static void probC()
{
Write("Problem C:\n");
var rand = new System.Random();
int n = 5 + rand.Next(3);
matrix A = makeRandomMatrix(n, n);
A.print("Make a random square matrix of random size: A = ");
qr_givens decomp_givens = new qr_givens(A);
qr_gs decomp_gs = new qr_gs(A);
Write("\nDo the Givens decomposition and store the restult in the matrix G, which cotains the elements of the component R in the upper triangular part, and the angles for the Givens rotations in the relevant sub-diagonal entries. Compare with the R matrix found from the Gramm-Schmitt method:");
decomp_givens.G.print("Givens G: ");
decomp_gs.R.print("Gram-Schmitt R: ");
Write("The upper triangular parts are the same.\n");
vector b = makeRandomVector(n);
b.print("\nMake a random vector b with the same size as A: b = ");
Write("\nCompare using the Givens rotations to apply Q^(T) to b, and doing the explicit matrix multiplication with the Q matrix found by the Gramm-Schmitt method:\n");
decomp_givens.applyQT(b).print("Givens: Q^(T)*b = ");
(decomp_gs.Q.transpose() * b).print("GS: Q^(T)*b = ");
vector x = decomp_givens.solve(b);
x.print("\nSolution to A*x=b using Givens: ");
(A * x - b).print("\nCheck solution satisfies A*x = b: A*x-b = ");
Write("\nFind the inverse of A, and check that A^(-1)*A is the identity matrix:\n");
decomp_givens.inverse().print("A^(-1)");
(decomp_givens.inverse() * A).print("A^(-1)*A = ");
}
static void probA2()
{
Write("\nProblem A2:\n");
// Need to make the tests for A2
var rand = new System.Random();
// Remember, square matrix:
Write("\nMake a random square matrix, A, with random dimmensions, and a random vector, b, of the same dimmension:\n");
int n = 2 + rand.Next(10);
matrix A = makeRandomMatrix(n, n);
vector b = makeRandomVector(n);
A.print("A = ");
b.print("b = ");
qr_gs decomposer = new qr_gs(A);
Write("\nSolve the system A*x = b for the vector x:\n");
//decomposer.Q.print("Decomposition Q: ");
//decomposer.R.print("Decomposition R: ");
//(decomposer.Q.transpose()*b).print("Q^(T)*b = ");
vector x = decomposer.solve(b);
x.print("Solution: x = ");
Write("\nCheck that the vector x satisfies A*x=b:\n");
(A * x - b).print("A*x-b = ");
}
static void probA1()
{
Write("Problem A1:\n");
var rand = new System.Random();
int m = 2 + rand.Next(6);
int n = m + rand.Next(6);
Write("First I create a random tall matrix with random dimmensions\n");
matrix A = makeRandomMatrix(n, m);
A.print("Random matrix A:");
qr_gs decomposer = new qr_gs(A);
Write("\nThen I decompose it into Q and R using the Gramm Schmitt method trough my qr_gs class:\n");
matrix Q = decomposer.Q;
matrix R = decomposer.R;
Q.print("Decomposition Q = ");
R.print("Decomposition R = ");
Write("\nCheck that Q^(T)Q is equal to the identity matrix:\n");
(Q.transpose() * Q).print("Q^(T)Q = ");
Write("\nCheck that Q*R = A, or equivalently that Q*R-A is a matrix of all zeros:\n");
(Q * R - A).print("Q*R-A");
}
public static matrix calculateSigma(data dat, Func <double, double>[] fs)
{
matrix A = calculateA(dat, fs);
qr_gs solver = new qr_gs(A.transpose() * A);
matrix sigma = solver.inverse();
return(sigma);
}
public static vector calculateC(data dat, Func <double, double>[] fs)
{
matrix A = calculateA(dat, fs);
vector b = calculateb(dat);
qr_gs solver = new qr_gs(A);
vector c = solver.solve(b);
return(c);
}
static void probB()
{
Write("\nProblem B:\n");
var rand = new System.Random();
int n = 3 + rand.Next(6);
matrix A = makeRandomMatrix(n, n);
qr_gs decomposer = new qr_gs(A);
matrix inverse = decomposer.inverse();
Write("\nMake a random square matrix A, with a random size:\n");
A.print("Random Matrix A: ");
Write("\nCalculate the inverse of A:\n");
inverse.print("Inverse of A: ");
Write("\nCheck that A*A^(-1) is equal to the identity matrix:\n");
(A * inverse).print("A*A^(-1): ");
}