FIX: Updates for Numba 0.49.0 (#531)

* FIX: Fix ModuleNotFoundError for Numba 0.49.0

* FIX: Fix errors in tests for `quad.py` when Numba 0.49.0 is used

* FIX: Fix errors in tests for `nelder_mead.py` when Numba 0.49.0 is used

* RFC: Fix PEP8 errors

Co-authored-by: QBatista <quentin.batista@mail.mcgill.ca>

quantecon/optimize/nelder_mead.py

@@ -220,7 +220,9 @@ def _nelder_mead_algorithm(fun, vertices, bounds=np.array([[], []]).T,
             break
 
         # Step 2: Reflection
-        x_r = x_bar + ρ * (x_bar - vertices[worst_val_idx])
+        # https://github.com/QuantEcon/QuantEcon.py/issues/530
+        temp = ρ * (x_bar - vertices[worst_val_idx])
+        x_r = x_bar + temp
         f_r = _neg_bounded_fun(fun, bounds, x_r, args=args)
 
         if f_r >= f_val[best_val_idx] and f_r < f_val[sort_ind[n-1]]:
@@ -230,7 +232,9 @@ def _nelder_mead_algorithm(fun, vertices, bounds=np.array([[], []]).T,
 
         # Step 3: Expansion
         elif f_r < f_val[best_val_idx]:
-            x_e = x_bar + χ * (x_r - x_bar)
+            # https://github.com/QuantEcon/QuantEcon.py/issues/530
+            temp = χ * (x_r - x_bar)
+            x_e = x_bar + temp
             f_e = _neg_bounded_fun(fun, bounds, x_e, args=args)
             if f_e < f_r:  # Greedy minimization
                 vertices[worst_val_idx] = x_e
@@ -242,11 +246,13 @@ def _nelder_mead_algorithm(fun, vertices, bounds=np.array([[], []]).T,
         # Step 4 & 5: Contraction and Shrink
         else:
             # Step 4: Contraction
+            # https://github.com/QuantEcon/QuantEcon.py/issues/530
+            temp = γ * (x_r - x_bar)
             if f_r < f_val[worst_val_idx]:  # Step 4.a: Outside Contraction
-                x_c = x_bar + γ * (x_r - x_bar)
+                x_c = x_bar + temp
                 LV_ratio_update = ργ
             else:  # Step 4.b: Inside Contraction
-                x_c = x_bar - γ * (x_r - x_bar)
+                x_c = x_bar - temp
                 LV_ratio_update = γ
 
             f_c = _neg_bounded_fun(fun, bounds, x_c, args=args)

quantecon/quad.py

@@ -21,6 +21,7 @@
            'qnwsimp', 'qnwtrap', 'qnwunif', 'quadrect', 'qnwbeta',
            'qnwgamma']
 
+
 @vectorize(nopython=True)
 def gammaln(x):
     return math.lgamma(x)
@@ -681,6 +682,7 @@ def _make_multidim_func(one_d_func, n, *args):
     nodes = gridmake(*nodes)
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwcheb1(n, a, b):
     """
@@ -729,6 +731,7 @@ def _qnwcheb1(n, a, b):
 
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwlege1(n, a, b):
     """
@@ -784,7 +787,10 @@ def _qnwlege1(n, a, b):
             p2 = p1
             p1 = ((2 * j - 1) * z * p2 - (j - 1) * p3) / j
 
-        pp = n * (z * p1 - p2)/(z * z - 1.0)
+        # https://github.com/QuantEcon/QuantEcon.py/issues/530
+        top = n * (z * p1 - p2)
+        bottom = z ** 2 - 1.0
+        pp = top / bottom
         z1 = z.copy()
         z = z1 - p1/pp
         if np.all(np.abs(z - z1) < 1e-14):
@@ -796,11 +802,13 @@ def _qnwlege1(n, a, b):
     nodes[i] = xm - xl * z
     nodes[- i - 1] = xm + xl * z
 
-    weights[i] = 2 * xl / ((1 - z * z) * pp * pp)
+    # https://github.com/QuantEcon/QuantEcon.py/issues/530
+    weights[i] = 2 * xl / ((1 - z ** 2) * pp * pp)
     weights[- i - 1] = weights[i]
 
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwnorm1(n):
     """
@@ -879,6 +887,7 @@ def _qnwnorm1(n):
 
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwsimp1(n, a, b):
     """
@@ -927,6 +936,7 @@ def _qnwsimp1(n, a, b):
 
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwtrap1(n, a, b):
     """
@@ -974,6 +984,7 @@ def _qnwtrap1(n, a, b):
 
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwbeta1(n, a=1.0, b=1.0):
     """
@@ -1090,13 +1101,14 @@ def _qnwbeta1(n, a=1.0, b=1.0):
         weights[i] = temp/(pp*p2)
 
     nodes = (1-nodes)/2
-    weights = weights * math.exp(gammaln(a+n) + gammaln(b+n)
-                                 - gammaln(n+1) - gammaln(n+ab+1))
-    weights = weights / (2*math.exp(gammaln(a+1) + gammaln(b+1)
-                         - gammaln(ab+2)))
+    weights = weights * math.exp(gammaln(a+n) + gammaln(b+n) -
+                                 gammaln(n+1) - gammaln(n+ab+1))
+    weights = weights / (2*math.exp(gammaln(a+1) + gammaln(b+1) -
+                         gammaln(ab+2)))
 
     return nodes, weights
 
+
 @jit(nopython=True)
 def _qnwgamma1(n, a=1.0, b=1.0, tol=3e-14):
     """

quantecon/util/numba.py

@@ -4,7 +4,10 @@
 """
 import numpy as np
 from numba import jit, generated_jit, types
-from numba.targets.linalg import _LAPACK
+try:
+    from numba.np.linalg import _LAPACK  # for Numba >= 0.49.0
+except ModuleNotFoundError:
+    from numba.targets.linalg import _LAPACK  # for Numba < 0.49.0
 
 
 # BLAS kinds as letters