public static int Main()
{
// int n=5;
int m = 4;
var rand = new Random(1);
// Assignment B
matrix B = new matrix(m, m);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < m; j++)
{
B[i, j] = 10 * (rand.NextDouble());
}
}
WriteLine("Assignment B: ");
B.print($"Square matrix A with size {m}x{m}, to do assigment B:");
var qr_B = new qrdecompositionGS(B);
var B_inv = qr_B.inverse();
B_inv.print("The invers matrix of A, B=:");
var bbinv = B * B_inv;
bbinv.print("A*B=I");
return(0);
}
public void lsfit(Func <double, double>[] fs, vector x, vector y, vector dy)
{
int n = x.size, m = fs.Length;
matrix A = new matrix(n, m);
vector b = new vector(n);
for (int i = 0; i < n; i++)
{
b[i] = y[i] / dy[i];
for (int k = 0; k < m; k++)
{
A[i, k] = fs[k](x[i]) / dy[i];
}
}
var qr_A = new qrdecompositionGS(A);
var c = qr_A.backsubstitution(qr_A.R, qr_A.Q.transpose() * b);
setC(c);
var R_inv = qr_A.inverse(qr_A.R);
// var R_inv = qr_A.backsubstitution(qr_A.R*(qr_A.Q.transpose()*qr_A.Q));
var S = R_inv * R_inv.transpose();
setS(S);
f = fs;
}
public static vector newton
(
Func <vector, vector> f, //takes the input vector x and retrun f(x)
vector xstart, //Starting point
double eps = 1e-3, //The accuracy goal, ||f(x)||< epsilon
double dx = 1e-6 //finite difference
)
{
vector x = xstart.copy();
int n = xstart.size;
vector fx = f(x);
vector y;
vector fy;
do
{
matrix J = new matrix(n, n);
for (int j = 0; j < n; j++)
{
x[j] += dx;
vector df = f(x) - fx;
for (int i = 0; i < n; i++)
{
J[i, j] = df[i] / dx;
}
x[j] -= dx;
}
var JQR = new qrdecompositionGS(J);
matrix B = JQR.inverse();
vector Dx = -B * fx;
double s = 1;
do
{
y = x + Dx * s;
fy = f(y);
if (fy.norm() < (1 - s / 2) * fx.norm())
{
break;
}
if (s < 1.0 / 32)
{
break;
}
s /= 2;
} while (true);
x = y;
fx = fy;
if (fx.norm() < eps)
{
break;
}
} while (true);
return(x);
}
// Assignment B
public matrix inverse()
{
int n = Q.size1, m = Q.size2;
matrix A_inv = new matrix(n, m);
vector e = new vector(n);
var qr_B = new qrdecompositionGS(Q * R);
for (int i = 0; i < n; i++)
{
e[i] = 1;
A_inv[i] = qr_B.solve(e);
e[i] = 0;
}
return(A_inv);
}
public static int Main()
{
int n = 5;
int m = 4;
matrix A = new matrix(n, m);
var rand = new Random(1);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
A[i, j] = 10 * (rand.NextDouble());
}
}
// A.1
WriteLine("Assignment A.1:");
A.print($"Matrix A {n}x{m}:");
var qr_A = new qrdecompositionGS(A);
var Q = qr_A.Q;
var R = qr_A.R;
R.print($"The upper triangular matrix R:");
var qq = Q.transpose() * Q;
qq.print($"Q^T Q =1: ");
var qr = Q * R;
qr.print($"Q*R=A: ");
if (A.approx(Q * R))
{
Write("Q*R=A, test passed\n");
}
else
{
Write("Q*R!=A, test failed\n");
}
WriteLine("");
// A.2
WriteLine("Assignment A.2:");
matrix A2 = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
A2[i, j] = 10 * (rand.NextDouble());
}
}
A2.print($"Matrix A {n}x{n}:");
var qr_A2 = new qrdecompositionGS(A2);
vector b = new vector(n);
for (int i = 0; i < n; i++)
{
b[i] = 10 * (rand.NextDouble());
}
b.print($"Vector b with size {n}: ");
var qrxb = qr_A2.solve(qr_A2.Q, b);
qrxb.print($"solve x for QRx=b:\nx = ");
var ax = A2 * qrxb;
ax.print("Ax = ");
WriteLine("which is equal to b.\n");
return(0);
}
