FIX: linprog_simplex: Fix bug in Phase 1

quantecon/optimize/linprog_simplex.py

@@ -163,14 +163,9 @@ def linprog_simplex(c, A_ub=np.empty((0, 0)), b_ub=np.empty((0,)),
 
  # Phase 1
  success, status, num_iter_1 = \
- solve_tableau(tableau, basis, max_iter, skip_aux=False,
- piv_options=piv_options)
+ solve_phase_1(tableau, basis, max_iter, piv_options=piv_options)
  num_iter += num_iter_1
- if not success: # max_iter exceeded
- return SimplexResult(x, lambd, fun, success, status, num_iter)
- if tableau[-1, -1] > piv_options.fea_tol: # Infeasible
- success = False
- status = 2
+ if not success:
  return SimplexResult(x, lambd, fun, success, status, num_iter)
 
  # Modify the criterion row for Phase 2
@@ -442,6 +437,50 @@ def solve_tableau(tableau, basis, max_iter=10**6, skip_aux=True,
  return success, status, num_iter
 
 
+@jit(nopython=True, cache=True)
+def solve_phase_1(tableau, basis, max_iter=10**6, piv_options=PivOptions()):
+ """
+ Perform the simplex algorithm for Phase 1 on a given tableau in
+ canonical form, by calling `solve_tableau` with `skip_aux=False`.
+
+ Parameters
+ ----------
+ See `solve_tableau`.
+
+ Returns
+ -------
+ See `solve_tableau`.
+
+ """
+ L = tableau.shape[0] - 1
+ nm = tableau.shape[1] - (L+1) # n + m
+
+ success, status, num_iter_1 = \
+ solve_tableau(tableau, basis, max_iter, skip_aux=False,
+ piv_options=piv_options)
+
+ if not success: # max_iter exceeded
+ return success, status, num_iter_1
+ if tableau[-1, -1] > piv_options.fea_tol: # Infeasible
+ success = False
+ status = 2
+ return success, status, num_iter_1
+
+ # Check artifial variables have been eliminated
+ tol_piv = piv_options.tol_piv
+ for i in range(L):
+ if basis[i] >= nm: # Artifial variable not eliminated
+ for j in range(nm):
+ if tableau[i, j] < -tol_piv or \
+ tableau[i, j] > tol_piv: # Treated nonzero
+ _pivoting(tableau, j, i)
+ basis[i] = j
+ num_iter_1 += 1
+ break
+
+ return success, status, num_iter_1
+
+
 @jit(nopython=True, cache=True)
 def _pivot_col(tableau, skip_aux, piv_options):
  """

quantecon/optimize/tests/test_linprog_simplex.py

@@ -239,3 +239,15 @@ def test_bug_8662(self):
  desired_fun = -36.0000000000
  res = linprog_simplex(c, A_ub=A_ub, b_ub=b_ub)
  _assert_success(res, c, b_ub=b_ub, desired_fun=desired_fun)
+
+
+class TestLinprogSimplex:
+ def test_phase_1_bug_725(self):
+ # Identified a bug in Phase 1
+ # https://github.com/QuantEcon/QuantEcon.py/issues/725
+ c = np.array([-4.09555556, 4.59044444])
+ A_ub = np.array([[1, 0.1], [-1, -0.1], [1, 1]])
+ b_ub = np.array([9.1, -0.1, 0.1])
+ desired_x = [0.1, 0]
+ res = linprog_simplex(c, A_ub=A_ub, b_ub=b_ub)
+ _assert_success(res, c, b_ub=b_ub, desired_x=desired_x)