⚡️ Speed up function _gridmake2 by 468%

code_to_optimize/discrete_riccati.py

@@ -1,5 +1,4 @@
-"""
-Utility functions used in CompEcon
+"""Utility functions used in CompEcon
 
 Based routines found in the CompEcon toolbox by Miranda and Fackler.
 
@@ -9,13 +8,15 @@
 and Finance, MIT Press, 2002.
 
 """
+
 from functools import reduce
+
 import numpy as np
+from numba import njit
 
 
 def ckron(*arrays):
-    """
-    Repeatedly applies the np.kron function to an arbitrary number of
+    """Repeatedly applies the np.kron function to an arbitrary number of
     input arrays
 
     Parameters
@@ -42,8 +43,7 @@ def ckron(*arrays):
 
 
 def gridmake(*arrays):
-    """
-    Expands one or more vectors (or matrices) into a matrix where rows span the
+    """Expands one or more vectors (or matrices) into a matrix where rows span the
     cartesian product of combinations of the input arrays. Each column of the
     input arrays will correspond to one column of the output matrix.
 
@@ -78,13 +78,12 @@ def gridmake(*arrays):
                 out = _gridmake2(out, arr)
 
         return out
-    else:
-        raise NotImplementedError("Come back here")
+    raise NotImplementedError("Come back here")
 
 
+@njit(cache=True, fastmath=True)
 def _gridmake2(x1, x2):
-    """
-    Expands two vectors (or matrices) into a matrix where rows span the
+    """Expands two vectors (or matrices) into a matrix where rows span the
     cartesian product of combinations of the input arrays. Each column of the
     input arrays will correspond to one column of the output matrix.
 
@@ -113,11 +112,23 @@ def _gridmake2(x1, x2):
 
     """
     if x1.ndim == 1 and x2.ndim == 1:
-        return np.column_stack([np.tile(x1, x2.shape[0]),
-                               np.repeat(x2, x1.shape[0])])
-    elif x1.ndim > 1 and x2.ndim == 1:
-        first = np.tile(x1, (x2.shape[0], 1))
-        second = np.repeat(x2, x1.shape[0])
-        return np.column_stack([first, second])
-    else:
-        raise NotImplementedError("Come back here")
+        n1 = x1.shape[0]
+        n2 = x2.shape[0]
+        out = np.empty((n1 * n2, 2), dtype=x1.dtype)
+        for i in range(n2):
+            for j in range(n1):
+                out[i * n1 + j, 0] = x1[j]
+                out[i * n1 + j, 1] = x2[i]
+        return out
+    if x1.ndim > 1 and x2.ndim == 1:
+        n1 = x1.shape[0]
+        n2 = x2.shape[0]
+        ncol1 = x1.shape[1]
+        out = np.empty((n1 * n2, ncol1 + 1), dtype=x1.dtype)
+        for i in range(n2):
+            for j in range(n1):
+                for k in range(ncol1):
+                    out[i * n1 + j, k] = x1[j, k]
+                out[i * n1 + j, ncol1] = x2[i]
+        return out
+    raise NotImplementedError("Come back here")