/// <summary>
/// Multiplies selected columns to form a matrix.
/// </summary>
/// <param name="mainDocument"></param>
/// <param name="srctable"></param>
/// <param name="selectedColumns"></param>
/// <returns>Null if successful, else the description of the error.</returns>
/// <remarks>The user must select an even number of columns. All columns of the first half of the selection
/// must have the same number of rows, and all columns of the second half of selection must also have the same
/// number of rows. The first half of selected columns form a matrix of dimensions(firstrowcount,halfselected), and the second half
/// of selected columns form a matrix of dimension(halfselected, secondrowcount). The resulting matrix has dimensions (firstrowcount,secondrowcount) and is
/// stored in a separate worksheet.</remarks>
public static string MultiplyColumnsToMatrix(
Altaxo.AltaxoDocument mainDocument,
Altaxo.Data.DataTable srctable,
IAscendingIntegerCollection selectedColumns
)
{
// check that there are columns selected
if(0==selectedColumns.Count)
return "You must select at least two columns to multiply!";
// selected columns must contain an even number of columns
if(0!=selectedColumns.Count%2)
return "You selected an odd number of columns. Please select an even number of columns to multiply!";
// all selected columns must be numeric columns
for(int i=0;i<selectedColumns.Count;i++)
{
if(!(srctable[selectedColumns[i]] is Altaxo.Data.INumericColumn))
return string.Format("The column[{0}] (name:{1}) is not a numeric column!",selectedColumns[i],srctable[selectedColumns[i]].Name);
}
int halfselect = selectedColumns.Count/2;
// check that all columns from the first half of selected colums contain the same
// number of rows
int rowsfirsthalf=int.MinValue;
for(int i=0;i<halfselect;i++)
{
int idx = selectedColumns[i];
if(rowsfirsthalf<0)
rowsfirsthalf = srctable[idx].Count;
else if(rowsfirsthalf != srctable[idx].Count)
return "The first half of selected columns have not all the same length!";
}
int rowssecondhalf=int.MinValue;
for(int i=halfselect;i<selectedColumns.Count;i++)
{
int idx = selectedColumns[i];
if(rowssecondhalf<0)
rowssecondhalf = srctable[idx].Count;
else if(rowssecondhalf != srctable[idx].Count)
return "The second half of selected columns have not all the same length!";
}
// now create the matrices to multiply from the
MatrixMath.REMatrix firstMat = new MatrixMath.REMatrix(rowsfirsthalf,halfselect);
for(int i=0;i<halfselect;i++)
{
Altaxo.Data.INumericColumn col = (Altaxo.Data.INumericColumn)srctable[selectedColumns[i]];
for(int j=0;j<rowsfirsthalf;j++)
firstMat[j,i] = col[j];
}
MatrixMath.BEMatrix secondMat = new MatrixMath.BEMatrix(halfselect,rowssecondhalf);
for(int i=0;i<halfselect;i++)
{
Altaxo.Data.INumericColumn col = (Altaxo.Data.INumericColumn)srctable[selectedColumns[i+halfselect]];
for(int j=0;j<rowssecondhalf;j++)
secondMat[i,j] = col[j];
}
// now multiply the two matrices
MatrixMath.BEMatrix resultMat = new MatrixMath.BEMatrix(rowsfirsthalf,rowssecondhalf);
MatrixMath.Multiply(firstMat,secondMat,resultMat);
// and store the result in a new worksheet
Altaxo.Data.DataTable table = new Altaxo.Data.DataTable("ResultMatrix of " + srctable.Name);
table.Suspend();
// first store the factors
for(int i=0;i<resultMat.Columns;i++)
{
Altaxo.Data.DoubleColumn col = new Altaxo.Data.DoubleColumn();
for(int j=0;j<resultMat.Rows;j++)
col[j] = resultMat[j,i];
table.DataColumns.Add(col,i.ToString());
}
table.Resume();
mainDocument.DataTableCollection.Add(table);
// create a new worksheet without any columns
Current.ProjectService.CreateNewWorksheet(table);
return null;
}
/// <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 matrixX, IROMatrix matrixY, int maxFactors)
{
int numberOfFactors = _calib.NumberOfFactors = Math.Min(matrixX.Columns, maxFactors);
MatrixMath.BEMatrix _xLoads = new MatrixMath.BEMatrix(0,0);
MatrixMath.BEMatrix _yLoads = new MatrixMath.BEMatrix(0,0);
MatrixMath.BEMatrix _W = new MatrixMath.BEMatrix(0,0);
MatrixMath.REMatrix _V = new MatrixMath.REMatrix(0,0);
_PRESS = VectorMath.CreateExtensibleVector(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;
}
/// <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;
}