256 lines
7.4 KiB
Python
256 lines
7.4 KiB
Python
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"""
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Unit test for Linear Programming via Simplex Algorithm.
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"""
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# TODO: add tests for:
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# https://github.com/scipy/scipy/issues/5400
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# https://github.com/scipy/scipy/issues/6690
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import numpy as np
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from numpy.testing import (
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assert_,
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assert_allclose,
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assert_equal)
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from .test_linprog import magic_square
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from scipy.optimize._remove_redundancy import _remove_redundancy_svd
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from scipy.optimize._remove_redundancy import _remove_redundancy_pivot_dense
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from scipy.optimize._remove_redundancy import _remove_redundancy_pivot_sparse
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from scipy.optimize._remove_redundancy import _remove_redundancy_id
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from scipy.sparse import csc_matrix
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def setup_module():
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np.random.seed(2017)
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def _assert_success(
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res,
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desired_fun=None,
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desired_x=None,
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rtol=1e-7,
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atol=1e-7):
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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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assert_(res.success)
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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(
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res.fun,
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desired_fun,
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err_msg="converged to an unexpected objective value",
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rtol=rtol,
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atol=atol)
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if desired_x is not None:
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assert_allclose(
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res.x,
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desired_x,
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err_msg="converged to an unexpected solution",
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rtol=rtol,
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atol=atol)
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def redundancy_removed(A, B):
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"""Checks whether a matrix contains only independent rows of another"""
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for rowA in A:
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# `rowA in B` is not a reliable check
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for rowB in B:
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if np.all(rowA == rowB):
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break
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else:
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return False
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return A.shape[0] == np.linalg.matrix_rank(A) == np.linalg.matrix_rank(B)
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class RRCommonTests:
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def test_no_redundancy(self):
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m, n = 10, 10
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A0 = np.random.rand(m, n)
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b0 = np.random.rand(m)
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A1, b1, status, message = self.rr(A0, b0)
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assert_allclose(A0, A1)
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assert_allclose(b0, b1)
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assert_equal(status, 0)
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def test_infeasible_zero_row(self):
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A = np.eye(3)
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A[1, :] = 0
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b = np.random.rand(3)
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 2)
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def test_remove_zero_row(self):
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A = np.eye(3)
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A[1, :] = 0
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b = np.random.rand(3)
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b[1] = 0
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 0)
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assert_allclose(A1, A[[0, 2], :])
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assert_allclose(b1, b[[0, 2]])
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def test_infeasible_m_gt_n(self):
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m, n = 20, 10
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A0 = np.random.rand(m, n)
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b0 = np.random.rand(m)
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A1, b1, status, message = self.rr(A0, b0)
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assert_equal(status, 2)
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def test_infeasible_m_eq_n(self):
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m, n = 10, 10
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A0 = np.random.rand(m, n)
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b0 = np.random.rand(m)
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A0[-1, :] = 2 * A0[-2, :]
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A1, b1, status, message = self.rr(A0, b0)
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assert_equal(status, 2)
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def test_infeasible_m_lt_n(self):
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m, n = 9, 10
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A0 = np.random.rand(m, n)
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b0 = np.random.rand(m)
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A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
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A1, b1, status, message = self.rr(A0, b0)
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assert_equal(status, 2)
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def test_m_gt_n(self):
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np.random.seed(2032)
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m, n = 20, 10
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A0 = np.random.rand(m, n)
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b0 = np.random.rand(m)
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x = np.linalg.solve(A0[:n, :], b0[:n])
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b0[n:] = A0[n:, :].dot(x)
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A1, b1, status, message = self.rr(A0, b0)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], n)
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assert_equal(np.linalg.matrix_rank(A1), n)
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def test_m_gt_n_rank_deficient(self):
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m, n = 20, 10
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A0 = np.zeros((m, n))
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A0[:, 0] = 1
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b0 = np.ones(m)
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A1, b1, status, message = self.rr(A0, b0)
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assert_equal(status, 0)
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assert_allclose(A1, A0[0:1, :])
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assert_allclose(b1, b0[0])
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def test_m_lt_n_rank_deficient(self):
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m, n = 9, 10
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A0 = np.random.rand(m, n)
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b0 = np.random.rand(m)
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A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
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b0[-1] = np.arange(m - 1).dot(b0[:-1])
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A1, b1, status, message = self.rr(A0, b0)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], 8)
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assert_equal(np.linalg.matrix_rank(A1), 8)
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def test_dense1(self):
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A = np.ones((6, 6))
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A[0, :3] = 0
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A[1, 3:] = 0
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A[3:, ::2] = -1
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A[3, :2] = 0
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A[4, 2:] = 0
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b = np.zeros(A.shape[0])
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A1, b1, status, message = self.rr(A, b)
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assert_(redundancy_removed(A1, A))
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assert_equal(status, 0)
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def test_dense2(self):
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A = np.eye(6)
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A[-2, -1] = 1
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A[-1, :] = 1
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b = np.zeros(A.shape[0])
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A1, b1, status, message = self.rr(A, b)
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assert_(redundancy_removed(A1, A))
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assert_equal(status, 0)
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def test_dense3(self):
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A = np.eye(6)
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A[-2, -1] = 1
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A[-1, :] = 1
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b = np.random.rand(A.shape[0])
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b[-1] = np.sum(b[:-1])
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A1, b1, status, message = self.rr(A, b)
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assert_(redundancy_removed(A1, A))
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assert_equal(status, 0)
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def test_m_gt_n_sparse(self):
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np.random.seed(2013)
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m, n = 20, 5
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p = 0.1
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A = np.random.rand(m, n)
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A[np.random.rand(m, n) > p] = 0
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rank = np.linalg.matrix_rank(A)
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b = np.zeros(A.shape[0])
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], rank)
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assert_equal(np.linalg.matrix_rank(A1), rank)
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def test_m_lt_n_sparse(self):
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np.random.seed(2017)
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m, n = 20, 50
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p = 0.05
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A = np.random.rand(m, n)
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A[np.random.rand(m, n) > p] = 0
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rank = np.linalg.matrix_rank(A)
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b = np.zeros(A.shape[0])
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], rank)
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assert_equal(np.linalg.matrix_rank(A1), rank)
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def test_m_eq_n_sparse(self):
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np.random.seed(2017)
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m, n = 100, 100
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p = 0.01
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A = np.random.rand(m, n)
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A[np.random.rand(m, n) > p] = 0
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rank = np.linalg.matrix_rank(A)
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b = np.zeros(A.shape[0])
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], rank)
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assert_equal(np.linalg.matrix_rank(A1), rank)
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def test_magic_square(self):
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A, b, c, numbers, _ = magic_square(3)
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], 23)
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assert_equal(np.linalg.matrix_rank(A1), 23)
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def test_magic_square2(self):
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A, b, c, numbers, _ = magic_square(4)
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A1, b1, status, message = self.rr(A, b)
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assert_equal(status, 0)
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assert_equal(A1.shape[0], 39)
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assert_equal(np.linalg.matrix_rank(A1), 39)
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class TestRRSVD(RRCommonTests):
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def rr(self, A, b):
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return _remove_redundancy_svd(A, b)
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class TestRRPivotDense(RRCommonTests):
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def rr(self, A, b):
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return _remove_redundancy_pivot_dense(A, b)
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class TestRRID(RRCommonTests):
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def rr(self, A, b):
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return _remove_redundancy_id(A, b)
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class TestRRPivotSparse(RRCommonTests):
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def rr(self, A, b):
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rr_res = _remove_redundancy_pivot_sparse(csc_matrix(A), b)
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A1, b1, status, message = rr_res
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return A1.toarray(), b1, status, message
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