diff --git "a/llava_next/lib/python3.10/site-packages/scipy/optimize/tests/test_linprog.py" "b/llava_next/lib/python3.10/site-packages/scipy/optimize/tests/test_linprog.py" new file mode 100644--- /dev/null +++ "b/llava_next/lib/python3.10/site-packages/scipy/optimize/tests/test_linprog.py" @@ -0,0 +1,2498 @@ +""" +Unit test for Linear Programming +""" +import sys +import platform + +import numpy as np +from numpy.testing import (assert_, assert_allclose, assert_equal, + assert_array_less, assert_warns, suppress_warnings) +from pytest import raises as assert_raises +from scipy.optimize import linprog, OptimizeWarning +from scipy.optimize._numdiff import approx_derivative +from scipy.sparse.linalg import MatrixRankWarning +from scipy.linalg import LinAlgWarning +from scipy._lib._util import VisibleDeprecationWarning +import scipy.sparse +import pytest + +has_umfpack = True +try: + from scikits.umfpack import UmfpackWarning +except ImportError: + has_umfpack = False + +has_cholmod = True +try: + import sksparse # noqa: F401 + from sksparse.cholmod import cholesky as cholmod # noqa: F401 +except ImportError: + has_cholmod = False + + +def _assert_iteration_limit_reached(res, maxiter): + assert_(not res.success, "Incorrectly reported success") + assert_(res.success < maxiter, "Incorrectly reported number of iterations") + assert_equal(res.status, 1, "Failed to report iteration limit reached") + + +def _assert_infeasible(res): + # res: linprog result object + assert_(not res.success, "incorrectly reported success") + assert_equal(res.status, 2, "failed to report infeasible status") + + +def _assert_unbounded(res): + # res: linprog result object + assert_(not res.success, "incorrectly reported success") + assert_equal(res.status, 3, "failed to report unbounded status") + + +def _assert_unable_to_find_basic_feasible_sol(res): + # res: linprog result object + + # The status may be either 2 or 4 depending on why the feasible solution + # could not be found. If the underlying problem is expected to not have a + # feasible solution, _assert_infeasible should be used. + assert_(not res.success, "incorrectly reported success") + assert_(res.status in (2, 4), "failed to report optimization failure") + + +def _assert_success(res, desired_fun=None, desired_x=None, + rtol=1e-8, atol=1e-8): + # res: linprog result object + # desired_fun: desired objective function value or None + # desired_x: desired solution or None + if not res.success: + msg = f"linprog status {res.status}, message: {res.message}" + raise AssertionError(msg) + + assert_equal(res.status, 0) + if desired_fun is not None: + assert_allclose(res.fun, desired_fun, + err_msg="converged to an unexpected objective value", + rtol=rtol, atol=atol) + if desired_x is not None: + assert_allclose(res.x, desired_x, + err_msg="converged to an unexpected solution", + rtol=rtol, atol=atol) + + +def magic_square(n): + """ + Generates a linear program for which integer solutions represent an + n x n magic square; binary decision variables represent the presence + (or absence) of an integer 1 to n^2 in each position of the square. + """ + + np.random.seed(0) + M = n * (n**2 + 1) / 2 + + numbers = np.arange(n**4) // n**2 + 1 + + numbers = numbers.reshape(n**2, n, n) + + zeros = np.zeros((n**2, n, n)) + + A_list = [] + b_list = [] + + # Rule 1: use every number exactly once + for i in range(n**2): + A_row = zeros.copy() + A_row[i, :, :] = 1 + A_list.append(A_row.flatten()) + b_list.append(1) + + # Rule 2: Only one number per square + for i in range(n): + for j in range(n): + A_row = zeros.copy() + A_row[:, i, j] = 1 + A_list.append(A_row.flatten()) + b_list.append(1) + + # Rule 3: sum of rows is M + for i in range(n): + A_row = zeros.copy() + A_row[:, i, :] = numbers[:, i, :] + A_list.append(A_row.flatten()) + b_list.append(M) + + # Rule 4: sum of columns is M + for i in range(n): + A_row = zeros.copy() + A_row[:, :, i] = numbers[:, :, i] + A_list.append(A_row.flatten()) + b_list.append(M) + + # Rule 5: sum of diagonals is M + A_row = zeros.copy() + A_row[:, range(n), range(n)] = numbers[:, range(n), range(n)] + A_list.append(A_row.flatten()) + b_list.append(M) + A_row = zeros.copy() + A_row[:, range(n), range(-1, -n - 1, -1)] = \ + numbers[:, range(n), range(-1, -n - 1, -1)] + A_list.append(A_row.flatten()) + b_list.append(M) + + A = np.array(np.vstack(A_list), dtype=float) + b = np.array(b_list, dtype=float) + c = np.random.rand(A.shape[1]) + + return A, b, c, numbers, M + + +def lpgen_2d(m, n): + """ -> A b c LP test: m*n vars, m+n constraints + row sums == n/m, col sums == 1 + https://gist.github.com/denis-bz/8647461 + """ + np.random.seed(0) + c = - np.random.exponential(size=(m, n)) + Arow = np.zeros((m, m * n)) + brow = np.zeros(m) + for j in range(m): + j1 = j + 1 + Arow[j, j * n:j1 * n] = 1 + brow[j] = n / m + + Acol = np.zeros((n, m * n)) + bcol = np.zeros(n) + for j in range(n): + j1 = j + 1 + Acol[j, j::n] = 1 + bcol[j] = 1 + + A = np.vstack((Arow, Acol)) + b = np.hstack((brow, bcol)) + + return A, b, c.ravel() + + +def very_random_gen(seed=0): + np.random.seed(seed) + m_eq, m_ub, n = 10, 20, 50 + c = np.random.rand(n)-0.5 + A_ub = np.random.rand(m_ub, n)-0.5 + b_ub = np.random.rand(m_ub)-0.5 + A_eq = np.random.rand(m_eq, n)-0.5 + b_eq = np.random.rand(m_eq)-0.5 + lb = -np.random.rand(n) + ub = np.random.rand(n) + lb[lb < -np.random.rand()] = -np.inf + ub[ub > np.random.rand()] = np.inf + bounds = np.vstack((lb, ub)).T + return c, A_ub, b_ub, A_eq, b_eq, bounds + + +def nontrivial_problem(): + c = [-1, 8, 4, -6] + A_ub = [[-7, -7, 6, 9], + [1, -1, -3, 0], + [10, -10, -7, 7], + [6, -1, 3, 4]] + b_ub = [-3, 6, -6, 6] + A_eq = [[-10, 1, 1, -8]] + b_eq = [-4] + x_star = [101 / 1391, 1462 / 1391, 0, 752 / 1391] + f_star = 7083 / 1391 + return c, A_ub, b_ub, A_eq, b_eq, x_star, f_star + + +def l1_regression_prob(seed=0, m=8, d=9, n=100): + ''' + Training data is {(x0, y0), (x1, y2), ..., (xn-1, yn-1)} + x in R^d + y in R + n: number of training samples + d: dimension of x, i.e. x in R^d + phi: feature map R^d -> R^m + m: dimension of feature space + ''' + np.random.seed(seed) + phi = np.random.normal(0, 1, size=(m, d)) # random feature mapping + w_true = np.random.randn(m) + x = np.random.normal(0, 1, size=(d, n)) # features + y = w_true @ (phi @ x) + np.random.normal(0, 1e-5, size=n) # measurements + + # construct the problem + c = np.ones(m+n) + c[:m] = 0 + A_ub = scipy.sparse.lil_matrix((2*n, n+m)) + idx = 0 + for ii in range(n): + A_ub[idx, :m] = phi @ x[:, ii] + A_ub[idx, m+ii] = -1 + A_ub[idx+1, :m] = -1*phi @ x[:, ii] + A_ub[idx+1, m+ii] = -1 + idx += 2 + A_ub = A_ub.tocsc() + b_ub = np.zeros(2*n) + b_ub[0::2] = y + b_ub[1::2] = -y + bnds = [(None, None)]*m + [(0, None)]*n + return c, A_ub, b_ub, bnds + + +def generic_callback_test(self): + # Check that callback is as advertised + last_cb = {} + + def cb(res): + message = res.pop('message') + complete = res.pop('complete') + + assert_(res.pop('phase') in (1, 2)) + assert_(res.pop('status') in range(4)) + assert_(isinstance(res.pop('nit'), int)) + assert_(isinstance(complete, bool)) + assert_(isinstance(message, str)) + + last_cb['x'] = res['x'] + last_cb['fun'] = res['fun'] + last_cb['slack'] = res['slack'] + last_cb['con'] = res['con'] + + c = np.array([-3, -2]) + A_ub = [[2, 1], [1, 1], [1, 0]] + b_ub = [10, 8, 4] + res = linprog(c, A_ub=A_ub, b_ub=b_ub, callback=cb, method=self.method) + + _assert_success(res, desired_fun=-18.0, desired_x=[2, 6]) + assert_allclose(last_cb['fun'], res['fun']) + assert_allclose(last_cb['x'], res['x']) + assert_allclose(last_cb['con'], res['con']) + assert_allclose(last_cb['slack'], res['slack']) + + +def test_unknown_solvers_and_options(): + c = np.array([-3, -2]) + A_ub = [[2, 1], [1, 1], [1, 0]] + b_ub = [10, 8, 4] + + assert_raises(ValueError, linprog, + c, A_ub=A_ub, b_ub=b_ub, method='ekki-ekki-ekki') + assert_raises(ValueError, linprog, + c, A_ub=A_ub, b_ub=b_ub, method='highs-ekki') + message = "Unrecognized options detected: {'rr_method': 'ekki-ekki-ekki'}" + with pytest.warns(OptimizeWarning, match=message): + linprog(c, A_ub=A_ub, b_ub=b_ub, + options={"rr_method": 'ekki-ekki-ekki'}) + + +def test_choose_solver(): + # 'highs' chooses 'dual' + c = np.array([-3, -2]) + A_ub = [[2, 1], [1, 1], [1, 0]] + b_ub = [10, 8, 4] + + res = linprog(c, A_ub, b_ub, method='highs') + _assert_success(res, desired_fun=-18.0, desired_x=[2, 6]) + + +def test_deprecation(): + with pytest.warns(DeprecationWarning): + linprog(1, method='interior-point') + with pytest.warns(DeprecationWarning): + linprog(1, method='revised simplex') + with pytest.warns(DeprecationWarning): + linprog(1, method='simplex') + + +def test_highs_status_message(): + res = linprog(1, method='highs') + msg = "Optimization terminated successfully. (HiGHS Status 7:" + assert res.status == 0 + assert res.message.startswith(msg) + + A, b, c, numbers, M = magic_square(6) + bounds = [(0, 1)] * len(c) + integrality = [1] * len(c) + options = {"time_limit": 0.1} + res = linprog(c=c, A_eq=A, b_eq=b, bounds=bounds, method='highs', + options=options, integrality=integrality) + msg = "Time limit reached. (HiGHS Status 13:" + assert res.status == 1 + assert res.message.startswith(msg) + + options = {"maxiter": 10} + res = linprog(c=c, A_eq=A, b_eq=b, bounds=bounds, method='highs-ds', + options=options) + msg = "Iteration limit reached. (HiGHS Status 14:" + assert res.status == 1 + assert res.message.startswith(msg) + + res = linprog(1, bounds=(1, -1), method='highs') + msg = "The problem is infeasible. (HiGHS Status 8:" + assert res.status == 2 + assert res.message.startswith(msg) + + res = linprog(-1, method='highs') + msg = "The problem is unbounded. (HiGHS Status 10:" + assert res.status == 3 + assert res.message.startswith(msg) + + from scipy.optimize._linprog_highs import _highs_to_scipy_status_message + status, message = _highs_to_scipy_status_message(58, "Hello!") + msg = "The HiGHS status code was not recognized. (HiGHS Status 58:" + assert status == 4 + assert message.startswith(msg) + + status, message = _highs_to_scipy_status_message(None, None) + msg = "HiGHS did not provide a status code. (HiGHS Status None: None)" + assert status == 4 + assert message.startswith(msg) + + +def test_bug_17380(): + linprog([1, 1], A_ub=[[-1, 0]], b_ub=[-2.5], integrality=[1, 1]) + + +A_ub = None +b_ub = None +A_eq = None +b_eq = None +bounds = None + +################ +# Common Tests # +################ + + +class LinprogCommonTests: + """ + Base class for `linprog` tests. Generally, each test will be performed + once for every derived class of LinprogCommonTests, each of which will + typically change self.options and/or self.method. Effectively, these tests + are run for many combination of method (simplex, revised simplex, and + interior point) and options (such as pivoting rule or sparse treatment). + """ + + ################## + # Targeted Tests # + ################## + + def test_callback(self): + generic_callback_test(self) + + def test_disp(self): + # test that display option does not break anything. + A, b, c = lpgen_2d(20, 20) + res = linprog(c, A_ub=A, b_ub=b, method=self.method, + options={"disp": True}) + _assert_success(res, desired_fun=-64.049494229) + + def test_docstring_example(self): + # Example from linprog docstring. + c = [-1, 4] + A = [[-3, 1], [1, 2]] + b = [6, 4] + x0_bounds = (None, None) + x1_bounds = (-3, None) + res = linprog(c, A_ub=A, b_ub=b, bounds=(x0_bounds, x1_bounds), + options=self.options, method=self.method) + _assert_success(res, desired_fun=-22) + + def test_type_error(self): + # (presumably) checks that linprog recognizes type errors + # This is tested more carefully in test__linprog_clean_inputs.py + c = [1] + A_eq = [[1]] + b_eq = "hello" + assert_raises(TypeError, linprog, + c, A_eq=A_eq, b_eq=b_eq, + method=self.method, options=self.options) + + def test_aliasing_b_ub(self): + # (presumably) checks that linprog does not modify b_ub + # This is tested more carefully in test__linprog_clean_inputs.py + c = np.array([1.0]) + A_ub = np.array([[1.0]]) + b_ub_orig = np.array([3.0]) + b_ub = b_ub_orig.copy() + bounds = (-4.0, np.inf) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-4, desired_x=[-4]) + assert_allclose(b_ub_orig, b_ub) + + def test_aliasing_b_eq(self): + # (presumably) checks that linprog does not modify b_eq + # This is tested more carefully in test__linprog_clean_inputs.py + c = np.array([1.0]) + A_eq = np.array([[1.0]]) + b_eq_orig = np.array([3.0]) + b_eq = b_eq_orig.copy() + bounds = (-4.0, np.inf) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=3, desired_x=[3]) + assert_allclose(b_eq_orig, b_eq) + + def test_non_ndarray_args(self): + # (presumably) checks that linprog accepts list in place of arrays + # This is tested more carefully in test__linprog_clean_inputs.py + c = [1.0] + A_ub = [[1.0]] + b_ub = [3.0] + A_eq = [[1.0]] + b_eq = [2.0] + bounds = (-1.0, 10.0) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=2, desired_x=[2]) + + def test_unknown_options(self): + c = np.array([-3, -2]) + A_ub = [[2, 1], [1, 1], [1, 0]] + b_ub = [10, 8, 4] + + def f(c, A_ub=None, b_ub=None, A_eq=None, + b_eq=None, bounds=None, options={}): + linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=options) + + o = {key: self.options[key] for key in self.options} + o['spam'] = 42 + + assert_warns(OptimizeWarning, f, + c, A_ub=A_ub, b_ub=b_ub, options=o) + + def test_integrality_without_highs(self): + # ensure that using `integrality` parameter without `method='highs'` + # raises warning and produces correct solution to relaxed problem + # source: https://en.wikipedia.org/wiki/Integer_programming#Example + A_ub = np.array([[-1, 1], [3, 2], [2, 3]]) + b_ub = np.array([1, 12, 12]) + c = -np.array([0, 1]) + + bounds = [(0, np.inf)] * len(c) + integrality = [1] * len(c) + + with np.testing.assert_warns(OptimizeWarning): + res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds, + method=self.method, integrality=integrality) + + np.testing.assert_allclose(res.x, [1.8, 2.8]) + np.testing.assert_allclose(res.fun, -2.8) + + def test_invalid_inputs(self): + + def f(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=None): + linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + # Test ill-formatted bounds + assert_raises(ValueError, f, [1, 2, 3], bounds=[(1, 2), (3, 4)]) + with np.testing.suppress_warnings() as sup: + sup.filter(VisibleDeprecationWarning, "Creating an ndarray from ragged") + assert_raises(ValueError, f, [1, 2, 3], bounds=[(1, 2), (3, 4), (3, 4, 5)]) + assert_raises(ValueError, f, [1, 2, 3], bounds=[(1, -2), (1, 2)]) + + # Test other invalid inputs + assert_raises(ValueError, f, [1, 2], A_ub=[[1, 2]], b_ub=[1, 2]) + assert_raises(ValueError, f, [1, 2], A_ub=[[1]], b_ub=[1]) + assert_raises(ValueError, f, [1, 2], A_eq=[[1, 2]], b_eq=[1, 2]) + assert_raises(ValueError, f, [1, 2], A_eq=[[1]], b_eq=[1]) + assert_raises(ValueError, f, [1, 2], A_eq=[1], b_eq=1) + + # this last check doesn't make sense for sparse presolve + if ("_sparse_presolve" in self.options and + self.options["_sparse_presolve"]): + return + # there aren't 3-D sparse matrices + + assert_raises(ValueError, f, [1, 2], A_ub=np.zeros((1, 1, 3)), b_eq=1) + + def test_sparse_constraints(self): + # gh-13559: improve error message for sparse inputs when unsupported + def f(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=None): + linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + np.random.seed(0) + m = 100 + n = 150 + A_eq = scipy.sparse.rand(m, n, 0.5) + x_valid = np.random.randn(n) + c = np.random.randn(n) + ub = x_valid + np.random.rand(n) + lb = x_valid - np.random.rand(n) + bounds = np.column_stack((lb, ub)) + b_eq = A_eq * x_valid + + if self.method in {'simplex', 'revised simplex'}: + # simplex and revised simplex should raise error + with assert_raises(ValueError, match=f"Method '{self.method}' " + "does not support sparse constraint matrices."): + linprog(c=c, A_eq=A_eq, b_eq=b_eq, bounds=bounds, + method=self.method, options=self.options) + else: + # other methods should succeed + options = {**self.options} + if self.method in {'interior-point'}: + options['sparse'] = True + + res = linprog(c=c, A_eq=A_eq, b_eq=b_eq, bounds=bounds, + method=self.method, options=options) + assert res.success + + def test_maxiter(self): + # test iteration limit w/ Enzo example + c = [4, 8, 3, 0, 0, 0] + A = [ + [2, 5, 3, -1, 0, 0], + [3, 2.5, 8, 0, -1, 0], + [8, 10, 4, 0, 0, -1]] + b = [185, 155, 600] + np.random.seed(0) + maxiter = 3 + res = linprog(c, A_eq=A, b_eq=b, method=self.method, + options={"maxiter": maxiter}) + _assert_iteration_limit_reached(res, maxiter) + assert_equal(res.nit, maxiter) + + def test_bounds_fixed(self): + + # Test fixed bounds (upper equal to lower) + # If presolve option True, test if solution found in presolve (i.e. + # number of iterations is 0). + do_presolve = self.options.get('presolve', True) + + res = linprog([1], bounds=(1, 1), + method=self.method, options=self.options) + _assert_success(res, 1, 1) + if do_presolve: + assert_equal(res.nit, 0) + + res = linprog([1, 2, 3], bounds=[(5, 5), (-1, -1), (3, 3)], + method=self.method, options=self.options) + _assert_success(res, 12, [5, -1, 3]) + if do_presolve: + assert_equal(res.nit, 0) + + res = linprog([1, 1], bounds=[(1, 1), (1, 3)], + method=self.method, options=self.options) + _assert_success(res, 2, [1, 1]) + if do_presolve: + assert_equal(res.nit, 0) + + res = linprog([1, 1, 2], A_eq=[[1, 0, 0], [0, 1, 0]], b_eq=[1, 7], + bounds=[(-5, 5), (0, 10), (3.5, 3.5)], + method=self.method, options=self.options) + _assert_success(res, 15, [1, 7, 3.5]) + if do_presolve: + assert_equal(res.nit, 0) + + def test_bounds_infeasible(self): + + # Test ill-valued bounds (upper less than lower) + # If presolve option True, test if solution found in presolve (i.e. + # number of iterations is 0). + do_presolve = self.options.get('presolve', True) + + res = linprog([1], bounds=(1, -2), method=self.method, options=self.options) + _assert_infeasible(res) + if do_presolve: + assert_equal(res.nit, 0) + + res = linprog([1], bounds=[(1, -2)], method=self.method, options=self.options) + _assert_infeasible(res) + if do_presolve: + assert_equal(res.nit, 0) + + res = linprog([1, 2, 3], bounds=[(5, 0), (1, 2), (3, 4)], + method=self.method, options=self.options) + _assert_infeasible(res) + if do_presolve: + assert_equal(res.nit, 0) + + def test_bounds_infeasible_2(self): + + # Test ill-valued bounds (lower inf, upper -inf) + # If presolve option True, test if solution found in presolve (i.e. + # number of iterations is 0). + # For the simplex method, the cases do not result in an + # infeasible status, but in a RuntimeWarning. This is a + # consequence of having _presolve() take care of feasibility + # checks. See issue gh-11618. + do_presolve = self.options.get('presolve', True) + simplex_without_presolve = not do_presolve and self.method == 'simplex' + + c = [1, 2, 3] + bounds_1 = [(1, 2), (np.inf, np.inf), (3, 4)] + bounds_2 = [(1, 2), (-np.inf, -np.inf), (3, 4)] + + if simplex_without_presolve: + def g(c, bounds): + res = linprog(c, bounds=bounds, + method=self.method, options=self.options) + return res + + with pytest.warns(RuntimeWarning): + with pytest.raises(IndexError): + g(c, bounds=bounds_1) + + with pytest.warns(RuntimeWarning): + with pytest.raises(IndexError): + g(c, bounds=bounds_2) + else: + res = linprog(c=c, bounds=bounds_1, + method=self.method, options=self.options) + _assert_infeasible(res) + if do_presolve: + assert_equal(res.nit, 0) + res = linprog(c=c, bounds=bounds_2, + method=self.method, options=self.options) + _assert_infeasible(res) + if do_presolve: + assert_equal(res.nit, 0) + + def test_empty_constraint_1(self): + c = [-1, -2] + res = linprog(c, method=self.method, options=self.options) + _assert_unbounded(res) + + def test_empty_constraint_2(self): + c = [-1, 1, -1, 1] + bounds = [(0, np.inf), (-np.inf, 0), (-1, 1), (-1, 1)] + res = linprog(c, bounds=bounds, + method=self.method, options=self.options) + _assert_unbounded(res) + # Unboundedness detected in presolve requires no iterations + if self.options.get('presolve', True): + assert_equal(res.nit, 0) + + def test_empty_constraint_3(self): + c = [1, -1, 1, -1] + bounds = [(0, np.inf), (-np.inf, 0), (-1, 1), (-1, 1)] + res = linprog(c, bounds=bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[0, 0, -1, 1], desired_fun=-2) + + def test_inequality_constraints(self): + # Minimize linear function subject to linear inequality constraints. + # http://www.dam.brown.edu/people/huiwang/classes/am121/Archive/simplex_121_c.pdf + c = np.array([3, 2]) * -1 # maximize + A_ub = [[2, 1], + [1, 1], + [1, 0]] + b_ub = [10, 8, 4] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-18, desired_x=[2, 6]) + + def test_inequality_constraints2(self): + # Minimize linear function subject to linear inequality constraints. + # http://www.statslab.cam.ac.uk/~ff271/teaching/opt/notes/notes8.pdf + # (dead link) + c = [6, 3] + A_ub = [[0, 3], + [-1, -1], + [-2, 1]] + b_ub = [2, -1, -1] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=5, desired_x=[2 / 3, 1 / 3]) + + def test_bounds_simple(self): + c = [1, 2] + bounds = (1, 2) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[1, 1]) + + bounds = [(1, 2), (1, 2)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[1, 1]) + + def test_bounded_below_only_1(self): + c = np.array([1.0]) + A_eq = np.array([[1.0]]) + b_eq = np.array([3.0]) + bounds = (1.0, None) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=3, desired_x=[3]) + + def test_bounded_below_only_2(self): + c = np.ones(3) + A_eq = np.eye(3) + b_eq = np.array([1, 2, 3]) + bounds = (0.5, np.inf) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=b_eq, desired_fun=np.sum(b_eq)) + + def test_bounded_above_only_1(self): + c = np.array([1.0]) + A_eq = np.array([[1.0]]) + b_eq = np.array([3.0]) + bounds = (None, 10.0) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=3, desired_x=[3]) + + def test_bounded_above_only_2(self): + c = np.ones(3) + A_eq = np.eye(3) + b_eq = np.array([1, 2, 3]) + bounds = (-np.inf, 4) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=b_eq, desired_fun=np.sum(b_eq)) + + def test_bounds_infinity(self): + c = np.ones(3) + A_eq = np.eye(3) + b_eq = np.array([1, 2, 3]) + bounds = (-np.inf, np.inf) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=b_eq, desired_fun=np.sum(b_eq)) + + def test_bounds_mixed(self): + # Problem has one unbounded variable and + # another with a negative lower bound. + c = np.array([-1, 4]) * -1 # maximize + A_ub = np.array([[-3, 1], + [1, 2]], dtype=np.float64) + b_ub = [6, 4] + x0_bounds = (-np.inf, np.inf) + x1_bounds = (-3, np.inf) + bounds = (x0_bounds, x1_bounds) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-80 / 7, desired_x=[-8 / 7, 18 / 7]) + + def test_bounds_equal_but_infeasible(self): + c = [-4, 1] + A_ub = [[7, -2], [0, 1], [2, -2]] + b_ub = [14, 0, 3] + bounds = [(2, 2), (0, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + def test_bounds_equal_but_infeasible2(self): + c = [-4, 1] + A_eq = [[7, -2], [0, 1], [2, -2]] + b_eq = [14, 0, 3] + bounds = [(2, 2), (0, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + def test_bounds_equal_no_presolve(self): + # There was a bug when a lower and upper bound were equal but + # presolve was not on to eliminate the variable. The bound + # was being converted to an equality constraint, but the bound + # was not eliminated, leading to issues in postprocessing. + c = [1, 2] + A_ub = [[1, 2], [1.1, 2.2]] + b_ub = [4, 8] + bounds = [(1, 2), (2, 2)] + + o = {key: self.options[key] for key in self.options} + o["presolve"] = False + + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + _assert_infeasible(res) + + def test_zero_column_1(self): + m, n = 3, 4 + np.random.seed(0) + c = np.random.rand(n) + c[1] = 1 + A_eq = np.random.rand(m, n) + A_eq[:, 1] = 0 + b_eq = np.random.rand(m) + A_ub = [[1, 0, 1, 1]] + b_ub = 3 + bounds = [(-10, 10), (-10, 10), (-10, None), (None, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-9.7087836730413404) + + def test_zero_column_2(self): + if self.method in {'highs-ds', 'highs-ipm'}: + # See upstream issue https://github.com/ERGO-Code/HiGHS/issues/648 + pytest.xfail() + + np.random.seed(0) + m, n = 2, 4 + c = np.random.rand(n) + c[1] = -1 + A_eq = np.random.rand(m, n) + A_eq[:, 1] = 0 + b_eq = np.random.rand(m) + + A_ub = np.random.rand(m, n) + A_ub[:, 1] = 0 + b_ub = np.random.rand(m) + bounds = (None, None) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_unbounded(res) + # Unboundedness detected in presolve + if self.options.get('presolve', True) and "highs" not in self.method: + # HiGHS detects unboundedness or infeasibility in presolve + # It needs an iteration of simplex to be sure of unboundedness + # Other solvers report that the problem is unbounded if feasible + assert_equal(res.nit, 0) + + def test_zero_row_1(self): + c = [1, 2, 3] + A_eq = [[0, 0, 0], [1, 1, 1], [0, 0, 0]] + b_eq = [0, 3, 0] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=3) + + def test_zero_row_2(self): + A_ub = [[0, 0, 0], [1, 1, 1], [0, 0, 0]] + b_ub = [0, 3, 0] + c = [1, 2, 3] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=0) + + def test_zero_row_3(self): + m, n = 2, 4 + c = np.random.rand(n) + A_eq = np.random.rand(m, n) + A_eq[0, :] = 0 + b_eq = np.random.rand(m) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + # Infeasibility detected in presolve + if self.options.get('presolve', True): + assert_equal(res.nit, 0) + + def test_zero_row_4(self): + m, n = 2, 4 + c = np.random.rand(n) + A_ub = np.random.rand(m, n) + A_ub[0, :] = 0 + b_ub = -np.random.rand(m) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + # Infeasibility detected in presolve + if self.options.get('presolve', True): + assert_equal(res.nit, 0) + + def test_singleton_row_eq_1(self): + c = [1, 1, 1, 2] + A_eq = [[1, 0, 0, 0], [0, 2, 0, 0], [1, 0, 0, 0], [1, 1, 1, 1]] + b_eq = [1, 2, 2, 4] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + # Infeasibility detected in presolve + if self.options.get('presolve', True): + assert_equal(res.nit, 0) + + def test_singleton_row_eq_2(self): + c = [1, 1, 1, 2] + A_eq = [[1, 0, 0, 0], [0, 2, 0, 0], [1, 0, 0, 0], [1, 1, 1, 1]] + b_eq = [1, 2, 1, 4] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=4) + + def test_singleton_row_ub_1(self): + c = [1, 1, 1, 2] + A_ub = [[1, 0, 0, 0], [0, 2, 0, 0], [-1, 0, 0, 0], [1, 1, 1, 1]] + b_ub = [1, 2, -2, 4] + bounds = [(None, None), (0, None), (0, None), (0, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + # Infeasibility detected in presolve + if self.options.get('presolve', True): + assert_equal(res.nit, 0) + + def test_singleton_row_ub_2(self): + c = [1, 1, 1, 2] + A_ub = [[1, 0, 0, 0], [0, 2, 0, 0], [-1, 0, 0, 0], [1, 1, 1, 1]] + b_ub = [1, 2, -0.5, 4] + bounds = [(None, None), (0, None), (0, None), (0, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=0.5) + + def test_infeasible(self): + # Test linprog response to an infeasible problem + c = [-1, -1] + A_ub = [[1, 0], + [0, 1], + [-1, -1]] + b_ub = [2, 2, -5] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + def test_infeasible_inequality_bounds(self): + c = [1] + A_ub = [[2]] + b_ub = 4 + bounds = (5, 6) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + # Infeasibility detected in presolve + if self.options.get('presolve', True): + assert_equal(res.nit, 0) + + def test_unbounded(self): + # Test linprog response to an unbounded problem + c = np.array([1, 1]) * -1 # maximize + A_ub = [[-1, 1], + [-1, -1]] + b_ub = [-1, -2] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_unbounded(res) + + def test_unbounded_below_no_presolve_corrected(self): + c = [1] + bounds = [(None, 1)] + + o = {key: self.options[key] for key in self.options} + o["presolve"] = False + + res = linprog(c=c, bounds=bounds, + method=self.method, + options=o) + if self.method == "revised simplex": + # Revised simplex has a special pathway for no constraints. + assert_equal(res.status, 5) + else: + _assert_unbounded(res) + + def test_unbounded_no_nontrivial_constraints_1(self): + """ + Test whether presolve pathway for detecting unboundedness after + constraint elimination is working. + """ + c = np.array([0, 0, 0, 1, -1, -1]) + A_ub = np.array([[1, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0], + [0, 0, 0, 0, 0, -1]]) + b_ub = np.array([2, -2, 0]) + bounds = [(None, None), (None, None), (None, None), + (-1, 1), (-1, 1), (0, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_unbounded(res) + if not self.method.lower().startswith("highs"): + assert_equal(res.x[-1], np.inf) + assert_equal(res.message[:36], + "The problem is (trivially) unbounded") + + def test_unbounded_no_nontrivial_constraints_2(self): + """ + Test whether presolve pathway for detecting unboundedness after + constraint elimination is working. + """ + c = np.array([0, 0, 0, 1, -1, 1]) + A_ub = np.array([[1, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 1]]) + b_ub = np.array([2, -2, 0]) + bounds = [(None, None), (None, None), (None, None), + (-1, 1), (-1, 1), (None, 0)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_unbounded(res) + if not self.method.lower().startswith("highs"): + assert_equal(res.x[-1], -np.inf) + assert_equal(res.message[:36], + "The problem is (trivially) unbounded") + + def test_cyclic_recovery(self): + # Test linprogs recovery from cycling using the Klee-Minty problem + # Klee-Minty https://www.math.ubc.ca/~israel/m340/kleemin3.pdf + c = np.array([100, 10, 1]) * -1 # maximize + A_ub = [[1, 0, 0], + [20, 1, 0], + [200, 20, 1]] + b_ub = [1, 100, 10000] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[0, 0, 10000], atol=5e-6, rtol=1e-7) + + def test_cyclic_bland(self): + # Test the effect of Bland's rule on a cycling problem + c = np.array([-10, 57, 9, 24.]) + A_ub = np.array([[0.5, -5.5, -2.5, 9], + [0.5, -1.5, -0.5, 1], + [1, 0, 0, 0]]) + b_ub = [0, 0, 1] + + # copy the existing options dictionary but change maxiter + maxiter = 100 + o = {key: val for key, val in self.options.items()} + o['maxiter'] = maxiter + + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + + if self.method == 'simplex' and not self.options.get('bland'): + # simplex cycles without Bland's rule + _assert_iteration_limit_reached(res, o['maxiter']) + else: + # other methods, including simplex with Bland's rule, succeed + _assert_success(res, desired_x=[1, 0, 1, 0]) + # note that revised simplex skips this test because it may or may not + # cycle depending on the initial basis + + def test_remove_redundancy_infeasibility(self): + # mostly a test of redundancy removal, which is carefully tested in + # test__remove_redundancy.py + m, n = 10, 10 + c = np.random.rand(n) + A_eq = np.random.rand(m, n) + b_eq = np.random.rand(m) + A_eq[-1, :] = 2 * A_eq[-2, :] + b_eq[-1] *= -1 + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "A_eq does not appear...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + ################# + # General Tests # + ################# + + def test_nontrivial_problem(self): + # Problem involves all constraint types, + # negative resource limits, and rounding issues. + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=f_star, desired_x=x_star) + + def test_lpgen_problem(self): + # Test linprog with a rather large problem (400 variables, + # 40 constraints) generated by https://gist.github.com/denis-bz/8647461 + A_ub, b_ub, c = lpgen_2d(20, 20) + + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "Solving system with option 'sym_pos'") + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-64.049494229) + + def test_network_flow(self): + # A network flow problem with supply and demand at nodes + # and with costs along directed edges. + # https://www.princeton.edu/~rvdb/542/lectures/lec10.pdf + c = [2, 4, 9, 11, 4, 3, 8, 7, 0, 15, 16, 18] + n, p = -1, 1 + A_eq = [ + [n, n, p, 0, p, 0, 0, 0, 0, p, 0, 0], + [p, 0, 0, p, 0, p, 0, 0, 0, 0, 0, 0], + [0, 0, n, n, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, p, p, 0, 0, p, 0], + [0, 0, 0, 0, n, n, n, 0, p, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, n, n, 0, 0, p], + [0, 0, 0, 0, 0, 0, 0, 0, 0, n, n, n]] + b_eq = [0, 19, -16, 33, 0, 0, -36] + with suppress_warnings() as sup: + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=755, atol=1e-6, rtol=1e-7) + + def test_network_flow_limited_capacity(self): + # A network flow problem with supply and demand at nodes + # and with costs and capacities along directed edges. + # http://blog.sommer-forst.de/2013/04/10/ + c = [2, 2, 1, 3, 1] + bounds = [ + [0, 4], + [0, 2], + [0, 2], + [0, 3], + [0, 5]] + n, p = -1, 1 + A_eq = [ + [n, n, 0, 0, 0], + [p, 0, n, n, 0], + [0, p, p, 0, n], + [0, 0, 0, p, p]] + b_eq = [-4, 0, 0, 4] + + with suppress_warnings() as sup: + # this is an UmfpackWarning but I had trouble importing it + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...") + sup.filter(OptimizeWarning, "A_eq does not appear...") + sup.filter(OptimizeWarning, "Solving system with option...") + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=14) + + def test_simplex_algorithm_wikipedia_example(self): + # https://en.wikipedia.org/wiki/Simplex_algorithm#Example + c = [-2, -3, -4] + A_ub = [ + [3, 2, 1], + [2, 5, 3]] + b_ub = [10, 15] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-20) + + def test_enzo_example(self): + # https://github.com/scipy/scipy/issues/1779 lp2.py + # + # Translated from Octave code at: + # http://www.ecs.shimane-u.ac.jp/~kyoshida/lpeng.htm + # and placed under MIT licence by Enzo Michelangeli + # with permission explicitly granted by the original author, + # Prof. Kazunobu Yoshida + c = [4, 8, 3, 0, 0, 0] + A_eq = [ + [2, 5, 3, -1, 0, 0], + [3, 2.5, 8, 0, -1, 0], + [8, 10, 4, 0, 0, -1]] + b_eq = [185, 155, 600] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=317.5, + desired_x=[66.25, 0, 17.5, 0, 183.75, 0], + atol=6e-6, rtol=1e-7) + + def test_enzo_example_b(self): + # rescued from https://github.com/scipy/scipy/pull/218 + c = [2.8, 6.3, 10.8, -2.8, -6.3, -10.8] + A_eq = [[-1, -1, -1, 0, 0, 0], + [0, 0, 0, 1, 1, 1], + [1, 0, 0, 1, 0, 0], + [0, 1, 0, 0, 1, 0], + [0, 0, 1, 0, 0, 1]] + b_eq = [-0.5, 0.4, 0.3, 0.3, 0.3] + + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "A_eq does not appear...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-1.77, + desired_x=[0.3, 0.2, 0.0, 0.0, 0.1, 0.3]) + + def test_enzo_example_c_with_degeneracy(self): + # rescued from https://github.com/scipy/scipy/pull/218 + m = 20 + c = -np.ones(m) + tmp = 2 * np.pi * np.arange(1, m + 1) / (m + 1) + A_eq = np.vstack((np.cos(tmp) - 1, np.sin(tmp))) + b_eq = [0, 0] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=0, desired_x=np.zeros(m)) + + def test_enzo_example_c_with_unboundedness(self): + # rescued from https://github.com/scipy/scipy/pull/218 + m = 50 + c = -np.ones(m) + tmp = 2 * np.pi * np.arange(m) / (m + 1) + # This test relies on `cos(0) -1 == sin(0)`, so ensure that's true + # (SIMD code or -ffast-math may cause spurious failures otherwise) + row0 = np.cos(tmp) - 1 + row0[0] = 0.0 + row1 = np.sin(tmp) + row1[0] = 0.0 + A_eq = np.vstack((row0, row1)) + b_eq = [0, 0] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_unbounded(res) + + def test_enzo_example_c_with_infeasibility(self): + # rescued from https://github.com/scipy/scipy/pull/218 + m = 50 + c = -np.ones(m) + tmp = 2 * np.pi * np.arange(m) / (m + 1) + A_eq = np.vstack((np.cos(tmp) - 1, np.sin(tmp))) + b_eq = [1, 1] + + o = {key: self.options[key] for key in self.options} + o["presolve"] = False + + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + _assert_infeasible(res) + + def test_basic_artificial_vars(self): + # Problem is chosen to test two phase simplex methods when at the end + # of phase 1 some artificial variables remain in the basis. + # Also, for `method='simplex'`, the row in the tableau corresponding + # with the artificial variables is not all zero. + c = np.array([-0.1, -0.07, 0.004, 0.004, 0.004, 0.004]) + A_ub = np.array([[1.0, 0, 0, 0, 0, 0], [-1.0, 0, 0, 0, 0, 0], + [0, -1.0, 0, 0, 0, 0], [0, 1.0, 0, 0, 0, 0], + [1.0, 1.0, 0, 0, 0, 0]]) + b_ub = np.array([3.0, 3.0, 3.0, 3.0, 20.0]) + A_eq = np.array([[1.0, 0, -1, 1, -1, 1], [0, -1.0, -1, 1, -1, 1]]) + b_eq = np.array([0, 0]) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=0, desired_x=np.zeros_like(c), + atol=2e-6) + + def test_optimize_result(self): + # check all fields in OptimizeResult + c, A_ub, b_ub, A_eq, b_eq, bounds = very_random_gen(0) + res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, options=self.options) + assert_(res.success) + assert_(res.nit) + assert_(not res.status) + if 'highs' not in self.method: + # HiGHS status/message tested separately + assert_(res.message == "Optimization terminated successfully.") + assert_allclose(c @ res.x, res.fun) + assert_allclose(b_eq - A_eq @ res.x, res.con, atol=1e-11) + assert_allclose(b_ub - A_ub @ res.x, res.slack, atol=1e-11) + for key in ['eqlin', 'ineqlin', 'lower', 'upper']: + if key in res.keys(): + assert isinstance(res[key]['marginals'], np.ndarray) + assert isinstance(res[key]['residual'], np.ndarray) + + ################# + # Bug Fix Tests # + ################# + + def test_bug_5400(self): + # https://github.com/scipy/scipy/issues/5400 + bounds = [ + (0, None), + (0, 100), (0, 100), (0, 100), (0, 100), (0, 100), (0, 100), + (0, 900), (0, 900), (0, 900), (0, 900), (0, 900), (0, 900), + (0, None), (0, None), (0, None), (0, None), (0, None), (0, None)] + + f = 1 / 9 + g = -1e4 + h = -3.1 + A_ub = np.array([ + [1, -2.99, 0, 0, -3, 0, 0, 0, -1, -1, 0, -1, -1, 1, 1, 0, 0, 0, 0], + [1, 0, -2.9, h, 0, -3, 0, -1, 0, 0, -1, 0, -1, 0, 0, 1, 1, 0, 0], + [1, 0, 0, h, 0, 0, -3, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 1, 1], + [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], + [0, 1.99, -1, -1, 0, 0, 0, -1, f, f, 0, 0, 0, g, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 2, -1, -1, 0, 0, 0, -1, f, f, 0, g, 0, 0, 0, 0], + [0, -1, 1.9, 2.1, 0, 0, 0, f, -1, -1, 0, 0, 0, 0, 0, g, 0, 0, 0], + [0, 0, 0, 0, -1, 2, -1, 0, 0, 0, f, -1, f, 0, 0, 0, g, 0, 0], + [0, -1, -1, 2.1, 0, 0, 0, f, f, -1, 0, 0, 0, 0, 0, 0, 0, g, 0], + [0, 0, 0, 0, -1, -1, 2, 0, 0, 0, f, f, -1, 0, 0, 0, 0, 0, g]]) + + b_ub = np.array([ + 0.0, 0, 0, 100, 100, 100, 100, 100, 100, 900, 900, 900, 900, 900, + 900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) + + c = np.array([-1.0, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]) + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, + "Solving system with option 'sym_pos'") + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=-106.63507541835018) + + def test_bug_6139(self): + # linprog(method='simplex') fails to find a basic feasible solution + # if phase 1 pseudo-objective function is outside the provided tol. + # https://github.com/scipy/scipy/issues/6139 + + # Note: This is not strictly a bug as the default tolerance determines + # if a result is "close enough" to zero and should not be expected + # to work for all cases. + + c = np.array([1, 1, 1]) + A_eq = np.array([[1., 0., 0.], [-1000., 0., - 1000.]]) + b_eq = np.array([5.00000000e+00, -1.00000000e+04]) + A_ub = -np.array([[0., 1000000., 1010000.]]) + b_ub = -np.array([10000000.]) + bounds = (None, None) + + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + _assert_success(res, desired_fun=14.95, + desired_x=np.array([5, 4.95, 5])) + + def test_bug_6690(self): + # linprog simplex used to violate bound constraint despite reporting + # success. + # https://github.com/scipy/scipy/issues/6690 + + A_eq = np.array([[0, 0, 0, 0.93, 0, 0.65, 0, 0, 0.83, 0]]) + b_eq = np.array([0.9626]) + A_ub = np.array([ + [0, 0, 0, 1.18, 0, 0, 0, -0.2, 0, -0.22], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0.43, 0, 0, 0, 0, 0, 0], + [0, -1.22, -0.25, 0, 0, 0, -2.06, 0, 0, 1.37], + [0, 0, 0, 0, 0, 0, 0, -0.25, 0, 0] + ]) + b_ub = np.array([0.615, 0, 0.172, -0.869, -0.022]) + bounds = np.array([ + [-0.84, -0.97, 0.34, 0.4, -0.33, -0.74, 0.47, 0.09, -1.45, -0.73], + [0.37, 0.02, 2.86, 0.86, 1.18, 0.5, 1.76, 0.17, 0.32, -0.15] + ]).T + c = np.array([ + -1.64, 0.7, 1.8, -1.06, -1.16, 0.26, 2.13, 1.53, 0.66, 0.28 + ]) + + with suppress_warnings() as sup: + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(OptimizeWarning, + "Solving system with option 'cholesky'") + sup.filter(OptimizeWarning, "Solving system with option 'sym_pos'") + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + desired_fun = -1.19099999999 + desired_x = np.array([0.3700, -0.9700, 0.3400, 0.4000, 1.1800, + 0.5000, 0.4700, 0.0900, 0.3200, -0.7300]) + _assert_success(res, desired_fun=desired_fun, desired_x=desired_x) + + # Add small tol value to ensure arrays are less than or equal. + atol = 1e-6 + assert_array_less(bounds[:, 0] - atol, res.x) + assert_array_less(res.x, bounds[:, 1] + atol) + + def test_bug_7044(self): + # linprog simplex failed to "identify correct constraints" (?) + # leading to a non-optimal solution if A is rank-deficient. + # https://github.com/scipy/scipy/issues/7044 + + A_eq, b_eq, c, _, _ = magic_square(3) + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "A_eq does not appear...") + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + desired_fun = 1.730550597 + _assert_success(res, desired_fun=desired_fun) + assert_allclose(A_eq.dot(res.x), b_eq) + assert_array_less(np.zeros(res.x.size) - 1e-5, res.x) + + def test_bug_7237(self): + # https://github.com/scipy/scipy/issues/7237 + # linprog simplex "explodes" when the pivot value is very + # close to zero. + + c = np.array([-1, 0, 0, 0, 0, 0, 0, 0, 0]) + A_ub = np.array([ + [1., -724., 911., -551., -555., -896., 478., -80., -293.], + [1., 566., 42., 937., 233., 883., 392., -909., 57.], + [1., -208., -894., 539., 321., 532., -924., 942., 55.], + [1., 857., -859., 83., 462., -265., -971., 826., 482.], + [1., 314., -424., 245., -424., 194., -443., -104., -429.], + [1., 540., 679., 361., 149., -827., 876., 633., 302.], + [0., -1., -0., -0., -0., -0., -0., -0., -0.], + [0., -0., -1., -0., -0., -0., -0., -0., -0.], + [0., -0., -0., -1., -0., -0., -0., -0., -0.], + [0., -0., -0., -0., -1., -0., -0., -0., -0.], + [0., -0., -0., -0., -0., -1., -0., -0., -0.], + [0., -0., -0., -0., -0., -0., -1., -0., -0.], + [0., -0., -0., -0., -0., -0., -0., -1., -0.], + [0., -0., -0., -0., -0., -0., -0., -0., -1.], + [0., 1., 0., 0., 0., 0., 0., 0., 0.], + [0., 0., 1., 0., 0., 0., 0., 0., 0.], + [0., 0., 0., 1., 0., 0., 0., 0., 0.], + [0., 0., 0., 0., 1., 0., 0., 0., 0.], + [0., 0., 0., 0., 0., 1., 0., 0., 0.], + [0., 0., 0., 0., 0., 0., 1., 0., 0.], + [0., 0., 0., 0., 0., 0., 0., 1., 0.], + [0., 0., 0., 0., 0., 0., 0., 0., 1.] + ]) + b_ub = np.array([ + 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., + 0., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1.]) + A_eq = np.array([[0., 1., 1., 1., 1., 1., 1., 1., 1.]]) + b_eq = np.array([[1.]]) + bounds = [(None, None)] * 9 + + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=108.568535, atol=1e-6) + + def test_bug_8174(self): + # https://github.com/scipy/scipy/issues/8174 + # The simplex method sometimes "explodes" if the pivot value is very + # close to zero. + A_ub = np.array([ + [22714, 1008, 13380, -2713.5, -1116], + [-4986, -1092, -31220, 17386.5, 684], + [-4986, 0, 0, -2713.5, 0], + [22714, 0, 0, 17386.5, 0]]) + b_ub = np.zeros(A_ub.shape[0]) + c = -np.ones(A_ub.shape[1]) + bounds = [(0, 1)] * A_ub.shape[1] + with suppress_warnings() as sup: + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + if self.options.get('tol', 1e-9) < 1e-10 and self.method == 'simplex': + _assert_unable_to_find_basic_feasible_sol(res) + else: + _assert_success(res, desired_fun=-2.0080717488789235, atol=1e-6) + + def test_bug_8174_2(self): + # Test supplementary example from issue 8174. + # https://github.com/scipy/scipy/issues/8174 + # https://stackoverflow.com/questions/47717012/linprog-in-scipy-optimize-checking-solution + c = np.array([1, 0, 0, 0, 0, 0, 0]) + A_ub = -np.identity(7) + b_ub = np.array([[-2], [-2], [-2], [-2], [-2], [-2], [-2]]) + A_eq = np.array([ + [1, 1, 1, 1, 1, 1, 0], + [0.3, 1.3, 0.9, 0, 0, 0, -1], + [0.3, 0, 0, 0, 0, 0, -2/3], + [0, 0.65, 0, 0, 0, 0, -1/15], + [0, 0, 0.3, 0, 0, 0, -1/15] + ]) + b_eq = np.array([[100], [0], [0], [0], [0]]) + + with suppress_warnings() as sup: + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(OptimizeWarning, "A_eq does not appear...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_fun=43.3333333331385) + + def test_bug_8561(self): + # Test that pivot row is chosen correctly when using Bland's rule + # This was originally written for the simplex method with + # Bland's rule only, but it doesn't hurt to test all methods/options + # https://github.com/scipy/scipy/issues/8561 + c = np.array([7, 0, -4, 1.5, 1.5]) + A_ub = np.array([ + [4, 5.5, 1.5, 1.0, -3.5], + [1, -2.5, -2, 2.5, 0.5], + [3, -0.5, 4, -12.5, -7], + [-1, 4.5, 2, -3.5, -2], + [5.5, 2, -4.5, -1, 9.5]]) + b_ub = np.array([0, 0, 0, 0, 1]) + res = linprog(c, A_ub=A_ub, b_ub=b_ub, options=self.options, + method=self.method) + _assert_success(res, desired_x=[0, 0, 19, 16/3, 29/3]) + + def test_bug_8662(self): + # linprog simplex used to report incorrect optimal results + # https://github.com/scipy/scipy/issues/8662 + c = [-10, 10, 6, 3] + A_ub = [[8, -8, -4, 6], + [-8, 8, 4, -6], + [-4, 4, 8, -4], + [3, -3, -3, -10]] + b_ub = [9, -9, -9, -4] + bounds = [(0, None), (0, None), (0, None), (0, None)] + desired_fun = 36.0000000000 + + with suppress_warnings() as sup: + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res1 = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + + # Set boundary condition as a constraint + A_ub.append([0, 0, -1, 0]) + b_ub.append(0) + bounds[2] = (None, None) + + with suppress_warnings() as sup: + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res2 = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + rtol = 1e-5 + _assert_success(res1, desired_fun=desired_fun, rtol=rtol) + _assert_success(res2, desired_fun=desired_fun, rtol=rtol) + + def test_bug_8663(self): + # exposed a bug in presolve + # https://github.com/scipy/scipy/issues/8663 + c = [1, 5] + A_eq = [[0, -7]] + b_eq = [-6] + bounds = [(0, None), (None, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[0, 6./7], desired_fun=5*6./7) + + def test_bug_8664(self): + # interior-point has trouble with this when presolve is off + # tested for interior-point with presolve off in TestLinprogIPSpecific + # https://github.com/scipy/scipy/issues/8664 + c = [4] + A_ub = [[2], [5]] + b_ub = [4, 4] + A_eq = [[0], [-8], [9]] + b_eq = [3, 2, 10] + with suppress_warnings() as sup: + sup.filter(RuntimeWarning) + sup.filter(OptimizeWarning, "Solving system with option...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_infeasible(res) + + def test_bug_8973(self): + """ + Test whether bug described at: + https://github.com/scipy/scipy/issues/8973 + was fixed. + """ + c = np.array([0, 0, 0, 1, -1]) + A_ub = np.array([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]]) + b_ub = np.array([2, -2]) + bounds = [(None, None), (None, None), (None, None), (-1, 1), (-1, 1)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + # solution vector x is not unique + _assert_success(res, desired_fun=-2) + # HiGHS IPM had an issue where the following wasn't true! + assert_equal(c @ res.x, res.fun) + + def test_bug_8973_2(self): + """ + Additional test for: + https://github.com/scipy/scipy/issues/8973 + suggested in + https://github.com/scipy/scipy/pull/8985 + review by @antonior92 + """ + c = np.zeros(1) + A_ub = np.array([[1]]) + b_ub = np.array([-2]) + bounds = (None, None) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[-2], desired_fun=0) + + def test_bug_10124(self): + """ + Test for linprog docstring problem + 'disp'=True caused revised simplex failure + """ + c = np.zeros(1) + A_ub = np.array([[1]]) + b_ub = np.array([-2]) + bounds = (None, None) + c = [-1, 4] + A_ub = [[-3, 1], [1, 2]] + b_ub = [6, 4] + bounds = [(None, None), (-3, None)] + o = {"disp": True} + o.update(self.options) + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + _assert_success(res, desired_x=[10, -3], desired_fun=-22) + + def test_bug_10349(self): + """ + Test for redundancy removal tolerance issue + https://github.com/scipy/scipy/issues/10349 + """ + A_eq = np.array([[1, 1, 0, 0, 0, 0], + [0, 0, 1, 1, 0, 0], + [0, 0, 0, 0, 1, 1], + [1, 0, 1, 0, 0, 0], + [0, 0, 0, 1, 1, 0], + [0, 1, 0, 0, 0, 1]]) + b_eq = np.array([221, 210, 10, 141, 198, 102]) + c = np.concatenate((0, 1, np.zeros(4)), axis=None) + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "A_eq does not appear...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options) + _assert_success(res, desired_x=[129, 92, 12, 198, 0, 10], desired_fun=92) + + @pytest.mark.skipif(sys.platform == 'darwin', + reason=("Failing on some local macOS builds, " + "see gh-13846")) + def test_bug_10466(self): + """ + Test that autoscale fixes poorly-scaled problem + """ + c = [-8., -0., -8., -0., -8., -0., -0., -0., -0., -0., -0., -0., -0.] + A_eq = [[1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], + [0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], + [0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0.], + [1., 0., 1., 0., 1., 0., -1., 0., 0., 0., 0., 0., 0.], + [1., 0., 1., 0., 1., 0., 0., 1., 0., 0., 0., 0., 0.], + [1., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], + [1., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], + [1., 0., 1., 0., 1., 0., 0., 0., 0., 0., 1., 0., 0.], + [0., 0., 1., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0.], + [0., 0., 1., 0., 1., 0., 0., 0., 0., 0., 0., 0., 1.]] + + b_eq = [3.14572800e+08, 4.19430400e+08, 5.24288000e+08, + 1.00663296e+09, 1.07374182e+09, 1.07374182e+09, + 1.07374182e+09, 1.07374182e+09, 1.07374182e+09, + 1.07374182e+09] + + o = {} + # HiGHS methods don't use autoscale option + if not self.method.startswith("highs"): + o = {"autoscale": True} + o.update(self.options) + + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "Solving system with option...") + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...") + sup.filter(RuntimeWarning, "divide by zero encountered...") + sup.filter(RuntimeWarning, "overflow encountered...") + sup.filter(RuntimeWarning, "invalid value encountered...") + sup.filter(LinAlgWarning, "Ill-conditioned matrix...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + assert_allclose(res.fun, -8589934560) + + def test_bug_20584(self): + """ + Test that when integrality is a list of all zeros, linprog gives the + same result as when it is an array of all zeros / integrality=None + """ + c = [1, 1] + A_ub = [[-1, 0]] + b_ub = [-2.5] + res1 = linprog(c, A_ub=A_ub, b_ub=b_ub, integrality=[0, 0]) + res2 = linprog(c, A_ub=A_ub, b_ub=b_ub, integrality=np.asarray([0, 0])) + res3 = linprog(c, A_ub=A_ub, b_ub=b_ub, integrality=None) + assert_equal(res1.x, res2.x) + assert_equal(res1.x, res3.x) + + +######################### +# Method-specific Tests # +######################### + + +@pytest.mark.filterwarnings("ignore::DeprecationWarning") +class LinprogSimplexTests(LinprogCommonTests): + method = "simplex" + + +@pytest.mark.filterwarnings("ignore::DeprecationWarning") +class LinprogIPTests(LinprogCommonTests): + method = "interior-point" + + def test_bug_10466(self): + pytest.skip("Test is failing, but solver is deprecated.") + + +@pytest.mark.filterwarnings("ignore::DeprecationWarning") +class LinprogRSTests(LinprogCommonTests): + method = "revised simplex" + + # Revised simplex does not reliably solve these problems. + # Failure is intermittent due to the random choice of elements to complete + # the basis after phase 1 terminates. In any case, linprog exists + # gracefully, reporting numerical difficulties. I do not think this should + # prevent revised simplex from being merged, as it solves the problems + # most of the time and solves a broader range of problems than the existing + # simplex implementation. + # I believe that the root cause is the same for all three and that this + # same issue prevents revised simplex from solving many other problems + # reliably. Somehow the pivoting rule allows the algorithm to pivot into + # a singular basis. I haven't been able to find a reference that + # acknowledges this possibility, suggesting that there is a bug. On the + # other hand, the pivoting rule is quite simple, and I can't find a + # mistake, which suggests that this is a possibility with the pivoting + # rule. Hopefully, a better pivoting rule will fix the issue. + + def test_bug_5400(self): + pytest.skip("Intermittent failure acceptable.") + + def test_bug_8662(self): + pytest.skip("Intermittent failure acceptable.") + + def test_network_flow(self): + pytest.skip("Intermittent failure acceptable.") + + +class LinprogHiGHSTests(LinprogCommonTests): + def test_callback(self): + # this is the problem from test_callback + def cb(res): + return None + c = np.array([-3, -2]) + A_ub = [[2, 1], [1, 1], [1, 0]] + b_ub = [10, 8, 4] + assert_raises(NotImplementedError, linprog, c, A_ub=A_ub, b_ub=b_ub, + callback=cb, method=self.method) + res = linprog(c, A_ub=A_ub, b_ub=b_ub, method=self.method) + _assert_success(res, desired_fun=-18.0, desired_x=[2, 6]) + + @pytest.mark.parametrize("options", + [{"maxiter": -1}, + {"disp": -1}, + {"presolve": -1}, + {"time_limit": -1}, + {"dual_feasibility_tolerance": -1}, + {"primal_feasibility_tolerance": -1}, + {"ipm_optimality_tolerance": -1}, + {"simplex_dual_edge_weight_strategy": "ekki"}, + ]) + def test_invalid_option_values(self, options): + def f(options): + linprog(1, method=self.method, options=options) + options.update(self.options) + assert_warns(OptimizeWarning, f, options=options) + + def test_crossover(self): + A_eq, b_eq, c, _, _ = magic_square(4) + bounds = (0, 1) + res = linprog(c, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, options=self.options) + # there should be nonzero crossover iterations for IPM (only) + assert_equal(res.crossover_nit == 0, self.method != "highs-ipm") + + @pytest.mark.fail_slow(5) + def test_marginals(self): + # Ensure lagrange multipliers are correct by comparing the derivative + # w.r.t. b_ub/b_eq/ub/lb to the reported duals. + c, A_ub, b_ub, A_eq, b_eq, bounds = very_random_gen(seed=0) + res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, options=self.options) + lb, ub = bounds.T + + # sensitivity w.r.t. b_ub + def f_bub(x): + return linprog(c, A_ub, x, A_eq, b_eq, bounds, + method=self.method).fun + + dfdbub = approx_derivative(f_bub, b_ub, method='3-point', f0=res.fun) + assert_allclose(res.ineqlin.marginals, dfdbub) + + # sensitivity w.r.t. b_eq + def f_beq(x): + return linprog(c, A_ub, b_ub, A_eq, x, bounds, + method=self.method).fun + + dfdbeq = approx_derivative(f_beq, b_eq, method='3-point', f0=res.fun) + assert_allclose(res.eqlin.marginals, dfdbeq) + + # sensitivity w.r.t. lb + def f_lb(x): + bounds = np.array([x, ub]).T + return linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method).fun + + with np.errstate(invalid='ignore'): + # approx_derivative has trouble where lb is infinite + dfdlb = approx_derivative(f_lb, lb, method='3-point', f0=res.fun) + dfdlb[~np.isfinite(lb)] = 0 + + assert_allclose(res.lower.marginals, dfdlb) + + # sensitivity w.r.t. ub + def f_ub(x): + bounds = np.array([lb, x]).T + return linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method).fun + + with np.errstate(invalid='ignore'): + dfdub = approx_derivative(f_ub, ub, method='3-point', f0=res.fun) + dfdub[~np.isfinite(ub)] = 0 + + assert_allclose(res.upper.marginals, dfdub) + + def test_dual_feasibility(self): + # Ensure solution is dual feasible using marginals + c, A_ub, b_ub, A_eq, b_eq, bounds = very_random_gen(seed=42) + res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, options=self.options) + + # KKT dual feasibility equation from Theorem 1 from + # http://www.personal.psu.edu/cxg286/LPKKT.pdf + resid = (-c + A_ub.T @ res.ineqlin.marginals + + A_eq.T @ res.eqlin.marginals + + res.upper.marginals + + res.lower.marginals) + assert_allclose(resid, 0, atol=1e-12) + + def test_complementary_slackness(self): + # Ensure that the complementary slackness condition is satisfied. + c, A_ub, b_ub, A_eq, b_eq, bounds = very_random_gen(seed=42) + res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, options=self.options) + + # KKT complementary slackness equation from Theorem 1 from + # http://www.personal.psu.edu/cxg286/LPKKT.pdf modified for + # non-zero RHS + assert np.allclose(res.ineqlin.marginals @ (b_ub - A_ub @ res.x), 0) + + +################################ +# Simplex Option-Specific Tests# +################################ + + +class TestLinprogSimplexDefault(LinprogSimplexTests): + + def setup_method(self): + self.options = {} + + def test_bug_5400(self): + pytest.skip("Simplex fails on this problem.") + + def test_bug_7237_low_tol(self): + # Fails if the tolerance is too strict. Here, we test that + # even if the solution is wrong, the appropriate error is raised. + pytest.skip("Simplex fails on this problem.") + + def test_bug_8174_low_tol(self): + # Fails if the tolerance is too strict. Here, we test that + # even if the solution is wrong, the appropriate warning is issued. + self.options.update({'tol': 1e-12}) + with pytest.warns(OptimizeWarning): + super().test_bug_8174() + + +class TestLinprogSimplexBland(LinprogSimplexTests): + + def setup_method(self): + self.options = {'bland': True} + + def test_bug_5400(self): + pytest.skip("Simplex fails on this problem.") + + def test_bug_8174_low_tol(self): + # Fails if the tolerance is too strict. Here, we test that + # even if the solution is wrong, the appropriate error is raised. + self.options.update({'tol': 1e-12}) + with pytest.raises(AssertionError): + with pytest.warns(OptimizeWarning): + super().test_bug_8174() + + +class TestLinprogSimplexNoPresolve(LinprogSimplexTests): + + def setup_method(self): + self.options = {'presolve': False} + + is_32_bit = np.intp(0).itemsize < 8 + is_linux = sys.platform.startswith('linux') + + @pytest.mark.xfail( + condition=is_32_bit and is_linux, + reason='Fails with warning on 32-bit linux') + def test_bug_5400(self): + super().test_bug_5400() + + def test_bug_6139_low_tol(self): + # Linprog(method='simplex') fails to find a basic feasible solution + # if phase 1 pseudo-objective function is outside the provided tol. + # https://github.com/scipy/scipy/issues/6139 + # Without ``presolve`` eliminating such rows the result is incorrect. + self.options.update({'tol': 1e-12}) + with pytest.raises(AssertionError, match='linprog status 4'): + return super().test_bug_6139() + + def test_bug_7237_low_tol(self): + pytest.skip("Simplex fails on this problem.") + + def test_bug_8174_low_tol(self): + # Fails if the tolerance is too strict. Here, we test that + # even if the solution is wrong, the appropriate warning is issued. + self.options.update({'tol': 1e-12}) + with pytest.warns(OptimizeWarning): + super().test_bug_8174() + + def test_unbounded_no_nontrivial_constraints_1(self): + pytest.skip("Tests behavior specific to presolve") + + def test_unbounded_no_nontrivial_constraints_2(self): + pytest.skip("Tests behavior specific to presolve") + + +####################################### +# Interior-Point Option-Specific Tests# +####################################### + + +class TestLinprogIPDense(LinprogIPTests): + options = {"sparse": False} + + # see https://github.com/scipy/scipy/issues/20216 for skip reason + @pytest.mark.skipif( + sys.platform == 'darwin', + reason="Fails on some macOS builds for reason not relevant to test" + ) + def test_bug_6139(self): + super().test_bug_6139() + +if has_cholmod: + class TestLinprogIPSparseCholmod(LinprogIPTests): + options = {"sparse": True, "cholesky": True} + + +if has_umfpack: + class TestLinprogIPSparseUmfpack(LinprogIPTests): + options = {"sparse": True, "cholesky": False} + + def test_network_flow_limited_capacity(self): + pytest.skip("Failing due to numerical issues on some platforms.") + + +class TestLinprogIPSparse(LinprogIPTests): + options = {"sparse": True, "cholesky": False, "sym_pos": False} + + @pytest.mark.skipif( + sys.platform == 'darwin', + reason="Fails on macOS x86 Accelerate builds (gh-20510)" + ) + @pytest.mark.xfail_on_32bit("This test is sensitive to machine epsilon level " + "perturbations in linear system solution in " + "_linprog_ip._sym_solve.") + def test_bug_6139(self): + super().test_bug_6139() + + @pytest.mark.xfail(reason='Fails with ATLAS, see gh-7877') + def test_bug_6690(self): + # Test defined in base class, but can't mark as xfail there + super().test_bug_6690() + + def test_magic_square_sparse_no_presolve(self): + # test linprog with a problem with a rank-deficient A_eq matrix + A_eq, b_eq, c, _, _ = magic_square(3) + bounds = (0, 1) + + with suppress_warnings() as sup: + if has_umfpack: + sup.filter(UmfpackWarning) + sup.filter(MatrixRankWarning, "Matrix is exactly singular") + sup.filter(OptimizeWarning, "Solving system with option...") + + o = {key: self.options[key] for key in self.options} + o["presolve"] = False + + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + _assert_success(res, desired_fun=1.730550597) + + def test_sparse_solve_options(self): + # checking that problem is solved with all column permutation options + A_eq, b_eq, c, _, _ = magic_square(3) + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "A_eq does not appear...") + sup.filter(OptimizeWarning, "Invalid permc_spec option") + o = {key: self.options[key] for key in self.options} + permc_specs = ('NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', + 'COLAMD', 'ekki-ekki-ekki') + # 'ekki-ekki-ekki' raises warning about invalid permc_spec option + # and uses default + for permc_spec in permc_specs: + o["permc_spec"] = permc_spec + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=o) + _assert_success(res, desired_fun=1.730550597) + + +class TestLinprogIPSparsePresolve(LinprogIPTests): + options = {"sparse": True, "_sparse_presolve": True} + + @pytest.mark.skipif( + sys.platform == 'darwin', + reason="Fails on macOS x86 Accelerate builds (gh-20510)" + ) + @pytest.mark.xfail_on_32bit("This test is sensitive to machine epsilon level " + "perturbations in linear system solution in " + "_linprog_ip._sym_solve.") + def test_bug_6139(self): + super().test_bug_6139() + + def test_enzo_example_c_with_infeasibility(self): + pytest.skip('_sparse_presolve=True incompatible with presolve=False') + + @pytest.mark.xfail(reason='Fails with ATLAS, see gh-7877') + def test_bug_6690(self): + # Test defined in base class, but can't mark as xfail there + super().test_bug_6690() + + +@pytest.mark.filterwarnings("ignore::DeprecationWarning") +class TestLinprogIPSpecific: + method = "interior-point" + # the following tests don't need to be performed separately for + # sparse presolve, sparse after presolve, and dense + + def test_solver_select(self): + # check that default solver is selected as expected + if has_cholmod: + options = {'sparse': True, 'cholesky': True} + elif has_umfpack: + options = {'sparse': True, 'cholesky': False} + else: + options = {'sparse': True, 'cholesky': False, 'sym_pos': False} + A, b, c = lpgen_2d(20, 20) + res1 = linprog(c, A_ub=A, b_ub=b, method=self.method, options=options) + res2 = linprog(c, A_ub=A, b_ub=b, method=self.method) # default solver + assert_allclose(res1.fun, res2.fun, + err_msg="linprog default solver unexpected result", + rtol=2e-15, atol=1e-15) + + def test_unbounded_below_no_presolve_original(self): + # formerly caused segfault in TravisCI w/ "cholesky":True + c = [-1] + bounds = [(None, 1)] + res = linprog(c=c, bounds=bounds, + method=self.method, + options={"presolve": False, "cholesky": True}) + _assert_success(res, desired_fun=-1) + + def test_cholesky(self): + # use cholesky factorization and triangular solves + A, b, c = lpgen_2d(20, 20) + res = linprog(c, A_ub=A, b_ub=b, method=self.method, + options={"cholesky": True}) # only for dense + _assert_success(res, desired_fun=-64.049494229) + + def test_alternate_initial_point(self): + # use "improved" initial point + A, b, c = lpgen_2d(20, 20) + with suppress_warnings() as sup: + sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...") + sup.filter(OptimizeWarning, "Solving system with option...") + sup.filter(LinAlgWarning, "Ill-conditioned matrix...") + res = linprog(c, A_ub=A, b_ub=b, method=self.method, + options={"ip": True, "disp": True}) + # ip code is independent of sparse/dense + _assert_success(res, desired_fun=-64.049494229) + + def test_bug_8664(self): + # interior-point has trouble with this when presolve is off + c = [4] + A_ub = [[2], [5]] + b_ub = [4, 4] + A_eq = [[0], [-8], [9]] + b_eq = [3, 2, 10] + with suppress_warnings() as sup: + sup.filter(RuntimeWarning) + sup.filter(OptimizeWarning, "Solving system with option...") + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options={"presolve": False}) + assert_(not res.success, "Incorrectly reported success") + + +######################################## +# Revised Simplex Option-Specific Tests# +######################################## + + +class TestLinprogRSCommon(LinprogRSTests): + options = {} + + def test_cyclic_bland(self): + pytest.skip("Intermittent failure acceptable.") + + def test_nontrivial_problem_with_guess(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=x_star) + _assert_success(res, desired_fun=f_star, desired_x=x_star) + assert_equal(res.nit, 0) + + def test_nontrivial_problem_with_unbounded_variables(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + bounds = [(None, None), (None, None), (0, None), (None, None)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=x_star) + _assert_success(res, desired_fun=f_star, desired_x=x_star) + assert_equal(res.nit, 0) + + def test_nontrivial_problem_with_bounded_variables(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + bounds = [(None, 1), (1, None), (0, None), (.4, .6)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=x_star) + _assert_success(res, desired_fun=f_star, desired_x=x_star) + assert_equal(res.nit, 0) + + def test_nontrivial_problem_with_negative_unbounded_variable(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + b_eq = [4] + x_star = np.array([-219/385, 582/385, 0, 4/10]) + f_star = 3951/385 + bounds = [(None, None), (1, None), (0, None), (.4, .6)] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=x_star) + _assert_success(res, desired_fun=f_star, desired_x=x_star) + assert_equal(res.nit, 0) + + def test_nontrivial_problem_with_bad_guess(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + bad_guess = [1, 2, 3, .5] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=bad_guess) + assert_equal(res.status, 6) + + def test_redundant_constraints_with_guess(self): + A, b, c, _, _ = magic_square(3) + p = np.random.rand(*c.shape) + with suppress_warnings() as sup: + sup.filter(OptimizeWarning, "A_eq does not appear...") + sup.filter(RuntimeWarning, "invalid value encountered") + sup.filter(LinAlgWarning) + res = linprog(c, A_eq=A, b_eq=b, method=self.method) + res2 = linprog(c, A_eq=A, b_eq=b, method=self.method, x0=res.x) + res3 = linprog(c + p, A_eq=A, b_eq=b, method=self.method, x0=res.x) + _assert_success(res2, desired_fun=1.730550597) + assert_equal(res2.nit, 0) + _assert_success(res3) + assert_(res3.nit < res.nit) # hot start reduces iterations + + +class TestLinprogRSBland(LinprogRSTests): + options = {"pivot": "bland"} + + +############################################ +# HiGHS-Simplex-Dual Option-Specific Tests # +############################################ + + +class TestLinprogHiGHSSimplexDual(LinprogHiGHSTests): + method = "highs-ds" + options = {} + + def test_lad_regression(self): + ''' + The scaled model should be optimal, i.e. not produce unscaled model + infeasible. See https://github.com/ERGO-Code/HiGHS/issues/494. + ''' + # Test to ensure gh-13610 is resolved (mismatch between HiGHS scaled + # and unscaled model statuses) + c, A_ub, b_ub, bnds = l1_regression_prob() + res = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=bnds, + method=self.method, options=self.options) + assert_equal(res.status, 0) + assert_(res.x is not None) + assert_(np.all(res.slack > -1e-6)) + assert_(np.all(res.x <= [np.inf if ub is None else ub + for lb, ub in bnds])) + assert_(np.all(res.x >= [-np.inf if lb is None else lb - 1e-7 + for lb, ub in bnds])) + + +################################### +# HiGHS-IPM Option-Specific Tests # +################################### + + +class TestLinprogHiGHSIPM(LinprogHiGHSTests): + method = "highs-ipm" + options = {} + + +################################### +# HiGHS-MIP Option-Specific Tests # +################################### + + +class TestLinprogHiGHSMIP: + method = "highs" + options = {} + + @pytest.mark.fail_slow(5) + @pytest.mark.xfail(condition=(sys.maxsize < 2 ** 32 and + platform.system() == "Linux"), + run=False, + reason="gh-16347") + def test_mip1(self): + # solve non-relaxed magic square problem (finally!) + # also check that values are all integers - they don't always + # come out of HiGHS that way + n = 4 + A, b, c, numbers, M = magic_square(n) + bounds = [(0, 1)] * len(c) + integrality = [1] * len(c) + + res = linprog(c=c*0, A_eq=A, b_eq=b, bounds=bounds, + method=self.method, integrality=integrality) + + s = (numbers.flatten() * res.x).reshape(n**2, n, n) + square = np.sum(s, axis=0) + np.testing.assert_allclose(square.sum(axis=0), M) + np.testing.assert_allclose(square.sum(axis=1), M) + np.testing.assert_allclose(np.diag(square).sum(), M) + np.testing.assert_allclose(np.diag(square[:, ::-1]).sum(), M) + + np.testing.assert_allclose(res.x, np.round(res.x), atol=1e-12) + + def test_mip2(self): + # solve MIP with inequality constraints and all integer constraints + # source: slide 5, + # https://www.cs.upc.edu/~erodri/webpage/cps/theory/lp/milp/slides.pdf + + # use all array inputs to test gh-16681 (integrality couldn't be array) + A_ub = np.array([[2, -2], [-8, 10]]) + b_ub = np.array([-1, 13]) + c = -np.array([1, 1]) + + bounds = np.array([(0, np.inf)] * len(c)) + integrality = np.ones_like(c) + + res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds, + method=self.method, integrality=integrality) + + np.testing.assert_allclose(res.x, [1, 2]) + np.testing.assert_allclose(res.fun, -3) + + def test_mip3(self): + # solve MIP with inequality constraints and all integer constraints + # source: https://en.wikipedia.org/wiki/Integer_programming#Example + A_ub = np.array([[-1, 1], [3, 2], [2, 3]]) + b_ub = np.array([1, 12, 12]) + c = -np.array([0, 1]) + + bounds = [(0, np.inf)] * len(c) + integrality = [1] * len(c) + + res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds, + method=self.method, integrality=integrality) + + np.testing.assert_allclose(res.fun, -2) + # two optimal solutions possible, just need one of them + assert np.allclose(res.x, [1, 2]) or np.allclose(res.x, [2, 2]) + + def test_mip4(self): + # solve MIP with inequality constraints and only one integer constraint + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + A_ub = np.array([[-1, -2], [-4, -1], [2, 1]]) + b_ub = np.array([14, -33, 20]) + c = np.array([8, 1]) + + bounds = [(0, np.inf)] * len(c) + integrality = [0, 1] + + res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds, + method=self.method, integrality=integrality) + + np.testing.assert_allclose(res.x, [6.5, 7]) + np.testing.assert_allclose(res.fun, 59) + + def test_mip5(self): + # solve MIP with inequality and inequality constraints + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + A_ub = np.array([[1, 1, 1]]) + b_ub = np.array([7]) + A_eq = np.array([[4, 2, 1]]) + b_eq = np.array([12]) + c = np.array([-3, -2, -1]) + + bounds = [(0, np.inf), (0, np.inf), (0, 1)] + integrality = [0, 1, 0] + + res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, + integrality=integrality) + + np.testing.assert_allclose(res.x, [0, 6, 0]) + np.testing.assert_allclose(res.fun, -12) + + # gh-16897: these fields were not present, ensure that they are now + assert res.get("mip_node_count", None) is not None + assert res.get("mip_dual_bound", None) is not None + assert res.get("mip_gap", None) is not None + + @pytest.mark.slow + @pytest.mark.timeout(120) # prerelease_deps_coverage_64bit_blas job + def test_mip6(self): + # solve a larger MIP with only equality constraints + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + A_eq = np.array([[22, 13, 26, 33, 21, 3, 14, 26], + [39, 16, 22, 28, 26, 30, 23, 24], + [18, 14, 29, 27, 30, 38, 26, 26], + [41, 26, 28, 36, 18, 38, 16, 26]]) + b_eq = np.array([7872, 10466, 11322, 12058]) + c = np.array([2, 10, 13, 17, 7, 5, 7, 3]) + + bounds = [(0, np.inf)]*8 + integrality = [1]*8 + + res = linprog(c=c, A_eq=A_eq, b_eq=b_eq, bounds=bounds, + method=self.method, integrality=integrality) + + np.testing.assert_allclose(res.fun, 1854) + + @pytest.mark.xslow + def test_mip_rel_gap_passdown(self): + # MIP taken from test_mip6, solved with different values of mip_rel_gap + # solve a larger MIP with only equality constraints + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + A_eq = np.array([[22, 13, 26, 33, 21, 3, 14, 26], + [39, 16, 22, 28, 26, 30, 23, 24], + [18, 14, 29, 27, 30, 38, 26, 26], + [41, 26, 28, 36, 18, 38, 16, 26]]) + b_eq = np.array([7872, 10466, 11322, 12058]) + c = np.array([2, 10, 13, 17, 7, 5, 7, 3]) + + bounds = [(0, np.inf)]*8 + integrality = [1]*8 + + mip_rel_gaps = [0.5, 0.25, 0.01, 0.001] + sol_mip_gaps = [] + for mip_rel_gap in mip_rel_gaps: + res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, + bounds=bounds, method=self.method, + integrality=integrality, + options={"mip_rel_gap": mip_rel_gap}) + final_mip_gap = res["mip_gap"] + # assert that the solution actually has mip_gap lower than the + # required mip_rel_gap supplied + assert final_mip_gap <= mip_rel_gap + sol_mip_gaps.append(final_mip_gap) + + # make sure that the mip_rel_gap parameter is actually doing something + # check that differences between solution gaps are declining + # monotonically with the mip_rel_gap parameter. np.diff does + # x[i+1] - x[i], so flip the array before differencing to get + # what should be a positive, monotone decreasing series of solution + # gaps + gap_diffs = np.diff(np.flip(sol_mip_gaps)) + assert np.all(gap_diffs >= 0) + assert not np.all(gap_diffs == 0) + + def test_semi_continuous(self): + # See issue #18106. This tests whether the solution is being + # checked correctly (status is 0) when integrality > 1: + # values are allowed to be 0 even if 0 is out of bounds. + + c = np.array([1., 1., -1, -1]) + bounds = np.array([[0.5, 1.5], [0.5, 1.5], [0.5, 1.5], [0.5, 1.5]]) + integrality = np.array([2, 3, 2, 3]) + + res = linprog(c, bounds=bounds, + integrality=integrality, method='highs') + + np.testing.assert_allclose(res.x, [0, 0, 1.5, 1]) + assert res.status == 0 + + +########################### +# Autoscale-Specific Tests# +########################### + + +@pytest.mark.filterwarnings("ignore::DeprecationWarning") +class AutoscaleTests: + options = {"autoscale": True} + + test_bug_6139 = LinprogCommonTests.test_bug_6139 + test_bug_6690 = LinprogCommonTests.test_bug_6690 + test_bug_7237 = LinprogCommonTests.test_bug_7237 + + +class TestAutoscaleIP(AutoscaleTests): + method = "interior-point" + + def test_bug_6139(self): + self.options['tol'] = 1e-10 + return AutoscaleTests.test_bug_6139(self) + + +class TestAutoscaleSimplex(AutoscaleTests): + method = "simplex" + + +class TestAutoscaleRS(AutoscaleTests): + method = "revised simplex" + + def test_nontrivial_problem_with_guess(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=x_star) + _assert_success(res, desired_fun=f_star, desired_x=x_star) + assert_equal(res.nit, 0) + + def test_nontrivial_problem_with_bad_guess(self): + c, A_ub, b_ub, A_eq, b_eq, x_star, f_star = nontrivial_problem() + bad_guess = [1, 2, 3, .5] + res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, + method=self.method, options=self.options, x0=bad_guess) + assert_equal(res.status, 6) + + +########################### +# Redundancy Removal Tests# +########################### + + +@pytest.mark.filterwarnings("ignore::DeprecationWarning") +class RRTests: + method = "interior-point" + LCT = LinprogCommonTests + # these are a few of the existing tests that have redundancy + test_RR_infeasibility = LCT.test_remove_redundancy_infeasibility + test_bug_10349 = LCT.test_bug_10349 + test_bug_7044 = LCT.test_bug_7044 + test_NFLC = LCT.test_network_flow_limited_capacity + test_enzo_example_b = LCT.test_enzo_example_b + + +class TestRRSVD(RRTests): + options = {"rr_method": "SVD"} + + +class TestRRPivot(RRTests): + options = {"rr_method": "pivot"} + + +class TestRRID(RRTests): + options = {"rr_method": "ID"}