public static int newton
(Func <vector, vector> f, ref vector x, double eps = 1e-3, double dx = 1e-7)
{
vector fx = f(x), z, fz;
int nsteps = 0;
while (++nsteps < 999)
{
matrix J = jacobian(f, x, fx);
qrdecomposition qrJ = new qrdecomposition(J);
vector Dx = qrJ.solve(-fx);
double s = 1;
do // backtracking linesearch
{
z = x + Dx * s;
fz = f(z);
if (fz.norm() < (1 - s / 2) * fx.norm())
{
break;
}
if (s < 1.0 / 32)
{
break;
}
}while((s /= 2) > 1.0 / 64);
x = z;
fx = fz;
if (fx.norm() < eps)
{
break;
}
}
return(nsteps);
}//broyden
static void Main()
{
int n = 7, m = n;
var A = new matrix(n, m);
var rnd = new System.Random();
for (int i = 0; i < A.size1; i++)
{
for (int j = 0; j < A.size2; j++)
{
A[i, j] = 2 * (rnd.NextDouble() - 1);
}
}
A.print("random matrix A:");
var b = new vector(m);
for (int i = 0; i < b.size; i++)
{
b[i] = rnd.NextDouble();
}
b.print("random vector b:\n");
var qra = new qrdecomposition(A);
var x = qra.solve(b);
x.print("solution x to system A*x=b:\n");
var Ax = A * x;
Ax.print("check: A*x (should be equal b):\n");
if (vector.approx(Ax, b))
{
WriteLine("test passed");
}
else
{
WriteLine("test failed");
}
var B = qra.inverse();
var C = (B * A);
C.print("A^-1*A=");
var D = (A * B);
D.print("A*A^-1=");
}