//constructor
//note to self: apparetly you can save functions as a array...
public olsf(vector x, vector y, vector dy, Func <double, double>[] f)
{
int len = x.size;
int m = f.Length;
vector b = new vector(len);
matrix A = new matrix(len, m);
for (int n = 0; n < len; n++)
{
b[n] = y[n] / dy[n];
for (int n1 = 0; n1 < m; n1++)
{
A[n, n1] = f[n1](x[n]) / dy[n];
} //end for
} //end for
gram_s gr = new gram_s(A);
c = gr.solve(b);
//coverient matrix:
gram_s gr1 = new gram_s(A.T * A);
Sigma = gr1.inverse();
vector dc1 = new vector(m);
for (int n1 = 0; n1 < m; n1++)
{
dc1[n1] = Sqrt(Sigma[n1, n1]);
} //end for
dc = dc1;
} //end constructor...
//function to find roots of f. x is the start guess..
public static vector newton(Func <vector, vector> f, vector x, double eps = 1e-3, double dx = 1e-7)
{
bool seed2 = true;
while (seed2)
{
//seed2=false;
//First the jacobian matrix J is calculated:
vector fx = f(x);
matrix J = new matrix(x.size, x.size);
for (int k = 0; k < x.size; k++) // for-loop over vector x
{
x[k] = x[k] + dx; //change x
vector df = (f(x) - fx) / dx; // the differnce in f(x)
for (int i = 0; i < x.size; i++)
{
J[i, k] = df[i]; // calculate the matrix element
} //end for
x[k] = x[k] - dx; // reset x
} // end for
// solving J*DX=-f(x)
gram_s GJ = new gram_s(J);
vector Dx = GJ.solve((-1) * fx); // using my own method to solve the equation ...
//calculating the step size s
double s = 2;
bool seed1 = true;
while (seed1)
{
s = s / 2;
if ((f(x + s * Dx).norm() < (1 - s / 2) * f(x).norm()) && (s < 1.0 / 64))
{
seed1 = false;
} //end if
} //end while
x = x + s * Dx; //calculate the new x!
//if((Dx.norm()<dx) && (f(x).norm() < eps)){
if (Dx.norm() < dx)
{
seed2 = false;
} //end if
else if (f(x).norm() < eps)
{
seed2 = false;
} //end else if
//seed2=false;
}//end while
return(x);
} //end newton...
public readonly vector c; //field
//constructor
//note to self: apparetly you can save functions as a array...
public olsf(vector x, vector y, vector dy, Func <double, double>[] f)
{
int len = x.size;
int m = f.Length;
vector b = new vector(len);
matrix A = new matrix(len, m);
for (int n = 0; n < len; n++)
{
b[n] = y[n] / dy[n];
for (int n1 = 0; n1 < m; n1++)
{
A[n, n1] = f[n1](x[n]) / dy[n];
} //end for
} //end for
gram_s gr = new gram_s(A);
c = gr.solve(b);
} //end constructor...
static int Main()
{
//generating a random matrix
matrix A = randmatrix(4, 3);
gram_s a1 = new gram_s(A);
matrix Q = a1.Q;
matrix R = a1.R;
WriteLine("Part A");
WriteLine($"i) in-place modified Gram-Schmidt");
WriteLine($"Random generated matrix A:");
for (int i = 0; i < A.size1; i++)
{
Write("\n");
for (int j = 0; j < A.size2; j++)
{
Write($"{A[i,j]} ");
}
}
Write("\n \n");
WriteLine("R-matrix takes the form:");
for (int i = 0; i < R.size1; i++)
{
Write("\n");
for (int n1 = 0; n1 < R.size2; n1++)
{
Write($"{R[i,n1]} ");
}
}
Write("\n \n");
WriteLine($"Test that Q^T*Q =1 :"); matrix qt = Q.T;
matrix Q1 = qt * Q;
for (int i = 0; i < Q1.size1; i++)
{
Write("\n");
for (int n1 = 0; n1 < Q1.size2; n1++)
{
Write($"{Q1[i,n1]} ");
}
}
Write("\n \n");
WriteLine("Test that QR=A");
matrix Q2 = Q * R;
for (int i = 0; i < Q2.size1; i++)
{
Write("\n");
for (int n1 = 0; n1 < Q2.size2; n1++)
{
Write($"{Q2[i,n1]} ");
}
}
Write("\n \n");
//end part i)
//new random matrix:
matrix A1 = randmatrix(4, 4);
//new random vector:
vector b = randvector(4);
//factorize A into QR:
gram_s a2 = new gram_s(A1);
matrix Qn = a2.Q;
matrix Rn = a2.R;
//solve QRx=b
vector x = a2.solve(b);
//test ax=b
vector ax = A1 * x;
WriteLine($"ii) Solve linear equation:");
WriteLine($"New random matrix A:");
WriteLine("Part A");
for (int i = 0; i < A1.size1; i++)
{
Write("\n");
for (int j = 0; j < A1.size2; j++)
{
Write($"{A1[i,j]} ");
}
}
Write("\n \n");
WriteLine($"random vector b:");
for (int i = 0; i < b.size; i++)
{
WriteLine($"{b[i]}");
}
Write("\n");
WriteLine($"A factorize into QR gives Q:");
for (int i = 0; i < Qn.size1; i++)
{
Write("\n");
for (int j = 0; j < Qn.size2; j++)
{
Write($"{Qn[i,j]} ");
}
}
Write("\n \n");
WriteLine($"and R:");
for (int i = 0; i < Rn.size1; i++)
{
Write("\n");
for (int j = 0; j < Rn.size2; j++)
{
Write($"{Rn[i,j]} ");
}
}
Write("\n \n");
WriteLine($"the system QRx=b was solved yeilding x:");
for (int i = 0; i < x.size; i++)
{
WriteLine($"{x[i]}");
}
Write("\n");
WriteLine($"Ax becomes:");
for (int i = 0; i < ax.size; i++)
{
WriteLine($"{ax[i]}");
}
Write("\n");
return(0);
}
