コード例 #1
0
    /// <summary>
    /// Partial least squares (PLS) decomposition of the matrizes X and Y.
    /// </summary>
    /// <param name="_X">The X ("spectrum") matrix, centered and preprocessed.</param>
    /// <param name="_Y">The Y ("concentration") matrix (centered).</param>
    /// <param name="numFactors">Number of factors to calculate.</param>
    /// <param name="xLoads">Returns the matrix of eigenvectors of X. Should be initially empty.</param>
    /// <param name="yLoads">Returns the matrix of eigenvectors of Y. Should be initially empty. </param>
    /// <param name="W">Returns the matrix of weighting values. Should be initially empty.</param>
    /// <param name="V">Returns the vector of cross products. Should be initially empty.</param>
    /// <param name="PRESS">If not null, the PRESS value of each factor is stored (vertically) here. </param>
    public static void ExecuteAnalysis(
      IROMatrix _X, // matrix of spectra (a spectra is a row of this matrix)
      IROMatrix _Y, // matrix of concentrations (a mixture is a row of this matrix)
      ref int numFactors,
      IBottomExtensibleMatrix xLoads, // out: the loads of the X matrix
      IBottomExtensibleMatrix yLoads, // out: the loads of the Y matrix
      IBottomExtensibleMatrix W, // matrix of weighting values
      IRightExtensibleMatrix V,  // matrix of cross products
      IExtensibleVector PRESS //vector of Y PRESS values
      )
    {
      // used variables:
      // n: number of spectra (number of tests, number of experiments)
      // p: number of slots (frequencies, ..) in each spectrum
      // m: number of constitutents (number of y values in each measurement)
      
      // X : n-p matrix of spectra (each spectra is a horizontal row)
      // Y : n-m matrix of concentrations


      const int maxIterations = 1500; // max number of iterations in one factorization step
      const double accuracy = 1E-12; // accuracy that should be reached between subsequent calculations of the u-vector



      // use the mean spectrum as first row of the W matrix
      MatrixMath.HorizontalVector mean = new MatrixMath.HorizontalVector(_X.Columns);
      //  MatrixMath.ColumnsToZeroMean(X,mean);
      //W.AppendBottom(mean);

      IMatrix X = new MatrixMath.BEMatrix(_X.Rows,_X.Columns);
      MatrixMath.Copy(_X,X);
      IMatrix Y = new MatrixMath.BEMatrix(_Y.Rows,_Y.Columns);
      MatrixMath.Copy(_Y,Y);

      IMatrix u_prev = null;
      IMatrix w = new MatrixMath.HorizontalVector(X.Columns); // horizontal vector of X (spectral) weighting
      IMatrix t = new MatrixMath.VerticalVector(X.Rows); // vertical vector of X  scores
      IMatrix u = new MatrixMath.VerticalVector(X.Rows); // vertical vector of Y scores
      IMatrix p = new MatrixMath.HorizontalVector(X.Columns); // horizontal vector of X loads
      IMatrix q = new MatrixMath.HorizontalVector(Y.Columns); // horizontal vector of Y loads

      int maxFactors = Math.Min(X.Columns,X.Rows);
      numFactors = numFactors<=0 ? maxFactors : Math.Min(numFactors,maxFactors);

      if(PRESS!=null)
      {
        PRESS.Append(new MatrixMath.Scalar(MatrixMath.SumOfSquares(Y))); // Press value for not decomposed Y
      }

      for(int nFactor=0; nFactor<numFactors; nFactor++)
      {
        //Console.WriteLine("Factor_{0}:",nFactor);
        //Console.WriteLine("X:"+X.ToString());
        //Console.WriteLine("Y:"+Y.ToString());

  
        // 1. Use as start vector for the y score the first column of the 
        // y-matrix
        MatrixMath.Submatrix(Y,u); // u is now a vertical vector of concentrations of the first constituents

        for(int iter=0;iter<maxIterations;iter++)
        {
          // 2. Calculate the X (spectrum) weighting vector
          MatrixMath.MultiplyFirstTransposed(u,X,w); // w is a horizontal vector

          // 3. Normalize w to unit length
          MatrixMath.NormalizeRows(w); // w now has unit length

          // 4. Calculate X (spectral) scores
          MatrixMath.MultiplySecondTransposed(X,w,t); // t is a vertical vector of n numbers

          // 5. Calculate the Y (concentration) loading vector
          MatrixMath.MultiplyFirstTransposed(t,Y,q); // q is a horizontal vector of m (number of constitutents)

          // 5.1 Normalize q to unit length
          MatrixMath.NormalizeRows(q);

          // 6. Calculate the Y (concentration) score vector u
          MatrixMath.MultiplySecondTransposed(Y,q,u); // u is a vertical vector of n numbers

          // 6.1 Compare
          // Compare this with the previous one 
          if(u_prev!=null && MatrixMath.IsEqual(u_prev,u,accuracy))
            break;
          if(u_prev==null)
            u_prev = new MatrixMath.VerticalVector(X.Rows);
          MatrixMath.Copy(u,u_prev); // stores the content of u in u_prev
        } // for all iterations

        // Store the scores of X
        //factors.AppendRight(t);


        // 7. Calculate the inner scalar (cross product)
        double length_of_t = MatrixMath.LengthOf(t); 
        MatrixMath.Scalar v = new MatrixMath.Scalar(0);
        MatrixMath.MultiplyFirstTransposed(u,t,v);
        if(length_of_t!=0)
          v = v/MatrixMath.Square(length_of_t); 
      
        // 8. Calculate the new loads for the X (spectral) matrix
        MatrixMath.MultiplyFirstTransposed(t,X,p); // p is a horizontal vector of loads
        // Normalize p by the spectral scores

        if(length_of_t!=0)
          MatrixMath.MultiplyScalar(p,1/MatrixMath.Square(length_of_t),p);

        // 9. Calculate the new residua for the X (spectral) and Y (concentration) matrix
        //MatrixMath.MultiplyScalar(t,length_of_t*v,t); // original t times the cross product

        MatrixMath.SubtractProductFromSelf(t,p,X);
        
        MatrixMath.MultiplyScalar(t,v,t); // original t times the cross product
        MatrixMath.SubtractProductFromSelf(t,q,Y); // to calculate residual Y

        // Store the loads of X and Y in the output result matrix
        xLoads.AppendBottom(p);
        yLoads.AppendBottom(q);
        W.AppendBottom(w);
        V.AppendRight(v);
    
        if(PRESS!=null)
        {
          double pressValue=MatrixMath.SumOfSquares(Y);
          PRESS.Append(new MatrixMath.Scalar(pressValue));
        }
        // Calculate SEPcv. If SEPcv is greater than for the actual number of factors,
        // break since the optimal number of factors was found. If not, repeat the calculations
        // with the residual matrizes for the next factor.
      } // for all factors
    }
コード例 #2
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    public static void Predict(
      IROMatrix XU, // unknown spectrum or spectra,  horizontal oriented
      IROMatrix xLoads, // x-loads matrix
      IROMatrix yLoads, // y-loads matrix
      IROMatrix W, // weighting matrix
      IROMatrix V,  // Cross product vector
      int numFactors, // number of factors to use for prediction
      IMatrix predictedY, // Matrix of predicted y-values, must be same number of rows as spectra
      IMatrix spectralResiduals // Matrix of spectral residuals, n rows x 1 column, can be zero
      )
    {

      // now predicting a "unkown" spectra
      MatrixMath.Scalar si = new MatrixMath.Scalar(0);
      MatrixMath.HorizontalVector Cu = new MatrixMath.HorizontalVector(yLoads.Columns);

      MatrixMath.HorizontalVector wi = new MatrixMath.HorizontalVector(XU.Columns);
      MatrixMath.HorizontalVector cuadd = new MatrixMath.HorizontalVector(yLoads.Columns);
      
      // xu holds a single spectrum extracted out of XU
      MatrixMath.HorizontalVector xu = new MatrixMath.HorizontalVector(XU.Columns);

      // xl holds temporarily a row of the xLoads matrix+
      MatrixMath.HorizontalVector xl = new MatrixMath.HorizontalVector(xLoads.Columns);


      int maxFactors = Math.Min(yLoads.Rows,numFactors);
      

      for(int nSpectrum=0;nSpectrum<XU.Rows;nSpectrum++)
      {
        MatrixMath.Submatrix(XU,xu,nSpectrum,0); // extract one spectrum to predict
        MatrixMath.ZeroMatrix(Cu); // Set Cu=0
        for(int i=0;i<maxFactors;i++)
        {
          //1. Calculate the unknown spectral score for a weighting vector
          MatrixMath.Submatrix(W,wi,i,0);
          MatrixMath.MultiplySecondTransposed(wi,xu,si);
          // take the y loading vector
          MatrixMath.Submatrix(yLoads,cuadd,i,0);
          // and multiply it with the cross product and the score
          MatrixMath.MultiplyScalar(cuadd,si*V[0,i],cuadd);
          // Add it to the predicted y-values
          MatrixMath.Add(Cu,cuadd,Cu);
          // remove the spectral contribution of the factor from the spectrum
          // TODO this is quite ineffective: in every loop we extract the xl vector, we have to find a shortcut for this!
          MatrixMath.Submatrix(xLoads,xl,i,0);
          MatrixMath.SubtractProductFromSelf(xl,(double)si,xu);
        }
        // xu now contains the spectral residual,
        // Cu now contains the predicted y values
        if(null!=predictedY)
        {
          MatrixMath.SetRow(Cu,0,predictedY,nSpectrum);
        }

        if(null!=spectralResiduals)
        {
          spectralResiduals[nSpectrum,0] = MatrixMath.SumOfSquares(xu);
        }

      } // for each spectrum in XU
    } // end partial-least-squares-predict
コード例 #3
0
ファイル: BivariateAkimaSpline.cs プロジェクト: Altaxo/Altaxo
		public double Interpolate(double x, double y)
		{
			MatrixMath.Scalar z = new MatrixMath.Scalar();
			this.itplbv_(_myX.Length, _myY.Length, _myX, _myY, _myZ, 1, new MatrixMath.Scalar(x), new MatrixMath.Scalar(y), z);
			return z;
		}