misc: make builtin grid unit spacing

devito/builtins/initializers.py

@@ -179,7 +179,9 @@ def fset(f, g):
     # Create the padded grid:
     objective_domain = ObjectiveDomain(lw)
     shape_padded = tuple([np.array(s) + 2*l for s, l in zip(shape, lw)])
-    grid = dv.Grid(shape=shape_padded, subdomains=objective_domain)
+    extent_padded = tuple([s-1 for s in shape_padded])
+    grid = dv.Grid(shape=shape_padded, subdomains=objective_domain,
+                   extent=extent_padded)
 
     f_c = dv.Function(name='f_c', grid=grid, space_order=2*max(lw), dtype=dtype)
     f_o = dv.Function(name='f_o', grid=grid, dtype=dtype)

devito/finite_differences/finite_difference.py

@@ -151,7 +151,7 @@ def make_derivative(expr, dim, fd_order, deriv_order, side, matvec, x0, coeffici
     expand = True if dim.is_Time else expand
 
     # The stencil indices
-    nweights, wdim = process_weights(weights, expr)
+    nweights, wdim, scale = process_weights(weights, expr, dim)
     indices, x0 = generate_indices(expr, dim, fd_order, side=side, matvec=matvec,
                                    x0=x0, nweights=nweights)
     # Finite difference weights corresponding to the indices. Computed via the
@@ -164,11 +164,6 @@ def make_derivative(expr, dim, fd_order, deriv_order, side, matvec, x0, coeffici
     # Enforce fixed precision FD coefficients to avoid variations in results
     weights = [sympify(w).evalf(_PRECISION) for w in weights]
 
-    # Adimensional weight from custom coeffs need to multiply by h^order
-    scale = None
-    if wdim is None and not weights[0].has(dim.spacing):
-        scale = dim.spacing**(-deriv_order)
-
     # Transpose the FD, if necessary
     if matvec == transpose:
         weights = weights[::-1]
@@ -213,6 +208,6 @@ def make_derivative(expr, dim, fd_order, deriv_order, side, matvec, x0, coeffici
 
         deriv = EvalDerivative(*terms, base=expr)
 
-    if scale is not None:
-        deriv = scale * deriv
+    if scale:
+        deriv = dim.spacing**(-deriv_order) * deriv
     return deriv

devito/finite_differences/tools.py

@@ -321,16 +321,21 @@ def make_shift_x0(shift, ndim):
                      "None, float or tuple with shape equal to %s" % (ndim,))
 
 
-def process_weights(weights, expr):
+def process_weights(weights, expr, dim):
     if weights is None:
-        return 0, None
+        return 0, None, False
     elif isinstance(weights, Function):
         if len(weights.dimensions) == 1:
-            return weights.shape[0], weights.dimensions[0]
+            return weights.shape[0], weights.dimensions[0], False
         wdim = {d for d in weights.dimensions if d not in expr.dimensions}
         assert len(wdim) == 1
         wdim = wdim.pop()
         shape = weights.shape
-        return shape[weights.dimensions.index(wdim)], wdim
+        return shape[weights.dimensions.index(wdim)], wdim, False
     else:
-        return len(list(weights)), None
+        # Adimensional weight from custom coeffs need to be multiplied by h^order
+        if not all(sympify(w).has(dim.spacing) for w in weights if w != 0):
+            scale = True
+        else:
+            scale = False
+        return len(list(weights)), None, scale