public static Vector GaussMethod(Matrix A, Vector F)
{
Vector RES;
MatrixСonverting.LeadingElementSelection(A);
MatrixСonverting.BringingMatrixToTopTriangle(A);
RES = Substitutions.BackRowSubstitution(A, F);
return(RES);
}
public static Vector QRMethod(Methods method, Matrix A, Vector F, out Matrix Q)
{
switch (method)
{
case Methods.Givens:
Givens(A, out Q);
break;
case Methods.Householder:
Householder(A, out Q);
break;
default:
throw new Exception("Need choice one method: Givens, Householder");
}
F = Q.MultTransMatrixVector(F);
Vector RES = Substitutions.BackRowSubstitution(A, F);
return(RES);
}
public static Vector LUMethod(Matrix A, Vector F)
{
Vector RES;
Matrix LU = new Matrix(A.M, A.N);
LU.Copy(A);
MatrixСonverting.BringingMatrixToTopTriangle(LU);
for (int i = 1; i < A.N; i++)
{
for (int j = 0; j < i; j++)
{
double sum = 0;
for (int k = 0; k < j; k++)
{
sum += LU.Elem[i][k] * LU.Elem[k][j];
}
LU.Elem[i][j] = (A.Elem[i][j] - sum) / LU.Elem[j][j];
}
}
Vector d = new Vector(A.N);
for (int i = 0; i < A.N; i++)
{
d.Elem[i] = LU.Elem[i][i];
LU.Elem[i][i] = 1;
}
Vector Y = Substitutions.DirectRowSubstitution(LU, F);
for (int i = 0; i < A.N; i++)
{
LU.Elem[i][i] = d.Elem[i];
}
RES = Substitutions.BackRowSubstitution(LU, Y);
return(RES);
}