import sys
sys.path.append('../')
from numethods import *


def demo_linear_solvers():
    A = Matrix([[4, -1, 0], [-1, 4, -1], [0, -1, 3]])
    b = Vector([15, 10, 10])

    print("LU:", LUDecomposition(A).solve(b))
    print("Gauss-Jordan:", GaussJordan(A).solve(b))
    print("Cholesky:", Cholesky(A).solve(b))
    print("Jacobi:", Jacobi(A, b, tol=1e-12).solve())
    print("Gauss-Seidel:", GaussSeidel(A, b, tol=1e-12).solve())

def demo_qr():
    A = Matrix([[2, -1], [1, 2], [1, 1]])

    b = Vector([1, 2, 3])

    # Factorization
    qr = QRHouseholder(A)
    Q, R = qr.Q, qr.R
    print("Q =", Q)
    print("R =", R)

    qrm = QRModifiedGramSchmidt(A)
    Qm, Rm = qrm.Q, qrm.R
    print("Qm =", Qm)
    print("Rm =", Rm)
    print("Q^T Q =", Q.T @ Q)
    print("Qm^T Qm =", Qm.T @ Qm)
    print("A=Qm Rm =", Qm @ Rm)
    print("A=Q R =", Q @ R)

    # Solve Ax = b (least squares, since A is tall)
    x_ls = LeastSquaresSolver(A, b).solve()
    print("Least squares solution:", x_ls)



def demo_roots():
    f = lambda x: x**2 - 2
    df = lambda x: 2 * x

    # Newton
    steps = NewtonRoot(f, df, x0=1.0).trace()
    print("Newton Method Trace (x^2 - 2):")
    print_trace(steps)

    # Secant
    steps = Secant(f, 0, 2).trace()
    print("\nSecant Method Trace (x^2 - 2):")
    print_trace(steps)

    # Bisection
    steps = Bisection(f, 0, 2).trace()
    print("\nBisection Method Trace (x^2 - 2):")
    print_trace(steps)

    # Fixed-point: solve
    g = lambda x: 0.5 * (x + 2 / x)
    steps = FixedPoint(g, 1.0).trace()
    print("\nFixed-Point Iteration Trace (x^2 - 2):")
    print_trace(steps)


def demo_interpolation():
    x = [0, 1, 2, 3]
    y = [1, 2, 0, 5]
    newt = NewtonInterpolation(x, y)
    lagr = LagrangeInterpolation(x, y)
    t = 1.5
    print("Newton interpolation at", t, "=", newt.evaluate(t))
    print("Lagrange interpolation at", t, "=", lagr.evaluate(t))

def demo_differentiation():
    f = lambda x: x**3  # f'(x) = 3x^2, f''(x) = 6x
    x0 = 2.0

    print("Forward  :", ForwardDiff(f, x0))
    print("Backward :", BackwardDiff(f, x0))
    print("Central  :", CentralDiff(f, x0))
    print("4th order:", CentralDiff4th(f, x0))
    print("Richardson:", RichardsonExtrap(f, x0))
    print("Second derivative:", SecondDerivative(f, x0))



if __name__ == "__main__":
    demo_linear_solvers()
    demo_roots()
    demo_interpolation()
    demo_qr()
    demo_differentiation()