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   "cell_type": "markdown",
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   "source": [
    "# Checking polytope feasibility\n",
    "\n",
    "It is useful to check problems and polytopes, whether they are empty before sampling or when encountering issues.\n",
    "For this purpose, hopsy provides simple functions, which we will show on examples in this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5bf6388c-1a8d-4f21-ae05-6995aa5791c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import hopsy\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "800d3e5f-53f8-49f6-a026-a3fb4d95f8db",
   "metadata": {},
   "source": [
    "## Example 1: empty polytope x < 1 and x > 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "72718950-f35e-41ba-a53d-34d6fce1296d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2023-11-30\n"
     ]
    }
   ],
   "source": [
    "empty_A = np.array([[1], [-1]])\n",
    "empty_b = np.array([1, -2])\n",
    "empty_problem = hopsy.Problem(empty_A, empty_b)\n",
    "\n",
    "# option 1: check np.arrays directly\n",
    "assert hopsy.is_polytope_empty(empty_A, empty_b) == True\n",
    "\n",
    "# option 2: check hopsy.Problem \n",
    "assert hopsy.is_problem_polytope_empty(empty_problem) == True"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8584a8ca-8f44-4726-9f75-612af2973b77",
   "metadata": {},
   "source": [
    "## Example 2: valid polytope x < 1 and x > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "70120e62-71be-49f9-acf0-b794d5178334",
   "metadata": {},
   "outputs": [],
   "source": [
    "valid_A = np.array([[1], [-1]])\n",
    "valid_b = np.array([1, 0])\n",
    "valid_problem = hopsy.Problem(valid_A, valid_b)\n",
    "\n",
    "# option 1: check np.arrays directly\n",
    "assert hopsy.is_polytope_empty(valid_A, valid_b) == False\n",
    "\n",
    "# option 2: check hopsy.Problem \n",
    "assert hopsy.is_problem_polytope_empty(valid_problem) == False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "571419cb-fb5e-4f6d-bfc6-7db15c28f748",
   "metadata": {},
   "source": [
    "## Example 3: invalid polytope x < 1 and x > 0 and x=5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c0aac3a5-a472-403f-8e4f-35e8617e79ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model in infeasible state, resetting lp\n",
      "Solver status: infeasible\n"
     ]
    }
   ],
   "source": [
    "valid_A = np.array([[1], [-1]])\n",
    "valid_b = np.array([1, 0])\n",
    "\n",
    "invalid_equality_constraint_matrix = np.array([[1]])\n",
    "invalid_equality_bounds = np.array([5])\n",
    "\n",
    "valid_problem = hopsy.Problem(valid_A, valid_b)\n",
    "\n",
    "# option 1: check np.arrays directly\n",
    "assert hopsy.is_polytope_empty(valid_A, valid_b, invalid_equality_constraint_matrix, invalid_equality_bounds) == True\n",
    "\n",
    "# option 2: There is no way to add invalid equality constraints using add_equality_constraints. hopsy will \n",
    "# directly raise a ValueError, because LP manipulations are required when simplifying added equality constraints, see PolyRound.\n",
    "try:\n",
    "    invalid_problem = hopsy.add_equality_constraints(valid_problem, A_eq=invalid_equality_constraint_matrix, b_eq=invalid_equality_bounds)\n",
    "except ValueError:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b5202072-f8a7-461e-a561-14d0328dc3f5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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