wave equation: add partial gpu support, warm up jit cache

Author: tkarna

examples/wave_equation.py

@@ -111,12 +111,14 @@ def run(n, backend, datatype, benchmark_mode):
     t_end = 1.0
 
     # coordinate arrays
+    sync()
     x_t_2d = fromfunction(
-        lambda i, j: xmin + i * dx + dx / 2, (nx, ny), dtype=dtype
+        lambda i, j: xmin + i * dx + dx / 2, (nx, ny), dtype=dtype, device=""
     )
     y_t_2d = fromfunction(
-        lambda i, j: ymin + j * dy + dy / 2, (nx, ny), dtype=dtype
+        lambda i, j: ymin + j * dy + dy / 2, (nx, ny), dtype=dtype, device=""
     )
+    sync()
 
     T_shape = (nx, ny)
     U_shape = (nx + 1, ny)
@@ -144,6 +146,22 @@ def run(n, backend, datatype, benchmark_mode):
     u2 = create_full(U_shape, 0.0, dtype)
     v2 = create_full(V_shape, 0.0, dtype)
 
+    # compute time step
+    alpha = 0.5
+    c = (g * h) ** 0.5
+    dt = alpha * dx / c
+    dt = t_export / int(math.ceil(t_export / dt))
+    nt = int(math.ceil(t_end / dt))
+    if benchmark_mode:
+        dt = 1e-5
+        nt = 100
+        t_export = dt * 25
+
+    info(f"Time step: {dt} s")
+    info(f"Total run time: {t_end} s, {nt} time steps")
+
+    sync()
+
     def exact_elev(t, x_t_2d, y_t_2d, lx, ly):
         """
         Exact solution for elevation field.
@@ -162,25 +180,6 @@ def exact_elev(t, x_t_2d, y_t_2d, lx, ly):
         sol_t = numpy.cos(2 * omega * t)
         return amp * sol_x * sol_y * sol_t
 
-    # inital elevation
-    e[:, :] = exact_elev(0.0, x_t_2d, y_t_2d, lx, ly)
-
-    # compute time step
-    alpha = 0.5
-    c = (g * h) ** 0.5
-    dt = alpha * dx / c
-    dt = t_export / int(math.ceil(t_export / dt))
-    nt = int(math.ceil(t_end / dt))
-    if benchmark_mode:
-        dt = 1e-5
-        nt = 100
-        t_export = dt * 25
-
-    info(f"Time step: {dt} s")
-    info(f"Total run time: {t_end} s, {nt} time steps")
-
-    sync()
-
     def rhs(u, v, e):
         """
         Evaluate right hand side of the equations
@@ -215,6 +214,16 @@ def step(u, v, e, u1, v1, e1, u2, v2, e2):
         v[:, 1:-1] = v[:, 1:-1] / 3.0 + 2.0 / 3.0 * (v2[:, 1:-1] + dt * dvdt)
         e[:, :] = e[:, :] / 3.0 + 2.0 / 3.0 * (e2[:, :] + dt * dedt)
 
+    # warm git cache
+    step(u, v, e, u1, v1, e1, u2, v2, e2)
+    sync()
+
+    # initial solution
+    e[:, :] = exact_elev(0.0, x_t_2d, y_t_2d, lx, ly).to_device(device)
+    u[:, :] = create_full(U_shape, 0.0, dtype)
+    v[:, :] = create_full(V_shape, 0.0, dtype)
+    sync()
+
     t = 0
     i_export = 0
     next_t_export = 0
@@ -226,9 +235,22 @@ def step(u, v, e, u1, v1, e1, u2, v2, e2):
         t = i * dt
 
         if t >= next_t_export - 1e-8:
-            _elev_max = np.max(e, all_axes)
-            _u_max = np.max(u, all_axes)
-            _total_v = np.sum(e + h, all_axes)
+            if device:
+                # FIXME gpu.memcpy to host requires identity layout
+                # FIXME reduction on gpu
+                # e_host = e.to_device()
+                # u_host = u.to_device()
+                # h_host = h.to_device()
+                # _elev_max = np.max(e_host, all_axes)
+                # _u_max = np.max(u_host, all_axes)
+                # _total_v = np.sum(e_host + h, all_axes)
+                _elev_max = 0
+                _u_max = 0
+                _total_v = 0
+            else:
+                _elev_max = np.max(e, all_axes)
+                _u_max = np.max(u, all_axes)
+                _total_v = np.sum(e + h, all_axes)
 
             elev_max = float(_elev_max)
             u_max = float(_u_max)
@@ -265,10 +287,17 @@ def step(u, v, e, u1, v1, e1, u2, v2, e2):
 
     e_exact = exact_elev(t, x_t_2d, y_t_2d, lx, ly)
     err2 = (e_exact - e) * (e_exact - e) * dx * dy / lx / ly
-    err_L2 = math.sqrt(float(np.sum(err2, all_axes)))
+    if device:
+        # FIXME gpu.memcpy to host requires identity layout
+        # FIXME reduction on gpu
+        # err2_host = err2.to_device()
+        # err_L2 = math.sqrt(float(np.sum(err2_host, all_axes)))
+        err_L2 = 0
+    else:
+        err_L2 = math.sqrt(float(np.sum(err2, all_axes)))
     info(f"L2 error: {err_L2:7.5e}")
 
-    if nx == 128 and ny == 128 and not benchmark_mode:
+    if nx == 128 and ny == 128 and not benchmark_mode and not device:
         if datatype == "f32":
             assert numpy.allclose(err_L2, 7.2235471e-03, rtol=1e-4)
         else: