/// <summary>
/// Estimates the least squares coefficients for the regression formula: Y = a + bX_1 + cX_2 + ... + dX_k
/// </summary>
/// <typeparam name="T">The type of observation values and the regression coefficients.</typeparam>
/// <typeparam name="C">The calculator for the observations' value type.</typeparam>
/// <param name="observationRows">The matrix of observations having rows in the following format: X_11 | X_12 | ... | X_1K | Y_1</param>
/// <returns>The vector of estimated least squares regression coefficients. Its first term is a free term, and all the following terms correspond to X_1, X_2 etc. up to X_k</returns>
public static Vector <T, C> EstimateLeastSquaresCoefficients <T, C>(Matrix <T, C> observationRows) where C : ICalc <T>, new()
{
Matrix <T, C> xMatrix = new Matrix_SDA <T, C>(observationRows.RowCount, observationRows.ColumnCount);
Matrix <T, C> yVector = observationRows.getSubMatrixAt(0, observationRows.ColumnCount - 1);
for (int i = 0; i < xMatrix.RowCount; i++)
{
xMatrix[i, 0] = Numeric <T, C> ._1;
for (int j = 1; j < xMatrix.ColumnCount; j++)
{
xMatrix[i, j] = observationRows[i, j - 1];
}
}
// TODO: transposition should NOT create a new matrix.
// write a new matrix class
Matrix <T, C> xTransposed = xMatrix.transposedMatrixCopy();
Matrix <T, C> result = (xTransposed * xMatrix).inverseMatrix_LUP_Factorization() * xTransposed * yVector;
IWinder winder = result.GetRowByRowWinder();
return(result.unwindToArray(winder));
}
/// <summary>
/// Winds a flat array onto current using the IWinder object.
/// The IWinder object is automatically reset before winding.
/// IWinder object and current matrix should be have the same dimension (i.e. row count and column count).
/// </summary>
/// <param name="winder">An IWinder object. Row and column count should match with current matrix.</param>
/// <param name="flatMatrix">A single-dimension matrix. Element count should match with current matrix.</param>
public void windFromArray(IWinder winder, T[] flatMatrix)
{
if (flatMatrix.Length != this.ElementCount)
{
throw new ArgumentException("The element count of the current matrix and the element count of the flat matrix must match.");
}
winder.reset();
for (int i = 0; i < this.ElementCount; i++)
{
this[winder.getNextIndexPair()] = flatMatrix[i];
}
}
// ------------------------------------------------------------------------------
// -----------------------------WINDING capabilities-----------------------------
public T[] unwindToArray(IWinder winder)
{
T[] temp = new T[this.ElementCount];
winder.reset();
for (int i = 0; i < this.ElementCount; i++)
{
temp[i] = this[winder.getNextIndexPair()];
}
return(temp);
}
