private _nVector HHStep1_2R(_mnMatrix matrix)
{
var resultAfterStep1 = HHStep1_1R(matrix);
var scalar = (1 / resultAfterStep1.Norm(resultAfterStep1));
var result = resultAfterStep1.MultiplyByScalar((1 / resultAfterStep1.Norm(resultAfterStep1)));
return(result);
}
private _nVector HHStep1_1R(_mnMatrix matrix)
{
var m = matrix.m;
var firstRow = matrix.GetRow(0);
var coefficient = Sign(firstRow.V(1)) * firstRow.Norm(firstRow);
var coefficientTimesUnitVector = iComponentVector(m).MultiplyByScalar(coefficient);
var resultAfterAdd = coefficientTimesUnitVector.Add(firstRow);
return(resultAfterAdd);
}
public _mnMatrix HouseholderRightSideResult(_mnMatrix mnMatrix, int i, int dim)
{
var U = HHStep1_2R(mnMatrix);
var result = mnMatrix.MultiplyByVector(U);
var multiplicationResult = result.mnMatrixTypeMultiplyWithAnotherVector(U);
var resultTimes2 = multiplicationResult.MultiplyByScalar(2);
var subtractionResult = mnMatrix.SubtractAnotherMatrix(resultTimes2);
if (i > 1)
{
AddToVHouseholder(U, subtractionResult, i, dim);
}
return(subtractionResult);
}
public void AddToVHouseholder(_nVector V, _mnMatrix mnMatrix, int i, int dim)
{
var vMatrix = V.MatrixTypeMultiplyWithMe();
var resultafterUMatrixTimes2 = vMatrix.MultiplyByScalar(2);
var identity = new nIdentityMatrix();
var finvlHouseholderMatrix = identity.ReturnNIdentityMatrix(i - 1)
.SubtractAnotherMatrix(resultafterUMatrixTimes2);
var matrixToAdd = identity.ReturnNIdentityMatrix(dim - 1);
matrixToAdd.InsertSubMatrix(finvlHouseholderMatrix, i - 1);
VHouseholderMatrices.Add(matrixToAdd);
//var maybe = matrixToAdd.MultiplyByAnotherMatrix(matrixToAdd.ReturnTranspose(matrixToAdd));
//var result = mnMatrix.MultiplyMeByNMatrix(matrixToAdd);
}
public static _mnMatrix GetQuadratureMatrix(int steps, double ds, double dt)
{
var rows = new List <_nVector>();
for (int t = 1; t <= steps; t++)
{
var doubleList = new List <double>();
for (int r = 0; r < steps; r++)
{
var temp = ds * Math.Pow(Math.E, (-1) * (ds * r) * (dt * t)); // At a specific time constant.
doubleList.Add(temp);
}
rows.Add(new _nVector(doubleList));
}
var matrix = new _mnMatrix(rows, steps, steps);
return(matrix);
}