240 lines
6.9 KiB
Python
240 lines
6.9 KiB
Python
"""
|
|
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
|
|
|
|
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
|
|
from scipy.optimize._remove_redundancy import _remove_redundancy_dense
|
|
from scipy.optimize._remove_redundancy import _remove_redundancy_sparse
|
|
from scipy.sparse import csc_matrix
|
|
|
|
|
|
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)
|
|
|
|
class RRCommonTests(object):
|
|
def test_no_redundancy(self):
|
|
m, n = 10, 10
|
|
A0 = np.random.rand(m, n)
|
|
b0 = np.random.rand(m)
|
|
A1, b1, status, message = self.rr(A0, b0)
|
|
assert_allclose(A0, A1)
|
|
assert_allclose(b0, b1)
|
|
assert_equal(status, 0)
|
|
|
|
def test_infeasible_zero_row(self):
|
|
A = np.eye(3)
|
|
A[1, :] = 0
|
|
b = np.random.rand(3)
|
|
A1, b1, status, message = self.rr(A, b)
|
|
assert_equal(status, 2)
|
|
|
|
def test_remove_zero_row(self):
|
|
A = np.eye(3)
|
|
A[1, :] = 0
|
|
b = np.random.rand(3)
|
|
b[1] = 0
|
|
A1, b1, status, message = self.rr(A, b)
|
|
assert_equal(status, 0)
|
|
assert_allclose(A1, A[[0, 2], :])
|
|
assert_allclose(b1, b[[0, 2]])
|
|
|
|
def test_infeasible_m_gt_n(self):
|
|
m, n = 20, 10
|
|
A0 = np.random.rand(m, n)
|
|
b0 = np.random.rand(m)
|
|
A1, b1, status, message = self.rr(A0, b0)
|
|
assert_equal(status, 2)
|
|
|
|
def test_infeasible_m_eq_n(self):
|
|
m, n = 10, 10
|
|
A0 = np.random.rand(m, n)
|
|
b0 = np.random.rand(m)
|
|
A0[-1, :] = 2 * A0[-2, :]
|
|
A1, b1, status, message = self.rr(A0, b0)
|
|
assert_equal(status, 2)
|
|
|
|
def test_infeasible_m_lt_n(self):
|
|
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 = self.rr(A0, b0)
|
|
assert_equal(status, 2)
|
|
|
|
def test_m_gt_n(self):
|
|
np.random.seed(2032)
|
|
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 = self.rr(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(self):
|
|
m, n = 20, 10
|
|
A0 = np.zeros((m, n))
|
|
A0[:, 0] = 1
|
|
b0 = np.ones(m)
|
|
A1, b1, status, message = self.rr(A0, b0)
|
|
assert_equal(status, 0)
|
|
assert_allclose(A1, A0[0:1, :])
|
|
assert_allclose(b1, b0[0])
|
|
|
|
def test_m_lt_n_rank_deficient(self):
|
|
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 = self.rr(A0, b0)
|
|
assert_equal(status, 0)
|
|
assert_equal(A1.shape[0], 8)
|
|
assert_equal(np.linalg.matrix_rank(A1), 8)
|
|
|
|
def test_dense1(self):
|
|
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 = self.rr(A, b)
|
|
assert_allclose(A1, A2)
|
|
assert_allclose(b1, b2)
|
|
assert_equal(status, 0)
|
|
|
|
def test_dense2(self):
|
|
A = np.eye(6)
|
|
A[-2, -1] = 1
|
|
A[-1, :] = 1
|
|
b = np.zeros(A.shape[0])
|
|
A1, b1, status, message = self.rr(A, b)
|
|
assert_allclose(A1, A[:-1, :])
|
|
assert_allclose(b1, b[:-1])
|
|
assert_equal(status, 0)
|
|
|
|
def test_dense3(self):
|
|
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 = self.rr(A, b)
|
|
assert_allclose(A1, A[:-1, :])
|
|
assert_allclose(b1, b[:-1])
|
|
assert_equal(status, 0)
|
|
|
|
def test_m_gt_n_sparse(self):
|
|
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 = self.rr(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(self):
|
|
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 = self.rr(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(self):
|
|
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 = self.rr(A, b)
|
|
assert_equal(status, 0)
|
|
assert_equal(A1.shape[0], rank)
|
|
assert_equal(np.linalg.matrix_rank(A1), rank)
|
|
|
|
def test_magic_square(self):
|
|
A, b, c, numbers = magic_square(3)
|
|
A1, b1, status, message = self.rr(A, b)
|
|
assert_equal(status, 0)
|
|
assert_equal(A1.shape[0], 23)
|
|
assert_equal(np.linalg.matrix_rank(A1), 23)
|
|
|
|
def test_magic_square2(self):
|
|
A, b, c, numbers = magic_square(4)
|
|
A1, b1, status, message = self.rr(A, b)
|
|
assert_equal(status, 0)
|
|
assert_equal(A1.shape[0], 39)
|
|
assert_equal(np.linalg.matrix_rank(A1), 39)
|
|
|
|
|
|
class TestRRSVD(RRCommonTests):
|
|
def rr(self, A, b):
|
|
return _remove_redundancy(A, b)
|
|
|
|
|
|
class TestRRPivotDense(RRCommonTests):
|
|
def rr(self, A, b):
|
|
return _remove_redundancy_dense(A, b)
|
|
|
|
|
|
class TestRRPivotSparse(RRCommonTests):
|
|
def rr(self, A, b):
|
|
A1, b1, status, message = _remove_redundancy_sparse(csc_matrix(A), b)
|
|
return A1.toarray(), b1, status, message
|