args = "x,y,z"
# really sloppy handling, use argparse
if len(sys.argv) > 1:
try:
N = int(sys.argv[1])
except:
raise Exception("argument must be an integer N (partition size in RK4)")
else:
N = 4
# just set verbosity based on size of N
v = (N < 5)
x0 = np.array([[1,1,1]]).T
x_sol = cm_rk4(case_one, args, x0, N, verbose=v)
# now just do some data
F, X = parse_symbolic(case_one, args)
# get F value at x*
F1 = F.subs(list(zip(X, x_sol)))
err = F1.norm() # wow, these methods are great
print("||F(x*)|| = ", err)
x_check = nsolve(F, X, (1,1,1))
print("solution according to sympy.solvers.nsolve:")
print(x_check.T)
#!/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)