C# PLS2 Scores And Loadings Example

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using System;
using System.IO;
using System.Threading;

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 m different 
  /// constituents 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 = {cij} be the nxm matrix where cij is the concentration of 
  /// the jth 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 PLS2ScoresAndLoadingsExample

    static void Main( string[] args )
      Thread.CurrentThread.CurrentCulture = new System.Globalization.CultureInfo( "en-US" );

      // Read in absorption data matrices. Well use A to calculate the
      // PLS model and predict concentrations using the absorption data
      // in A1
      var A = new DoubleMatrix( new StreamReader( "chemometricX.dat" ));
      var A1 = new DoubleMatrix( new StreamReader( "chemometricX1.dat" ) );
      var C = new DoubleMatrix( new StreamReader( "chemometricY.dat" ));

      int numComponents = 3;
      var pls = new PLS2();
      Console.WriteLine( "\nCalculating..." );
      pls.Calculate( A, C, numComponents );

      // Check that the PLS computation succeeded.
      Console.WriteLine( "Is it good? " + pls.IsGood );

      // The scores and loadings availability and access are specific
      // the particular PLS algorithm used. We used the NIPALS algorithm,
      // which is the default, so we must retrieve the algorithm object
      // from the PLS object and extract the scores and loadings from it.
      var alg = (PLS2NipalsAlgorithm) pls.Calculator;

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

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

      // Get concentration weighted scores
      DoubleMatrix U = alg.ResponseScores;
      Console.WriteLine( "\nConcentration Weighted Scores ------------------\n" );
      for ( int i = 0; i < numComponents; ++i )
        Console.WriteLine( "concentration score {0} \n{1} \n", i, U.Col( i ).ToString( "G5" ) );

      // Get concentration loadings
      DoubleMatrix By = alg.ResponseLoadings;
      Console.WriteLine( "\nConcentration Loadings ------------------------------\n" );
      for ( int i = 0; i < numComponents; ++i )
        Console.WriteLine( "concentration loading {0} \n{1} \n", i, By.Col( i ).ToString( "G5" ) );

      // Prediction using the coefficients matrix. Predict the constituent 
      // concentrations from a vector of spectral responses.
      // The coefficient matrix, B, can be used for prediction as follows:
      // Let Cu be the predicted concentrations 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)B.
      DoubleVector Cbar = alg.ResponseMean;
      DoubleVector Abar = alg.PredictorMean;
      DoubleMatrix B = alg.Coefficients;

      DoubleVector Au = A1.Row( 0 );
      DoubleVector Cu = Cbar + NMathFunctions.TransposeProduct( B, ( Au - Abar ) );
      Console.WriteLine( "Prediction Using Coefficient Matrix ------------------\n" );
      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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