e-002   5.38e+000    3.3291e-001    7.1569e-001 -0.08 0.02 1.00
    3    3.5251e-001    8.0993e-002   4.35e+000    1.9357e-001    5.1145e-001 -0.16 -0.08 -0.55 1.00
    4   -6.8485e-002    2.4032e-001  -2.85e-001   -5.4009e-001    4.0312e-001 -0.04 0.00 0.02 -0.10 1.00
    5   -1.1181e+001    1.0533e+000  -1.06e+001   -1.3248e+001   -9.1140e+000 -0.60 -0.38 -0.11 0.12 -0.62 1.00

Optimized: Logistic(((((((1.3837834757792504 * BI_RADS) + (0.04848326870703262 * Age)) + (0.5242993934295344 * Shape)) + (0.35251072256817134 * Margin)) + (-0.06848513367625395 * Density)) + -11.180915607397576))

p_opt: 6.41213e-002 2.12684e+002
Successful: True, NumIters: 3, NumFuncEvals: 44, NumJacEvals: 0
SSR: 1.1954e+003  s: 1.0934e+001 AICc: 19.0 BIC: 17.5 MDL: 21.5
Para       Estimate      Std. error     z Score          Lower          Upper Correlation matrix
    0    6.4121e-002    8.7112e-003   7.36e+000    4.4711e-002    8.3531e-002 1.00
    1    2.1268e+002    7.1607e+000   2.97e+001    1.9673e+002    2.2864e+002 0.78 1.00

Optimized: ((x0 / (0.06412128166090875 + x0)) * 212.68374312341493)

Passed!  - Failed:     0, Passed:     3, Skipped:     0, Total:     3, Duration: 274 ms - HEAL.NonlinearRegression.Console.Tests.dll (net6.0)

Run the tests for profile likelihood confidence intervals:

dotnet test --filter "(FullyQualifiedName~ProfilePuromycin|FullyQualifiedName~ProfileMammography)"
Starting test execution, please wait...
A total of 1 test files matched the specified pattern.

profile-based marginal confidence intervals (alpha=0.05)
p0    1.3838e+000    1.0586e+000    1.7270e+000
p1    4.8483e-002    3.3810e-002    6.3677e-002
p2    5.2430e-001    3.3325e-001    7.1665e-001
p3    3.5251e-001    1.9415e-001    5.1249e-001
p4   -6.8485e-002   -5.3640e-001    4.0944e-001
p5   -1.1181e+001   -1.3314e+001   -9.1744e+000

profile-based marginal confidence intervals (alpha=0.05)
p0    6.4121e-002    4.6920e-002    8.6157e-002
p1    2.1268e+002    1.9730e+002    2.2929e+002

Passed!  - Failed:     0, Passed:     2, Skipped:     0, Total:     2, Duration: 5 s - HEAL.NonlinearRegression.Console.Tests.dll (net6.0)


To call the library you have to provide an expression for the model as well as a dataset to fit to.

var x = new double[,] { { 0.02 }, { 0.02 }, { 0.06 }, { 0.06 }, { 0.11 }, { 0.11 }, { 0.22 }, { 0.22 }, { 0.56 }, { 0.56 }, { 1.10 }, { 1.10 } };
var y = new double[] {76, 47, 97, 107, 123, 139, 159, 152, 191, 201, 207, 200 };

var nlr = new NonlinearRegression();
nlr.Fit("0.1 * x0 / (1.0f + 0.1 * x0)", new[] { "x0" }, LikelihoodEnum.Gaussian, x, y);
var prediction = nlr.PredictWithIntervals(x, IntervalEnum.LaplaceApproximation);
System.Console.WriteLine($"pred: {prediction[0, 0]}, low: {prediction[0, 2]}, high: {prediction[0, 3]}");


The implementation uses alglib (https://alglib.net) for linear algebra and nonlinear least squares fitting. Alglib is licensed under GPL2+ and includes code from other projects. Commercial licenses for alglib are available.


The code is licensed under the conditions of the GPL version 3.

Product Compatible and additional computed target framework versions.
.NET net5.0 was computed.  net5.0-windows was computed.  net6.0 was computed.  net6.0-android was computed.  net6.0-ios was computed.  net6.0-maccatalyst was computed.  net6.0-macos was computed.  net6.0-tvos was computed.  net6.0-windows was computed.  net7.0 was computed.  net7.0-android was computed.  net7.0-ios was computed.  net7.0-maccatalyst was computed.  net7.0-macos was computed.  net7.0-tvos was computed.  net7.0-windows was computed.  net8.0 was computed.  net8.0-android was computed.  net8.0-ios was computed.  net8.0-maccatalyst was computed.  net8.0-macos was computed.  net8.0-tvos was computed.  net8.0-windows was computed. 
.NET Core netcoreapp3.0 was computed.  netcoreapp3.1 was computed. 
.NET Standard netstandard2.1 is compatible. 
MonoAndroid monoandroid was computed. 
MonoMac monomac was computed. 
MonoTouch monotouch was computed. 
Tizen tizen60 was computed. 
Xamarin.iOS xamarinios was computed. 
Xamarin.Mac xamarinmac was computed. 
Xamarin.TVOS xamarintvos was computed. 
Xamarin.WatchOS xamarinwatchos was computed. 
Compatible target framework(s)
Additional computed target framework(s)
Learn more about Target Frameworks and .NET Standard.

NuGet packages

This package is not used by any NuGet packages.

GitHub repositories

This package is not used by any popular GitHub repositories.

Version Downloads Last updated
0.1.0-rc.2 79 4/3/2023
0.1.0-rc.1 70 3/31/2023