update from symmetry

src/Integrator.jl

@@ -56,6 +56,33 @@ end
     return nothing
 end
 
+@inline function RK4b(rhs!::F, dt::Real, reg1, reg2, reg3, reg4, params, t::Real,
+                     indices::CartesianIndices, N) where {F}
+    rhs!(reg4, reg1, params.h, N, t)
+    @inbounds @fastmath @avx for i in indices
+        reg3[i] = dt * reg4[i]
+        reg1[i] = reg1[i] + reg3[i] / 2
+        reg2[i] = reg3[i]
+    end
+    rhs!(reg4, reg1, params.h, N, t)
+    @inbounds @fastmath @avx for i in indices
+        reg3[i] = dt * reg4[i]
+        reg1[i] = reg1[i] + (reg3[i] - reg2[i]) / 2
+    end
+    rhs!(reg4, reg1, params.h, N, t)
+    @inbounds @fastmath @avx for i in indices
+        reg3[i] = dt * reg4[i] - reg3[i] / 2
+        reg1[i] = reg1[i] + reg3[i]
+        reg2[i] = reg2[i] / 6 - reg3[i]
+    end
+    rhs!(reg4, reg1, params.h, N, t)
+    @inbounds @fastmath @avx for i in indices
+        reg3[i] = dt * reg4[i] + reg3[i] + reg3[i]
+        reg1[i] = reg1[i] + reg2[i] + reg3[i] / 6
+    end
+    return nothing
+end
+
 function solve(rhs, statevector, params, t, grid, save_every, folder)
     # istr = get_iter_str(0, t.ncells + 1)
     base_dir = base_path(folder)
@@ -98,23 +125,25 @@ function solve(rhs, statevector, params, t, grid, save_every, folder)
 
     println("saving every=", save_every)
 
-    # nt = t.ncells + 1
-    # dt = spacing(t)
-    # indices = CartesianIndices(statevector)
-    # params = (grid=grid, dt=dt, ti=coords(t), params...)
+    nt = t.ncells + 1
+    dt = spacing(t)
+    indices = CartesianIndices(statevector)
+    params = (grid=grid, dt=dt, ti=coords(t), params...)
     # InputOutput.write_metadata(base_dir, params, save_every, sims_dir)
-    # for (i, ti) in enumerate(params.ti)
-    #     i -= 1
-    #     if i == 0
-    #         continue
-    #     end
-    #     println("Iteration = ", i, "/", t.ncells)
-    #     @time RK4(rhs, dt, statevector, reg2, reg3, reg4, params, ti, indices, N)
-    #     if i % save_every == 0
-    #         InputOutput.writevtk(statevector, sims_dir, xcoord, ti, i, pvd)
-    #     end
-    # end
-
+    for (i, ti) in enumerate(coords(t)[2:end])
+        # println("Iteration = ", i, "/", t.ncells)
+        if (i==1)  global wtime0 = Base.time()  end
+        RK4(rhs, dt, statevector, reg2, reg3, reg4, params, ti, indices, N)
+        # RK4(ODE.rhs_batch!, dt, statevector, reg2, reg3, reg4, params, ti, indices, N)
+        # if i % save_every == 0
+        #     InputOutput.writevtk(statevector, sims_dir, xcoord, ti, i, pvd)
+        # end
+    end
+    wtime    = Base.time()-wtime0
+    A_eff    = (3*2)/1e9*N*N*sizeof(Data.Number)
+    wtime_it = wtime/(nt)                        # Execution time per iteration [s]
+    T_eff    = A_eff/wtime_it                       # Effective memory throughput [GB/s]
+    println("Total steps=$nt, time=$wtime sec (@ T_eff = $(round(T_eff, sigdigits=2)) GB/s)")
     # InputOutput.save_pvd(pvd)
     return nothing
 end