C# PLS1 Scores And Loadings Example

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using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.Examples.CSharp
  /// <summary>
  /// This is a .NET example in C# showing Partial Least Squares (PLS) scores
  /// and loadings.  
  /// In chemometrics one often wishes to know the chemical composition of a
  /// sample of, say, a gas or liquid. One common technique is to study the absorption
  /// spectrum of light passing through the sample. Partial Least Squares (PLS) 
  /// is often used to construct a predictive model in this situation. Suppose we 
  /// wish to measure the concentration of a constituent in the
  /// substance and that we look at n different absorption spectra (an absorption
  /// spectra measures the amount of light absorbed at each wavelength). Pick p
  /// different wavelengths in the absorption spectra and let A = {aij} be the 
  /// be the nxp matrix where aij is the absorption measurement at the jth 
  /// wavelength in the ith sample. And let C = {ci} be the m vector where
  /// ci is the concentration of the constituent in the ith sample.
  /// This example constructs a predictive model for C given A using PLS. In
  /// particular the scores and loadings for the response variable, C, and the
  /// predictor variable, A, are examined.
  /// </summary>
  class PLS1ScoresAndLoadingsExample
    static void Main( string[] args )
      var rng = new RandGenUniform( 0x124 );
      rng.LowerBound = 0.1;
      rng.UpperBound = 1.1;
      int n = 7; // number of samples (spectra)
      int p = 10; // number of data points (wavelength)
      int f = 4;  // number of PLS eigenvectors

      var A = new DoubleMatrix( n, p, rng ); // spectral absorbances
      var C = new DoubleVector( n, rng );    // constituent concentrations
      var pls = new PLS1();

      Console.WriteLine( "Performing calculation..." );
      pls.Calculate( A, C, f );

      Console.WriteLine( "Is it good? {0}\n", pls.IsGood );

      var alg = (PLS1NipalsAlgorithm) pls.Calculator;

      // Get the spectral scores
      DoubleMatrix S = alg.Scores;
      Console.WriteLine( "Spectral Scores ------------------------------\n" );
      for ( int i = 0; i < f; ++i )
        Console.WriteLine( "spectral score {0}\n{1}\n", i, S.Col( i ).ToString( "G5" ) );

      // Get spectral loadings
      DoubleMatrix Bx = alg.Loadings;
      Console.WriteLine( "Spectral Loadings ------------------------------\n" );
      for ( int i = 0; i < f; ++i )
        Console.WriteLine( "spectral loading {0}\n{1}\n", i, Bx.Col( i ).ToString( "G5" ) );

      // Predict the constituent concentrations from a vector of spectral responses.
      // The regression vector, r, can be used for prediction as follows:
      // Let Cu be the predicted concentration for the spectral response
      // vector Au, let Abar the mean of the spectral data and Cbar be the mean
      // of the concentrations data used to create the model. Then
      // Cu = Cbar + (Au - Abar)r.
      var Au = new DoubleVector( p, rng ); // spectral responses
      double Cbar = alg.ResponseMean;
      DoubleVector Abar = alg.PredictorMean;
      DoubleVector r = alg.RegressionVector;

      double Cu = Cbar + NMathFunctions.Dot( ( Au - Abar ), r );
      Console.WriteLine( "Prediction Using Regression Vector ------------------" );
      Console.WriteLine( "Predicted concentrations for spectral response \n\n{0} \n\nis \n\n{1}", Au.ToString( "G5" ), Cu );

      Console.WriteLine( "Press Enter Key" );

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