/// <summary>
/// // At this point U has been calculated including the norm of U being multiplied to U. Therefore, when we multiply U by itself it is in fact the norm times itself , and amounts to VT*V
/// </summary>
/// <param name="matrix"></param>
/// <returns></returns>
public _nMatrix HouseholderResult(_nMatrix matrix, int i, int dim)
{
var U = HHStep1_2(matrix);
var result = U.MultiplyByMatrix(matrix);
var multiplicationResult = U.MatrixTypeMultiplyWithAnotherVector(result);
var resultTimes2 = multiplicationResult.MultiplyByScalar(2);
var subtractionResult = matrix.SubtractAnotherMatrix(resultTimes2);
if (i > 1)
{
AddToUHouseholder(U, subtractionResult, i, dim);
}
return(subtractionResult);
}
private static void AddNextPowerTermToMatrixSeries(_nMatrix copy, ref _nMatrix temp, int i)
{
int remainder = 0;
Math.DivRem(i, 2, out remainder);
if (remainder == 0)
{
var tmp = MatrixToThePowerN(i, copy);
//ZeroOutRightUptoI(tmp, i);
temp = temp.AddAnotherMatrix(tmp);
}
else
{
var tmp = MatrixToThePowerN(i, copy);
//ZeroOutRightUptoI(tmp, i);
temp = temp.SubtractAnotherMatrix(tmp);
}
}