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I am searching for the global minimum of a certain function and trying to use its gradient (here same as Jacobin) to guide the step counter. However, my x is fix and so is my gradient. I am also trying to retrieve the fastest way possible the first x for which f(x)<1, therefore I am using a constraint.

• How can I update the x input and the Jacobin ?


• My f(x)<1 is not being very effective, so is there any alternative to achieve my requirement?

This is my code (more or less):

class MyBounds(object):
 def __init__(self, xmax=[2*np.pi, 2*np.pi, 2*np.pi, 2*np.pi, 1.2, 1.2, 1.2, 1.2], xmin=[0, 0, 0, 0, 0, 0, 0, 0] ):
 self.xmax = np.array(xmax)
 self.xmin = np.array(xmin)

 def __call__(self, **kwargs):
 x = kwargs["x_new"]
 tmax = bool(np.all(x <= self.xmax))
 tmin = bool(np.all(x >= self.xmin))
 return tmax and tmin

class MyTakeStep(object):
 def __init__(self, stepsize=1):
 self.stepsize = stepsize

 def compute_step(self, jacobi_matrix, x, i):
 if jacobi_matrix[i] < 0: r = np.random.uniform(0, 2*np.pi-x[i])
 elif jacobi_matrix[i] > 0: r = np.random.uniform(0-x[i], 0)
 else : r = 0
 return r

 def __call__(self, x):
 print("ENTERING fROM CALL")
 print("THIS IS X: ", x)
 jacobi_matrix = jacobian(x)
 print("x : ", x)
 print("jacobi: ", jacobi_matrix)
 x[0] += self.compute_step(jacobi_matrix, x, 0)
 x[1] += self.compute_step(jacobi_matrix, x, 1)
 x[2] += self.compute_step(jacobi_matrix, x, 2)
 x[3] += self.compute_step(jacobi_matrix, x, 3)
 x[4] += self.compute_step(jacobi_matrix, x, 4)
 x[5] += self.compute_step(jacobi_matrix, x, 5)
 x[6] += self.compute_step(jacobi_matrix, x, 6)
 x[7] += self.compute_step(jacobi_matrix, x, 7)
 print("newx : ", x)
 return x

def f(x):
 # objective function componenets
 result = g1
 result += g2
 result += g3
 return result

def jacobian(x):
 print("input_list in Jacobi: ", x)

 # define full derivatives
 dG_dphi = dg1_dphi + dg2_dphi + dg3_dphi
 dG_dr = dg1_dr + dg2_dr + dg3_dr
 gradient = np.hstack((dG_dphi, dG_dr))

 print("G: ", gradient.shape, gradient, " n")
 return gradient

def callback(x, f, accept):
 print("x: %65s | f: %5s | accept: %5s" % (str([round(e,3) for e in x]), str(round(f, 3)), accept))

def hopping_solver(min_f, min_x, input_excitation):
 # define bounds
 mybounds = MyBounds()
 mytakestep = MyTakeStep()
 comb = [deg2rad(phi) for phi in input_excitation[:4]] + input_excitation[4:]
 print("comb: ", comb)
 min_f = 10
 tol = 0
 cons = 'type':'ineq','fun': lambda x: 1-f(x)
 k = "method":'Nelder-Mead', 'constraints': cons, 'jac': jacobian, 'tol': tol
 optimal_c = optimize.basinhopping(f,
 x0 = comb,
 niter = 1000000,
 T = 8,
 stepsize = 1,
 minimizer_kwargs = k,
 take_step = mytakestep,
 accept_test = mybounds,
 callback = callback,
 interval = 100000,
 disp = True,
 niter_success = None)
 print(optimal_c)
 min_x, min_f = optimal_c['x'], optimal_c['fun']
 comb = min_x
 sol = np.array(list([np.rad2deg(phi) for phi in list(optimal_c['x'][:4])]) + list(optimal_c['x'][4:]))
 min_x = sol
 return min_x, min_f

Any help is much appreciated, thank you in advance.