/// <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);
}
