/// <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;
    }
示例#2
0
    /// <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;
    }