from newtons_for_systems import solve_nonlinear_system
args = "a,b"
table = [(75, 1.),
(80, .99),
(85, .833),
(90, .612),
(95, .412)]
fi_spec = "{} - b*({})^a"
case_two = [fi_spec.format(*pair) for pair in table]
# make g(a,b) term
squared = "+".join(("({})^2".format(fi) for fi in case_two))
# solve_nonlinear_system() expects a list :/
squared_case_two = [squared,]
# make an initial guess a, b = 1, 1 idk
x0 = np.array([[1,1]]).T
print("x0 == ", x0.T, "\n\n\n")
x_sol = solve_nonlinear_system(squared_case_two, args, x0, M=1000,
x_convergence=True, ε=10e-3)
#x_sol = solve_nonlinear_system(case_two, args, x0, M=1000, ε=10e-9, x_convergence=True)
#!/usr/bin/env python3
import numpy as np
from newtons_for_systems import solve_nonlinear_system
from continuation import cm_rk4
system = ["4*x1^2 - 20*x1 + (1/4)*x2^2 + 8",
"(1/2)*x1*x2^2 + 2*x1 - 5*x2 + 8"]
args = "x1, x2"
x0 = np.array([[0,0]]).T
print("newton's method (one iteration)")
x_a = solve_nonlinear_system(system, args, x0, M=1)
print("(newton's method):", x_a.T)
print("*"*40)
print("continuation method (one iteration)")
x_c = cm_rk4(system, args, x0, N=1, verbose=False)
print("x^(1) = ", x_c.T)
