/// <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
/// <summary> /// Makes a PCA (a principal component analysis) of the table or the selected columns / rows and stores the results in a newly created table. /// </summary> /// <param name="mainDocument">The main document of the application.</param> /// <param name="srctable">The table where the data come from.</param> /// <param name="selectedColumns">The selected columns.</param> /// <param name="selectedRows">The selected rows.</param> /// <param name="bHorizontalOrientedSpectrum">True if a spectrum is a single row, False if a spectrum is a single column.</param> /// <param name="maxNumberOfFactors">The maximum number of factors to calculate.</param> /// <returns></returns> public static string PrincipalComponentAnalysis( Altaxo.AltaxoDocument mainDocument, Altaxo.Data.DataTable srctable, IAscendingIntegerCollection selectedColumns, IAscendingIntegerCollection selectedRows, bool bHorizontalOrientedSpectrum, int maxNumberOfFactors ) { bool bUseSelectedColumns = (null != selectedColumns && 0 != selectedColumns.Count); int prenumcols = bUseSelectedColumns ? selectedColumns.Count : srctable.DataColumns.ColumnCount; // check for the number of numeric columns int numcols = 0; for (int i = 0; i < prenumcols; i++) { int idx = bUseSelectedColumns ? selectedColumns[i] : i; if (srctable[i] is Altaxo.Data.INumericColumn) { numcols++; } } // check the number of rows bool bUseSelectedRows = (null != selectedRows && 0 != selectedRows.Count); int numrows; if (bUseSelectedRows) { numrows = selectedRows.Count; } else { numrows = 0; for (int i = 0; i < numcols; i++) { int idx = bUseSelectedColumns ? selectedColumns[i] : i; numrows = Math.Max(numrows, srctable[idx].Count); } } // check that both dimensions are at least 2 - otherwise PCA is not possible if (numrows < 2) { return("At least two rows are neccessary to do Principal Component Analysis!"); } if (numcols < 2) { return("At least two numeric columns are neccessary to do Principal Component Analysis!"); } // Create a matrix of appropriate dimensions and fill it MatrixMath.BEMatrix matrixX; if (bHorizontalOrientedSpectrum) { matrixX = new MatrixMath.BEMatrix(numrows, numcols); int ccol = 0; // current column in the matrix for (int i = 0; i < prenumcols; i++) { int colidx = bUseSelectedColumns ? selectedColumns[i] : i; Altaxo.Data.INumericColumn col = srctable[colidx] as Altaxo.Data.INumericColumn; if (null != col) { for (int j = 0; j < numrows; j++) { int rowidx = bUseSelectedRows ? selectedRows[j] : j; matrixX[j, ccol] = col[rowidx]; } ++ccol; } } } // end if it was a horizontal oriented spectrum else // if it is a vertical oriented spectrum { matrixX = new MatrixMath.BEMatrix(numcols, numrows); int ccol = 0; // current column in the matrix for (int i = 0; i < prenumcols; i++) { int colidx = bUseSelectedColumns ? selectedColumns[i] : i; Altaxo.Data.INumericColumn col = srctable[colidx] as Altaxo.Data.INumericColumn; if (null != col) { for (int j = 0; j < numrows; j++) { int rowidx = bUseSelectedRows ? selectedRows[j] : j; matrixX[ccol, j] = col[rowidx]; } ++ccol; } } } // if it was a vertical oriented spectrum // now do PCA with the matrix MatrixMath.REMatrix factors = new MatrixMath.REMatrix(0, 0); MatrixMath.BEMatrix loads = new MatrixMath.BEMatrix(0, 0); MatrixMath.BEMatrix residualVariances = new MatrixMath.BEMatrix(0, 0); MatrixMath.HorizontalVector meanX = new MatrixMath.HorizontalVector(matrixX.Columns); // first, center the matrix MatrixMath.ColumnsToZeroMean(matrixX, meanX); MatrixMath.NIPALS_HO(matrixX, maxNumberOfFactors, 1E-9, factors, loads, residualVariances); // now we have to create a new table where to place the calculated factors and loads // we will do that in a vertical oriented manner, i.e. even if the loads are // here in horizontal vectors: in our table they are stored in (vertical) columns Altaxo.Data.DataTable table = new Altaxo.Data.DataTable("PCA of " + srctable.Name); // Fill the Table table.Suspend(); // first of all store the meanscore { double meanScore = MatrixMath.LengthOf(meanX); MatrixMath.NormalizeRows(meanX); Altaxo.Data.DoubleColumn col = new Altaxo.Data.DoubleColumn(); for (int i = 0; i < factors.Rows; i++) { col[i] = meanScore; } table.DataColumns.Add(col, "MeanFactor", Altaxo.Data.ColumnKind.V, 0); } // first store the factors for (int i = 0; i < factors.Columns; i++) { Altaxo.Data.DoubleColumn col = new Altaxo.Data.DoubleColumn(); for (int j = 0; j < factors.Rows; j++) { col[j] = factors[j, i]; } table.DataColumns.Add(col, "Factor" + i.ToString(), Altaxo.Data.ColumnKind.V, 1); } // now store the mean of the matrix { Altaxo.Data.DoubleColumn col = new Altaxo.Data.DoubleColumn(); for (int j = 0; j < meanX.Columns; j++) { col[j] = meanX[0, j]; } table.DataColumns.Add(col, "MeanLoad", Altaxo.Data.ColumnKind.V, 2); } // now store the loads - careful - they are horizontal in the matrix for (int i = 0; i < loads.Rows; i++) { Altaxo.Data.DoubleColumn col = new Altaxo.Data.DoubleColumn(); for (int j = 0; j < loads.Columns; j++) { col[j] = loads[i, j]; } table.DataColumns.Add(col, "Load" + i.ToString(), Altaxo.Data.ColumnKind.V, 3); } // now store the residual variances, they are vertical in the vector { Altaxo.Data.DoubleColumn col = new Altaxo.Data.DoubleColumn(); for (int i = 0; i < residualVariances.Rows; i++) { col[i] = residualVariances[i, 0]; } table.DataColumns.Add(col, "ResidualVariance", Altaxo.Data.ColumnKind.V, 4); } table.Resume(); mainDocument.DataTableCollection.Add(table); // create a new worksheet without any columns Current.ProjectService.CreateNewWorksheet(table); return(null); }