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"""
Unit test for Linear Programming via Simplex Algorithm.
"""
# TODO: add tests for:
# https://github.com/scipy/scipy/issues/5400
# https://github.com/scipy/scipy/issues/6690
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import (
assert_,
assert_allclose,
assert_equal)
from .test_linprog import magic_square
from scipy.optimize._remove_redundancy import _remove_redundancy
def setup_module():
np.random.seed(2017)
def _assert_success(
res,
desired_fun=None,
desired_x=None,
rtol=1e-7,
atol=1e-7):
# res: linprog result object
# desired_fun: desired objective function value or None
# desired_x: desired solution or None
assert_(res.success)
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 test_no_redundancy():
m, n = 10, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_allclose(A0, A1)
assert_allclose(b0, b1)
assert_equal(status, 0)
def test_infeasible_zero_row():
A = np.eye(3)
A[1, :] = 0
b = np.random.rand(3)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 2)
def test_remove_zero_row():
A = np.eye(3)
A[1, :] = 0
b = np.random.rand(3)
b[1] = 0
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_allclose(A1, A[[0, 2], :])
assert_allclose(b1, b[[0, 2]])
def test_infeasible_m_gt_n():
m, n = 20, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_infeasible_m_eq_n():
m, n = 10, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = 2 * A0[-2, :]
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_infeasible_m_lt_n():
m, n = 9, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_m_gt_n():
m, n = 20, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
x = np.linalg.solve(A0[:n, :], b0[:n])
b0[n:] = A0[n:, :].dot(x)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_equal(A1.shape[0], n)
assert_equal(np.linalg.matrix_rank(A1), n)
def test_m_gt_n_rank_deficient():
m, n = 20, 10
A0 = np.zeros((m, n))
A0[:, 0] = 1
b0 = np.ones(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_allclose(A1, A0[0:1, :])
assert_allclose(b1, b0[0])
def test_m_lt_n_rank_deficient():
m, n = 9, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
b0[-1] = np.arange(m - 1).dot(b0[:-1])
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_equal(A1.shape[0], 8)
assert_equal(np.linalg.matrix_rank(A1), 8)
def test_dense1():
A = np.ones((6, 6))
A[0, :3] = 0
A[1, 3:] = 0
A[3:, ::2] = -1
A[3, :2] = 0
A[4, 2:] = 0
b = np.zeros(A.shape[0])
A2 = A[[0, 1, 3, 4], :]
b2 = np.zeros(4)
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A2)
assert_allclose(b1, b2)
assert_equal(status, 0)
def test_dense2():
A = np.eye(6)
A[-2, -1] = 1
A[-1, :] = 1
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A[:-1, :])
assert_allclose(b1, b[:-1])
assert_equal(status, 0)
def test_dense3():
A = np.eye(6)
A[-2, -1] = 1
A[-1, :] = 1
b = np.random.rand(A.shape[0])
b[-1] = np.sum(b[:-1])
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A[:-1, :])
assert_allclose(b1, b[:-1])
assert_equal(status, 0)
def test_m_gt_n_sparse():
np.random.seed(2013)
m, n = 20, 5
p = 0.1
A = np.random.rand(m, n)
A[np.random.rand(m, n) > p] = 0
rank = np.linalg.matrix_rank(A)
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], rank)
assert_equal(np.linalg.matrix_rank(A1), rank)
def test_m_lt_n_sparse():
np.random.seed(2017)
m, n = 20, 50
p = 0.05
A = np.random.rand(m, n)
A[np.random.rand(m, n) > p] = 0
rank = np.linalg.matrix_rank(A)
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], rank)
assert_equal(np.linalg.matrix_rank(A1), rank)
def test_m_eq_n_sparse():
np.random.seed(2017)
m, n = 100, 100
p = 0.01
A = np.random.rand(m, n)
A[np.random.rand(m, n) > p] = 0
rank = np.linalg.matrix_rank(A)
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], rank)
assert_equal(np.linalg.matrix_rank(A1), rank)
def test_magic_square():
A, b, c, numbers = magic_square(3)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], 23)
assert_equal(np.linalg.matrix_rank(A1), 23)
def test_magic_square2():
A, b, c, numbers = magic_square(4)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], 39)
assert_equal(np.linalg.matrix_rank(A1), 39)
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