From 019a1b5a667b1455aeb2f7fcc8f94fb0aac16495 Mon Sep 17 00:00:00 2001 From: KeShih Date: Sat, 6 Jul 2024 22:00:16 +0800 Subject: [PATCH 1/2] Add pulp_based_impl.py and pulp_impl_test.py --- dingo/pulp_based_impl.py | 449 +++++++++ poetry.lock | 1896 ++++++++++++++++++++++---------------- pyproject.toml | 2 + tests/pulp_impl_test.py | 80 ++ 4 files changed, 1647 insertions(+), 780 deletions(-) create mode 100644 dingo/pulp_based_impl.py create mode 100644 tests/pulp_impl_test.py diff --git a/dingo/pulp_based_impl.py b/dingo/pulp_based_impl.py new file mode 100644 index 00000000..60d54c64 --- /dev/null +++ b/dingo/pulp_based_impl.py @@ -0,0 +1,449 @@ +# dingo : a python library for metabolic networks sampling and analysis +# dingo is part of GeomScale project + +# Copyright (c) 2024 Ke Shi + +# Licensed under GNU LGPL.3, see LICENCE file + +import pulp as pl +import numpy as np +import math +import sys + +solver_name = "HiGHS" + +def dot(c, x): + """A function to get the dot product of variables vector x and coefficients vector c + faster than pl.lpDot and pl.lpSum + """ + return pl.LpAffineExpression( + (x[j], c[j]) for j in range(len(c)) if abs(c[j]) > 1e-10 + ) + + +def fba(lb, ub, S, c): + """A Python function to perform fba using PuLP LP modeler + Returns an optimal solution and its value for the following linear program: + max c*v, subject to, + Sv = 0, lb <= v <= ub + + Keyword arguments: + lb -- lower bounds for the fluxes, i.e., a n-dimensional vector + ub -- upper bounds for the fluxes, i.e., a n-dimensional vector + S -- the mxn stoichiometric matrix, s.t. Sv = 0 + c -- the linear objective function, i.e., a n-dimensional vector + """ + + if lb.size != S.shape[1] or ub.size != S.shape[1]: + raise Exception( + "The number of reactions must be equal to the number of given flux bounds." + ) + if c.size != S.shape[1]: + raise Exception( + "The length of the lineart objective function must be equal to the number of reactions." + ) + + m = S.shape[0] + n = S.shape[1] + optimum_value = 0 + optimum_sol = np.zeros(n) + + try: + # Create a model + model = pl.LpProblem("FBA", pl.LpMaximize) + + # Create variables and set lb <= v <= ub + v = [pl.LpVariable(f"v{i}", lowBound=lb[i], upBound=ub[i]) for i in range(n)] + + # Add the constraints Sv = 0 + for i in range(m): + model += dot(S[i], v) == 0 + + # Set the objective function + model += dot(c, v) + + # Optimize model + solver = pl.getSolver(solver_name, msg=0) + model.solve(solver) + + # If optimized + status = model.status + if status == pl.LpStatusOptimal: + optimum_value = pl.value(model.objective) + optimum_sol = np.array([v[i].value() for i in range(n)]) + + return optimum_sol, optimum_value + + except pl.PulpSolverError as e: + print(f"Solver Error: {e}") + except Exception as e: + print(f"An error occurred: {e}") + + +def fva(lb, ub, S, c, opt_percentage=100): + """A Python function to perform fva using PuLP LP modeler + Returns the value of the optimal solution for all the following linear programs: + min/max v_i, for all coordinates i=1,...,n, subject to, + Sv = 0, lb <= v <= ub + + Keyword arguments: + lb -- lower bounds for the fluxes, i.e., a n-dimensional vector + ub -- upper bounds for the fluxes, i.e., a n-dimensional vector + S -- the mxn stoichiometric matrix, s.t. Sv = 0 + c -- the objective function to maximize + opt_percentage -- consider solutions that give you at least a certain + percentage of the optimal solution (default is to consider + optimal solutions only) + """ + + if lb.size != S.shape[1] or ub.size != S.shape[1]: + raise Exception( + "The number of reactions must be equal to the number of given flux bounds." + ) + + # declare the tolerance that gurobi and highs works properly (we found it experimentally) + tol = 1e-06 + + m = S.shape[0] + n = S.shape[1] + + max_biomass_flux_vector, max_biomass_objective = fba(lb, ub, S, c) + + min_fluxes = [] + max_fluxes = [] + + adjusted_opt_threshold = ( + (opt_percentage / 100) * tol * math.floor(max_biomass_objective / tol) + ) + + try: + # Create a model + model = pl.LpProblem("FVA", pl.LpMinimize) + + # Create variables and set lb <= v <= ub + v = [pl.LpVariable(f"v{i}", lowBound=lb[i], upBound=ub[i]) for i in range(n)] + + # Add the constraints Sv = 0 + for i in range(m): + model += dot(S[i], v) == 0 + + # add an additional constraint to impose solutions with at least `opt_percentage` of the optimal solution + model += dot(c, v) >= adjusted_opt_threshold + + for i in range(n): + # Set the objective function + model.objective = v[i] + + # Optimize model + solver = pl.getSolver(solver_name, msg=0) + model.solve(solver) + + # If optimized + if model.status == pl.LpStatusOptimal: + # Get the min objective value + min_objective = pl.value(model.objective) + min_fluxes.append(min_objective) + else: + min_fluxes.append(lb[i]) + + # Likewise, for the maximum + model.objective = -v[i] + + # Optimize model + solver = pl.getSolver(solver_name, msg=0) + model.solve(solver) + + # Again if optimized + if model.status == pl.LpStatusOptimal: + # Get the max objective value + max_objective = -pl.value(model.objective) + max_fluxes.append(max_objective) + else: + max_fluxes.append(ub[i]) + + # Make lists of fluxes numpy arrays + min_fluxes = np.asarray(min_fluxes) + max_fluxes = np.asarray(max_fluxes) + + return ( + min_fluxes, + max_fluxes, + max_biomass_flux_vector, + max_biomass_objective, + ) + + except pl.PulpSolverError as e: + print(f"Solver Error: {e}") + except Exception as e: + print(f"An error occurred: {e}") + + +def inner_ball(A, b): + """A Python function to compute the maximum inscribed ball in the given polytope using PuLP LP modeler + Returns the optimal solution for the following linear program: + max r, subject to, + a_ix + r||a_i|| <= b, i=1,...,n + + Keyword arguments: + A -- an mxn matrix that contains the normal vectors of the facets of the polytope row-wise + b -- a m-dimensional vector + """ + + extra_column = [] + + m = A.shape[0] + n = A.shape[1] + + for i in range(A.shape[0]): + entry = np.linalg.norm(A[i]) + extra_column.append(entry) + + column = np.asarray(extra_column) + A_expand = np.c_[A, column] + + model = pl.LpProblem("Inner_Ball", pl.LpMaximize) + + # Create variables where x[n] is the radius + x = [pl.LpVariable(f"x{i}") for i in range(n + 1)] + + # Add the constraints a_ix + r||a_i|| <= b + for i in range(m): + model += dot(A_expand[i], x) <= b[i] + + # Set the objective function + model += x[n] + + # Optimize model + solver = pl.getSolver(solver_name, msg=0) + model.solve(solver) + + # Get the center point and the radius of max ball from the solution of LP + point = [x[i].value() for i in range(n)] + # its last element is the radius + r = x[n].value() + + # And check whether the computed radius is negative + if r < 0: + print( + "The radius calculated has negative value. The polytope is infeasible or something went wrong with the solver" + ) + else: + return point, r + + +def set_model(x, lb, ub, Aeq, beq, A, b): + """ + A helper function of remove_redundant_facets function + Create a PuLP model with given PuLP variables, bounds, equality constraints, and inequality constraints + but without an objective function. + """ + + model = pl.LpProblem() + + # Set the bounds for the variables + for i in range(len(x)): + x[i].lowBound = lb[i] + x[i].upBound = ub[i] + + # Add the equality constraints + for i in range(Aeq.shape[0]): + model += dot(Aeq[i], x) == beq[i] + + # Add the inequality constraints + for i in range(A.shape[0]): + model += dot(A[i], x) <= b[i] + + return model + + +def remove_redundant_facets(lb, ub, S, c, opt_percentage=100): + """A function to find and remove the redundant facets and to find + the facets with very small offset and to set them as equalities + + Keyword arguments: + lb -- lower bounds for the fluxes, i.e., a n-dimensional vector + ub -- upper bounds for the fluxes, i.e., a n-dimensional vector + S -- the mxn stoichiometric matrix, s.t. Sv = 0 + c -- the objective function to maximize + opt_percentage -- consider solutions that give you at least a certain + percentage of the optimal solution (default is to consider + optimal solutions only) + """ + + if lb.size != S.shape[1] or ub.size != S.shape[1]: + raise Exception( + "The number of reactions must be equal to the number of given flux bounds." + ) + + # TODO + # declare the tolerance that gurobi works properly + redundant_facet_tol = 1e-07 + tol = 1e-06 + + m = S.shape[0] + n = S.shape[1] + + # [v,-v] <= [ub,-lb] + A = np.zeros((2 * n, n), dtype="float") + A[0:n] = np.eye(n) + A[n:] -= np.eye(n, n, dtype="float") + + b = np.concatenate((ub, -lb), axis=0) + b = np.ascontiguousarray(b, dtype="float") + + beq = np.zeros(m) + + Aeq_res = S + beq_res = np.array(beq) + b_res = [] + A_res = np.empty((0, n), float) + + max_biomass_flux_vector, max_biomass_objective = fba(lb, ub, S, c) + val = -np.floor(max_biomass_objective / tol) * tol * opt_percentage / 100 + + try: + # Create variables for the model + v = [pl.LpVariable(f"v{i}") for i in range(n)] + + # initialize + indices_iter = range(n) + removed = 1 + offset = 1 + facet_left_removed = np.zeros(n, dtype=bool) + facet_right_removed = np.zeros(n, dtype=bool) + + # Loop until no redundant facets are found + while removed > 0 or offset > 0: + removed = 0 + offset = 0 + indices = indices_iter + indices_iter = [] + + Aeq = np.array(Aeq_res) + beq = np.array(beq_res) + + A_res = np.empty((0, n), dtype=float) + b_res = [] + + model_iter = set_model(v, lb, ub, Aeq, beq, np.array([-c]), [val]) + + for i in indices: + + redundant_facet_right = True + redundant_facet_left = True + + for j in range(n): + v[j].lowBound = lb[j] + v[j].upBound = ub[j] + + # maximize v_i (right) + model_iter.objective = -v[i] + + solver = pl.getSolver(solver_name, msg=0) + model_iter.solve(solver) + + # if optimized + if model_iter.status == pl.LpStatusOptimal: + # get the maximum objective value + max_objective = -pl.value(model_iter.objective) + else: + max_objective = ub[i] + + # if this facet was not removed in a previous iteration + if not facet_right_removed[i]: + # Relax the inequality + v[i].upBound = ub[i] + 1 + + solver = pl.getSolver(solver_name, msg=0) + model_iter.solve(solver) + + # Reset the inequality + v[i].upBound = ub[i] + + if model_iter.status == pl.LpStatusOptimal: + # Get the max objective value with relaxed inequality + max_objective2 = -pl.value(model_iter.objective) + if np.abs(max_objective2 - max_objective) > redundant_facet_tol: + redundant_facet_right = False + else: + removed += 1 + facet_right_removed[i] = True + + # minimum v_i (left) + model_iter.objective = v[i] + solver = pl.getSolver(solver_name, msg=0) + model_iter.solve(solver) + + # If optimized + if model_iter.status == pl.LpStatusOptimal: + # Get the min objective value + min_objective = pl.value(model_iter.objective) + else: + min_objective = lb[i] + + # if this facet was not removed in a previous iteration + if not facet_left_removed[i]: + # Relax the inequality + v[i].lowBound = lb[i] - 1 + + solver = pl.getSolver(solver_name, msg=0) + model_iter.solve(solver) + + # Reset the inequality + v[i].lowBound = lb[i] + + if model_iter.status == pl.LpStatusOptimal: + # Get the min objective value with relaxed inequality + min_objective2 = pl.value(model_iter.objective) + if ( + np.abs(min_objective2 - min_objective) + > redundant_facet_tol + ): + redundant_facet_left = False + else: + removed += 1 + facet_left_removed[i] = True + + if (not redundant_facet_left) or (not redundant_facet_right): + width = abs(max_objective - min_objective) + + # Check whether the offset in this dimension is small (and set an equality) + if width < redundant_facet_tol: + offset += 1 + Aeq_res = np.vstack((Aeq_res, A[i])) + beq_res = np.append(beq_res, min(max_objective, min_objective)) + # Remove the bounds on this dimension + ub[i] = sys.float_info.max + lb[i] = -sys.float_info.max + else: + # store this dimension + indices_iter.append(i) + + if not redundant_facet_left: + # Not a redundant inequality + A_res = np.append(A_res, np.array([A[n + i]]), axis=0) + b_res.append(b[n + i]) + else: + lb[i] = -sys.float_info.max + + if not redundant_facet_right: + # Not a redundant inequality + A_res = np.append(A_res, np.array([A[i]]), axis=0) + b_res.append(b[i]) + else: + ub[i] = sys.float_info.max + else: + # Remove the bounds on this dimension + ub[i] = sys.float_info.max + lb[i] = -sys.float_info.max + + b_res = np.asarray(b_res, dtype="float") + A_res = np.asarray(A_res, dtype="float") + A_res = np.ascontiguousarray(A_res, dtype="float") + + return A_res, b_res, Aeq_res, beq_res + + except pl.PulpSolverError as e: + print(f"Solver Error: {e}") + except Exception as e: + print(f"An error occurred: {e}") diff --git a/poetry.lock b/poetry.lock index 598593c5..94092038 100644 --- a/poetry.lock +++ b/poetry.lock @@ -2,24 +2,26 @@ [[package]] name = "anyio" -version = "3.6.2" +version = "4.4.0" 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+content-hash = "9f205ed2ecfdb51557d19c915fed2505d6e5ad10ae25ab65bfa2f6147d26f03a" diff --git a/pyproject.toml b/pyproject.toml index 2e83c04e..748a5290 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -17,6 +17,8 @@ matplotlib = "^3.4.1" cobra = "^0.26.0" plotly = "^5.11.0" kaleido = "0.2.1" +pulp = {git = "https://github.com/coin-or/pulp.git", branch = "master"} +highspy = "^1.7.0" [tool.poetry.dev-dependencies] diff --git a/tests/pulp_impl_test.py b/tests/pulp_impl_test.py new file mode 100644 index 00000000..88c6ed9d --- /dev/null +++ b/tests/pulp_impl_test.py @@ -0,0 +1,80 @@ +# dingo : a python library for metabolic networks sampling and analysis +# dingo is part of GeomScale project + +# Copyright (c) 2024 Ke Shi + +# Licensed under GNU LGPL.3, see LICENCE file + +import unittest +import os +import numpy as np +from dingo import MetabolicNetwork, PolytopeSampler +from dingo.pulp_based_impl import fba, fva, inner_ball, remove_redundant_facets + +class TestFastMethods(unittest.TestCase): + def test_inner_ball(self): + + m = 2 + n = 5 + + A = np.zeros((2 * n, n), dtype="float") + A[0:n] = np.eye(n) + A[n:] -= np.eye(n, n, dtype="float") + b = np.ones(2 * n, dtype="float") + + max_ball = inner_ball(A, b) + + self.assertTrue(abs(max_ball[1] - 1) < 1e-08) + + def test_fva(self): + + current_directory = os.getcwd() + input_file_json = current_directory + "/ext_data/e_coli_core.json" + + model = MetabolicNetwork.from_json(input_file_json) + + res = fva( + model.lb, + model.ub, + model.S, + model.objective_function, + model.parameters["opt_percentage"], + ) + + self.assertTrue(abs(res[3] - 0.8739215069684305) < 1e-08) + self.assertEqual(res[0].size, 95) + self.assertEqual(res[1].size, 95) + + def test_remove_redundant_facets(self): + current_directory = os.getcwd() + input_file_json = current_directory + "/ext_data/e_coli_core.json" + + model = MetabolicNetwork.from_json(input_file_json) + + A, b, Aeq, beq = remove_redundant_facets( + model.lb, + model.ub, + model.S, + model.objective_function, + model.parameters["opt_percentage"], + ) + + self.assertEqual(A.shape[0], 25) + self.assertEqual(A.shape[1], 95) + self.assertEqual(Aeq.shape[0], 76) + self.assertEqual(Aeq.shape[1], 95) + + def test_fast_fba(self): + + current_directory = os.getcwd() + input_file_json = current_directory + "/ext_data/e_coli_core.json" + + model = MetabolicNetwork.from_json(input_file_json) + + res = fba(model._lb, model._ub, model._S, model._objective_function) + + self.assertTrue(abs(res[1] - 0.8739215069684305) < 1e-08) + + +if __name__ == "__main__": + unittest.main() From 0f73df7645e7c3ab42d795c3e1c714baf35a9592 Mon Sep 17 00:00:00 2001 From: KeShih Date: Fri, 26 Jul 2024 21:54:37 +0800 Subject: [PATCH 2/2] Add pyoptInterface_based_impl.py --- dingo/pyoptInterface_based_impl.py | 480 +++++++++++++++++++++++++++++ 1 file changed, 480 insertions(+) create mode 100644 dingo/pyoptInterface_based_impl.py diff --git a/dingo/pyoptInterface_based_impl.py b/dingo/pyoptInterface_based_impl.py new file mode 100644 index 00000000..3e659af2 --- /dev/null +++ b/dingo/pyoptInterface_based_impl.py @@ -0,0 +1,480 @@ +import pyoptinterface as poi +from pyoptinterface import highs, gurobi, copt, mosek +import numpy as np +import math +import sys + +SOLVER = gurobi + +solver_map = { + "highs": highs, + "gurobi": gurobi, + "copt": copt, + "mosek": mosek, +} + +def dot(c, x): + return poi.quicksum(c[i] * x[i] for i in range(len(x)) if abs(c[i]) > 1e-12) + + +def fba(lb, ub, S, c): + """A Python function to perform fba using PuLP LP modeler + Returns an optimal solution and its value for the following linear program: + max c*v, subject to, + Sv = 0, lb <= v <= ub + + Keyword arguments: + lb -- lower bounds for the fluxes, i.e., a n-dimensional vector + ub -- upper bounds for the fluxes, i.e., a n-dimensional vector + S -- the mxn stoichiometric matrix, s.t. Sv = 0 + c -- the linear objective function, i.e., a n-dimensional vector + """ + + if lb.size != S.shape[1] or ub.size != S.shape[1]: + raise Exception( + "The number of reactions must be equal to the number of given flux bounds." + ) + if c.size != S.shape[1]: + raise Exception( + "The length of the linear objective function must be equal to the number of reactions." + ) + + m = S.shape[0] + n = S.shape[1] + optimum_value = 0 + optimum_sol = np.zeros(n) + try: + # Create a model + model = SOLVER.Model() + model.set_model_attribute(poi.ModelAttribute.Silent, True) + + # Create variables and set lb <= v <= ub + v = np.empty(n, dtype=object) + for i in range(n): + v[i] = model.add_variable(lb=lb[i], ub=ub[i]) + + # Add the constraints Sv = 0 + for i in range(m): + model.add_linear_constraint( + dot(S[i],v), poi.Eq, 0 + ) + + # Set the objective function + obj = dot(c,v) + model.set_objective(obj, sense=poi.ObjectiveSense.Maximize) + + # Optimize model + model.optimize() + + # If optimized + status = model.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + optimum_value = model.get_value(obj) + for i in range(n): + optimum_sol[i] = model.get_value(v[i]) + return optimum_sol, optimum_value + + except poi.TerminationStatusCode.NUMERICAL_ERROR as e: + print(f"A numerical error occurred: {e}") + except poi.TerminationStatusCode.OTHER_ERROR as e: + print(f"An error occurred: {e}") + except Exception as e: + print(f"An unexpected error occurred: {e}") + + +def fva(lb, ub, S, c, opt_percentage=100): + """A Python function to perform fva using PuLP LP modeler + Returns the value of the optimal solution for all the following linear programs: + min/max v_i, for all coordinates i=1,...,n, subject to, + Sv = 0, lb <= v <= ub + + Keyword arguments: + lb -- lower bounds for the fluxes, i.e., a n-dimensional vector + ub -- upper bounds for the fluxes, i.e., a n-dimensional vector + S -- the mxn stoichiometric matrix, s.t. Sv = 0 + c -- the objective function to maximize + opt_percentage -- consider solutions that give you at least a certain + percentage of the optimal solution (default is to consider + optimal solutions only) + """ + + if lb.size != S.shape[1] or ub.size != S.shape[1]: + raise Exception( + "The number of reactions must be equal to the number of given flux bounds." + ) + + # declare the tolerance that highs, gurobi and copt works properly (we found it experimentally) + tol = 1e-06 + + m = S.shape[0] + n = S.shape[1] + + max_biomass_flux_vector, max_biomass_objective = fba(lb, ub, S, c) + + min_fluxes = [] + max_fluxes = [] + + adjusted_opt_threshold = ( + (opt_percentage / 100) * tol * math.floor(max_biomass_objective / tol) + ) + + try: + # Create a model + model = SOLVER.Model() + model.set_model_attribute(poi.ModelAttribute.Silent, True) + + # Create variables and set lb <= v <= ub + v = np.empty(n, dtype=object) + for i in range(n): + v[i] = model.add_variable(lb=lb[i], ub=ub[i]) + + # Add the constraints Sv = 0 + for i in range(m): + model.add_linear_constraint( + dot(S[i],v), poi.Eq, 0 + ) + + # add an additional constraint to impose solutions with at least `opt_percentage` of the optimal solution + model.add_linear_constraint( + dot(c,v), poi.Geq, adjusted_opt_threshold + ) + + for i in range(n): + # Set the objective function + obj = poi.ExprBuilder(v[i]) + + model.set_objective(obj, sense=poi.ObjectiveSense.Minimize) + + # Optimize model + model.optimize() + + # If optimized + status = model.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + # Get the min objective value + min_objective = model.get_value(v[i]) + min_fluxes.append(min_objective) + else: + min_fluxes.append(lb[i]) + + # Likewise, for the maximum, optimize model + model.set_objective(obj, sense=poi.ObjectiveSense.Maximize) + + # Again if optimized + model.optimize() + status = model.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + # Get the max objective value + max_objective = model.get_value(v[i]) + max_fluxes.append(max_objective) + else: + max_fluxes.append(ub[i]) + + # Make lists of fluxes numpy arrays + min_fluxes = np.asarray(min_fluxes) + max_fluxes = np.asarray(max_fluxes) + + return ( + min_fluxes, + max_fluxes, + max_biomass_flux_vector, + max_biomass_objective, + ) + + except poi.TerminationStatusCode.NUMERICAL_ERROR as e: + print(f"A numerical error occurred: {e}") + except poi.TerminationStatusCode.OTHER_ERROR as e: + print(f"An error occurred: {e}") + except Exception as e: + print(f"An unexpected error occurred: {e}") + + +def inner_ball(A, b): + """A Python function to compute the maximum inscribed ball in the given polytope using PuLP LP modeler + Returns the optimal solution for the following linear program: + max r, subject to, + a_ix + r||a_i|| <= b, i=1,...,n + + Keyword arguments: + A -- an mxn matrix that contains the normal vectors of the facets of the polytope row-wise + b -- a m-dimensional vector + """ + + extra_column = [] + + m = A.shape[0] + n = A.shape[1] + + for i in range(A.shape[0]): + entry = np.linalg.norm(A[i]) + extra_column.append(entry) + + column = np.asarray(extra_column) + A_expand = np.c_[A, column] + + model = SOLVER.Model() + model.set_model_attribute(poi.ModelAttribute.Silent, True) + + # Create variables where x[n] is the radius + x = np.empty(n+1, dtype=object) + for i in range(n+1): + x[i] = model.add_variable() + + # Add the constraints a_ix + r||a_i|| <= b + for i in range(m): + model.add_linear_constraint( + dot(A_expand[i], x) ,poi.Leq, b[i] + ) + + # Set the objective function + obj = poi.ExprBuilder(x[n]) + model.set_objective(obj, sense=poi.ObjectiveSense.Maximize) + + # Optimize model + model.optimize() + + # Get the center point and the radius of max ball from the solution of LP + point = [model.get_value(x[i]) for i in range(n)] + + # Get radius + r = model.get_value(obj) + + # And check whether the computed radius is negative + if r < 0: + print( + "The radius calculated has negative value. The polytope is infeasible or something went wrong with the solver" + ) + else: + return point, r + + +def set_model(n, Aeq, beq, A, b): + """ + A helper function of remove_redundant_facets function + Create a PuLP model with given PuLP variables, equality constraints, and inequality constraints + but without an objective function. + """ + # Create a model + model = SOLVER.Model() + model.set_model_attribute(poi.ModelAttribute.Silent, True) + + # Create variables + x = model.add_variables(range(n)) + + # Add the equality constraints + for i in range(Aeq.shape[0]): + model.add_linear_constraint( + dot(Aeq[i], x), poi.Eq, beq[i] + ) + + # Add the inequality constraints + for i in range(A.shape[0]): + model.add_linear_constraint( + dot(A[i], x), poi.Leq, b[i] + ) + + return model,x + + +def remove_redundant_facets(lb, ub, S, c, opt_percentage=100): + """A function to find and remove the redundant facets and to find + the facets with very small offset and to set them as equalities + + Keyword arguments: + lb -- lower bounds for the fluxes, i.e., a n-dimensional vector + ub -- upper bounds for the fluxes, i.e., a n-dimensional vector + S -- the mxn stoichiometric matrix, s.t. Sv = 0 + c -- the objective function to maximize + opt_percentage -- consider solutions that give you at least a certain + percentage of the optimal solution (default is to consider + optimal solutions only) + """ + + if lb.size != S.shape[1] or ub.size != S.shape[1]: + raise Exception( + "The number of reactions must be equal to the number of given flux bounds." + ) + + # TODO + # declare the tolerance that gurobi works properly + redundant_facet_tol = 1e-07 + tol = 1e-06 + + m = S.shape[0] + n = S.shape[1] + + # [v,-v] <= [ub,-lb] + A = np.zeros((2 * n, n), dtype="float") + A[0:n] = np.eye(n) + A[n:] -= np.eye(n, n, dtype="float") + + b = np.concatenate((ub, -lb), axis=0) + b = np.ascontiguousarray(b, dtype="float") + + beq = np.zeros(m) + + Aeq_res = S + beq_res = np.array(beq) + b_res = [] + A_res = np.empty((0, n), float) + + max_biomass_flux_vector, max_biomass_objective = fba(lb, ub, S, c) + val = -np.floor(max_biomass_objective / tol) * tol * opt_percentage / 100 + + start = np.zeros(n) + + try: + + # initialize + indices_iter = range(n) + removed = 1 + offset = 1 + facet_left_removed = np.zeros(n, dtype=bool) + facet_right_removed = np.zeros(n, dtype=bool) + + # Loop until no redundant facets are found + while removed > 0 or offset > 0: + removed = 0 + offset = 0 + indices = indices_iter + indices_iter = [] + + Aeq = np.array(Aeq_res) + beq = np.array(beq_res) + + A_res = np.empty((0, n), dtype=float) + b_res = [] + + model_iter, v = set_model(n, Aeq, beq, np.array([-c]), [val]) + + for j in range(n): + model_iter.set_variable_attribute(v[j], poi.VariableAttribute.PrimalStart,max_biomass_flux_vector[j]) + + for i in indices: + + redundant_facet_right = True + redundant_facet_left = True + + for j in range(n): + model_iter.set_variable_attribute(v[j], poi.VariableAttribute.LowerBound, lb[j]) + model_iter.set_variable_attribute(v[j], poi.VariableAttribute.UpperBound, ub[j]) + + # objective function + obj = poi.ExprBuilder(v[i]) + + # maximize v_i (right) + model_iter.set_objective(obj, sense=poi.ObjectiveSense.Maximize) + model_iter.optimize() + + # if optimized + status = model_iter.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + # get the maximum objective value + max_objective = model_iter.get_value(obj) + else: + max_objective = ub[i] + + # if this facet was not removed in a previous iteration + if not facet_right_removed[i]: + # Relax the inequality + model_iter.set_variable_attribute(v[i], poi.VariableAttribute.UpperBound, ub[i]+1) + + # Solve the model + model_iter.optimize() + + status = model_iter.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + # Get the max objective value with relaxed inequality + + max_objective2 = model_iter.get_value(obj) + if np.abs(max_objective2 - max_objective) > redundant_facet_tol: + redundant_facet_right = False + else: + removed += 1 + facet_right_removed[i] = True + + # Reset the inequality + model_iter.set_variable_attribute(v[i], poi.VariableAttribute.UpperBound, ub[i]) + + # minimum v_i (left) + model_iter.set_objective(obj, sense=poi.ObjectiveSense.Minimize) + model_iter.optimize() + + # If optimized + status = model_iter.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + # Get the min objective value + min_objective = model_iter.get_value(obj) + else: + min_objective = lb[i] + + # if this facet was not removed in a previous iteration + if not facet_left_removed[i]: + # Relax the inequality + model_iter.set_variable_attribute(v[i], poi.VariableAttribute.LowerBound, lb[i]-1) + + # Solve the model + model_iter.optimize() + + status = model_iter.get_model_attribute(poi.ModelAttribute.TerminationStatus) + if status == poi.TerminationStatusCode.OPTIMAL: + # Get the min objective value with relaxed inequality + min_objective2 = model_iter.get_value(obj) + if ( + np.abs(min_objective2 - min_objective) + > redundant_facet_tol + ): + redundant_facet_left = False + else: + removed += 1 + facet_left_removed[i] = True + + # Reset the inequality + # model_iter.set_variable_attribute(v[i], poi.VariableAttribute.LowerBound, lb[i]) + + if (not redundant_facet_left) or (not redundant_facet_right): + width = abs(max_objective - min_objective) + + # Check whether the offset in this dimension is small (and set an equality) + if width < redundant_facet_tol: + offset += 1 + Aeq_res = np.vstack((Aeq_res, A[i])) + beq_res = np.append(beq_res, min(max_objective, min_objective)) + # Remove the bounds on this dimension + ub[i] = sys.float_info.max + lb[i] = -sys.float_info.max + else: + # store this dimension + indices_iter.append(i) + + if not redundant_facet_left: + # Not a redundant inequality + A_res = np.append(A_res, np.array([A[n + i]]), axis=0) + b_res.append(b[n + i]) + else: + lb[i] = -sys.float_info.max + + if not redundant_facet_right: + # Not a redundant inequality + A_res = np.append(A_res, np.array([A[i]]), axis=0) + b_res.append(b[i]) + else: + ub[i] = sys.float_info.max + else: + # Remove the bounds on this dimension + ub[i] = sys.float_info.max + lb[i] = -sys.float_info.max + + b_res = np.asarray(b_res, dtype="float") + A_res = np.asarray(A_res, dtype="float") + A_res = np.ascontiguousarray(A_res, dtype="float") + # print(b_res) + # print(beq_res) + return A_res, b_res, Aeq_res, beq_res + + except poi.TerminationStatusCode.NUMERICAL_ERROR as e: + print(f"A numerical error occurred: {e}") + except poi.TerminationStatusCode.OTHER_ERROR as e: + print(f"An error occurred: {e}") + except Exception as e: + print(f"An unexpected error occurred: {e}") \ No newline at end of file