glpk.glp_add_cols(lp, 2) # two unknowns: x and y glpk.glp_set_col_bnds(lp, 1, glpk.GLP_DB, 0., 1.) # 0 <= x <= 1 glpk.glp_set_col_bnds(lp, 2, glpk.GLP_DB, 0., 1.) # 0 <= y <= 1 glpk.glp_add_rows(lp, 2) # 2 constraints matrix_row_index = glpk.intArray(5) matrix_column_index = glpk.intArray(5) matrix_content = glpk.doubleArray(5) # First constraint: x + y >= 1. matrix_row_index[1] = 1; matrix_column_index[1] = 1; matrix_content[1] = 1.; matrix_row_index[2] = 1; matrix_column_index[2] = 2; matrix_content[2] = 1.; glpk.glp_set_row_bnds(lp, 1, glpk.GLP_LO, 1., 0.) # Second constraint: - x + y >= -0.5. matrix_row_index[3] = 2; matrix_column_index[3] = 1; matrix_content[3] = -1.; matrix_row_index[4] = 2; matrix_column_index[4] = 2; matrix_content[4] = 1.; glpk.glp_set_row_bnds(lp, 2, glpk.GLP_LO, -0.5, 0.) # Load them glpk.glp_load_matrix(lp, 4, matrix_row_index, matrix_column_index, matrix_content) # Cost function: 0.5 x + y glpk.glp_set_obj_coef(lp, 1, 0.5) glpk.glp_set_obj_coef(lp, 2, 1.) # Solve the linear programming problem options = glpk.glp_smcp() glpk.glp_init_smcp(options) options.msg_lev = glpk.GLP_MSG_ERR options.meth = glpk.GLP_DUAL glpk.glp_simplex(lp, options) print "Computed optimum: x = ", glpk.glp_get_col_prim(lp, 1), ", y = ", glpk.glp_get_col_prim(lp, 2) ,", obj = ", glpk.glp_get_obj_val(lp) print "Expected optimum: x = 0.75, y = 0.25, obj = 0.625" glpk.glp_delete_prob(lp)
def get_alpha_LB(self, mu, safeguard=True):
self.load_reduced_data_structures()
lp = glpk.glp_create_prob()
glpk.glp_set_obj_dir(lp, glpk.GLP_MIN)
Qa = self.parametrized_problem.Qa
N = self.N
M_e = self.M_e
if M_e < 0:
M_e = N
if M_e > len(self.C_J):
M_e = len(self.C_J) # = N
M_p = self.M_p
if M_p < 0:
M_p = N
if M_p > len(self.complement_C_J):
M_p = len(self.complement_C_J)
# 1. Linear program unknowns: Qa variables, y_1, ..., y_{Q_a}
glpk.glp_add_cols(lp, Qa)
# 2. Range: constrain the variables to be in the bounding box (note: GLPK indexing starts from 1)
for qa in range(Qa):
if self.B_min[qa] < self.B_max[qa]: # the usual case
glpk.glp_set_col_bnds(lp, qa + 1, glpk.GLP_DB, self.B_min[qa], self.B_max[qa])
elif self.B_min[qa] == self.B_max[qa]: # unlikely, but possible
glpk.glp_set_col_bnds(lp, qa + 1, glpk.GLP_FX, self.B_min[qa], self.B_max[qa])
else: # there is something wrong in the bounding box: set as unconstrained variable
print "Warning: wrong bounding box for affine expansion element #", qa
glpk.glp_set_col_bnds(lp, qa + 1, glpk.GLP_FR, 0., 0.)
# 3. Add two different sets of constraints
glpk.glp_add_rows(lp, M_e + M_p)
array_size = (M_e + M_p)*Qa
matrix_row_index = glpk.intArray(array_size + 1) # + 1 since GLPK indexing starts from 1
matrix_column_index = glpk.intArray(array_size + 1)
matrix_content = glpk.doubleArray(array_size + 1)
glpk_container_size = 0
# 3a. Add constraints: a constraint is added for the closest samples to mu in C_J
closest_C_J_indices = self.closest_parameters(M_e, self.C_J, mu)
for j in range(M_e):
# Overwrite parameter values
omega = self.xi_train[ self.C_J[ closest_C_J_indices[j] ] ]
self.parametrized_problem.setmu(omega)
current_theta_a = self.parametrized_problem.compute_theta_a()
# Assemble the LHS of the constraint
for qa in range(Qa):
matrix_row_index[glpk_container_size + 1] = int(j + 1)
matrix_column_index[glpk_container_size + 1] = int(qa + 1)
matrix_content[glpk_container_size + 1] = current_theta_a[qa]
glpk_container_size += 1
# Assemble the RHS of the constraint
glpk.glp_set_row_bnds(lp, j + 1, glpk.GLP_LO, self.alpha_J[ closest_C_J_indices[j] ], 0.)
closest_C_J_indices = None
# 3b. Add constraints: also constrain the closest point in the complement of C_J,
# with RHS depending on previously computed lower bounds
closest_complement_C_J_indices = self.closest_parameters(M_p, self.complement_C_J, mu)
for j in range(M_p):
nu = self.xi_train[ self.complement_C_J[ closest_complement_C_J_indices[j] ] ]
self.parametrized_problem.setmu(nu)
current_theta_a = self.parametrized_problem.compute_theta_a()
# Assemble first the LHS
for qa in range(Qa):
matrix_row_index[glpk_container_size + 1] = int(M_e + j + 1)
matrix_column_index[glpk_container_size + 1] = int(qa + 1)
matrix_content[glpk_container_size + 1] = current_theta_a[qa]
glpk_container_size += 1
# ... and then the RHS
glpk.glp_set_row_bnds(lp, M_e + j + 1, glpk.GLP_LO, self.alpha_LB_on_xi_train[ self.complement_C_J[ closest_complement_C_J_indices[j] ] ], 0.)
closest_complement_C_J_indices = None
# Load the assembled LHS
glpk.glp_load_matrix(lp, array_size, matrix_row_index, matrix_column_index, matrix_content)
# 4. Add cost function coefficients
self.parametrized_problem.setmu(mu)
current_theta_a = self.parametrized_problem.compute_theta_a()
for qa in range(Qa):
glpk.glp_set_obj_coef(lp, qa + 1, current_theta_a[qa])
# 5. Solve the linear programming problem
options = glpk.glp_smcp()
glpk.glp_init_smcp(options)
options.msg_lev = glpk.GLP_MSG_ERR
options.meth = glpk.GLP_DUAL
glpk.glp_simplex(lp, options)
alpha_LB = glpk.glp_get_obj_val(lp)
glpk.glp_delete_prob(lp)
# 6. If a safeguard is requested (when called in the online stage of the RB method),
# we check the resulting value of alpha_LB. In order to avoid divisions by zero
# or taking the square root of a negative number, we allow an inefficient evaluation.
if safeguard == True:
tol = 1e-10
alpha_UB = self.get_alpha_UB(mu)
if alpha_LB/alpha_UB < tol:
print "SCM warning: alpha_LB is <= 0 at mu = " + str(mu) + ".",
print "Please consider a larger Nmax for SCM. Meanwhile, a truth",
print "eigensolve is performed."
(alpha_LB, discarded1, discarded2) = self.truth_coercivity_constant()
if alpha_LB/alpha_UB > 1 + tol:
print "SCM warning: alpha_LB is > alpha_UB at mu = " + str(mu) + ".",
print "This should never happen!"
return alpha_LB
matrix_content[1] = 1.
matrix_row_index[2] = 1
matrix_column_index[2] = 2
matrix_content[2] = 1.
glpk.glp_set_row_bnds(lp, 1, glpk.GLP_LO, 1., 0.)
# Second constraint: - x + y >= -0.5.
matrix_row_index[3] = 2
matrix_column_index[3] = 1
matrix_content[3] = -1.
matrix_row_index[4] = 2
matrix_column_index[4] = 2
matrix_content[4] = 1.
glpk.glp_set_row_bnds(lp, 2, glpk.GLP_LO, -0.5, 0.)
# Load them
glpk.glp_load_matrix(lp, 4, matrix_row_index, matrix_column_index,
matrix_content)
# Cost function: 0.5 x + y
glpk.glp_set_obj_coef(lp, 1, 0.5)
glpk.glp_set_obj_coef(lp, 2, 1.)
# Solve the linear programming problem
options = glpk.glp_smcp()
glpk.glp_init_smcp(options)
options.msg_lev = glpk.GLP_MSG_ERR
options.meth = glpk.GLP_DUAL
glpk.glp_simplex(lp, options)
print "Computed optimum: x = ", glpk.glp_get_col_prim(
lp, 1), ", y = ", glpk.glp_get_col_prim(
lp, 2), ", obj = ", glpk.glp_get_obj_val(lp)
print "Expected optimum: x = 0.75, y = 0.25, obj = 0.625"
glpk.glp_delete_prob(lp)
def get_alpha_LB(self, mu, safeguard=True):
self.load_red_data_structures()
lp = glpk.glp_create_prob()
glpk.glp_set_obj_dir(lp, glpk.GLP_MIN)
Qa = self.parametrized_problem.Qa
N = self.N
M_e = self.M_e
if M_e < 0:
M_e = N
if M_e > len(self.C_J):
M_e = len(self.C_J) # = N
M_p = self.M_p
if M_p < 0:
M_p = N
if M_p > len(self.complement_C_J):
M_p = len(self.complement_C_J)
# 1. Linear program unknowns: Qa variables, y_1, ..., y_{Q_a}
glpk.glp_add_cols(lp, Qa)
# 2. Range: constrain the variables to be in the bounding box (note: GLPK indexing starts from 1)
for qa in range(Qa):
if self.B_min[qa] < self.B_max[qa]: # the usual case
glpk.glp_set_col_bnds(lp, qa + 1, glpk.GLP_DB, self.B_min[qa], self.B_max[qa])
elif self.B_min[qa] == self.B_max[qa]: # unlikely, but possible
glpk.glp_set_col_bnds(lp, qa + 1, glpk.GLP_FX, self.B_min[qa], self.B_max[qa])
else: # there is something wrong in the bounding box: set as unconstrained variable
print "Warning: wrong bounding box for affine expansion element #", qa
glpk.glp_set_col_bnds(lp, qa + 1, glpk.GLP_FR, 0., 0.)
# 3. Add two different sets of constraints
glpk.glp_add_rows(lp, M_e + M_p)
array_size = (M_e + M_p)*Qa
matrix_row_index = glpk.intArray(array_size + 1) # + 1 since GLPK indexing starts from 1
matrix_column_index = glpk.intArray(array_size + 1)
matrix_content = glpk.doubleArray(array_size + 1)
glpk_container_size = 0
# 3a. Add constraints: a constraint is added for the closest samples to mu in C_J
closest_C_J_indices = self.closest_parameters(M_e, self.C_J, mu)
for j in range(M_e):
# Overwrite parameter values
omega = self.xi_train[ self.C_J[ closest_C_J_indices[j] ] ]
self.parametrized_problem.setmu(omega)
current_theta_a = self.parametrized_problem.compute_theta_a()
# Assemble the LHS of the constraint
for qa in range(Qa):
matrix_row_index[glpk_container_size + 1] = int(j + 1)
matrix_column_index[glpk_container_size + 1] = int(qa + 1)
matrix_content[glpk_container_size + 1] = current_theta_a[qa]
glpk_container_size += 1
# Assemble the RHS of the constraint
glpk.glp_set_row_bnds(lp, j + 1, glpk.GLP_LO, self.alpha_J[ closest_C_J_indices[j] ], 0.)
closest_C_J_indices = None
# 3b. Add constraints: also constrain the closest point in the complement of C_J,
# with RHS depending on previously computed lower bounds
closest_complement_C_J_indices = self.closest_parameters(M_p, self.complement_C_J, mu)
for j in range(M_p):
nu = self.xi_train[ self.complement_C_J[ closest_complement_C_J_indices[j] ] ]
self.parametrized_problem.setmu(nu)
current_theta_a = self.parametrized_problem.compute_theta_a()
# Assemble first the LHS
for qa in range(Qa):
matrix_row_index[glpk_container_size + 1] = int(M_e + j + 1)
matrix_column_index[glpk_container_size + 1] = int(qa + 1)
matrix_content[glpk_container_size + 1] = current_theta_a[qa]
glpk_container_size += 1
# ... and then the RHS
glpk.glp_set_row_bnds(lp, M_e + j + 1, glpk.GLP_LO, self.alpha_LB_on_xi_train[ self.complement_C_J[ closest_complement_C_J_indices[j] ] ], 0.)
closest_complement_C_J_indices = None
# Load the assembled LHS
glpk.glp_load_matrix(lp, array_size, matrix_row_index, matrix_column_index, matrix_content)
# 4. Add cost function coefficients
self.parametrized_problem.setmu(mu)
current_theta_a = self.parametrized_problem.compute_theta_a()
for qa in range(Qa):
glpk.glp_set_obj_coef(lp, qa + 1, current_theta_a[qa])
# 5. Solve the linear programming problem
options = glpk.glp_smcp()
glpk.glp_init_smcp(options)
options.msg_lev = glpk.GLP_MSG_ERR
options.meth = glpk.GLP_DUAL
glpk.glp_simplex(lp, options)
alpha_LB = glpk.glp_get_obj_val(lp)
glpk.glp_delete_prob(lp)
# 6. If a safeguard is requested (when called in the online stage of the RB method),
# we check the resulting value of alpha_LB. In order to avoid divisions by zero
# or taking the square root of a negative number, we allow an inefficient evaluation.
if safeguard == True:
tol = 1e-10
alpha_UB = self.get_alpha_UB(mu)
if alpha_LB/alpha_UB < tol:
print "SCM warning: alpha_LB is <= 0 at mu = " + str(mu) + ".",
print "Please consider a larger Nmax for SCM. Meanwhile, a truth",
print "eigensolve is performed."
(alpha_LB, discarded1, discarded2) = self.truth_coercivity_constant()
if alpha_LB/alpha_UB > 1 + tol:
print "SCM warning: alpha_LB is > alpha_UB at mu = " + str(mu) + ".",
print "This should never happen!"
return alpha_LB