public lsfit(vector x, vector y, vector dy, Func <double, double>[] fs)
{
f = fs;
int n = x.size, m = fs.Length;
// Console.WriteLine($"n: {n} m: {m}\n");
var A = new matrix(n, m);
var b = new vector(n);
for (int i = 0; i < n; i++)
{
b[i] = y[i] / dy[i]; // Equation (7) in chapter
for (int k = 0; k < m; k++)
{
A[i, k] = f[k](x[i]) / dy[i]; // Equation (7) in chapter
}
}
var q = new gramschmidt(A); // We use the Gram-Schmidt routine to decompose A
c = q.solve(b); // We solve the system
var ai = q.inverse();
sigma = ai * ai.T; // equation (14) in chapter to determine the covariance matrix
}
static void Main()
{
var rnd = new Random(1);
int n = 4;
var A = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
A[i, j] = 2 * (rnd.NextDouble() - 0.5);
}
}
A.print("Matrix inverse.\nRandom square matrix A:");
var qra = new gramschmidt(A);
var B = qra.inverse();
B.print("\nThe inverse of A, A^-1:");
var Id = new matrix(n, n);
for (int i = 0; i < n; i++)
{
Id[i, i] = 1;
}
var C = A * B;
C.print("\ncheck: A*A^-1:");
if (Id.approx(A * B))
{
Write("\nA*A^-1 = Id, test passed\n");
}
else
{
Write("\nA*A^-1 != Id, test failed\n");
}
var D = B * A;
D.print("\ncheck: A^-1*A=");
if (Id.approx(B * A))
{
Write("\nA^-1*A = I, test passed\n");
}
else
{
Write("\nA^-1*A != I, test failed\n");
}
}
static void Main()
{
var rnd = new Random(1);
int n = 4;
var A = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
A[i, j] = 2 * (rnd.NextDouble() - 0.5);
}
}
A.print("Solution of a linear system Ax=b:\nRandom square matrix A:");
var b = new vector(n);
for (int i = 0; i < n; i++)
{
b[i] = 2 * (rnd.NextDouble() - 0.5);
}
b.print("random right-hand-side vector b:\n");
var qra = new gramschmidt(A);
var x = qra.solve(b);
x.print("solution x to equation Ax=b:\n");
var C = A * x;
C.print("check: A*x=\n");
if (b.approx(A * x))
{
Write("A*x=b, test passed\n");
}
else
{
Write("A*x!=b, test failed\n");
}
}
static void Main()
{
int n = 4, m = 3;
matrix A = new matrix(n, m); /* Construction of a random matrix A */
var rnd = new Random(1);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
A[i, j] = 2 * (rnd.NextDouble() - 0.5);
}
}
A.print($"QR-decomposition:\nrandom {n}x{m} matrix A:");
var qra = new gramschmidt(A);
var Q = qra.Q;
var R = qra.R;
Q.print("matrix Q:");
R.print("matrix R:");
matrix qtq = (Q.T * Q);
qtq.print("Q^T*Q:");
matrix qr = (Q * R);
qr.print("Q*R:");
if (A.approx(Q * R))
{
Write("Q*R=A, test passed\n");
}
else
{
Write("Q*R!=A, test failed\n");
}
}
