public static void CalculatePRESS(
IROMatrix <double> yLoads,
IROMatrix <double> xScores,
int numberOfFactors,
out IROVector <double> press)
{
int numMeasurements = yLoads.RowCount;
IExtensibleVector <double> PRESS = VectorMath.CreateExtensibleVector <double>(numberOfFactors + 1);
var UtY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(yLoads.RowCount, yLoads.ColumnCount);
var predictedY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(yLoads.RowCount, yLoads.ColumnCount);
press = PRESS;
MatrixMath.MultiplyFirstTransposed(xScores, yLoads, UtY);
// now calculate PRESS by predicting the y
// using yp = U (w*(1/w)) U' y
// of course w*1/w is the identity matrix, but we use only the first factors, so using a cutted identity matrix
// we precalculate the last term U'y = UtY
// and multiplying with one row of U in every factor step, summing up the predictedY
PRESS[0] = MatrixMath.SumOfSquares(yLoads);
for (int nf = 0; nf < numberOfFactors; nf++)
{
for (int cn = 0; cn < yLoads.ColumnCount; cn++)
{
for (int k = 0; k < yLoads.RowCount; k++)
{
predictedY[k, cn] += xScores[k, nf] * UtY[nf, cn];
}
}
PRESS[nf + 1] = MatrixMath.SumOfSquaredDifferences(yLoads, predictedY);
}
}
/// <summary>
/// Fits a data set linear to a given function base.
/// </summary>
/// <param name="xarr">The array of x values of the data set.</param>
/// <param name="yarr">The array of y values of the data set.</param>
/// <param name="stddev">The array of y standard deviations of the data set. Can be null if the standard deviation is unkown.</param>
/// <param name="numberOfData">The number of data points (may be smaller than the array sizes of the data arrays).</param>
/// <param name="numberOfParameter">The number of parameters to fit == size of the function base.</param>
/// <param name="evaluateFunctionBase">The function base used to fit.</param>
/// <param name="threshold">A treshold value (usually 1E-5) used to chop the unimportant singular values away.</param>
public LinearFitBySvd(
double[] xarr,
double[] yarr,
double[] stddev,
int numberOfData,
int numberOfParameter,
FunctionBaseEvaluator evaluateFunctionBase,
double threshold)
{
var u = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(numberOfData, numberOfParameter);
double[] functionBase = new double[numberOfParameter];
// Fill the function base matrix (rows: numberOfData, columns: numberOfParameter)
// and scale also y
for (int i = 0; i < numberOfData; i++)
{
evaluateFunctionBase(xarr[i], functionBase);
for (int j = 0; j < numberOfParameter; j++)
{
u[i, j] = functionBase[j];
}
}
Calculate(
u,
VectorMath.ToROVector(yarr),
VectorMath.ToROVector(stddev),
numberOfData,
numberOfParameter,
threshold);
}
public static void GetSpectralResiduals(
IROMatrix <double> matrixX,
IROMatrix <double> xLoads,
IROMatrix <double> yLoads,
IROMatrix <double> xScores,
IReadOnlyList <double> crossProduct,
int numberOfFactors,
IMatrix <double> spectralResiduals)
{
int numX = xLoads.ColumnCount;
int numY = yLoads.ColumnCount;
int numM = yLoads.RowCount;
var reconstructedSpectra = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(matrixX.RowCount, matrixX.ColumnCount);
MatrixMath.ZeroMatrix(reconstructedSpectra);
for (int nf = 0; nf < numberOfFactors; nf++)
{
double scale = crossProduct[nf];
for (int m = 0; m < numM; m++)
{
for (int k = 0; k < numX; k++)
{
reconstructedSpectra[m, k] += scale * xScores[m, nf] * xLoads[nf, k];
}
}
}
for (int m = 0; m < numM; m++)
{
spectralResiduals[m, 0] = MatrixMath.SumOfSquaredDifferences(
MatrixMath.ToROSubMatrix(matrixX, m, 0, 1, matrixX.ColumnCount),
MatrixMath.ToROSubMatrix(reconstructedSpectra, m, 0, 1, matrixX.ColumnCount));
}
}
/// <summary>
/// Creates an analyis from preprocessed spectra and preprocessed concentrations.
/// </summary>
/// <param name="matrixX">The spectral matrix (each spectrum is a row in the matrix). They must at least be centered.</param>
/// <param name="matrixY">The matrix of concentrations (each experiment is a row in the matrix). They must at least be centered.</param>
/// <param name="maxFactors">Maximum number of factors for analysis.</param>
/// <returns>A regression object, which holds all the loads and weights neccessary for further calculations.</returns>
protected override void AnalyzeFromPreprocessedWithoutReset(IROMatrix <double> matrixX, IROMatrix <double> matrixY, int maxFactors)
{
int numberOfFactors = _calib.NumberOfFactors = Math.Min(matrixX.ColumnCount, maxFactors);
IMatrix <double> helperY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(matrixY.RowCount, 1);
_PRESS = null;
for (int i = 0; i < matrixY.ColumnCount; i++)
{
MatrixMath.Submatrix(matrixY, helperY, 0, i);
var r = PLS2Regression.CreateFromPreprocessed(matrixX, helperY, maxFactors);
IPLS2CalibrationModel cal = r.CalibrationModel;
_calib.NumberOfFactors = Math.Min(_calib.NumberOfFactors, cal.NumberOfFactors);
_calib.XLoads[i] = cal.XLoads;
_calib.YLoads[i] = cal.YLoads;
_calib.XWeights[i] = cal.XWeights;
_calib.CrossProduct[i] = cal.CrossProduct;
if (_PRESS == null)
{
_PRESS = VectorMath.CreateExtensibleVector <double>(r.PRESS.Length);
}
VectorMath.Add(_PRESS, r.PRESS, _PRESS);
}
}
public static void GetPredictionScoreMatrix(
IROMatrix <double> xLoads,
IROMatrix <double> yLoads,
IROMatrix <double> xScores,
IReadOnlyList <double> crossProduct,
int numberOfFactors,
IMatrix <double> predictionScores)
{
int numX = xLoads.ColumnCount;
int numY = yLoads.ColumnCount;
int numM = yLoads.RowCount;
var UtY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(xScores.ColumnCount, yLoads.ColumnCount);
MatrixMath.MultiplyFirstTransposed(xScores, yLoads, UtY);
MatrixMath.ZeroMatrix(predictionScores);
for (int nf = 0; nf < numberOfFactors; nf++)
{
double scale = 1 / crossProduct[nf];
for (int cn = 0; cn < numY; cn++)
{
for (int k = 0; k < numX; k++)
{
predictionScores[k, cn] += scale * xLoads[nf, k] * UtY[nf, cn];
}
}
}
}
/// <summary>
/// Calculates the prediction scores (for use withthe preprocessed spectra).
/// </summary>
/// <param name="numFactors">Number of factors used to calculate the prediction scores.</param>
/// <param name="predictionScores">Supplied matrix for holding the prediction scores.</param>
protected override void InternalGetPredictionScores(int numFactors, IMatrix <double> predictionScores)
{
IMatrix <double> pred = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(predictionScores.RowCount, 1);
for (int i = 0; i < _calib.NumberOfY; i++)
{
PLS2Regression.GetPredictionScoreMatrix(_calib.XLoads[i], _calib.YLoads[i], _calib.XWeights[i], _calib.CrossProduct[i], numFactors, pred);
MatrixMath.SetColumn(pred, predictionScores, i);
}
}
public CrossValidationResult(int numberOfPoints, int numberOfY, int numberOfFactors, bool multipleSpectralResiduals)
{
_predictedY = new IMatrix <double> [numberOfFactors + 1];
_spectralResidual = new IMatrix <double> [numberOfFactors + 1];
_crossPRESS = VectorMath.CreateExtensibleVector <double>(numberOfFactors + 1);
for (int i = 0; i <= numberOfFactors; i++)
{
_predictedY[i] = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(numberOfPoints, numberOfY);
_spectralResidual[i] = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(numberOfPoints, multipleSpectralResiduals ? numberOfY : 1);
}
}
/// <summary>
/// Creates an analyis from preprocessed spectra and preprocessed concentrations.
/// </summary>
/// <param name="matrixX">The spectral matrix (each spectrum is a row in the matrix). They must at least be centered.</param>
/// <param name="matrixY">The matrix of concentrations (each experiment is a row in the matrix). They must at least be centered.</param>
/// <param name="maxFactors">Maximum number of factors for analysis.</param>
/// <returns>A regression object, which holds all the loads and weights neccessary for further calculations.</returns>
protected override void AnalyzeFromPreprocessedWithoutReset(IROMatrix <double> matrixX, IROMatrix <double> matrixY, int maxFactors)
{
int numFactors = Math.Min(matrixX.ColumnCount, maxFactors);
ExecuteAnalysis(matrixX, matrixY, ref numFactors, out var xLoads, out var xScores, out var V);
var yLoads = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(matrixY.RowCount, matrixY.ColumnCount);
MatrixMath.Copy(matrixY, yLoads);
_calib.NumberOfFactors = numFactors;
_calib.XLoads = xLoads;
_calib.YLoads = yLoads;
_calib.XScores = xScores;
_calib.CrossProduct = V;
}
public static void CalculateXLeverageFromPreprocessed(
IROMatrix <double> xScores,
int numberOfFactors,
IMatrix <double> leverage)
{
var subscores = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(xScores.RowCount, numberOfFactors);
MatrixMath.Submatrix(xScores, subscores);
var decompose = new MatrixMath.SingularValueDecomposition(subscores);
for (int i = 0; i < xScores.RowCount; i++)
{
leverage[i, 0] = decompose.HatDiagonal[i];
}
}
/// <summary>
/// Creates an analyis from preprocessed spectra and preprocessed concentrations.
/// </summary>
/// <param name="matrixX">The spectral matrix (each spectrum is a row in the matrix). They must at least be centered.</param>
/// <param name="matrixY">The matrix of concentrations (each experiment is a row in the matrix). They must at least be centered.</param>
/// <param name="maxFactors">Maximum number of factors for analysis.</param>
/// <returns>A regression object, which holds all the loads and weights neccessary for further calculations.</returns>
protected override void AnalyzeFromPreprocessedWithoutReset(IROMatrix <double> matrixX, IROMatrix <double> matrixY, int maxFactors)
{
int numberOfFactors = _calib.NumberOfFactors = Math.Min(matrixX.ColumnCount, maxFactors);
var _xLoads = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(0, 0);
var _yLoads = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(0, 0);
var _W = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(0, 0);
var _V = new MatrixMath.TopSpineJaggedArrayMatrix <double>(0, 0);
_PRESS = VectorMath.CreateExtensibleVector <double>(0);
ExecuteAnalysis(matrixX, matrixY, ref numberOfFactors, _xLoads, _yLoads, _W, _V, _PRESS);
_calib.NumberOfFactors = Math.Min(_calib.NumberOfFactors, numberOfFactors);
_calib.XLoads = _xLoads;
_calib.YLoads = _yLoads;
_calib.XWeights = _W;
_calib.CrossProduct = _V;
}
public static void ExecuteAnalysis(
IROMatrix <double> X, // matrix of spectra (a spectra is a row of this matrix)
IROMatrix <double> Y, // matrix of concentrations (a mixture is a row of this matrix)
ref int numFactors,
out IROMatrix <double> xLoads, // out: the loads of the X matrix
out IROMatrix <double> xScores, // matrix of weighting values
out IROVector <double> V // vector of cross products
)
{
var matrixX = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(X.RowCount, X.ColumnCount);
MatrixMath.Copy(X, matrixX);
var decompose = new MatrixMath.SingularValueDecomposition(matrixX);
numFactors = Math.Min(numFactors, matrixX.ColumnCount);
numFactors = Math.Min(numFactors, matrixX.RowCount);
xLoads = JaggedArrayMath.ToTransposedROMatrix(decompose.V, Y.RowCount, X.ColumnCount);
xScores = JaggedArrayMath.ToMatrix(decompose.U, Y.RowCount, Y.RowCount);
V = VectorMath.ToROVector(decompose.Diagonal, numFactors);
}
private static void CalculatePRESS(
IROMatrix <double> Y, // matrix of concentrations (a mixture is a row of this matrix)
IROMatrix <double> xLoads, // out: the loads of the X matrix
IROMatrix <double> xScores, // matrix of weighting values
IReadOnlyList <double> V, // vector of cross products
int maxNumberOfFactors,
IVector <double> PRESS //vector of Y PRESS values
)
{
var U = xScores;
var UtY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(Y.RowCount, Y.ColumnCount);
MatrixMath.MultiplyFirstTransposed(U, Y, UtY);
var predictedY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(Y.RowCount, Y.ColumnCount);
var subU = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(Y.RowCount, 1);
var subY = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(Y.RowCount, Y.ColumnCount);
PRESS[0] = MatrixMath.SumOfSquares(Y);
int numFactors = Math.Min(maxNumberOfFactors, V.Count);
// now calculate PRESS by predicting the y
// using yp = U (w*(1/w)) U' y
// of course w*1/w is the identity matrix, but we use only the first factors, so using a cutted identity matrix
// we precalculate the last term U'y = UtY
// and multiplying with one row of U in every factor step, summing up the predictedY
for (int nf = 0; nf < numFactors; nf++)
{
for (int cn = 0; cn < Y.ColumnCount; cn++)
{
for (int k = 0; k < Y.RowCount; k++)
{
predictedY[k, cn] += U[k, nf] * UtY[nf, cn];
}
}
PRESS[nf + 1] = MatrixMath.SumOfSquaredDifferences(Y, predictedY);
}
}
} // end partial-least-squares-predict
public static void CalculateXLeverageFromPreprocessed(
IROMatrix <double> matrixX,
IROMatrix <double> W, // weighting matrix
int numFactors, // number of factors to use for prediction
IMatrix <double> leverage, // Matrix of predicted y-values, must be same number of rows as spectra
int leverageColumn
)
{
// get the score matrix
var weights = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(numFactors, W.ColumnCount);
MatrixMath.Submatrix(W, weights, 0, 0);
var scoresMatrix = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(matrixX.RowCount, weights.RowCount);
MatrixMath.MultiplySecondTransposed(matrixX, weights, scoresMatrix);
MatrixMath.SingularValueDecomposition decomposition = MatrixMath.GetSingularValueDecomposition(scoresMatrix);
for (int i = 0; i < matrixX.RowCount; i++)
{
leverage[i, leverageColumn] = decomposition.HatDiagonal[i];
}
}
public static void Predict(
IROMatrix <double> matrixX,
IROMatrix <double> xLoads,
IROMatrix <double> yLoads,
IROMatrix <double> xScores,
IReadOnlyList <double> crossProduct,
int numberOfFactors,
IMatrix <double> predictedY,
IMatrix <double> spectralResiduals)
{
int numX = xLoads.ColumnCount;
int numY = yLoads.ColumnCount;
int numM = yLoads.RowCount;
var predictionScores = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(numX, numY);
GetPredictionScoreMatrix(xLoads, yLoads, xScores, crossProduct, numberOfFactors, predictionScores);
MatrixMath.Multiply(matrixX, predictionScores, predictedY);
if (null != spectralResiduals)
{
GetSpectralResiduals(matrixX, xLoads, yLoads, xScores, crossProduct, numberOfFactors, spectralResiduals);
}
}
/// <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 <double> _X, // matrix of spectra (a spectra is a row of this matrix)
IROMatrix <double> _Y, // matrix of concentrations (a mixture is a row of this matrix)
ref int numFactors,
IBottomExtensibleMatrix <double> xLoads, // out: the loads of the X matrix
IBottomExtensibleMatrix <double> yLoads, // out: the loads of the Y matrix
IBottomExtensibleMatrix <double> W, // matrix of weighting values
IRightExtensibleMatrix <double> V, // matrix of cross products
IExtensibleVector <double> 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
var mean = new MatrixMath.MatrixWithOneRow <double>(_X.ColumnCount);
// MatrixMath.ColumnsToZeroMean(X,mean);
//W.AppendBottom(mean);
var X = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(_X.RowCount, _X.ColumnCount);
MatrixMath.Copy(_X, X);
var Y = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(_Y.RowCount, _Y.ColumnCount);
MatrixMath.Copy(_Y, Y);
IMatrix <double> u_prev = null;
var w = new MatrixMath.MatrixWithOneRow <double>(X.ColumnCount); // horizontal vector of X (spectral) weighting
var t = new MatrixMath.MatrixWithOneColumn <double>(X.RowCount); // vertical vector of X scores
var u = new MatrixMath.MatrixWithOneColumn <double>(X.RowCount); // vertical vector of Y scores
var p = new MatrixMath.MatrixWithOneRow <double>(X.ColumnCount); // horizontal vector of X loads
var q = new MatrixMath.MatrixWithOneRow <double>(Y.ColumnCount); // horizontal vector of Y loads
int maxFactors = Math.Min(X.ColumnCount, X.RowCount);
numFactors = numFactors <= 0 ? maxFactors : Math.Min(numFactors, maxFactors);
if (PRESS != null)
{
PRESS.Append(new MatrixMath.ScalarAsMatrix <double>(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.MatrixWithOneColumn <double>(X.RowCount);
}
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);
var v = new MatrixMath.ScalarAsMatrix <double>(0);
MatrixMath.MultiplyFirstTransposed(u, t, (IVector <double>)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.ScalarAsMatrix <double>(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
}
/// <summary>
/// Fits a data set linear to a given x base.
/// </summary>
/// <param name="xbase">The matrix of x values of the data set. Dimensions: numberOfData x numberOfParameters. The matrix is changed during calculation!</param>
/// <param name="yarr">The array of y values of the data set.</param>
/// <param name="stddev">The array of y standard deviations of the data set. Can be null if the standard deviation is unkown.</param>
/// <param name="numberOfData">The number of data points (may be smaller than the array sizes of the data arrays).</param>
/// <param name="numberOfParameter">The number of parameters to fit == size of the function base.</param>
/// <param name="threshold">A treshold value (usually 1E-5) used to chop the unimportant singular values away.</param>
public LinearFitBySvd Calculate(
IROMatrix <double> xbase, // NumberOfData, NumberOfParameters
IReadOnlyList <double> yarr,
IReadOnlyList <double> stddev,
int numberOfData,
int numberOfParameter,
double threshold)
{
_numberOfParameter = numberOfParameter;
_numberOfFreeParameter = numberOfParameter;
_numberOfData = numberOfData;
_parameter = new double[numberOfParameter];
_residual = new double[numberOfData];
_predicted = new double[numberOfData];
_reducedPredictionVariance = new double[numberOfData];
double[] scaledY = new double[numberOfData];
// Calculated some useful values
_yMean = Mean(yarr, 0, _numberOfData);
_yCorrectedSumOfSquares = CorrectedSumOfSquares(yarr, _yMean, 0, _numberOfData);
var u = new MatrixMath.LeftSpineJaggedArrayMatrix <double>(numberOfData, numberOfParameter);
// Fill the function base matrix (rows: numberOfData, columns: numberOfParameter)
// and scale also y
if (null == stddev)
{
for (int i = 0; i < numberOfData; i++)
{
for (int j = 0; j < numberOfParameter; j++)
{
u[i, j] = xbase[i, j];
}
scaledY[i] = yarr[i];
}
}
else
{
for (int i = 0; i < numberOfData; i++)
{
double scale = 1 / stddev[i];
for (int j = 0; j < numberOfParameter; j++)
{
u[i, j] = scale * xbase[i, j];
}
scaledY[i] = scale * yarr[i];
}
}
_decomposition = MatrixMath.GetSingularValueDecomposition(u);
// set singular values < thresholdLevel to zero
// ChopSingularValues makes only sense if all columns of the x matrix have the same variance
//decomposition.ChopSingularValues(1E-5);
// recalculate the parameters with the chopped singular values
_decomposition.Backsubstitution(scaledY, _parameter);
_chiSquare = 0;
for (int i = 0; i < numberOfData; i++)
{
double ypredicted = 0;
for (int j = 0; j < numberOfParameter; j++)
{
ypredicted += _parameter[j] * xbase[i, j];
}
double deviation = yarr[i] - ypredicted;
_predicted[i] = ypredicted;
_residual[i] = deviation;
_chiSquare += deviation * deviation;
}
_covarianceMatrix = _decomposition.GetCovariances();
//calculate the reduced prediction variance x'(X'X)^(-1)x
for (int i = 0; i < numberOfData; i++)
{
double total = 0;
for (int j = 0; j < numberOfParameter; j++)
{
double sum = 0;
for (int k = 0; k < numberOfParameter; k++)
{
sum += _covarianceMatrix[j][k] * u[i, k];
}
total += u[i, j] * sum;
}
_reducedPredictionVariance[i] = total;
}
return(this);
}
