def demo_conjugate_gradient_search():
def F(x):
u = x[0]
v = x[1]
return 10 * u**2 - 16 * u * v + 8 * v**2 + 8 * u - 16 * v + 16
def J(x):
u = x[0]
v = x[1]
return [20 * u - 16 * v + 8, -16 * u + 16 * v - 16]
def H(x):
u = x[0]
v = x[1]
return [[20, -16], [-16, 16]]
A = np.matrix([[20, -16], [-16, 16]])
b = np.matrix([[-8], [16]])
#x0 = [[2.5], [2.5]]
x0 = [2.5, 2.5]
min = conjugate_gradient_search(F, J, x0)
print('The minimum is: (%.2f, %.2f, %.2f)' %
(min[0], min[1], F([min[0], min[1]])))
plot3d_with_mins(F, [0, 5], [0, 5], mins=[min])
def demo_mv_newton():
def F(x, y):
return x**4 + y**4 + 2 * x**2 * y**2 + 6 * x * y - 4 * x - 4 * y + 1
# Jacobian
def J(x, y):
return [
4 * x**3 + 4 * x * y**2 + 6 * y - 4,
4 * y**3 + 4 * x**2 * y + 6 * x - 4
]
# Hessian
def H(x, y):
return [[12 * x**2 + 4 * y**2, 8 * x * y + 6],
[8 * x * y + 6, 12 * y**2 + 4 * x**2]]
print('Plotting both minimums...')
starting_guesses = [[-1, 1], [1, -1]]
mins = multivariate_newtons_multi_guess(J, H, starting_guesses)
plot3d_with_mins(F, mins=mins)
print('Plotting only one minimum...')
starting_guess = [-1, 1]
min = multivariate_newtons(J, H, starting_guess)
plot3d_with_mins(F, mins=[min])
def main():
'''
x, y = opt.multivariate_newtons(J, H, [-1.9, 2], 0.5e-15)
print('(%.20f, %.20f)' % (x, y))
opt.plot3d_with_mins(F, [-2, 2], [-1, 3], [[-1.9, 2], [x, y]])
x, y = opt.weakest_line(F, J, [-1.9, 2], tolerance=0.5e-15)
print('(%.20f, %.20f)' % (x, y))
opt.plot3d_with_mins(F, [-2, 2], [-1, 3], [[-1.9, 2], [x, y]])
x, y = opt.steepest_descent_gss(F, J, [-1.9, 2], tolerance=0.5e-15)
print('(%.20f, %.20f)' % (x, y))
opt.plot3d_with_mins(F, [-2, 2], [-1, 3], [[-1.9, 2], [x, y]])
'''
# v = opt.nelder_mead(F, [-1.9, 2], 3, xtol=0.5e-10, ftol=0.5e-10)
# print(v)
# x = v[0]
# y = v[1]
# print('(%.20f, %.20f)' % (x, y))
# opt.plot3d_with_mins(F, [-2, 2], [-1, 3], [[-1.9, 2], [x, y]])
v = opt.conjugate_gradient_search(F, J, [-1.9, 2])
x = v[0]
y = v[1]
print('(%.20f, %.20f)' % (x, y))
opt.plot3d_with_mins(F, [-2, 2], [-1, 3], [[-1.9, 2], [x, y]])
def demo_weakest_line():
def F(x, y):
return x**4 + y**4 + 2 * x**2 * y**2 + 6 * x * y - 4 * x - 4 * y + 1
# Jacobian
def J(x, y):
return [
4 * x**3 + 4 * x * y**2 + 6 * y - 4,
4 * y**3 + 4 * x**2 * y + 6 * x - 4
]
x0 = [-1, 1]
min = weakest_line(F, J, x0)
plot3d_with_mins(F, mins=[min])
def demo_weakest_line_gss():
def F(x, y):
return x**4 + y**4 + 2 * x**2 * y**2 + 6 * x * y - 4 * x - 4 * y + 1
# Jacobian
def J(x, y):
return [
4 * x**3 + 4 * x * y**2 + 6 * y - 4,
4 * y**3 + 4 * x**2 * y + 6 * x - 4
]
def H(x, y):
return [[12 * x**2 + 4 * y**2, 8 * x * y + 6],
[8 * x * y + 6, 12 * y**2 + 4 * x**2]]
x0 = [-1, 1]
min = []
min.append(steepest_descent_gss(F, J, x0))
#min.append(weakest_line(F, J, x0))
#min.append(multivariate_newtons(J,H,x0))
plot3d_with_mins(F, mins=min)
print(min)