1019 lines
39 KiB
Python
1019 lines
39 KiB
Python
"""
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Unit test for Linear Programming
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"""
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy.testing import assert_, assert_allclose, assert_equal
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from pytest import raises as assert_raises
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from scipy.optimize import linprog, OptimizeWarning
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from scipy._lib._numpy_compat import _assert_warns, suppress_warnings
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from scipy.sparse.linalg import MatrixRankWarning
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import pytest
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def magic_square(n):
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np.random.seed(0)
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M = n * (n**2 + 1) / 2
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numbers = np.arange(n**4) // n**2 + 1
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numbers = numbers.reshape(n**2, n, n)
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zeros = np.zeros((n**2, n, n))
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A_list = []
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b_list = []
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# Rule 1: use every number exactly once
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for i in range(n**2):
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A_row = zeros.copy()
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A_row[i, :, :] = 1
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A_list.append(A_row.flatten())
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b_list.append(1)
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# Rule 2: Only one number per square
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for i in range(n):
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for j in range(n):
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A_row = zeros.copy()
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A_row[:, i, j] = 1
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A_list.append(A_row.flatten())
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b_list.append(1)
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# Rule 3: sum of rows is M
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for i in range(n):
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A_row = zeros.copy()
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A_row[:, i, :] = numbers[:, i, :]
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A_list.append(A_row.flatten())
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b_list.append(M)
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# Rule 4: sum of columns is M
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for i in range(n):
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A_row = zeros.copy()
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A_row[:, :, i] = numbers[:, :, i]
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A_list.append(A_row.flatten())
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b_list.append(M)
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# Rule 5: sum of diagonals is M
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A_row = zeros.copy()
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A_row[:, range(n), range(n)] = numbers[:, range(n), range(n)]
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A_list.append(A_row.flatten())
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b_list.append(M)
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A_row = zeros.copy()
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A_row[:, range(n), range(-1, -n - 1, -1)] = \
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numbers[:, range(n), range(-1, -n - 1, -1)]
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A_list.append(A_row.flatten())
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b_list.append(M)
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A = np.array(np.vstack(A_list), dtype=float)
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b = np.array(b_list, dtype=float)
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c = np.random.rand(A.shape[1])
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return A, b, c, numbers
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def lpgen_2d(m, n):
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""" -> A b c LP test: m*n vars, m+n constraints
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row sums == n/m, col sums == 1
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https://gist.github.com/denis-bz/8647461
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"""
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np.random.seed(0)
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c = - np.random.exponential(size=(m, n))
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Arow = np.zeros((m, m * n))
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brow = np.zeros(m)
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for j in range(m):
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j1 = j + 1
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Arow[j, j * n:j1 * n] = 1
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brow[j] = n / m
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Acol = np.zeros((n, m * n))
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bcol = np.zeros(n)
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for j in range(n):
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j1 = j + 1
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Acol[j, j::n] = 1
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bcol[j] = 1
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A = np.vstack((Arow, Acol))
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b = np.hstack((brow, bcol))
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return A, b, c.ravel()
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def _assert_infeasible(res):
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# res: linprog result object
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assert_(not res.success, "incorrectly reported success")
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assert_equal(res.status, 2, "failed to report infeasible status")
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def _assert_unbounded(res):
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# res: linprog result object
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assert_(not res.success, "incorrectly reported success")
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assert_equal(res.status, 3, "failed to report unbounded status")
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def _assert_success(res, desired_fun=None, desired_x=None,
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rtol=1e-8, atol=1e-8):
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# res: linprog result object
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# desired_fun: desired objective function value or None
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# desired_x: desired solution or None
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if not res.success:
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msg = "linprog status {0}, message: {1}".format(res.status,
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res.message)
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raise AssertionError(msg)
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assert_equal(res.status, 0)
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if desired_fun is not None:
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assert_allclose(res.fun, desired_fun,
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err_msg="converged to an unexpected objective value",
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rtol=rtol, atol=atol)
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if desired_x is not None:
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assert_allclose(res.x, desired_x,
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err_msg="converged to an unexpected solution",
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rtol=rtol, atol=atol)
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class LinprogCommonTests(object):
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def test_aliasing_b_ub(self):
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c = np.array([1.0])
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A_ub = np.array([[1.0]])
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b_ub_orig = np.array([3.0])
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b_ub = b_ub_orig.copy()
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bounds = (-4.0, np.inf)
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=bounds,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=-4, desired_x=[-4])
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assert_allclose(b_ub_orig, b_ub)
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def test_aliasing_b_eq(self):
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c = np.array([1.0])
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A_eq = np.array([[1.0]])
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b_eq_orig = np.array([3.0])
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b_eq = b_eq_orig.copy()
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bounds = (-4.0, np.inf)
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res = linprog(c, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=3, desired_x=[3])
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assert_allclose(b_eq_orig, b_eq)
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def test_bounds_second_form_unbounded_below(self):
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c = np.array([1.0])
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A_eq = np.array([[1.0]])
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b_eq = np.array([3.0])
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bounds = (None, 10.0)
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res = linprog(c, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=3, desired_x=[3])
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def test_bounds_second_form_unbounded_above(self):
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c = np.array([1.0])
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A_eq = np.array([[1.0]])
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b_eq = np.array([3.0])
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bounds = (1.0, None)
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res = linprog(c, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=3, desired_x=[3])
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def test_non_ndarray_args(self):
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c = [1.0]
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A_ub = [[1.0]]
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b_ub = [3.0]
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A_eq = [[1.0]]
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b_eq = [2.0]
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bounds = (-1.0, 10.0)
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
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bounds=bounds, method=self.method, options=self.options)
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_assert_success(res, desired_fun=2, desired_x=[2])
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def test_linprog_upper_bound_constraints(self):
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# Maximize a linear function subject to only linear upper bound
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# constraints.
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# http://www.dam.brown.edu/people/huiwang/classes/am121/Archive/simplex_121_c.pdf
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c = np.array([3, 2]) * -1 # maximize
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A_ub = [[2, 1],
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[1, 1],
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[1, 0]]
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b_ub = [10, 8, 4]
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res = (linprog(c, A_ub=A_ub, b_ub=b_ub,
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method=self.method, options=self.options))
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_assert_success(res, desired_fun=-18, desired_x=[2, 6])
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def test_linprog_mixed_constraints(self):
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# Minimize linear function subject to non-negative variables.
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# http://www.statslab.cam.ac.uk/~ff271/teaching/opt/notes/notes8.pdf
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c = [6, 3]
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A_ub = [[0, 3],
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[-1, -1],
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[-2, 1]]
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b_ub = [2, -1, -1]
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res = linprog(c, A_ub=A_ub, b_ub=b_ub,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=5, desired_x=[2 / 3, 1 / 3])
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def test_linprog_cyclic_recovery(self):
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# Test linprogs recovery from cycling using the Klee-Minty problem
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# Klee-Minty http://www.math.ubc.ca/~israel/m340/kleemin3.pdf
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c = np.array([100, 10, 1]) * -1 # maximize
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A_ub = [[1, 0, 0],
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[20, 1, 0],
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[200, 20, 1]]
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b_ub = [1, 100, 10000]
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res = linprog(c, A_ub=A_ub, b_ub=b_ub,
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method=self.method, options=self.options)
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_assert_success(res, desired_x=[0, 0, 10000], atol=5e-6, rtol=1e-7)
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def test_linprog_cyclic_bland(self):
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# Test the effect of Bland's rule on a cycling problem
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c = np.array([-10, 57, 9, 24.])
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A_ub = np.array([[0.5, -5.5, -2.5, 9],
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[0.5, -1.5, -0.5, 1],
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[1, 0, 0, 0]])
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b_ub = [0, 0, 1]
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# "interior-point" will succeed, "simplex" will fail
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, options=dict(maxiter=100),
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method=self.method)
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if self.method == "simplex":
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assert_(not res.success)
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res = linprog(c, A_ub=A_ub, b_ub=b_ub,
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options=dict(maxiter=100, bland=True,),
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method=self.method)
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_assert_success(res, desired_x=[1, 0, 1, 0])
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def test_linprog_cyclic_bland_bug_8561(self):
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# Test that pivot row is chosen correctly when using Bland's rule
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c = np.array([7, 0, -4, 1.5, 1.5])
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A_ub = np.array([
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[4, 5.5, 1.5, 1.0, -3.5],
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[1, -2.5, -2, 2.5, 0.5],
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[3, -0.5, 4, -12.5, -7],
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[-1, 4.5, 2, -3.5, -2],
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[5.5, 2, -4.5, -1, 9.5]])
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b_ub = np.array([0, 0, 0, 0, 1])
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if self.method == "simplex":
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res = linprog(c, A_ub=A_ub, b_ub=b_ub,
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options=dict(maxiter=100, bland=True),
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method=self.method)
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else:
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, options=dict(maxiter=100),
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method=self.method)
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_assert_success(res, desired_x=[0, 0, 19, 16/3, 29/3])
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def test_linprog_unbounded(self):
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# Test linprog response to an unbounded problem
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c = np.array([1, 1]) * -1 # maximize
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A_ub = [[-1, 1],
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[-1, -1]]
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b_ub = [-1, -2]
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res = linprog(c, A_ub=A_ub, b_ub=b_ub,
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method=self.method, options=self.options)
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_assert_unbounded(res)
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def test_linprog_infeasible(self):
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# Test linrpog response to an infeasible problem
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c = [-1, -1]
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A_ub = [[1, 0],
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[0, 1],
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[-1, -1]]
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b_ub = [2, 2, -5]
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res = linprog(c, A_ub=A_ub, b_ub=b_ub,
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method=self.method, options=self.options)
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_assert_infeasible(res)
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def test_nontrivial_problem(self):
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# Test linprog for a problem involving all constraint types,
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# negative resource limits, and rounding issues.
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c = [-1, 8, 4, -6]
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A_ub = [[-7, -7, 6, 9],
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[1, -1, -3, 0],
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[10, -10, -7, 7],
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[6, -1, 3, 4]]
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b_ub = [-3, 6, -6, 6]
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A_eq = [[-10, 1, 1, -8]]
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b_eq = [-4]
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=7083 / 1391,
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desired_x=[101 / 1391, 1462 / 1391, 0, 752 / 1391])
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def test_negative_variable(self):
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# Test linprog with a problem with one unbounded variable and
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# another with a negative lower bound.
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c = np.array([-1, 4]) * -1 # maximize
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A_ub = np.array([[-3, 1],
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[1, 2]], dtype=np.float64)
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A_ub_orig = A_ub.copy()
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b_ub = [6, 4]
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x0_bounds = (-np.inf, np.inf)
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x1_bounds = (-3, np.inf)
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=(x0_bounds, x1_bounds),
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method=self.method, options=self.options)
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assert_equal(A_ub, A_ub_orig) # user input not overwritten
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_assert_success(res, desired_fun=-80 / 7, desired_x=[-8 / 7, 18 / 7])
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def test_large_problem(self):
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# Test linprog simplex with a rather large problem (400 variables,
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# 40 constraints) generated by https://gist.github.com/denis-bz/8647461
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A, b, c = lpgen_2d(20, 20)
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res = linprog(c, A_ub=A, b_ub=b,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=-64.049494229)
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def test_network_flow(self):
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# A network flow problem with supply and demand at nodes
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# and with costs along directed edges.
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# https://www.princeton.edu/~rvdb/542/lectures/lec10.pdf
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c = [2, 4, 9, 11, 4, 3, 8, 7, 0, 15, 16, 18]
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n, p = -1, 1
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A_eq = [
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[n, n, p, 0, p, 0, 0, 0, 0, p, 0, 0],
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[p, 0, 0, p, 0, p, 0, 0, 0, 0, 0, 0],
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[0, 0, n, n, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, p, p, 0, 0, p, 0],
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[0, 0, 0, 0, n, n, n, 0, p, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, n, n, 0, 0, p],
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[0, 0, 0, 0, 0, 0, 0, 0, 0, n, n, n]]
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b_eq = [0, 19, -16, 33, 0, 0, -36]
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res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=755, atol=1e-6, rtol=1e-7)
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def test_network_flow_limited_capacity(self):
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# A network flow problem with supply and demand at nodes
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# and with costs and capacities along directed edges.
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# http://blog.sommer-forst.de/2013/04/10/
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cost = [2, 2, 1, 3, 1]
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bounds = [
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[0, 4],
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[0, 2],
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[0, 2],
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[0, 3],
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[0, 5]]
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n, p = -1, 1
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A_eq = [
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[n, n, 0, 0, 0],
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[p, 0, n, n, 0],
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[0, p, p, 0, n],
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[0, 0, 0, p, p]]
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b_eq = [-4, 0, 0, 4]
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if self.method == "simplex":
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# Including the callback here ensures the solution can be
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# calculated correctly, even when phase 1 terminated
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# with some of the artificial variables as pivots
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# (i.e. basis[:m] contains elements corresponding to
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# the artificial variables)
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res = linprog(c=cost, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
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method=self.method, options=self.options,
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callback=lambda x, **kwargs: None)
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else:
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with suppress_warnings() as sup:
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sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...")
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sup.filter(OptimizeWarning, "A_eq does not appear...")
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sup.filter(OptimizeWarning, "Solving system with option...")
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res = linprog(c=cost, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=14)
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def test_simplex_algorithm_wikipedia_example(self):
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# http://en.wikipedia.org/wiki/Simplex_algorithm#Example
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Z = [-2, -3, -4]
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A_ub = [
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[3, 2, 1],
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[2, 5, 3]]
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b_ub = [10, 15]
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res = linprog(c=Z, A_ub=A_ub, b_ub=b_ub,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=-20)
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def test_enzo_example(self):
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# http://projects.scipy.org/scipy/attachment/ticket/1252/lp2.py
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#
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# Translated from Octave code at:
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# http://www.ecs.shimane-u.ac.jp/~kyoshida/lpeng.htm
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# and placed under MIT licence by Enzo Michelangeli
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# with permission explicitly granted by the original author,
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# Prof. Kazunobu Yoshida
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c = [4, 8, 3, 0, 0, 0]
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A_eq = [
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[2, 5, 3, -1, 0, 0],
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[3, 2.5, 8, 0, -1, 0],
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[8, 10, 4, 0, 0, -1]]
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b_eq = [185, 155, 600]
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res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
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method=self.method, options=self.options)
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_assert_success(res, desired_fun=317.5,
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desired_x=[66.25, 0, 17.5, 0, 183.75, 0],
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atol=6e-6, rtol=1e-7)
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def test_enzo_example_b(self):
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# rescued from https://github.com/scipy/scipy/pull/218
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c = [2.8, 6.3, 10.8, -2.8, -6.3, -10.8]
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A_eq = [[-1, -1, -1, 0, 0, 0],
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[0, 0, 0, 1, 1, 1],
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[1, 0, 0, 1, 0, 0],
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[0, 1, 0, 0, 1, 0],
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[0, 0, 1, 0, 0, 1]]
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b_eq = [-0.5, 0.4, 0.3, 0.3, 0.3]
|
|
if self.method == "simplex":
|
|
# Including the callback here ensures the solution can be
|
|
# calculated correctly.
|
|
res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options,
|
|
callback=lambda x, **kwargs: None)
|
|
else:
|
|
with suppress_warnings() as sup:
|
|
sup.filter(OptimizeWarning, "A_eq does not appear...")
|
|
res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
|
|
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=c, A_eq=A_eq, b_eq=b_eq,
|
|
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)
|
|
A_eq = np.vstack((np.cos(tmp) - 1, np.sin(tmp)))
|
|
b_eq = [0, 0]
|
|
res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
|
|
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]
|
|
if self.method == "simplex":
|
|
res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options)
|
|
else:
|
|
res = linprog(c=c, A_eq=A_eq, b_eq=b_eq, method=self.method,
|
|
options={"presolve": False})
|
|
_assert_infeasible(res)
|
|
|
|
def test_unknown_options_or_solver(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)
|
|
|
|
_assert_warns(OptimizeWarning, f,
|
|
c, A_ub=A_ub, b_ub=b_ub, options=dict(spam='42'))
|
|
|
|
assert_raises(ValueError, linprog,
|
|
c, A_ub=A_ub, b_ub=b_ub, method='ekki-ekki-ekki')
|
|
|
|
def test_no_constraints(self):
|
|
res = linprog([-1, -2], method=self.method, options=self.options)
|
|
if self.method == "simplex":
|
|
# Why should x be 0,0? inf,inf is more correct, IMO
|
|
assert_equal(res.x, [0, 0])
|
|
_assert_unbounded(res)
|
|
|
|
def test_simple_bounds(self):
|
|
res = linprog([1, 2], bounds=(1, 2),
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_x=[1, 1])
|
|
res = linprog([1, 2], bounds=[(1, 2), (1, 2)],
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_x=[1, 1])
|
|
|
|
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)
|
|
|
|
for bad_bound in [[(5, 0), (1, 2), (3, 4)],
|
|
[(1, 2), (3, 4)],
|
|
[(1, 2), (3, 4), (3, 4, 5)],
|
|
[(1, 2), (np.inf, np.inf), (3, 4)],
|
|
[(1, 2), (-np.inf, -np.inf), (3, 4)],
|
|
]:
|
|
assert_raises(ValueError, f, [1, 2, 3], bounds=bad_bound)
|
|
|
|
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)
|
|
|
|
if ("_sparse_presolve" in self.options and
|
|
self.options["_sparse_presolve"]):
|
|
return
|
|
# this test doesn't make sense for sparse presolve
|
|
# there aren't 3D sparse matrices
|
|
assert_raises(ValueError, f, [1, 2], A_ub=np.zeros((1, 1, 3)), b_eq=1)
|
|
|
|
def test_basic_artificial_vars(self):
|
|
# Test if linprog succeeds when at the end of Phase 1 some artificial
|
|
# variables remain basic, and the row in T corresponding to 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=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=0, desired_x=np.zeros_like(c),
|
|
atol=2e-6)
|
|
|
|
def test_empty_constraint_2(self):
|
|
res = linprog([1, -1, 1, -1],
|
|
bounds=[(0, np.inf), (-np.inf, 0), (-1, 1), (-1, 1)],
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_x=[0, 0, -1, 1], desired_fun=-2)
|
|
|
|
def test_zero_row_2(self):
|
|
A_eq = [[0, 0, 0], [1, 1, 1], [0, 0, 0]]
|
|
b_eq = [0, 3, 0]
|
|
c = [1, 2, 3]
|
|
res = linprog(c=c, A_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=3)
|
|
|
|
def test_zero_row_4(self):
|
|
A_ub = [[0, 0, 0], [1, 1, 1], [0, 0, 0]]
|
|
b_ub = [0, 3, 0]
|
|
c = [1, 2, 3]
|
|
res = linprog(c=c, A_ub=A_ub, b_ub=b_ub,
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=0)
|
|
|
|
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
|
|
res = linprog(c, A_ub, b_ub, A_eq, b_eq,
|
|
bounds=[(-10, 10), (-10, 10),
|
|
(-10, None), (None, None)],
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=-9.7087836730413404)
|
|
|
|
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_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=4)
|
|
|
|
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]
|
|
res = linprog(c, A_ub=A_ub, b_ub=b_ub,
|
|
bounds=[(None, None), (0, None), (0, None), (0, None)],
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=0.5)
|
|
|
|
def test_remove_redundancy_infeasibility(self):
|
|
m, n = 10, 10
|
|
c = np.random.rand(n)
|
|
A0 = np.random.rand(m, n)
|
|
b0 = np.random.rand(m)
|
|
A0[-1, :] = 2 * A0[-2, :]
|
|
b0[-1] *= -1
|
|
with suppress_warnings() as sup:
|
|
sup.filter(OptimizeWarning, "A_eq does not appear...")
|
|
res = linprog(c, A_eq=A0, b_eq=b0,
|
|
method=self.method, options=self.options)
|
|
_assert_infeasible(res)
|
|
|
|
def test_bounded_below_only(self):
|
|
A = np.eye(3)
|
|
b = np.array([1, 2, 3])
|
|
c = np.ones(3)
|
|
res = linprog(c, A_eq=A, b_eq=b, bounds=(0.5, np.inf),
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_x=b, desired_fun=np.sum(b))
|
|
|
|
def test_bounded_above_only(self):
|
|
A = np.eye(3)
|
|
b = np.array([1, 2, 3])
|
|
c = np.ones(3)
|
|
res = linprog(c, A_eq=A, b_eq=b, bounds=(-np.inf, 4),
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_x=b, desired_fun=np.sum(b))
|
|
|
|
def test_unbounded_below_and_above(self):
|
|
A = np.eye(3)
|
|
b = np.array([1, 2, 3])
|
|
c = np.ones(3)
|
|
res = linprog(c, A_eq=A, b_eq=b, bounds=(-np.inf, np.inf),
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_x=b, desired_fun=np.sum(b))
|
|
|
|
def test_bug_8663(self):
|
|
A = [[0, -7]]
|
|
b = [-6]
|
|
c = [1, 5]
|
|
bounds = [(0, None), (None, None)]
|
|
res = linprog(c, A_eq=A, b_eq=b, bounds=bounds,
|
|
method=self.method, options=self.options)
|
|
_assert_success(res,
|
|
desired_x=[0, 6./7],
|
|
desired_fun=5*6./7)
|
|
|
|
|
|
class TestLinprogSimplex(LinprogCommonTests):
|
|
method = "simplex"
|
|
options = {}
|
|
|
|
def test_callback(self):
|
|
# Check that callback is as advertised
|
|
callback_complete = [False]
|
|
last_xk = []
|
|
|
|
def cb(xk, **kwargs):
|
|
kwargs.pop('tableau')
|
|
assert_(isinstance(kwargs.pop('phase'), int))
|
|
assert_(isinstance(kwargs.pop('nit'), int))
|
|
|
|
i, j = kwargs.pop('pivot')
|
|
assert_(np.isscalar(i))
|
|
assert_(np.isscalar(j))
|
|
|
|
basis = kwargs.pop('basis')
|
|
assert_(isinstance(basis, np.ndarray))
|
|
assert_(basis.dtype == np.int_)
|
|
|
|
complete = kwargs.pop('complete')
|
|
assert_(isinstance(complete, bool))
|
|
if complete:
|
|
last_xk.append(xk)
|
|
callback_complete[0] = True
|
|
else:
|
|
assert_(not callback_complete[0])
|
|
|
|
# no more kwargs
|
|
assert_(not kwargs)
|
|
|
|
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_(callback_complete[0])
|
|
assert_allclose(last_xk[0], res.x)
|
|
|
|
|
|
class BaseTestLinprogIP(LinprogCommonTests):
|
|
method = "interior-point"
|
|
|
|
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=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds,
|
|
method=self.method)
|
|
_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=c, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
|
|
method=self.method)
|
|
_assert_infeasible(res)
|
|
|
|
def test_magic_square_bug_7044(self):
|
|
# test linprog with a problem with a rank-deficient A_eq matrix
|
|
A, b, c, N = magic_square(3)
|
|
with suppress_warnings() as sup:
|
|
sup.filter(OptimizeWarning, "A_eq does not appear...")
|
|
res = linprog(c, A_eq=A, b_eq=b, bounds=(0, 1),
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=1.730550597)
|
|
|
|
def test_bug_6690(self):
|
|
# 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:
|
|
sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...")
|
|
sup.filter(OptimizeWarning, "Solving system with option...")
|
|
sol = 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_success(sol, desired_fun=-1.191, rtol=1e-6)
|
|
|
|
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, 1.99, -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, 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])
|
|
|
|
res = linprog(c, A_ub, b_ub, bounds=bounds,
|
|
method=self.method, options=self.options)
|
|
_assert_success(res, desired_fun=-106.63507541835018)
|
|
|
|
def test_empty_constraint_1(self):
|
|
# detected in presolve?
|
|
res = linprog([-1, 1, -1, 1],
|
|
bounds=[(0, np.inf), (-np.inf, 0), (-1, 1), (-1, 1)],
|
|
method=self.method, options=self.options)
|
|
_assert_unbounded(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_singleton_row_eq_1(self):
|
|
# detected in presolve?
|
|
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_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options)
|
|
_assert_infeasible(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_singleton_row_ub_1(self):
|
|
# detected in presolve?
|
|
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]
|
|
res = linprog(c, A_ub=A_ub, b_ub=b_ub,
|
|
bounds=[(None, None), (0, None), (0, None), (0, None)],
|
|
method=self.method, options=self.options)
|
|
_assert_infeasible(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_zero_column_2(self):
|
|
# detected in presolve?
|
|
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)
|
|
res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds=(None, None),
|
|
method=self.method, options=self.options)
|
|
_assert_unbounded(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_zero_row_1(self):
|
|
# detected in presolve?
|
|
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=c, A_eq=A_eq, b_eq=b_eq,
|
|
method=self.method, options=self.options)
|
|
_assert_infeasible(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_zero_row_3(self):
|
|
# detected in presolve?
|
|
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=c, A_ub=A_ub, b_ub=b_ub,
|
|
method=self.method, options=self.options)
|
|
_assert_infeasible(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_infeasible_ub(self):
|
|
# detected in presolve?
|
|
c = [1]
|
|
A_ub = [[2]]
|
|
b_ub = 4
|
|
bounds = (5, 6)
|
|
res = linprog(c=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds,
|
|
method=self.method, options=self.options)
|
|
_assert_infeasible(res)
|
|
assert_equal(res.nit, 0)
|
|
|
|
def test_type_error(self):
|
|
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_equal_bounds_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=c, A_ub=A_ub, b_ub=b_ub, bounds=bounds,
|
|
method=self.method, options=o)
|
|
_assert_infeasible(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)
|
|
_assert_unbounded(res)
|
|
|
|
def test_bug_8664(self):
|
|
# Weak test. Ideally should _detect infeasibility_ for all options.
|
|
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...")
|
|
o = {key: self.options[key] for key in self.options}
|
|
o["presolve"] = False
|
|
res = linprog(c, A_ub, b_ub, A_eq, b_eq, options=o,
|
|
method=self.method)
|
|
assert_(not res.success, "incorrectly reported success")
|
|
|
|
|
|
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_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):
|
|
# Test with a rather large problem (400 variables,
|
|
# 40 constraints) generated by https://gist.github.com/denis-bz/8647461
|
|
# 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):
|
|
# Test with a rather large problem (400 variables,
|
|
# 40 constraints) generated by https://gist.github.com/denis-bz/8647461
|
|
# 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...")
|
|
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_maxiter(self):
|
|
# Test with a rather large problem (400 variables,
|
|
# 40 constraints) generated by https://gist.github.com/denis-bz/8647461
|
|
# test iteration limit
|
|
A, b, c = lpgen_2d(20, 20)
|
|
maxiter = np.random.randint(6) + 1 # problem takes 7 iterations
|
|
res = linprog(c, A_ub=A, b_ub=b, method=self.method,
|
|
options={"maxiter": maxiter})
|
|
# maxiter is independent of sparse/dense
|
|
assert_equal(res.status, 1)
|
|
assert_equal(res.nit, maxiter)
|
|
|
|
def test_disp(self):
|
|
# Test with a rather large problem (400 variables,
|
|
# 40 constraints) generated by https://gist.github.com/denis-bz/8647461
|
|
# 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})
|
|
# disp is independent of sparse/dense
|
|
_assert_success(res, desired_fun=-64.049494229)
|
|
|
|
def test_callback(self):
|
|
def f():
|
|
pass
|
|
assert_raises(NotImplementedError, linprog, c=1, callback=f,
|
|
method=self.method)
|
|
|
|
|
|
class TestLinprogIPSparse(BaseTestLinprogIP):
|
|
options = {"sparse": True}
|
|
|
|
@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(TestLinprogIPSparse, self).test_bug_6690()
|
|
|
|
def test_magic_square_sparse_no_presolve(self):
|
|
# test linprog with a problem with a rank-deficient A_eq matrix
|
|
A, b, c, N = magic_square(3)
|
|
with suppress_warnings() as sup:
|
|
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_eq=A, b_eq=b, bounds=(0, 1),
|
|
options=o, method=self.method)
|
|
_assert_success(res, desired_fun=1.730550597)
|
|
|
|
def test_sparse_solve_options(self):
|
|
A, b, c, N = 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')
|
|
for permc_spec in permc_specs:
|
|
o["permc_spec"] = permc_spec
|
|
res = linprog(c, A_eq=A, b_eq=b, bounds=(0, 1),
|
|
method=self.method, options=o)
|
|
_assert_success(res, desired_fun=1.730550597)
|
|
|
|
|
|
class TestLinprogIPDense(BaseTestLinprogIP):
|
|
options = {"sparse": False}
|
|
|
|
|
|
class TestLinprogIPSparsePresolve(BaseTestLinprogIP):
|
|
options = {"sparse": True, "_sparse_presolve": True}
|
|
|
|
@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(TestLinprogIPSparsePresolve, self).test_bug_6690()
|