Coverage for robust\robustify_large_posynomial.py : 0%

from __future__ import absolute_import 

from __future__ import division 

from builtins import map 

from builtins import zip 

from builtins import range 

from builtins import object 

import numpy as np 

from gpkit import Variable, Monomial, SignomialsEnabled 

from gpkit.nomials import NomialMap 

from .robust_gp_tools import RobustGPTools 

class RobustifyLargePosynomial(object): 

def __init__(self, p, type_of_uncertainty_set, number_of_stds, setting): 

self.p = p 

self.type_of_uncertainty_set = type_of_uncertainty_set 

self.number_of_stds = number_of_stds 

self.setting = setting 

@staticmethod 

def merge_mesh_grid(array, n): 

""" 

A method used in perturbation_function method, allows easy computation of the 

output at the regression points 

:param array: The multidimensional array we need to make simpler (1D) 

:param n: The total number of interesting points 

:return: The simplified array 

""" 

if n == 1: 

return [array] 

else: 

output = [] 

for i in range(len(array)): 

output = output + RobustifyLargePosynomial. \ 

merge_mesh_grid(array[i], n / (len(array) + 0.0)) 

return output 

@staticmethod 

def perturbation_function(perturbation_vector, type_of_uncertainty_set, number_of_regression_points): 

""" 

A method used to do the linear regression 

:param type_of_uncertainty_set: the type of uncertainty set 

:param perturbation_vector: A list representing the perturbation associated 

with each uncertain parameter 

:param number_of_regression_points: The number of regression points 

per dimension 

:return: the regression coefficients and intercept 

""" 

dim = len(perturbation_vector) 

result, input_list = [], [] 

if type_of_uncertainty_set == 'box' or type_of_uncertainty_set == 'one norm' or dim == 1: 

if dim == 1: 

x = [np.linspace(-1, 1, number_of_regression_points)] 

else: 

x = np.meshgrid(*[np.linspace(-1, 1, number_of_regression_points)] * dim) 

for _ in range(number_of_regression_points ** dim): 

input_list.append([]) 

for i in range(dim): 

temp = RobustifyLargePosynomial.merge_mesh_grid(x[i], number_of_regression_points ** dim) 

for j in range(number_of_regression_points ** dim): 

input_list[j].append(temp[j]) 

else: 

theta_mesh_grid = np.meshgrid(*[np.linspace(0, 2*np.pi - 2*np.pi/number_of_regression_points, 

number_of_regression_points)] * (dim - 1)) 

thetas_list = [] 

for _ in range(number_of_regression_points ** (dim - 1)): 

thetas_list.append([]) 

for i in range(dim - 1): 

temp = RobustifyLargePosynomial.merge_mesh_grid(theta_mesh_grid[i], number_of_regression_points ** (dim - 1)) 

for j in range(number_of_regression_points ** (dim - 1)): 

thetas_list[j].append(temp[j]) 

for i in range(number_of_regression_points ** (dim - 1)): 

an_input_list = [] 

for j in range(dim): 

product = 1 

for k in range(j): 

product *= np.cos(thetas_list[i][k]) 

if j != dim - 1: 

product *= np.sin(thetas_list[i][j]) 

an_input_list.append(product) 

input_list.append(an_input_list) 

num_of_inputs = len(input_list) 

for i in range(num_of_inputs): 

output = 1 

for j in range(dim): 

if perturbation_vector[j] != 0: 

output = output * perturbation_vector[j] ** input_list[i][j] 

result.append(output) 

max_index, max_value, min_index, min_value = None, -np.inf, None, np.inf 

for i, element in enumerate(result): 

if element < min_value: 

min_value = element 

min_index = i 

if element >= max_value: 

max_value = element 

max_index = i 

tol = float(0) 

the_index = -1 

while tol <= 1e-4: 

the_index += 1 

tol = abs(input_list[min_index][the_index] - input_list[max_index][the_index]) 

capital_a = [] 

b = [] 

y_m_i = input_list[min_index][the_index] - input_list[max_index][the_index] 

back_count = 0 

for k in range(num_of_inputs): 

if k != max_index and k != min_index: 

capital_a.append([]) 

y_ratio = (input_list[k][the_index] - input_list[max_index][the_index])/y_m_i 

b.append(result[k] + max_value*(y_ratio - 1) - min_value*y_ratio) 

for l in range(dim): 

if l != the_index: 

y_k_l = input_list[k][l] - input_list[max_index][l] 

y_m_l = input_list[min_index][l] - input_list[max_index][l] 

capital_a[k-back_count].append(y_k_l - y_m_l*y_ratio) 

else: 

back_count += 1 

capital_a_trans = list(map(list, list(zip(*capital_a)))) 

capital_b = np.dot(capital_a_trans, capital_a) 

r_h_s = np.dot(capital_a_trans, b) 

try: 

solution = list(np.linalg.solve(capital_b, r_h_s)) 

l1 = 0 

l2 = 0 

the_sum = 0 

while l1 < dim - 1: 

if l2 != the_index: 

y_m_l = input_list[min_index][l2] - input_list[max_index][l2] 

the_sum += solution[l1]*y_m_l 

l1 += 1 

l2 += 1 

a_i = (min_value - max_value - the_sum)/y_m_i 

coeff = solution[0:the_index] + [a_i] + solution[the_index:len(solution)] 

the_sum = 0 

for l in range(dim): 

the_sum += coeff[l]*input_list[max_index][l] 

intercept = max_value - the_sum 

except np.linalg.LinAlgError: 

coeff = [(min_value - max_value)/y_m_i] 

intercept = max_value - coeff[0]*input_list[max_index][the_index] 

return coeff, intercept 

def linearize_perturbations(self, p_uncertain_vars, number_of_regression_points): 

""" 

A method used to linearize uncertain exponential functions 

:param p_uncertain_vars: the uncertain variables in the posynomial 

:param number_of_regression_points: The number of regression points per dimension 

:return: The linear regression of all the exponential functions, and the mean vector 

""" 

center, scale = [], [] 

mean_vector = [] 

coeff, intercept = [], [] 

for i in range(len(p_uncertain_vars)): 

eta_min, eta_max = RobustGPTools.generate_etas(p_uncertain_vars[i]) 

center.append((eta_min + eta_max) / 2.0) 

scale.append(eta_max - center[i]) 

perturbation_matrix = [] 

for i in range(len(self.p.exps)): 

only_uncertain_vars_monomial_exps = RobustGPTools.\ 

only_uncertain_vars_monomial(self.p.exps[i]) 

perturbation_matrix.append([]) 

mon_uncertain_vars = [var for var in only_uncertain_vars_monomial_exps 

if RobustGPTools.is_directly_uncertain(var)] 

mean = 1 

for j, var in enumerate(p_uncertain_vars): 

if var.key in mon_uncertain_vars: 

mean = mean * np.exp(center[j]*only_uncertain_vars_monomial_exps.get(var.key)) 

perturbation_matrix[i].append(np.exp(only_uncertain_vars_monomial_exps.get(var.key) * scale[j])) 

else: 

perturbation_matrix[i].append(0) 

coeff.append([]) 

intercept.append([]) 

coeff[i], intercept[i] = RobustifyLargePosynomial. \ 

perturbation_function(perturbation_matrix[i], self.type_of_uncertainty_set, number_of_regression_points) 

mean_vector.append(mean) 

return coeff, intercept, mean_vector 

def no_coefficient_monomials(self): 

""" 

separates the monomials in a posynomial into a list of monomials 

:return: The list of monomials 

""" 

monmaps = [NomialMap({exp: 1.}) for exp, c in self.hmap.items()] 

for monmap in monmaps: 

monmap.units = self.p.hmap.units 

mons = [Monomial(monmap) for monmap in monmaps] 

return mons 

@staticmethod 

def generate_robust_constraints(gamma, type_of_uncertainty_set, 

monomials, perturbation_matrix, 

intercept, mean_vector, enable_sp, m): 

""" 

:param gamma: controls the size of the uncertainty set 

:param type_of_uncertainty_set: box, elliptical, or one norm 

:param monomials: the list of monomials 

:param perturbation_matrix: the matrix of perturbations 

:param intercept: the list of intercepts 

:param mean_vector: the list of means 

:param enable_sp: whether or not we prefer sp solutions 

:param m: the index 

:return: the robust set of constraints 

""" 

constraints = [] 

s_main = Variable("s_%s" % m) 

if type_of_uncertainty_set == 'box' or type_of_uncertainty_set == 'one norm': 

constraints += [sum([a * b for a, b in 

zip([a * b for a, b in 

zip(mean_vector, intercept)], monomials)]) + gamma * s_main <= 1] 

elif type_of_uncertainty_set == 'elliptical': 

constraints += [sum([a * b for a, b in 

zip([c * d for c, d in 

zip(mean_vector, intercept)], monomials)]) + gamma * s_main ** 0.5 <= 1] 

ss = [] 

for i in range(len(perturbation_matrix[0])): 

positive_pert, negative_pert = [], [] 

positive_monomials, negative_monomials = [], [] 

if type_of_uncertainty_set == 'box' or type_of_uncertainty_set == 'elliptical': 

s = Variable("s^%s_%s" % (i, m)) 

ss.append(s) 

else: 

s = s_main 

for j in range(len(perturbation_matrix)): 

if perturbation_matrix[j][i] > 0: 

positive_pert.append(mean_vector[j] * perturbation_matrix[j][i]) 

positive_monomials.append(monomials[j]) 

elif perturbation_matrix[j][i] < 0: 

negative_pert.append(-mean_vector[j] * perturbation_matrix[j][i]) 

negative_monomials.append(monomials[j]) 

if enable_sp: 

with SignomialsEnabled(): 

if type_of_uncertainty_set == 'box' or type_of_uncertainty_set == 'one norm': 

if negative_pert and not positive_pert: 

constraints += [sum([a * b for a, b in 

zip(negative_pert, negative_monomials)]) <= s] 

elif positive_pert and not negative_pert: 

constraints += [sum([a * b for a, b in 

zip(positive_pert, positive_monomials)]) <= s] 

else: 

constraints += [sum([a * b for a, b in 

zip(positive_pert, positive_monomials)]) - 

sum([a * b for a, b in 

zip(negative_pert, negative_monomials)]) <= s] 

constraints += [sum([a * b for a, b in 

zip(negative_pert, negative_monomials)]) - 

sum([a * b for a, b in 

zip(positive_pert, positive_monomials)]) <= s] 

elif type_of_uncertainty_set == 'elliptical': 

if negative_pert and not positive_pert: 

constraints += [(sum([a * b for a, b in 

zip(negative_pert, negative_monomials)]))**2 <= s] 

elif positive_pert and not negative_pert: 

constraints += [(sum([a * b for a, b in 

zip(positive_pert, positive_monomials)]))**2 <= s] 

else: 

dummiest = Variable() 

constraints += [dummiest**2 <= s] 

constraints += [(sum([a * b for a, b in zip(positive_pert, positive_monomials)]) - 

(sum([a * b for a, b in zip(negative_pert, negative_monomials)]))) <= dummiest] 

constraints += [(sum([a * b for a, b in zip(negative_pert, negative_monomials)]) - 

(sum([a * b for a, b in zip(positive_pert, positive_monomials)]))) <= dummiest] 

else: 

if type_of_uncertainty_set == 'box' or type_of_uncertainty_set == 'one norm': 

if positive_pert: 

constraints += [sum([a * b for a, b in 

zip(positive_pert, positive_monomials)]) <= s] 

if negative_pert: 

constraints += [sum([a * b for a, b in 

zip(negative_pert, negative_monomials)]) <= s] 

elif type_of_uncertainty_set == 'elliptical': 

constraints += [sum([a * b for a, b in 

zip(positive_pert, positive_monomials)]) ** 2 

+ sum([a * b for a, b in 

zip(negative_pert, negative_monomials)]) ** 2 <= s] 

if type_of_uncertainty_set == 'box' or type_of_uncertainty_set == 'elliptical': 

constraints.append(sum(ss) <= s_main) 

return constraints 

def robustify_large_posynomial(self, type_of_uncertainty_set, m, 

setting): 

""" 

generate a safe approximation for large posynomials with uncertain coefficients 

:param type_of_uncertainty_set: 'box', elliptical, or 'one norm' 

:param m: Index 

:param setting: robustness setting 

:return: set of robust constraints 

""" 

p_direct_uncertain_vars = [var for var in self.p.varkeys if RobustGPTools.is_directly_uncertain(var)] 

p_indirect_uncertain_vars = [var for var in self.p.varkeys if RobustGPTools.is_indirectly_uncertain(var)] 

new_direct_uncertain_vars = [] 

for var in p_indirect_uncertain_vars: 

new_direct_uncertain_vars += list(RobustGPTools.\ 

replace_indirect_uncertain_variable_by_equivalent(var.key.rel, 1).keys()) 

new_direct_uncertain_vars = [var for var in new_direct_uncertain_vars 

if RobustGPTools.is_directly_uncertain(var)] 

p_uncertain_vars = list(set(p_direct_uncertain_vars) | set(new_direct_uncertain_vars)) 

if (not p_uncertain_vars and not p_indirect_uncertain_vars) or setting.get('gamma') == 0: 

return [self.p <= 1] 

perturbation_matrix, intercept, mean_vector = \ 

self.linearize_perturbations(p_uncertain_vars, setting.get('numberOfRegressionPoints')) 

monomials = self.no_coefficient_monomials() 

constraints = RobustifyLargePosynomial. \ 

generate_robust_constraints(setting.get('gamma'), type_of_uncertainty_set, monomials, 

perturbation_matrix, intercept, 

mean_vector, setting.get('enableSP'), m) 

return constraints 

if __name__ == '__main__': 

pass