/// <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
}
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
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;
}
