def cm_rk4(F_strings, F_args, x0, N, verbose=True):
#you should really do this in a decorator
if verbose:
fs = sys.stdout # this is default for the print function
else:
fs = open(os.devnull, 'w')
F, X = parse_symbolic(F_strings, F_args)
print("system parsed successfully...", file=fs)
J = F.jacobian(X) # symbolic jacobian matrix
print("jacobian found", end=" ", file=fs)
Jinv = J.inv() # calculate inverse (method can be specified)
print("...and inverted!", end=" ", file=fs)
#Jinv.simplify() # simplify symbolic expression (for logging)
# note that this occurs in place!
#print("...and simplified!", end=" ", file=fs)
print("\n", file=fs)
# get a value for F_0 = F(x0)
F0 = F.subs(list(zip(X, x0)))
print("initial system calculated", file=fs)
# x`(λ) = [J(x(λ)]^(-1) * F0
# this is an nx1 matrix that describes the set of differential equations
# dx_i / dλ = [x`(λ)]_i
xpl = -Jinv.multiply(F0) # matmul syntax is different within sympy
print("ODE system x`(λ) calculated", file=fs)
print("...and simplified", file=fs)
print("running RK4 with N={}".format(N), file=fs)
# pass everything to RK4 (including verbosity setting)
x_sol = rk4(xpl, X, x0, N, verbose=verbose)
# do you need to close /dev/null?
if not verbose:
try:
fs.close()
except:
pass # this is bad code
return x_sol
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)
