batuhan-basoglu/Vehicle-Anti-Theft-Face-Recognition-System
1
1
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions
Vehicle-Anti-Theft-Face-Rec.../venv/Lib/site-packages/scipy/optimize/tests/test_linprog.py

1776 lines
69 KiB
Python
Raw Normal View History

Fixed database typo and removed unnecessary class identifier.
2020-10-14 14:10:37 +00:00
"""
Unit test for Linear Programming
"""
import sys
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.sparse.linalg import MatrixRankWarning
from scipy.linalg import LinAlgWarning
import pytest
has_umfpack = True
try:
from scikits.umfpack import UmfpackWarning
except ImportError:
has_umfpack = False
has_cholmod = True
try:
import sksparse
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 undelying 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 = "linprog status {0}, message: {1}".format(res.status,
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
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 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 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_solver():
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')
A_ub = None
b_ub = None
A_eq = None
b_eq = None
bounds = None
################
# Common Tests #
################
class LinprogCommonTests(object):
"""
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_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)
# Removed [(5, 0), (1, 2), (3, 4)]: these are invalid bounds but should be subject to a check in _presolve, not in _clean_inputs.
# The optimization should exit with an 'infeasible problem' error, not with a ValueError
# Same for [(1, 2), (np.inf, np.inf), (3, 4)] and [(1, 2), (-np.inf, -np.inf), (3, 4)]
for bad_bound in [[(1, 2), (3, 4)],
[(1, 2), (3, 4), (3, 4, 5)],
]:
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)
# 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_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):
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):
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)
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)
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)
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_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)
#################
# 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, N = 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)
_assert_success(res, desired_x=[2, -2, 0, -1, 1], desired_fun=-2)
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)
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 = {"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)
#########################
# Method-specific Tests #
#########################
class LinprogSimplexTests(LinprogCommonTests):
method = "simplex"
class LinprogIPTests(LinprogCommonTests):
method = "interior-point"
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.")
################################
# Simplex Option-Specific Tests#
################################
class TestLinprogSimplexDefault(LinprogSimplexTests):
def setup_method(self):
self.options = {}
def test_bug_5400(self):
with pytest.raises(ValueError):
super(TestLinprogSimplexDefault, self).test_bug_5400()
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.
self.options.update({'tol': 1e-12})
with pytest.raises(ValueError):
super(TestLinprogSimplexDefault, self).test_bug_7237()
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(TestLinprogSimplexDefault, self).test_bug_8174()
class TestLinprogSimplexBland(LinprogSimplexTests):
def setup_method(self):
self.options = {'bland': True}
def test_bug_5400(self):
with pytest.raises(ValueError):
super(TestLinprogSimplexBland, self).test_bug_5400()
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(TestLinprogSimplexBland, self).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(TestLinprogSimplexNoPresolve, self).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(ValueError):
return super(TestLinprogSimplexNoPresolve, self).test_bug_6139()
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.
self.options.update({'tol': 1e-12})
with pytest.raises(ValueError):
super(TestLinprogSimplexNoPresolve, self).test_bug_7237()
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(TestLinprogSimplexNoPresolve, self).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}
if has_cholmod:
class TestLinprogIPSparseCholmod(LinprogIPTests):
options = {"sparse": True, "cholesky": True}
if has_umfpack:
class TestLinprogIPSparseUmfpack(LinprogIPTests):
options = {"sparse": True, "cholesky": False}
def test_bug_10466(self):
pytest.skip("Autoscale doesn't fix everything, and that's OK.")
class TestLinprogIPSparse(LinprogIPTests):
options = {"sparse": True, "cholesky": False, "sym_pos": False}
@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(TestLinprogIPSparse, self).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(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_eq, b_eq, c, N = 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, 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')
# '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.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(TestLinprogIPSparsePresolve, self).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(TestLinprogIPSparsePresolve, self).test_bug_6690()
class TestLinprogIPSpecific(object):
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=1e-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_maxiter(self):
# 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_iteration_limit_reached(res, maxiter)
assert_equal(res.nit, maxiter)
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, N = 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"}
###########################
# Autoscale-Specific Tests#
###########################
class AutoscaleTests(object):
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)
Reference in a new issue Copy permalink