public static vector newton(Func <vector, vector> f, vector x, double epsilon = 1e-3, double dx = 1e-7)
{
vector res = x.copy();
var n = res.size;
var J = new matrix(n, n);
while (true)
{
var fx = f(res);
for (int j = 0; j < n; j++)
{
res[j] += dx;
var df = f(res) - fx;
for (int i = 0; i < n; i++)
{
J[i, j] = df[i] / dx;
}
res[j] -= dx;
}
var J_qr = LinEq.QrGsDecomp(J);
var Dx = LinEq.QrGsSolve(J_qr, -fx);
// Dx.print();
double s = 2;
vector y, fy;
double comp_norm;
while (true)
{
s /= 2;
y = res + Dx * s;
fy = f(y);
comp_norm = fy.norm();
if (comp_norm < (1 - s / 2) * comp_norm | s < 0.02)
{
break;
}
}
res = y;
fx = fy;
comp_norm = Dx.norm();
if (comp_norm < dx | comp_norm < epsilon)
{
break;
}
}
return(res);
}
public void fit(Func <double, double>[] fs, vector x, vector y, vector dy)
{
var n = x.size;
var m = fs.Length;
var A = new matrix(n, m);
var b = new vector(n);
for (int i = 0; i < n; i++)
{
b[i] = y[i] / dy[i];
for (int j = 0; j < m; j++)
{
A[i, j] = fs[j](x[i]) / dy[i];
}
}
var qrData = LinEq.QrGsDecomp(A);
c = LinEq.QrGsSolve(qrData, b);
var inverse_R = LinEq.inverse(LinEq.QrGsDecomp(qrData.R));
S = inverse_R * inverse_R.T;
}
public static void Main()
{
// matrix A = new matrix(6, 4);
// for(int i = 0; i < A.size1; i++)
// {
// for(int j = 0; j < A.size2; j++)
// {
// A[i, j] = fixRand.NextDouble();
// }
// }
// A.print();
// var data = LinEq.QrGsDecomp(A);
// data.Q.print();
// data.R.print();
// var qtq = data.Q.transpose()*data.Q;
// qtq.print();
// var Ares = data.Q*data.R;
// Ares.print();
Console.WriteLine("Testing A)");
Random fixRand = new Random(0);
matrix A = new matrix(5, 5);
vector B = new vector(5);
for (int i = 0; i < A.size1; i++)
{
for (int j = 0; j < A.size2; j++)
{
A[j][i] = fixRand.NextDouble();
}
}
for (int i = 0; i < B.size; i++)
{
B[i] = fixRand.NextDouble();
}
Console.WriteLine("The random Square matrix A");
A.print();
Console.WriteLine("The random Vector B for the Linear system Ax=B");
B.print();
var data = LinEq.QrGsDecomp(A);
Console.WriteLine("The matrix Q");
data.Q.print();
Console.WriteLine("The matrix R");
data.R.print();
var res = LinEq.QrGsSolve(data, B);
Console.WriteLine("Solution to the system QRx=b");
res.print();
var check = A * res;
Console.WriteLine("Ax=b, should be equal to the random vector B");
check.print();
// Random fixRand = new Random(0);
Console.WriteLine("Testing B)");
matrix Aforinverse = new matrix(5, 5);
for (int i = 0; i < Aforinverse.size1; i++)
{
for (int j = 0; j < Aforinverse.size2; j++)
{
Aforinverse[i, j] = fixRand.NextDouble();
}
}
Console.WriteLine("Random square matrix A for inversion");
Aforinverse.print();
var dataB = LinEq.QrGsDecomp(Aforinverse);
var Bforinverse = LinEq.inverse(dataB);
var Cforinverse = Aforinverse * Bforinverse;
Console.WriteLine("AA^-1 = I");
Cforinverse.print();
}
