tests/test_fvm.py

+import sympy as sp
+import pystencils as ps
+import numpy as np
+import pytest
+from itertools import product
+from pystencils.rng import random_symbol
+from pystencils.astnodes import SympyAssignment
+from pystencils.node_collection import NodeCollection
+
+
+def advection_diffusion(dim: int):
+    # parameters
+    if dim == 2:
+        L = (32, 32)
+    elif dim == 3:
+        L = (16, 16, 16)
+
+    dh = ps.create_data_handling(domain_size=L, periodicity=True, default_target=ps.Target.CPU)
+
+    n_field = dh.add_array('n', values_per_cell=1)
+    j_field = dh.add_array('j', values_per_cell=3 ** dim // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+    velocity_field = dh.add_array('v', values_per_cell=dim)
+
+    D = 0.0666
+    time = 100
+
+    def grad(f):
+        return sp.Matrix([ps.fd.diff(f, i) for i in range(dim)])
+
+    flux_eq = - D * grad(n_field)
+    fvm_eq = ps.fd.FVM1stOrder(n_field, flux=flux_eq)
+
+    vof_adv = ps.fd.VOF(j_field, velocity_field, n_field)
+
+    # merge calculation of advection and diffusion terms
+    flux = []
+    for adv, div in zip(vof_adv, fvm_eq.discrete_flux(j_field)):
+        assert adv.lhs == div.lhs
+        flux.append(ps.Assignment(adv.lhs, adv.rhs + div.rhs))
+
+    flux_kernel = ps.create_staggered_kernel(flux).compile()
+
+    pde_kernel = ps.create_kernel(fvm_eq.discrete_continuity(j_field)).compile()
+
+    sync_conc = dh.synchronization_function([n_field.name])
+
+    # analytical density calculation
+    def density(pos: np.ndarray, time: int, D: float):
+        return (4 * np.pi * D * time)**(-dim / 2) * \
+            np.exp(-np.sum(np.square(pos), axis=-1) / (4 * D * time))
+
+    pos = np.zeros((*L, dim))
+    xpos = np.arange(-L[0] // 2, L[0] // 2)
+    ypos = np.arange(-L[1] // 2, L[1] // 2)
+
+    if dim == 2:
+        pos[..., 1], pos[..., 0] = np.meshgrid(xpos, ypos)
+    elif dim == 3:
+        zpos = np.arange(-L[2] // 2, L[2] // 2)
+        pos[..., 2], pos[..., 1], pos[..., 0] = np.meshgrid(xpos, ypos, zpos)
+    pos += 0.5
+
+    def run(velocity: np.ndarray, time: int):
+        dh.fill(n_field.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(j_field.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+
+        # set initial values for velocity and density
+        for i in range(dim):
+            dh.fill(velocity_field.name, velocity[i], i, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(n_field.name, 0)
+        if dim == 2:
+            start = ps.make_slice[L[0] // 2 - 1:L[0] // 2 + 1, L[1] // 2 - 1:L[1] // 2 + 1]
+        else:
+            start = ps.make_slice[L[0] // 2 - 1:L[0] // 2 + 1, L[1] // 2 - 1:L[1] // 2 + 1,
+                                  L[2] // 2 - 1:L[2] // 2 + 1]
+        dh.fill(n_field.name, 2**-dim, slice_obj=start)
+
+        sync_conc()
+        for i in range(time):
+            dh.run_kernel(flux_kernel)
+            dh.run_kernel(pde_kernel)
+            sync_conc()
+
+        sim_density = dh.gather_array(n_field.name)
+        
+        # check that mass was conserved
+        assert np.isclose(sim_density.sum(), 1)
+        assert np.all(sim_density > 0)
+        
+        # check that the maximum is in the right place
+        peak = np.unravel_index(np.argmax(sim_density, axis=None), sim_density.shape)
+        assert np.allclose(peak, np.array(L) // 2 - 0.5 + velocity * time, atol=0.5)
+        
+        # check the concentration profile
+        if np.linalg.norm(velocity) == 0:
+            calc_density = density(pos - velocity * time, time, D)
+            target = [time, D]
+        
+            pytest.importorskip('scipy.optimize')
+            from scipy.optimize import curve_fit
+            popt, _ = curve_fit(lambda x, t, D: density(x - velocity * time, t, D),
+                                pos.reshape(-1, dim),
+                                sim_density.reshape(-1),
+                                p0=target)
+        
+            assert np.isclose(popt[0], time, rtol=0.1)
+            assert np.isclose(popt[1], D, rtol=0.1)
+            assert np.allclose(calc_density, sim_density, atol=1e-4)
+
+    return lambda v: run(np.array(v), time)
+
+
+advection_diffusion.runners = {}
+
+
+@pytest.mark.parametrize("velocity", list(product([0, -0.047, 0.041], [0, -0.031, 0.023])))
+def test_advection_diffusion_2d(velocity):
+    if 2 not in advection_diffusion.runners:
+        advection_diffusion.runners[2] = advection_diffusion(2)
+    advection_diffusion.runners[2](velocity)
+
+
+@pytest.mark.parametrize("velocity", list(product([0, -0.047, 0.041], [0, -0.031, 0.023], [0, -0.017, 0.011])))
+@pytest.mark.longrun
+def test_advection_diffusion_3d(velocity):
+    if 3 not in advection_diffusion.runners:
+        advection_diffusion.runners[3] = advection_diffusion(3)
+    advection_diffusion.runners[3](velocity)
+
+
+def advection_diffusion_fluctuations(dim: int):
+    # parameters
+    if dim == 2:
+        L = (32, 32)
+        stencil_factor = np.sqrt(1 / (1 + np.sqrt(2)))
+    elif dim == 3:
+        L = (16, 16, 16)
+        stencil_factor = np.sqrt(1 / (1 + 2 * np.sqrt(2) + 4.0 / 3.0 * np.sqrt(3)))
+
+    dh = ps.create_data_handling(domain_size=L, periodicity=True, default_target=ps.Target.CPU)
+
+    n_field = dh.add_array('n', values_per_cell=1)
+    j_field = dh.add_array('j', values_per_cell=3 ** dim // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+    velocity_field = dh.add_array('v', values_per_cell=dim)
+
+    D = 0.00666
+    time = 10000
+
+    def grad(f):
+        return sp.Matrix([ps.fd.diff(f, i) for i in range(dim)])
+
+    flux_eq = - D * grad(n_field)
+    fvm_eq = ps.fd.FVM1stOrder(n_field, flux=flux_eq)
+
+    vof_adv = ps.fd.VOF(j_field, velocity_field, n_field)
+
+    # merge calculation of advection and diffusion terms
+    flux = []
+    for adv, div in zip(vof_adv, fvm_eq.discrete_flux(j_field)):
+        assert adv.lhs == div.lhs
+        flux.append(ps.Assignment(adv.lhs, adv.rhs + div.rhs))
+    flux = ps.AssignmentCollection(flux)
+
+    rng_symbol_gen = random_symbol(flux.subexpressions, dim=dh.dim)
+    for i in range(len(flux.main_assignments)):
+        n = j_field.staggered_stencil[i]
+        assert flux.main_assignments[i].lhs == j_field.staggered_access(n)
+        
+        # calculate mean density
+        dens = (n_field.neighbor_vector(n) + n_field.center_vector)[0] / 2
+        # multyply by smoothed haviside function so that fluctuation will not get bigger that the density
+        dens *= sp.Max(0, sp.Min(1.0, n_field.neighbor_vector(n)[0]) * sp.Min(1.0, n_field.center_vector[0]))
+        
+        # lenght of the vector
+        length = sp.sqrt(len(j_field.staggered_stencil[i]))
+        
+        # amplitude of the random fluctuations
+        fluct = sp.sqrt(2 * dens * D) * sp.sqrt(1 / length) * stencil_factor
+        # add fluctuations
+        fluct *= 2 * (next(rng_symbol_gen) - 0.5) * sp.sqrt(3)
+        
+        flux.main_assignments[i] = ps.Assignment(flux.main_assignments[i].lhs, flux.main_assignments[i].rhs + fluct)
+    
+    # Add the folding to the flux, so that the random numbers persist through the ghostlayers.
+    fold = {ps.astnodes.LoopOverCoordinate.get_loop_counter_symbol(i):
+            ps.astnodes.LoopOverCoordinate.get_loop_counter_symbol(i) % L[i] for i in range(len(L))}
+    flux.subs(fold)
+
+    flux_kernel = ps.create_staggered_kernel(flux).compile()
+
+    pde_kernel = ps.create_kernel(fvm_eq.discrete_continuity(j_field)).compile()
+
+    sync_conc = dh.synchronization_function([n_field.name])
+
+    # analytical density distribution calculation
+    def P(rho, density_init):
+        res = []
+        for r in rho:
+            res.append(np.power(density_init, r) * np.exp(-density_init) / np.math.gamma(r + 1))
+        return np.array(res)
+
+    def run(density_init: float, velocity: np.ndarray, time: int):
+        dh.fill(n_field.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(j_field.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+
+        # set initial values for velocity and density
+        for i in range(dim):
+            dh.fill(velocity_field.name, velocity[i], i, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(n_field.name, density_init)
+
+        measurement_intervall = 10
+        warm_up = 1000
+        data = []
+
+        sync_conc()
+        for i in range(warm_up):
+            dh.run_kernel(flux_kernel, seed=42, time_step=i)
+            dh.run_kernel(pde_kernel)
+            sync_conc()
+
+        for i in range(time):
+            dh.run_kernel(flux_kernel, seed=42, time_step=i + warm_up)
+            dh.run_kernel(pde_kernel)
+            sync_conc()
+            if(i % measurement_intervall == 0):
+                data = np.append(data, dh.gather_array(n_field.name).ravel(), 0)
+
+        # test mass conservation
+        np.testing.assert_almost_equal(dh.gather_array(n_field.name).mean(), density_init)
+
+        n_bins = 50
+
+        density_value, bins = np.histogram(data, density=True, bins=n_bins)
+        bins_mean = bins[:-1] + (bins[1:] - bins[:-1]) / 2
+        analytical_value = P(bins_mean, density_init)
+        print(density_value - analytical_value)
+        np.testing.assert_allclose(density_value, analytical_value, atol=2e-3)
+
+    return lambda density_init, v: run(density_init, np.array(v), time)
+
+
+advection_diffusion_fluctuations.runners = {}
+
+
+@pytest.mark.parametrize("velocity", list(product([0, 0.00041], [0, -0.00031])))
+@pytest.mark.parametrize("density", [27.0, 56.5])
+@pytest.mark.longrun
+def test_advection_diffusion_fluctuation_2d(density, velocity):
+    if 2 not in advection_diffusion_fluctuations.runners:
+        advection_diffusion_fluctuations.runners[2] = advection_diffusion_fluctuations(2)
+    advection_diffusion_fluctuations.runners[2](density, velocity)
+
+
+@pytest.mark.parametrize("velocity", [(0.0, 0.0, 0.0), (0.00043, -0.00017, 0.00028)])
+@pytest.mark.parametrize("density", [27.0, 56.5])
+@pytest.mark.longrun
+def test_advection_diffusion_fluctuation_3d(density, velocity):
+    if 3 not in advection_diffusion_fluctuations.runners:
+        advection_diffusion_fluctuations.runners[3] = advection_diffusion_fluctuations(3)
+    advection_diffusion_fluctuations.runners[3](density, velocity)
+
+
+def diffusion_reaction(fluctuations: bool):
+    # parameters
+    L = (32, 32)
+    stencil_factor = np.sqrt(1 / (1 + np.sqrt(2)))
+
+    dh = ps.create_data_handling(domain_size=L, periodicity=True, default_target=ps.Target.CPU)
+
+    species = 2
+    n_fields = []
+    j_fields = []
+    r_flux_fields = []
+    for i in range(species):
+        n_fields.append(dh.add_array(f'n_{i}', values_per_cell=1))
+        j_fields.append(dh.add_array(f'j_{i}', values_per_cell=3 ** dh.dim // 2,
+                                     field_type=ps.FieldType.STAGGERED_FLUX))
+        r_flux_fields.append(dh.add_array(f'r_{i}', values_per_cell=1))
+    velocity_field = dh.add_array('v', values_per_cell=dh.dim)
+
+    D = 0.00666
+    time = 1000
+    r_order = [2.0, 0.0]
+    r_rate_const = 0.00001
+    r_coefs = [-2, 1]
+
+    def grad(f):
+        return sp.Matrix([ps.fd.diff(f, i) for i in range(dh.dim)])
+
+    flux_eq = - D * grad(n_fields[0])
+    fvm_eq = ps.fd.FVM1stOrder(n_fields[0], flux=flux_eq)
+    vof_adv = ps.fd.VOF(j_fields[0], velocity_field, n_fields[0])
+    continuity_assignments = fvm_eq.discrete_continuity(j_fields[0])
+    # merge calculation of advection and diffusion terms
+    flux = []
+    for adv, div in zip(vof_adv, fvm_eq.discrete_flux(j_fields[0])):
+        assert adv.lhs == div.lhs
+        flux.append(ps.Assignment(adv.lhs, adv.rhs + div.rhs))
+    flux = ps.AssignmentCollection(flux)
+
+    if(fluctuations):
+        rng_symbol_gen = random_symbol(flux.subexpressions, dim=dh.dim)
+        for i in range(len(flux.main_assignments)):
+            n = j_fields[0].staggered_stencil[i]
+            assert flux.main_assignments[i].lhs == j_fields[0].staggered_access(n)
+            
+            # calculate mean density
+            dens = (n_fields[0].neighbor_vector(n) + n_fields[0].center_vector)[0] / 2
+            # multyply by smoothed haviside function so that fluctuation will not get bigger that the density
+            dens *= sp.Max(0,
+                           sp.Min(1.0, n_fields[0].neighbor_vector(n)[0]) * sp.Min(1.0, n_fields[0].center_vector[0]))
+            
+            # lenght of the vector
+            length = sp.sqrt(len(j_fields[0].staggered_stencil[i]))
+            
+            # amplitude of the random fluctuations
+            fluct = sp.sqrt(2 * dens * D) * sp.sqrt(1 / length) * stencil_factor
+            # add fluctuations
+            fluct *= 2 * (next(rng_symbol_gen) - 0.5) * sp.sqrt(3)
+            flux.main_assignments[i] = ps.Assignment(flux.main_assignments[i].lhs, flux.main_assignments[i].rhs + fluct)
+        
+        # Add the folding to the flux, so that the random numbers persist through the ghostlayers.
+        fold = {ps.astnodes.LoopOverCoordinate.get_loop_counter_symbol(i):
+                ps.astnodes.LoopOverCoordinate.get_loop_counter_symbol(i) % L[i] for i in range(len(L))}
+        flux.subs(fold)
+
+    r_flux = NodeCollection([SympyAssignment(j_fields[i].center, 0) for i in range(species)])
+    reaction = r_rate_const
+    for i in range(species):
+        reaction *= sp.Pow(n_fields[i].center, r_order[i])
+    new_assignments = []
+    if fluctuations:
+        rng_symbol_gen = random_symbol(new_assignments, dim=dh.dim)
+        reaction_fluctuations = sp.sqrt(sp.Abs(reaction)) * 2 * (next(rng_symbol_gen) - 0.5) * sp.sqrt(3)
+        reaction_fluctuations *= sp.Min(1, sp.Abs(reaction**2))
+    else:
+        reaction_fluctuations = 0.0
+    for i in range(species):
+        r_flux.all_assignments[i] = SympyAssignment(
+            r_flux_fields[i].center, (reaction + reaction_fluctuations) * r_coefs[i])
+    [r_flux.all_assignments.insert(0, new) for new in new_assignments]
+
+    continuity_assignments = [SympyAssignment(*assignment.args) for assignment in continuity_assignments]
+    continuity_assignments.append(SympyAssignment(n_fields[0].center, n_fields[0].center + r_flux_fields[0].center))
+
+    flux_kernel = ps.create_staggered_kernel(flux).compile()
+    reaction_kernel = ps.create_kernel(r_flux).compile()
+
+    config = ps.CreateKernelConfig(allow_double_writes=True)
+    pde_kernel = ps.create_kernel(continuity_assignments, config=config).compile()
+
+    sync_conc = dh.synchronization_function([n_fields[0].name, n_fields[1].name])
+
+    def f(t, r, n0, fac, fluctuations):
+        """Calculates the amount of product created after a certain time of a reaction with form xA -> B
+
+        Args:
+            t: Time of the reation
+            r: Reaction rate constant
+            n0: Initial density of the 
+            fac: Reaction order of A (this in most cases equals the stochometric coefficient x)
+            fluctuations: Boolian whether fluctuations were included during the reaction.
+        """
+        if fluctuations:
+            return 1 / fac * (n0 + n0 / (n0 - (n0 + 1) * np.exp(fac * r * t)))
+        return 1 / fac * (n0 - (1 / (fac * r * t + (1 / n0))))
+
+    def run(density_init: float, velocity: np.ndarray, time: int):
+        for i in range(species):
+            dh.fill(n_fields[i].name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+            dh.fill(j_fields[i].name, 0.0, ghost_layers=True, inner_ghost_layers=True)
+            dh.fill(r_flux_fields[i].name, 0.0, ghost_layers=True, inner_ghost_layers=True)
+
+        # set initial values for velocity and density
+        for i in range(dh.dim):
+            dh.fill(velocity_field.name, velocity[i], i, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(n_fields[0].name, density_init)
+        dh.fill(n_fields[1].name, 0.0)
+
+        measurement_intervall = 10
+        data = []
+        
+        sync_conc()
+        for i in range(time):
+            if(i % measurement_intervall == 0):
+                data.append([i, dh.gather_array(n_fields[1].name).mean(), dh.gather_array(n_fields[0].name).mean()])
+            dh.run_kernel(reaction_kernel, seed=41, time_step=i)
+            for s_idx in range(species):
+                flux_kernel(n_0=dh.cpu_arrays[n_fields[s_idx].name],
+                            j_0=dh.cpu_arrays[j_fields[s_idx].name],
+                            v=dh.cpu_arrays[velocity_field.name], seed=42 + s_idx, time_step=i)
+                pde_kernel(n_0=dh.cpu_arrays[n_fields[s_idx].name],
+                           j_0=dh.cpu_arrays[j_fields[s_idx].name],
+                           r_0=dh.cpu_arrays[r_flux_fields[s_idx].name])
+            sync_conc()
+
+        data = np.array(data).transpose()
+        x = data[0]
+        analytical_value = f(x, r_rate_const, density_init, abs(r_coefs[0]), fluctuations)
+
+        # test mass conservation
+        np.testing.assert_almost_equal(
+            dh.gather_array(n_fields[0].name).mean() + 2 * dh.gather_array(n_fields[1].name).mean(), density_init)
+
+        r_tol = 2e-3
+        if fluctuations:
+            r_tol = 3e-2
+        np.testing.assert_allclose(data[1], analytical_value, rtol=r_tol)
+
+    return lambda density_init, v: run(density_init, np.array(v), time)
+
+
+advection_diffusion_fluctuations.runners = {}
+
+
+@pytest.mark.parametrize("velocity", list(product([0, 0.0041], [0, -0.0031])))
+@pytest.mark.parametrize("density", [27.0, 56.5])
+@pytest.mark.parametrize("fluctuations", [False, True])
+@pytest.mark.longrun
+def test_diffusion_reaction(fluctuations, density, velocity):
+    diffusion_reaction.runner = diffusion_reaction(fluctuations)
+    diffusion_reaction.runner(density, velocity)
+
+
+def VOF2(j: ps.field.Field, v: ps.field.Field, ρ: ps.field.Field, simplify=True):
+    """Volume-of-fluid discretization of advection
+
+    Args:
+        j: the staggered field to write the fluxes to. Should have a D2Q9/D3Q27 stencil. Other stencils work too, but
+           incur a small error (D2Q5/D3Q7: v^2, D3Q19: v^3).
+        v: the flow velocity field
+        ρ: the quantity to advect
+        simplify: whether to simplify the generated expressions (slow, but makes them much more readable and faster)
+    """
+    dim = j.spatial_dimensions
+    assert ps.FieldType.is_staggered(j)
+    
+    def assume_velocity(e):
+        if not simplify:
+            return e
+        repl = {}
+        for c in e.atoms(sp.StrictGreaterThan, sp.GreaterThan):
+            if isinstance(c.lhs, ps.field.Field.Access) and c.lhs.field == v and isinstance(c.rhs, sp.Number):
+                if c.rhs <= -1:
+                    repl[c] = True
+                elif c.rhs >= 1:
+                    repl[c] = False
+        for c in e.atoms(sp.StrictLessThan, sp.LessThan):
+            if isinstance(c.lhs, ps.field.Field.Access) and c.lhs.field == v and isinstance(c.rhs, sp.Number):
+                if c.rhs >= 1:
+                    repl[c] = True
+                elif c.rhs <= -1:
+                    repl[c] = False
+        for c in e.atoms(sp.Equality):
+            if isinstance(c.lhs, ps.field.Field.Access) and c.lhs.field == v and isinstance(c.rhs, sp.Number):
+                if c.rhs <= -1 or c.rhs >= 1:
+                    repl[c] = False
+        return e.subs(repl)
+    
+    class AABB:
+        def __init__(self, corner0, corner1):
+            self.dim = len(corner0)
+            self.minCorner = sp.zeros(self.dim, 1)
+            self.maxCorner = sp.zeros(self.dim, 1)
+            for i in range(self.dim):
+                self.minCorner[i] = sp.Piecewise((corner0[i], corner0[i] < corner1[i]), (corner1[i], True))
+                self.maxCorner[i] = sp.Piecewise((corner1[i], corner0[i] < corner1[i]), (corner0[i], True))
+
+        def intersect(self, other):
+            minCorner = [sp.Max(self.minCorner[d], other.minCorner[d]) for d in range(self.dim)]
+            maxCorner = [sp.Max(minCorner[d], sp.Min(self.maxCorner[d], other.maxCorner[d]))
+                         for d in range(self.dim)]
+            return AABB(minCorner, maxCorner)
+
+        @property
+        def volume(self):
+            v = sp.prod([self.maxCorner[d] - self.minCorner[d] for d in range(self.dim)])
+            if simplify:
+                return sp.simplify(assume_velocity(v.rewrite(sp.Piecewise)))
+            else:
+                return v
+    
+    fluxes = []
+    cell = AABB([-0.5] * dim, [0.5] * dim)
+    cell_s = AABB(sp.Matrix([-0.5] * dim) + v.center_vector, sp.Matrix([0.5] * dim) + v.center_vector)
+    for d, neighbor in enumerate(j.staggered_stencil):
+        c = sp.Matrix(ps.stencil.direction_string_to_offset(neighbor)[:dim])
+        cell_n = AABB(sp.Matrix([-0.5] * dim) + c, sp.Matrix([0.5] * dim) + c)
+        cell_ns = AABB(sp.Matrix([-0.5] * dim) + c + v.neighbor_vector(neighbor),
+                       sp.Matrix([0.5] * dim) + c + v.neighbor_vector(neighbor))
+        fluxes.append(assume_velocity(ρ.center_vector * cell_s.intersect(cell_n).volume
+                                      - ρ.neighbor_vector(neighbor) * cell_ns.intersect(cell).volume))
+    
+    assignments = []
+    for i, d in enumerate(j.staggered_stencil):
+        for lhs, rhs in zip(j.staggered_vector_access(d).values(), fluxes[i].values()):
+            assignments.append(ps.Assignment(lhs, rhs))
+    return assignments
+
+
+@pytest.mark.parametrize("dim", [2, 3])
+def test_advection(dim):
+    L = (8,) * dim
+    dh = ps.create_data_handling(L, periodicity=True, default_target=ps.Target.CPU)
+    c = dh.add_array('c', values_per_cell=1)
+    j = dh.add_array('j', values_per_cell=3 ** dh.dim // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+    u = dh.add_array('u', values_per_cell=dh.dim)
+    
+    dh.cpu_arrays[c.name][:] = (np.random.random([l + 2 for l in L]))
+    dh.cpu_arrays[u.name][:] = (np.random.random([l + 2 for l in L] + [dim]) - 0.5) / 5
+    
+    vof1 = ps.create_kernel(ps.fd.VOF(j, u, c)).compile()
+    dh.fill(j.name, np.nan, ghost_layers=True)
+    dh.run_kernel(vof1)
+    j1 = dh.gather_array(j.name).copy()
+    
+    vof2 = ps.create_kernel(VOF2(j, u, c, simplify=False)).compile()
+    dh.fill(j.name, np.nan, ghost_layers=True)
+    dh.run_kernel(vof2)
+    j2 = dh.gather_array(j.name)
+    
+    assert np.allclose(j1, j2)
+
+
+@pytest.mark.parametrize("stencil", ["D2Q5", "D2Q9"])
+def test_ek(stencil):
+
+    # parameters
+
+    L = (40, 40)
+    D = sp.Symbol("D")
+    z = sp.Symbol("z")
+
+    # data structures
+
+    dh = ps.create_data_handling(L, periodicity=True, default_target=ps.Target.CPU)
+    c = dh.add_array('c', values_per_cell=1)
+    j = dh.add_array('j', values_per_cell=int(stencil[-1]) // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+    Phi = dh.add_array('Φ', values_per_cell=1)
+
+    # perform automatic discretization
+
+    def Gradient(f):
+        return sp.Matrix([ps.fd.diff(f, i) for i in range(dh.dim)])
+
+    flux_eq = -D * Gradient(c) + D * z * c.center * Gradient(Phi)
+
+    disc = ps.fd.FVM1stOrder(c, flux_eq)
+    flux_assignments = disc.discrete_flux(j)
+    continuity_assignments = disc.discrete_continuity(j)
+
+    # manual discretization
+
+    x_staggered = - c[-1, 0] + c[0, 0] + z * (c[-1, 0] + c[0, 0]) / 2 * (Phi[-1, 0] - Phi[0, 0])
+    y_staggered = - c[0, -1] + c[0, 0] + z * (c[0, -1] + c[0, 0]) / 2 * (Phi[0, -1] - Phi[0, 0])
+    xy_staggered = (- c[-1, -1] + c[0, 0]) / sp.sqrt(2) + \
+        z * (c[-1, -1] + c[0, 0]) / 2 * (Phi[-1, -1] - Phi[0, 0]) / sp.sqrt(2)
+    xY_staggered = (- c[-1, 1] + c[0, 0]) / sp.sqrt(2) + \
+        z * (c[-1, 1] + c[0, 0]) / 2 * (Phi[-1, 1] - Phi[0, 0]) / sp.sqrt(2)
+    A0 = (1 + sp.sqrt(2) if j.index_shape[0] == 4 else 1)
+
+    jj = j.staggered_access
+    divergence = -1 * sum([jj(d) for d in j.staggered_stencil
+                          + [ps.stencil.inverse_direction_string(d) for d in j.staggered_stencil]])
+
+    update = [ps.Assignment(c.center, c.center + divergence)]
+    flux = [ps.Assignment(j.staggered_access("W"), D * x_staggered / A0),
+            ps.Assignment(j.staggered_access("S"), D * y_staggered / A0)]
+    if j.index_shape[0] == 4:
+        flux += [ps.Assignment(j.staggered_access("SW"), D * xy_staggered / A0),
+                 ps.Assignment(j.staggered_access("NW"), D * xY_staggered / A0)]
+
+    # compare
+
+    for a, b in zip(flux, flux_assignments):
+        assert a.lhs == b.lhs
+        assert sp.simplify(a.rhs - b.rhs) == 0
+    for a, b in zip(update, continuity_assignments):
+        assert a.lhs == b.lhs
+        assert a.rhs == b.rhs
+
+# TODO: test source
+
+
+@pytest.mark.parametrize("stencil", ["D2Q5", "D2Q9", "D3Q7", "D3Q19", "D3Q27"])
+@pytest.mark.parametrize("derivative", [0, 1])
+def test_flux_stencil(stencil, derivative):
+    L = (40, ) * int(stencil[1])
+    dh = ps.create_data_handling(L, periodicity=True, default_target=ps.Target.CPU)
+    c = dh.add_array('c', values_per_cell=1)
+    j = dh.add_array('j', values_per_cell=int(stencil[3:]) // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+
+    def Gradient(f):
+        return sp.Matrix([ps.fd.diff(f, i) for i in range(dh.dim)])
+
+    eq = [sp.Matrix([sp.Symbol(f"a_{i}") * c.center for i in range(dh.dim)]), Gradient(c)][derivative]
+    disc = ps.fd.FVM1stOrder(c, flux=eq)
+
+    # check the continuity
+    continuity_assignments = disc.discrete_continuity(j)
+    assert [len(a.rhs.atoms(ps.field.Field.Access)) for a in continuity_assignments] == \
+           [int(stencil[3:])] * len(continuity_assignments)
+
+    # check the flux
+    flux_assignments = disc.discrete_flux(j)
+    assert [len(a.rhs.atoms(ps.field.Field.Access)) for a in flux_assignments] == [2] * len(flux_assignments)
+
+
+@pytest.mark.parametrize("stencil", ["D2Q5", "D2Q9", "D3Q7", "D3Q19", "D3Q27"])
+def test_source_stencil(stencil):
+    L = (40, ) * int(stencil[1])
+    dh = ps.create_data_handling(L, periodicity=True, default_target=ps.Target.CPU)
+    c = dh.add_array('c', values_per_cell=1)
+    j = dh.add_array('j', values_per_cell=int(stencil[3:]) // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+
+    continuity_ref = ps.fd.FVM1stOrder(c).discrete_continuity(j)
+
+    for eq in [c.center] + [ps.fd.diff(c, i) for i in range(dh.dim)]:
+        disc = ps.fd.FVM1stOrder(c, source=eq)
+        diff = sp.simplify(disc.discrete_continuity(j)[0].rhs - continuity_ref[0].rhs)
+        if type(eq) is ps.field.Field.Access:
+            assert len(diff.atoms(ps.field.Field.Access)) == 1
+        else:
+            assert len(diff.atoms(ps.field.Field.Access)) == 2
+
+
+def test_fvm_staggered_simplification():
+    D = sp.Symbol("D")
+    data_type = "float64"
+
+    c = ps.fields(f"c: {data_type}[2D]", layout='fzyx')
+    j = ps.fields(f"j(2): {data_type}[2D]", layout='fzyx', field_type=ps.FieldType.STAGGERED_FLUX)
+
+    grad_c = sp.Matrix([ps.fd.diff(c, i) for i in range(c.spatial_dimensions)])
+
+    ek = ps.fd.FVM1stOrder(c, flux=-D * grad_c)
+
+    ast = ps.create_staggered_kernel(ek.discrete_flux(j))
+    code = ps.get_code_str(ast)
+
+    assert '_size_c_0 - 1 < _size_c_0 - 1' not in code

tests/test_global_definitions.py

+import sympy
+
+import pystencils.astnodes
+from pystencils.backends.cbackend import CBackend
+from pystencils.typing import TypedSymbol
+
+
+class BogusDeclaration(pystencils.astnodes.Node):
+    """Base class for all AST nodes."""
+
+    def __init__(self, parent=None):
+        self.parent = parent
+
+    @property
+    def args(self):
+        """Returns all arguments/children of this node."""
+        return set()
+
+    @property
+    def symbols_defined(self):
+        """Set of symbols which are defined by this node."""
+        return {TypedSymbol('Foo', 'double')}
+
+    @property
+    def undefined_symbols(self):
+        """Symbols which are used but are not defined inside this node."""
+        set()
+
+    def subs(self, subs_dict):
+        """Inplace! substitute, similar to sympy's but modifies the AST inplace."""
+        for a in self.args:
+            a.subs(subs_dict)
+
+    @property
+    def func(self):
+        return self.__class__
+
+    def atoms(self, arg_type):
+        """Returns a set of all descendants recursively, which are an instance of the given type."""
+        result = set()
+        for arg in self.args:
+            if isinstance(arg, arg_type):
+                result.add(arg)
+            result.update(arg.atoms(arg_type))
+        return result
+
+
+class BogusUsage(pystencils.astnodes.Node):
+    """Base class for all AST nodes."""
+
+    def __init__(self, requires_global: bool, parent=None):
+        self.parent = parent
+        if requires_global:
+            self.required_global_declarations = [BogusDeclaration()]
+
+    @property
+    def args(self):
+        """Returns all arguments/children of this node."""
+        return set()
+
+    @property
+    def symbols_defined(self):
+        """Set of symbols which are defined by this node."""
+        return set()
+
+    @property
+    def undefined_symbols(self):
+        """Symbols which are used but are not defined inside this node."""
+        return {TypedSymbol('Foo', 'double')}
+
+    def subs(self, subs_dict):
+        """Inplace! substitute, similar to sympy's but modifies the AST inplace."""
+        for a in self.args:
+            a.subs(subs_dict)
+
+    @property
+    def func(self):
+        return self.__class__
+
+    def atoms(self, arg_type):
+        """Returns a set of all descendants recursively, which are an instance of the given type."""
+        result = set()
+        for arg in self.args:
+            if isinstance(arg, arg_type):
+                result.add(arg)
+            result.update(arg.atoms(arg_type))
+        return result
+
+
+def test_global_definitions_with_global_symbol():
+    # Teach our printer to print new ast nodes
+    CBackend._print_BogusUsage = lambda _, __: "// Bogus would go here"
+    CBackend._print_BogusDeclaration = lambda _, __: "// Declaration would go here"
+
+    z, x, y = pystencils.fields("z, y, x: [2d]")
+
+    normal_assignments = pystencils.AssignmentCollection([pystencils.Assignment(
+        z[0, 0], x[0, 0] * x[0, 0] * y[0, 0])], [])
+
+    ast = pystencils.create_kernel(normal_assignments)
+    print(pystencils.show_code(ast))
+    ast.body.append(BogusUsage(requires_global=True))
+    print(pystencils.show_code(ast))
+    kernel = ast.compile()
+    assert kernel is not None
+
+    assert TypedSymbol('Foo', 'double') not in [p.symbol for p in ast.get_parameters()]
+
+
+def test_global_definitions_without_global_symbol():
+    # Teach our printer to print new ast nodes
+    CBackend._print_BogusUsage = lambda _, __: "// Bogus would go here"
+    CBackend._print_BogusDeclaration = lambda _, __: "// Declaration would go here"
+
+    z, x, y = pystencils.fields("z, y, x: [2d]")
+
+    normal_assignments = pystencils.AssignmentCollection([pystencils.Assignment(
+        z[0, 0], x[0, 0] * x[0, 0] * y[0, 0])], [])
+
+    ast = pystencils.create_kernel(normal_assignments)
+    print(pystencils.show_code(ast))
+    ast.body.append(BogusUsage(requires_global=False))
+    print(pystencils.show_code(ast))
+    kernel = ast.compile()
+    assert kernel is not None
+
+    assert TypedSymbol('Foo', 'double') in [p.symbol for p in ast.get_parameters()]

pystencils_tests/test_cudagpu.py → tests/test_gpu.py

+import pytest
+
 import numpy as np
 import sympy as sp
-from pystencils import Field, Assignment, fields
-from pystencils.simp import sympy_cse_on_assignment_list
-from pystencils.gpucuda.indexing import LineIndexing
-from pystencils.slicing import remove_ghost_layers, add_ghost_layers, make_slice
-from pystencils.gpucuda import make_python_function, create_cuda_kernel, BlockIndexing
-import pycuda.gpuarray as gpuarray
+import math
 from scipy.ndimage import convolve
 
+from pystencils import Assignment, Field, fields, CreateKernelConfig, create_kernel, Target, get_code_str
+from pystencils.gpu import BlockIndexing
+from pystencils.simp import sympy_cse_on_assignment_list
+from pystencils.slicing import add_ghost_layers, make_slice, remove_ghost_layers, normalize_slice
+
+try:
+    import cupy as cp
+    device_numbers = range(cp.cuda.runtime.getDeviceCount())
+except ImportError:
+    device_numbers = []
+    cp = None
+
 
 def test_averaging_kernel():
+    pytest.importorskip('cupy')
     size = (40, 55)
     src_arr = np.random.rand(*size)
     src_arr = add_ghost_layers(src_arr)
@@ -20,13 +30,14 @@ def test_averaging_kernel():
     update_rule = Assignment(dst_field[0, 0],
                              (src_field[0, 1] + src_field[0, -1] + src_field[1, 0] + src_field[-1, 0]) / 4)
 
-    ast = create_cuda_kernel(sympy_cse_on_assignment_list([update_rule]))
-    kernel = make_python_function(ast)
+    config = CreateKernelConfig(target=Target.GPU)
+    ast = create_kernel(sympy_cse_on_assignment_list([update_rule]), config=config)
+    kernel = ast.compile()
 
-    gpu_src_arr = gpuarray.to_gpu(src_arr)
-    gpu_dst_arr = gpuarray.to_gpu(dst_arr)
+    gpu_src_arr = cp.asarray(src_arr)
+    gpu_dst_arr = cp.asarray(dst_arr)
     kernel(src=gpu_src_arr, dst=gpu_dst_arr)
-    gpu_dst_arr.get(dst_arr)
+    dst_arr = gpu_dst_arr.get()
 
     stencil = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]]) / 4.0
     reference = convolve(remove_ghost_layers(src_arr), stencil, mode='constant', cval=0.0)
@@ -35,24 +46,26 @@ def test_averaging_kernel():
 
 
 def test_variable_sized_fields():
+    pytest.importorskip('cupy')
     src_field = Field.create_generic('src', spatial_dimensions=2)
     dst_field = Field.create_generic('dst', spatial_dimensions=2)
 
     update_rule = Assignment(dst_field[0, 0],
                              (src_field[0, 1] + src_field[0, -1] + src_field[1, 0] + src_field[-1, 0]) / 4)
 
-    ast = create_cuda_kernel(sympy_cse_on_assignment_list([update_rule]))
-    kernel = make_python_function(ast)
+    config = CreateKernelConfig(target=Target.GPU)
+    ast = create_kernel(sympy_cse_on_assignment_list([update_rule]), config=config)
+    kernel = ast.compile()
 
     size = (3, 3)
     src_arr = np.random.rand(*size)
     src_arr = add_ghost_layers(src_arr)
     dst_arr = np.zeros_like(src_arr)
 
-    gpu_src_arr = gpuarray.to_gpu(src_arr)
-    gpu_dst_arr = gpuarray.to_gpu(dst_arr)
+    gpu_src_arr = cp.asarray(src_arr)
+    gpu_dst_arr = cp.asarray(dst_arr)
     kernel(src=gpu_src_arr, dst=gpu_dst_arr)
-    gpu_dst_arr.get(dst_arr)
+    dst_arr = gpu_dst_arr.get()
 
     stencil = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]]) / 4.0
     reference = convolve(remove_ghost_layers(src_arr), stencil, mode='constant', cval=0.0)
@@ -61,6 +74,7 @@ def test_variable_sized_fields():
 
 
 def test_multiple_index_dimensions():
+    pytest.importorskip('cupy')
     """Sums along the last axis of a numpy array"""
     src_size = (7, 6, 4)
     dst_size = src_size[:2]
@@ -74,13 +88,14 @@ def test_multiple_index_dimensions():
     update_rule = Assignment(dst_field[0, 0],
                              sum([src_field[offset[0], offset[1]](i) for i in range(src_size[-1])]))
 
-    ast = create_cuda_kernel([update_rule])
-    kernel = make_python_function(ast)
+    config = CreateKernelConfig(target=Target.GPU)
+    ast = create_kernel([update_rule], config=config)
+    kernel = ast.compile()
 
-    gpu_src_arr = gpuarray.to_gpu(src_arr)
-    gpu_dst_arr = gpuarray.to_gpu(dst_arr)
+    gpu_src_arr = cp.asarray(src_arr)
+    gpu_dst_arr = cp.asarray(dst_arr)
     kernel(src=gpu_src_arr, dst=gpu_dst_arr)
-    gpu_dst_arr.get(dst_arr)
+    dst_arr = gpu_dst_arr.get()
 
     reference = np.zeros_like(dst_arr)
     gl = np.max(np.abs(np.array(offset, dtype=int)))
@@ -92,6 +107,7 @@ def test_multiple_index_dimensions():
 
 
 def test_ghost_layer():
+    pytest.importorskip('cupy')
     size = (6, 5)
     src_arr = np.ones(size)
     dst_arr = np.zeros_like(src_arr)
@@ -100,13 +116,15 @@ def test_ghost_layer():
 
     update_rule = Assignment(dst_field[0, 0], src_field[0, 0])
     ghost_layers = [(1, 2), (2, 1)]
-    ast = create_cuda_kernel([update_rule], ghost_layers=ghost_layers, indexing_creator=LineIndexing)
-    kernel = make_python_function(ast)
 
-    gpu_src_arr = gpuarray.to_gpu(src_arr)
-    gpu_dst_arr = gpuarray.to_gpu(dst_arr)
+    config = CreateKernelConfig(target=Target.GPU, ghost_layers=ghost_layers, gpu_indexing="line")
+    ast = create_kernel(sympy_cse_on_assignment_list([update_rule]), config=config)
+    kernel = ast.compile()
+
+    gpu_src_arr = cp.asarray(src_arr)
+    gpu_dst_arr = cp.asarray(dst_arr)
     kernel(src=gpu_src_arr, dst=gpu_dst_arr)
-    gpu_dst_arr.get(dst_arr)
+    dst_arr = gpu_dst_arr.get()
 
     reference = np.zeros_like(src_arr)
     reference[ghost_layers[0][0]:-ghost_layers[0][1], ghost_layers[1][0]:-ghost_layers[1][1]] = 1
@@ -114,25 +132,29 @@ def test_ghost_layer():
 
 
 def test_setting_value():
+    pytest.importorskip('cupy')
     arr_cpu = np.arange(25, dtype=np.float64).reshape(5, 5)
-    arr_gpu = gpuarray.to_gpu(arr_cpu)
+    arr_gpu = cp.asarray(arr_cpu)
 
     iteration_slice = make_slice[:, :]
     f = Field.create_generic("f", 2)
     update_rule = [Assignment(f(0), sp.Symbol("value"))]
-    ast = create_cuda_kernel(update_rule, iteration_slice=iteration_slice, indexing_creator=LineIndexing)
 
-    kernel = make_python_function(ast)
+    config = CreateKernelConfig(target=Target.GPU, gpu_indexing="line", iteration_slice=iteration_slice)
+    ast = create_kernel(sympy_cse_on_assignment_list(update_rule), config=config)
+    kernel = ast.compile()
+
     kernel(f=arr_gpu, value=np.float64(42.0))
     np.testing.assert_equal(arr_gpu.get(), np.ones((5, 5)) * 42.0)
 
 
 def test_periodicity():
-    from pystencils.gpucuda.periodicity import get_periodic_boundary_functor as periodic_gpu
+    pytest.importorskip('cupy')
+    from pystencils.gpu.periodicity import get_periodic_boundary_functor as periodic_gpu
     from pystencils.slicing import get_periodic_boundary_functor as periodic_cpu
 
     arr_cpu = np.arange(50, dtype=np.float64).reshape(5, 5, 2)
-    arr_gpu = gpuarray.to_gpu(arr_cpu)
+    arr_gpu = cp.asarray(arr_cpu)
 
     periodicity_stencil = [(1, 0), (-1, 0), (1, 1)]
     periodic_gpu_kernel = periodic_gpu(periodicity_stencil, (5, 5), 1, 2)
@@ -141,22 +163,95 @@ def test_periodicity():
     cpu_result = np.copy(arr_cpu)
     periodic_cpu_kernel(cpu_result)
 
-    gpu_result = np.copy(arr_cpu)
     periodic_gpu_kernel(pdfs=arr_gpu)
-    arr_gpu.get(gpu_result)
+    gpu_result = arr_gpu.get()
     np.testing.assert_equal(cpu_result, gpu_result)
 
 
-def test_block_size_limiting():
-    res = BlockIndexing.limit_block_size_to_device_maximum((4096, 4096, 4096))
-    assert all(r < 4096 for r in res)
-
-
-def test_block_indexing():
+@pytest.mark.parametrize("device_number", device_numbers)
+def test_block_indexing(device_number):
+    pytest.importorskip('cupy')
     f = fields("f: [3D]")
-    bi = BlockIndexing(f, make_slice[:, :, :], block_size=(16, 8, 2), permute_block_size_dependent_on_layout=False)
+    s = normalize_slice(make_slice[:, :, :], f.spatial_shape)
+    bi = BlockIndexing(s, f.layout, block_size=(16, 8, 2),
+                       permute_block_size_dependent_on_layout=False)
     assert bi.call_parameters((3, 2, 32))['block'] == (3, 2, 32)
     assert bi.call_parameters((32, 2, 32))['block'] == (16, 2, 8)
 
-    bi = BlockIndexing(f, make_slice[:, :, :], block_size=(32, 1, 1), permute_block_size_dependent_on_layout=False)
+    bi = BlockIndexing(s, f.layout, block_size=(32, 1, 1),
+                       permute_block_size_dependent_on_layout=False)
     assert bi.call_parameters((1, 16, 16))['block'] == (1, 16, 2)
+
+    bi = BlockIndexing(s, f.layout, block_size=(16, 8, 2),
+                       maximum_block_size="auto", device_number=device_number)
+
+    # This function should be used if number of needed registers is known. Can be determined with func.num_regs
+    registers_per_thread = 1000
+    blocks = bi.limit_block_size_by_register_restriction([1024, 1024, 1], registers_per_thread)
+
+    if cp.cuda.runtime.is_hip:
+        max_registers_per_block = cp.cuda.runtime.deviceGetAttribute(71, device_number)
+    else:
+        device = cp.cuda.Device(device_number)
+        da = device.attributes
+        max_registers_per_block = da.get("MaxRegistersPerBlock")
+
+    assert np.prod(blocks) * registers_per_thread < max_registers_per_block
+
+
+@pytest.mark.parametrize('gpu_indexing', ("block", "line"))
+@pytest.mark.parametrize('layout', ("C", "F"))
+@pytest.mark.parametrize('shape', ((5, 5, 5, 5), (3, 17, 387, 4), (23, 44, 21, 11)))
+def test_four_dimensional_kernel(gpu_indexing, layout, shape):
+    pytest.importorskip('cupy')
+    n_elements = np.prod(shape)
+
+    arr_cpu = np.arange(n_elements, dtype=np.float64).reshape(shape, order=layout)
+    arr_gpu = cp.asarray(arr_cpu)
+
+    iteration_slice = make_slice[:, :, :, :]
+    f = Field.create_from_numpy_array("f", arr_cpu)
+    update_rule = [Assignment(f.center, sp.Symbol("value"))]
+
+    config = CreateKernelConfig(target=Target.GPU, gpu_indexing=gpu_indexing, iteration_slice=iteration_slice)
+    ast = create_kernel(update_rule, config=config)
+    kernel = ast.compile()
+
+    kernel(f=arr_gpu, value=np.float64(42.0))
+    np.testing.assert_equal(arr_gpu.get(), np.ones(shape) * 42.0)
+
+
+@pytest.mark.parametrize('start', (1, 5))
+@pytest.mark.parametrize('end', (-1, -2, -3, -4))
+@pytest.mark.parametrize('step', (1, 2, 3, 4))
+@pytest.mark.parametrize('shape', ([55, 60], [77, 101, 80], [44, 64, 66]))
+def test_guards_with_iteration_slices(start, end, step, shape):
+    iter_slice = tuple([slice(start, end, step)] * len(shape))
+
+    kernel_config_gpu = CreateKernelConfig(target=Target.GPU, iteration_slice=iter_slice)
+    field_1 = fields(f"f(1) : double{list(shape)}")
+    assignment = Assignment(field_1.center, 1)
+    ast = create_kernel(assignment, config=kernel_config_gpu)
+    code_str = get_code_str(ast)
+
+    test_strings = list()
+    iteration_ranges = list()
+    for i, s in enumerate(iter_slice):
+        e = ((shape[i] + end) - s.start) / s.step
+        e = math.ceil(e) + s.start
+        test_strings.append(f"{s.start} < {e}")
+
+        a = s.start
+        counter = 0
+        while a < e:
+            a += 1
+            counter += 1
+        iteration_ranges.append(counter)
+
+    # check if the expected if statement is in the GPU code
+    for s in test_strings:
+        assert s in code_str
+
+    # check if these bounds lead to same lengths as the range function would produce
+    for i in range(len(iter_slice)):
+        assert iteration_ranges[i] == len(range(iter_slice[i].start, shape[i] + end, iter_slice[i].step))

tests/test_half_precision.py

+import pytest
+import platform
+
+import numpy as np
+import pystencils as ps
+
+
+@pytest.mark.parametrize('target', (ps.Target.CPU, ps.Target.GPU))
+def test_half_precison(target):
+    if target == ps.Target.CPU:
+        if not platform.machine() in ['arm64', 'aarch64']:
+            pytest.xfail("skipping half precision test on non arm platform")
+
+        if 'clang' not in ps.cpu.cpujit.get_compiler_config()['command']:
+            pytest.xfail("skipping half precision because clang compiler is not used")
+
+    if target == ps.Target.GPU:
+        pytest.importorskip("cupy")
+
+    dh = ps.create_data_handling(domain_size=(10, 10), default_target=target)
+
+    f1 = dh.add_array("f1", values_per_cell=1, dtype=np.float16)
+    dh.fill("f1", 1.0, ghost_layers=True)
+    f2 = dh.add_array("f2", values_per_cell=1, dtype=np.float16)
+    dh.fill("f2", 2.0, ghost_layers=True)
+
+    f3 = dh.add_array("f3", values_per_cell=1, dtype=np.float16)
+    dh.fill("f3", 0.0, ghost_layers=True)
+
+    up = ps.Assignment(f3.center, f1.center + 2.1 * f2.center)
+
+    config = ps.CreateKernelConfig(target=dh.default_target, default_number_float=np.float32)
+    ast = ps.create_kernel(up, config=config)
+
+    kernel = ast.compile()
+
+    dh.run_kernel(kernel)
+    dh.all_to_cpu()
+
+    assert np.all(dh.cpu_arrays[f3.name] == 5.2)
+    assert dh.cpu_arrays[f3.name].dtype == np.float16

tests/test_helpful_errors.py

+"""
+
+"""
+
+import pytest
+
+from pystencils.astnodes import Block
+from pystencils.backends.cbackend import CustomCodeNode, get_headers
+
+
+def test_headers_have_quotes_or_brackets():
+    class ErrorNode1(CustomCodeNode):
+
+        def __init__(self):
+            super().__init__("", [], [])
+            self.headers = ["iostream"]
+
+    class ErrorNode2(CustomCodeNode):
+        headers = ["<iostream>", "foo"]
+
+        def __init__(self):
+            super().__init__("", [], [])
+            self.headers = ["<iostream>", "foo"]
+
+    class OkNode3(CustomCodeNode):
+
+        def __init__(self):
+            super().__init__("", [], [])
+            self.headers = ["<iostream>", '"foo"']
+
+    with pytest.raises(AssertionError, match='.* does not follow the pattern .*'):
+        get_headers(Block([ErrorNode1()]))
+
+    with pytest.raises(AssertionError, match='.* does not follow the pattern .*'):
+        get_headers(ErrorNode2())
+
+    get_headers(OkNode3())

tests/test_indexed_kernels.py

+import sympy as sp
+import numpy as np
+import pytest
+
+import pystencils as ps
+from pystencils import Assignment, Field, CreateKernelConfig, create_kernel, Target
+from pystencils.transformations import filtered_tree_iteration
+from pystencils.typing import BasicType, FieldPointerSymbol, PointerType, TypedSymbol
+
+
+@pytest.mark.parametrize('target', [ps.Target.CPU, ps.Target.GPU])
+def test_indexed_kernel(target):
+    if target == Target.GPU:
+        pytest.importorskip("cupy")
+        import cupy as cp
+
+    arr = np.zeros((3, 4))
+    dtype = np.dtype([('x', int), ('y', int), ('value', arr.dtype)])
+    index_arr = np.zeros((3,), dtype=dtype)
+    index_arr[0] = (0, 2, 3.0)
+    index_arr[1] = (1, 3, 42.0)
+    index_arr[2] = (2, 1, 5.0)
+
+    indexed_field = Field.create_from_numpy_array('index', index_arr)
+    normal_field = Field.create_from_numpy_array('f', arr)
+    update_rule = Assignment(normal_field[0, 0], indexed_field('value'))
+
+    config = CreateKernelConfig(target=target, index_fields=[indexed_field])
+    ast = create_kernel([update_rule], config=config)
+    kernel = ast.compile()
+
+    if target == Target.CPU:
+        kernel(f=arr, index=index_arr)
+    else:
+        gpu_arr = cp.asarray(arr)
+        gpu_index_arr = cp.ndarray(index_arr.shape, dtype=index_arr.dtype)
+        gpu_index_arr.set(index_arr)
+        kernel(f=gpu_arr, index=gpu_index_arr)
+        arr = gpu_arr.get()
+    for i in range(index_arr.shape[0]):
+        np.testing.assert_allclose(arr[index_arr[i]['x'], index_arr[i]['y']], index_arr[i]['value'], atol=1e-13)
+
+
+@pytest.mark.parametrize('index_size', ("fixed", "variable"))
+@pytest.mark.parametrize('array_size', ("3D", "2D", "10, 12", "13, 17, 19"))
+@pytest.mark.parametrize('target', (ps.Target.CPU, ps.Target.GPU))
+@pytest.mark.parametrize('dtype', ("float64", "float32"))
+def test_indexed_domain_kernel(index_size, array_size, target, dtype):
+    dtype = BasicType(dtype)
+
+    f = ps.fields(f'f(1): {dtype.numpy_dtype.name}[{array_size}]')
+    g = ps.fields(f'g(1): {dtype.numpy_dtype.name}[{array_size}]')
+
+    index = TypedSymbol("index", dtype=BasicType(np.int16))
+    if index_size == "variable":
+        index_src = TypedSymbol("_size_src", dtype=BasicType(np.int16))
+        index_dst = TypedSymbol("_size_dst", dtype=BasicType(np.int16))
+    else:
+        index_src = 16
+        index_dst = 16
+    pointer_type = PointerType(dtype, const=False, restrict=True, double_pointer=True)
+    const_pointer_type = PointerType(dtype, const=True, restrict=True, double_pointer=True)
+
+    src = sp.IndexedBase(TypedSymbol(f"_data_{f.name}", dtype=const_pointer_type), shape=index_src)
+    dst = sp.IndexedBase(TypedSymbol(f"_data_{g.name}", dtype=pointer_type), shape=index_dst)
+
+    update_rule = [ps.Assignment(FieldPointerSymbol("f", dtype, const=True), src[index + 1]),
+                   ps.Assignment(FieldPointerSymbol("g", dtype, const=False), dst[index + 1]),
+                   ps.Assignment(g.center, f.center)]
+
+    ast = ps.create_kernel(update_rule, target=target)
+
+    code = ps.get_code_str(ast)
+    assert f"const {dtype.c_name} * RESTRICT _data_f = (({dtype.c_name} * RESTRICT const)(_data_f[index + 1]));" in code
+    assert f"{dtype.c_name} * RESTRICT  _data_g = (({dtype.c_name} * RESTRICT )(_data_g[index + 1]));" in code
+
+    if target == Target.CPU:
+        assert code.count("for") == f.spatial_dimensions + 1
+

pystencils_tests/test_jacobi_cbackend.py → tests/test_jacobi_cbackend.py

 import numpy as np
-from pystencils import show_code
-from pystencils.transformations import move_constants_before_loop, make_loop_over_domain, resolve_field_accesses
-from pystencils.field import Field
-from pystencils.astnodes import SympyAssignment, Block
+
+from pystencils import get_code_obj
+from pystencils.astnodes import Block, KernelFunction, SympyAssignment
 from pystencils.cpu import make_python_function
+from pystencils.field import Field
+from pystencils.enums import Target, Backend
+from pystencils.transformations import (
+    make_loop_over_domain, move_constants_before_loop, resolve_field_accesses)
 
 
 def test_jacobi_fixed_field_size():
@@ -19,7 +22,8 @@ def test_jacobi_fixed_field_size():
 
     jacobi = SympyAssignment(d[0, 0], (f[1, 0] + f[-1, 0] + f[0, 1] + f[0, -1]) / 4)
     body = Block([jacobi])
-    ast_node = make_loop_over_domain(body, "kernel")
+    loop_node, gl_info = make_loop_over_domain(body)
+    ast_node = KernelFunction(loop_node, Target.CPU, Backend.C, make_python_function, ghost_layers=gl_info)
     resolve_field_accesses(ast_node)
     move_constants_before_loop(ast_node)
 
@@ -28,12 +32,12 @@ def test_jacobi_fixed_field_size():
             dst_field_py[x, y] = 0.25 * (src_field_py[x - 1, y] + src_field_py[x + 1, y] +
                                          src_field_py[x, y - 1] + src_field_py[x, y + 1])
 
-    kernel = make_python_function(ast_node)
+    kernel = ast_node.compile()
     kernel(f=src_field_c, d=dst_field_c)
     error = np.sum(np.abs(dst_field_py - dst_field_c))
     np.testing.assert_allclose(error, 0.0, atol=1e-13)
 
-    code_display = show_code(ast_node)
+    code_display = get_code_obj(ast_node)
     assert 'for' in str(code_display)
     assert 'for' in code_display._repr_html_()
 
@@ -44,7 +48,8 @@ def test_jacobi_variable_field_size():
     d = Field.create_generic("d", 3)
     jacobi = SympyAssignment(d[0, 0, 0], (f[1, 0, 0] + f[-1, 0, 0] + f[0, 1, 0] + f[0, -1, 0]) / 4)
     body = Block([jacobi])
-    ast_node = make_loop_over_domain(body, "kernel")
+    loop_node, gl_info = make_loop_over_domain(body)
+    ast_node = KernelFunction(loop_node, Target.CPU, Backend.C, make_python_function, ghost_layers=gl_info)
     resolve_field_accesses(ast_node)
     move_constants_before_loop(ast_node)
 
@@ -53,13 +58,13 @@ def test_jacobi_variable_field_size():
     dst_field_c = np.zeros(size)
     dst_field_py = np.zeros(size)
 
-    for x in range(1, size[0]-1):
-        for y in range(1, size[1]-1):
-            for z in range(1, size[2]-1):
+    for x in range(1, size[0] - 1):
+        for y in range(1, size[1] - 1):
+            for z in range(1, size[2] - 1):
                 dst_field_py[x, y, z] = 0.25 * (src_field_py[x - 1, y, z] + src_field_py[x + 1, y, z] +
                                                 src_field_py[x, y - 1, z] + src_field_py[x, y + 1, z])
 
-    kernel = make_python_function(ast_node)
+    kernel = ast_node.compile()
     kernel(f=src_field_c, d=dst_field_c)
-    error = np.sum(np.abs(dst_field_py-dst_field_c))
+    error = np.sum(np.abs(dst_field_py - dst_field_c))
     np.testing.assert_allclose(error, 0.0, atol=1e-13)

tests/test_json_backend.py

+# -*- coding: utf-8 -*-
+#
+# Copyright © 2019 Stephan Seitz <stephan.seitz@fau.de>
+#
+# Distributed under terms of the GPLv3 license.
+
+"""
+
+"""
+
+import sympy
+
+import pystencils
+from pystencils.backends.json import print_json, print_yaml, write_json, write_yaml
+import tempfile
+
+
+def test_json_backend():
+
+    z, y, x = pystencils.fields("z, y, x: [20,40]")
+    a = sympy.Symbol('a')
+
+    assignments = pystencils.AssignmentCollection({
+        z[0, 0]: x[0, 0] * a * x[0, 0] * y[0, 0]
+    })
+
+    ast = pystencils.create_kernel(assignments)
+
+    pj = print_json(ast)
+    # print(pj)
+    py = print_yaml(ast)
+    # print(py)
+
+    temp_dir = tempfile.TemporaryDirectory()
+    write_json(temp_dir.name + '/test.json', ast)
+    write_yaml(temp_dir.name + '/test.yaml', ast)

tests/test_json_serializer.py

+"""
+Test the pystencils-specific JSON encoder and serializer as used in the Database class.
+"""
+
+import numpy as np
+import tempfile
+
+from pystencils.config import CreateKernelConfig
+from pystencils import Target, Field
+from pystencils.runhelper.db import Database, PystencilsJsonSerializer
+
+
+def test_json_serializer():
+
+    dtype = np.float32
+
+    index_arr = np.zeros((3,), dtype=dtype)
+    indexed_field = Field.create_from_numpy_array('index', index_arr)
+
+    # create pystencils config
+    config = CreateKernelConfig(target=Target.CPU, function_name='dummy_config', data_type=dtype,
+                                index_fields=[indexed_field])
+
+    # create dummy database
+    temp_dir = tempfile.TemporaryDirectory()
+    db = Database(file=temp_dir.name, serializer_info=('pystencils_serializer', PystencilsJsonSerializer))
+
+    db.save(params={'config': config}, result={'test': 'dummy'})

tests/test_jupyter_extensions.ipynb

+%% Cell type:code id: tags:
+
+``` python
+from pystencils.session import *
+```
+
+%% Cell type:code id: tags:
+
+``` python
+dh = ps.create_data_handling(domain_size=(256, 256), periodicity=True)
+c_field = dh.add_array('c')
+dh.fill("c", 0.0, ghost_layers=True)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+for x in range(129):
+    for y in range(258):
+        dh.cpu_arrays['c'][x, y] = 1.0
+```
+
+%% Cell type:code id: tags:
+
+``` python
+plt.scalar_field(dh.cpu_arrays["c"])
+```
+
+%% Output
+
+    <matplotlib.image.AxesImage at 0x117081c10>
+
+
+
+%% Cell type:code id: tags:
+
+``` python
+ur = ps.Assignment(c_field[0, 0], c_field[1, 0])
+config = ps.CreateKernelConfig(target=dh.default_target, cpu_openmp=False, skip_independence_check=True)
+ast = ps.create_kernel(ur, config=config)
+kernel = ast.compile()
+```
+
+%% Cell type:code id: tags:
+
+``` python
+c_sync = dh.synchronization_function_cpu(['c'])
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def timeloop(steps=10):
+    for i in range(steps):
+        c_sync()
+        dh.run_kernel(kernel)
+    return dh.gather_array('c')
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ps.jupyter.set_display_mode('video')
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ani = ps.plot.scalar_field_animation(timeloop, rescale=True, frames=12)
+ps.jupyter.display_animation(ani)
+```
+
+%% Output
+
+    <IPython.core.display.HTML object>
+
+%% Cell type:code id: tags:
+
+``` python
+ps.jupyter.set_display_mode('image_update')
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ani = ps.plot.scalar_field_animation(timeloop, rescale=True, frames=12)
+ps.jupyter.display_animation(ani)
+```
+
+%% Output
+
+
+
+%% Cell type:code id: tags:
+
+``` python
+def grid_update_function(image):
+    for i in range(40):
+        c_sync()
+        dh.run_kernel(kernel)
+    return dh.gather_array('c')
+```
+
+%% Cell type:code id: tags:
+
+``` python
+animation = ps.jupyter.make_imshow_animation(dh.cpu_arrays["c"], grid_update_function, frames=300)
+```
+
+%% Output
+
+
+
+%% Cell type:code id: tags:
+
+``` python
+ps.jupyter.set_display_mode("video")
+ps.jupyter.set_display_mode("window")
+ps.jupyter.set_display_mode("image_update")
+ps.jupyter.activate_ipython()
+```
+
+%% Output
+
+    ---------------------------------------------------------------------------
+    ImportError                               Traceback (most recent call last)
+Cell     In[14], line 2
+          1 ps.jupyter.set_display_mode("video")
+    ----> 2 ps.jupyter.set_display_mode("window")
+          3 ps.jupyter.set_display_mode("image_update")
+          4 ps.jupyter.activate_ipython()
+File     ~/pystencils/pystencils/src/pystencils/jupyter.py:115, in set_display_mode(mode)
+        113     display_animation_func = display_as_html_video
+        114 elif animation_display_mode == 'window':
+    --> 115     ipython.magic("matplotlib qt")
+        116     display_animation_func = display_in_extra_window
+        117 elif animation_display_mode == 'image_update':
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/IPython/core/interactiveshell.py:2539, in InteractiveShell.magic(self, arg_s)
+       2537 magic_name, _, magic_arg_s = arg_s.partition(' ')
+       2538 magic_name = magic_name.lstrip(prefilter.ESC_MAGIC)
+    -> 2539 return self.run_line_magic(magic_name, magic_arg_s, _stack_depth=2)
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/IPython/core/interactiveshell.py:2417, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
+       2415     kwargs['local_ns'] = self.get_local_scope(stack_depth)
+       2416 with self.builtin_trap:
+    -> 2417     result = fn(*args, **kwargs)
+       2419 # The code below prevents the output from being displayed
+       2420 # when using magics with decodator @output_can_be_silenced
+       2421 # when the last Python token in the expression is a ';'.
+       2422 if getattr(fn, magic.MAGIC_OUTPUT_CAN_BE_SILENCED, False):
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/IPython/core/magics/pylab.py:99, in PylabMagics.matplotlib(self, line)
+         97     print("Available matplotlib backends: %s" % backends_list)
+         98 else:
+    ---> 99     gui, backend = self.shell.enable_matplotlib(args.gui.lower() if isinstance(args.gui, str) else args.gui)
+        100     self._show_matplotlib_backend(args.gui, backend)
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3603, in InteractiveShell.enable_matplotlib(self, gui)
+       3599         print('Warning: Cannot change to a different GUI toolkit: %s.'
+       3600                 ' Using %s instead.' % (gui, self.pylab_gui_select))
+       3601         gui, backend = pt.find_gui_and_backend(self.pylab_gui_select)
+    -> 3603 pt.activate_matplotlib(backend)
+       3604 configure_inline_support(self, backend)
+       3606 # Now we must activate the gui pylab wants to use, and fix %run to take
+       3607 # plot updates into account
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/IPython/core/pylabtools.py:360, in activate_matplotlib(backend)
+        355 # Due to circular imports, pyplot may be only partially initialised
+        356 # when this function runs.
+        357 # So avoid needing matplotlib attribute-lookup to access pyplot.
+        358 from matplotlib import pyplot as plt
+    --> 360 plt.switch_backend(backend)
+        362 plt.show._needmain = False
+        363 # We need to detect at runtime whether show() is called by the user.
+        364 # For this, we wrap it into a decorator which adds a 'called' flag.
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/matplotlib/pyplot.py:271, in switch_backend(newbackend)
+        268 # have to escape the switch on access logic
+        269 old_backend = dict.__getitem__(rcParams, 'backend')
+    --> 271 backend_mod = importlib.import_module(
+        272     cbook._backend_module_name(newbackend))
+        274 required_framework = _get_required_interactive_framework(backend_mod)
+        275 if required_framework is not None:
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/importlib/__init__.py:126, in import_module(name, package)
+        124             break
+        125         level += 1
+    --> 126 return _bootstrap._gcd_import(name[level:], package, level)
+File     <frozen importlib._bootstrap>:1204, in _gcd_import(name, package, level)
+File     <frozen importlib._bootstrap>:1176, in _find_and_load(name, import_)
+File     <frozen importlib._bootstrap>:1147, in _find_and_load_unlocked(name, import_)
+File     <frozen importlib._bootstrap>:690, in _load_unlocked(spec)
+File     <frozen importlib._bootstrap_external>:940, in exec_module(self, module)
+File     <frozen importlib._bootstrap>:241, in _call_with_frames_removed(f, *args, **kwds)
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/matplotlib/backends/backend_qt5agg.py:7
+          4 from .. import backends
+          6 backends._QT_FORCE_QT5_BINDING = True
+    ----> 7 from .backend_qtagg import (    # noqa: F401, E402 # pylint: disable=W0611
+          8     _BackendQTAgg, FigureCanvasQTAgg, FigureManagerQT, NavigationToolbar2QT,
+          9     FigureCanvasAgg, FigureCanvasQT)
+         12 @_BackendQTAgg.export
+         13 class _BackendQT5Agg(_BackendQTAgg):
+         14     pass
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/matplotlib/backends/backend_qtagg.py:9
+          5 import ctypes
+          7 from matplotlib.transforms import Bbox
+    ----> 9 from .qt_compat import QT_API, _enum
+         10 from .backend_agg import FigureCanvasAgg
+         11 from .backend_qt import QtCore, QtGui, _BackendQT, FigureCanvasQT
+File     /opt/local/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/site-packages/matplotlib/backends/qt_compat.py:135
+        133         break
+        134     else:
+    --> 135         raise ImportError(
+        136             "Failed to import any of the following Qt binding modules: {}"
+        137             .format(", ".join(_ETS.values())))
+        138 else:  # We should not get there.
+        139     raise AssertionError(f"Unexpected QT_API: {QT_API}")
+    ImportError: Failed to import any of the following Qt binding modules: PyQt6, PySide6, PyQt5, PySide2

tests/test_logarithm.py

+import pytest
+import numpy as np
+import sympy as sp
+
+import pystencils as ps
+
+
+@pytest.mark.parametrize('dtype', ["float64", "float32"])
+def test_log(dtype):
+    a = sp.Symbol("a")
+    x = ps.fields(f'x: {dtype}[1d]')
+
+    assignments = ps.AssignmentCollection({x.center(): sp.log(a)})
+
+    ast = ps.create_kernel(assignments)
+    code = ps.get_code_str(ast)
+    kernel = ast.compile()
+
+    # ps.show_code(ast)
+
+    if dtype == "float64":
+        assert "float" not in code
+
+    array = np.zeros((10,), dtype=dtype)
+    kernel(x=array, a=100)
+    assert np.allclose(array, 4.60517019)

pystencils_tests/test_loop_cutting.py → tests/test_loop_cutting.py

-import sympy as sp
 import numpy as np
+import sympy as sp
+
+import pytest
+
 import pystencils as ps
-from pystencils import Field
-from pystencils.cpu import create_kernel, make_python_function
+import pystencils.astnodes as ast
+from pystencils.field import Field, FieldType
 from pystencils.astnodes import Conditional, LoopOverCoordinate, SympyAssignment
+from pystencils.cpu import create_kernel, make_python_function
 from pystencils.kernelcreation import create_staggered_kernel
-from pystencils.transformations import move_constants_before_loop
-import pystencils.astnodes as ast
-from pystencils.transformations import simplify_conditionals, cleanup_blocks, cut_loop
+from pystencils.transformations import (
+    cleanup_blocks, cut_loop, move_constants_before_loop, simplify_conditionals)
 
 
 def offsets_in_plane(normal_plane, offset_int, dimension):
@@ -33,9 +36,9 @@ def test_staggered_iteration():
     s_arr_ref = s_arr.copy()
 
     fields_fixed = (Field.create_from_numpy_array('f', f_arr),
-                    Field.create_from_numpy_array('s', s_arr, index_dimensions=1))
+                    Field.create_from_numpy_array('s', s_arr, index_dimensions=1, field_type=FieldType.STAGGERED))
     fields_var = (Field.create_generic('f', 2),
-                  Field.create_generic('s', 2, index_dimensions=1))
+                  Field.create_generic('s', 2, index_dimensions=1, index_shape=(dim,), field_type=FieldType.STAGGERED))
 
     for f, s in [fields_var, fields_fixed]:
         # --- Manual
@@ -47,14 +50,18 @@ def test_staggered_iteration():
                                  sum(f[o] for o in offsets_in_plane(d, -1, dim)))
             cond = sp.And(*[conditions[i] for i in range(dim) if d != i])
             eqs.append(Conditional(cond, eq))
-        func = create_kernel(eqs, ghost_layers=[(1, 0), (1, 0), (1, 0)]).compile()
+        # TODO: correct type hint
+        config = ps.CreateKernelConfig(target=ps.Target.CPU, ghost_layers=[(1, 0), (1, 0), (1, 0)])
+        func = ps.create_kernel(eqs, config=config).compile()
 
         # --- Built-in optimized
         expressions = []
         for d in range(dim):
             expressions.append(sum(f[o] for o in offsets_in_plane(d, 0, dim)) -
                                sum(f[o] for o in offsets_in_plane(d, -1, dim)))
-        func_optimized = create_staggered_kernel(s, expressions).compile()
+        assignments = [ps.Assignment(s.staggered_access(d), expressions[i]) for i, d in enumerate(s.staggered_stencil)]
+        func_optimized = create_staggered_kernel(assignments).compile()
+        pytest.importorskip('islpy')
         assert not func_optimized.ast.atoms(Conditional), "Loop cutting optimization did not work"
 
         func(f=f_arr, s=s_arr_ref)
@@ -69,12 +76,13 @@ def test_staggered_iteration_manual():
     s_arr_ref = s_arr.copy()
 
     f = Field.create_from_numpy_array('f', f_arr)
-    s = Field.create_from_numpy_array('s', s_arr, index_dimensions=1)
+    s = Field.create_from_numpy_array('s', s_arr, index_dimensions=1, field_type=FieldType.STAGGERED)
 
     eqs = []
 
     counters = [LoopOverCoordinate.get_loop_counter_symbol(i) for i in range(dim)]
     conditions = [counters[i] < f.shape[i] - 1 for i in range(dim)]
+    conditions2 = counters[0] > f.shape[0] + 5
 
     for d in range(dim):
         eq = SympyAssignment(s(d), sum(f[o] for o in offsets_in_plane(d, 0, dim)) -
@@ -82,7 +90,13 @@ def test_staggered_iteration_manual():
         cond = sp.And(*[conditions[i] for i in range(dim) if d != i])
         eqs.append(Conditional(cond, eq))
 
-    kernel_ast = create_kernel(eqs, ghost_layers=[(1, 0), (1, 0), (1, 0)])
+    # this conditional should vanish entirely because it is never true
+    eq = SympyAssignment(s(0), f[0, 0])
+    cond = sp.And(*[conditions2])
+    eqs.append(Conditional(cond, eq))
+
+    config = ps.CreateKernelConfig(target=ps.Target.CPU, ghost_layers=[(1, 0), (1, 0), (1, 0)])
+    kernel_ast = ps.create_kernel(eqs, config=config)
 
     func = make_python_function(kernel_ast)
     func(f=f_arr, s=s_arr_ref)
@@ -97,6 +111,7 @@ def test_staggered_iteration_manual():
     move_constants_before_loop(kernel_ast.body)
     cleanup_blocks(kernel_ast.body)
 
+    pytest.importorskip('islpy')
     assert not kernel_ast.atoms(Conditional), "Loop cutting optimization did not work"
 
     func_optimized = make_python_function(kernel_ast)
@@ -106,11 +121,14 @@ def test_staggered_iteration_manual():
 
 def test_staggered_gpu():
     dim = 2
-    f, s = ps.fields("f, s({dim}): double[{dim}D]".format(dim=dim))
+    f = ps.fields(f"f: double[{dim}D]")
+    s = ps.fields("s({dim}): double[{dim}D]".format(dim=dim), field_type=FieldType.STAGGERED)
     expressions = [(f[0, 0] + f[-1, 0]) / 2,
                    (f[0, 0] + f[0, -1]) / 2]
-    kernel_ast = ps.create_staggered_kernel(s, expressions, target='gpu', gpu_exclusive_conditions=True)
+    assignments = [ps.Assignment(s.staggered_access(d), expressions[i]) for i, d in enumerate(s.staggered_stencil)]
+    kernel_ast = ps.create_staggered_kernel(assignments, target=ps.Target.GPU, gpu_exclusive_conditions=True)
     assert len(kernel_ast.atoms(Conditional)) == 4
 
-    kernel_ast = ps.create_staggered_kernel(s, expressions, target='gpu', gpu_exclusive_conditions=False)
+    assignments = [ps.Assignment(s.staggered_access(d), expressions[i]) for i, d in enumerate(s.staggered_stencil)]
+    kernel_ast = ps.create_staggered_kernel(assignments, target=ps.Target.GPU, gpu_exclusive_conditions=False)
     assert len(kernel_ast.atoms(Conditional)) == 3

tests/test_match_subs_for_assignment_collection.py

+# -*- coding: utf-8 -*-
+#
+# Copyright © 2019 Stephan Seitz <stephan.seitz@fau.de>
+#
+# Distributed under terms of the GPLv3 license.
+
+"""
+
+"""
+
+import sympy as sp
+
+import pystencils
+from pystencils.typing import TypedSymbol, BasicType
+
+
+def test_wild_typed_symbol():
+    x = pystencils.fields('x:  float32[3d]')
+    typed_symbol = TypedSymbol('a', BasicType('float64'))
+
+    assert x.center().match(sp.Wild('w1'))
+    assert typed_symbol.match(sp.Wild('w1'))
+
+    wild_ceiling = sp.ceiling(sp.Wild('w1'))
+    assert sp.ceiling(x.center()).match(wild_ceiling)
+    assert sp.ceiling(typed_symbol).match(wild_ceiling)
+
+
+def test_replace_and_subs_for_assignment_collection():
+
+    x, y = pystencils.fields('x, y:  float32[3d]')
+    a, b, c, d = sp.symbols('a, b, c, d')
+
+    assignments = pystencils.AssignmentCollection({
+        a: sp.floor(1),
+        b: 2,
+        c: a + c,
+        y.center(): sp.ceiling(x.center()) + sp.floor(x.center())
+    })
+
+    expected_assignments = pystencils.AssignmentCollection({
+        a: sp.floor(3),
+        b: 2,
+        c: a + c,
+        y.center(): sp.ceiling(x.center()) + sp.floor(x.center())
+    })
+
+    assert expected_assignments == assignments.replace(1, 3)
+    assert expected_assignments == assignments.subs({1: 3})
+
+    expected_assignments = pystencils.AssignmentCollection({
+        d: sp.floor(1),
+        b: 2,
+        c: d + c,
+        y.center(): sp.ceiling(x.center()) + sp.floor(x.center())
+    })
+
+    print(expected_assignments)
+    print(assignments.subs(a, d))
+    assert expected_assignments == assignments.subs(a, d)
+
+
+def test_match_for_assignment_collection():
+
+    x, y = pystencils.fields('x, y:  float32[3d]')
+    a, b, c, d = sp.symbols('a, b, c, d')
+
+    assignments = pystencils.AssignmentCollection({
+        a: sp.floor(1),
+        b: 2,
+        c: a + c,
+        y.center(): sp.ceiling(x.center()) + sp.floor(x.center())
+    })
+
+    w1 = sp.Wild('w1')
+    w2 = sp.Wild('w2')
+    w3 = sp.Wild('w3')
+
+    wild_ceiling = sp.ceiling(w1)
+    wild_addition = w1 + w2
+
+    assert assignments.match(pystencils.Assignment(w3, wild_ceiling + w2))[w1] == x.center()
+    assert assignments.match(pystencils.Assignment(w3, wild_ceiling + w2)) == {
+        w3: y.center(),
+        w2: sp.floor(x.center()),
+        w1: x.center()
+    }
+    assert assignments.find(wild_ceiling) == {sp.ceiling(x.center())}
+    assert len([a for a in assignments.find(wild_addition) if isinstance(a, sp.Add)]) == 2

tests/test_math_functions.py

+import pytest
+import sympy as sp
+import numpy as np
+import pystencils as ps
+from pystencils.fast_approximation import fast_division
+
+
+@pytest.mark.parametrize('dtype', ["float64", "float32"])
+@pytest.mark.parametrize('func', [sp.Pow, sp.atan2])
+@pytest.mark.parametrize('target', [ps.Target.CPU, ps.Target.GPU])
+def test_two_arguments(dtype, func, target):
+    if target == ps.Target.GPU:
+        pytest.importorskip("cupy")
+    dh = ps.create_data_handling(domain_size=(10, 10), periodicity=True, default_target=target)
+
+    x = dh.add_array('x', values_per_cell=1, dtype=dtype)
+    dh.fill("x", 0.0, ghost_layers=True)
+    y = dh.add_array('y', values_per_cell=1, dtype=dtype)
+    dh.fill("y", 1.0, ghost_layers=True)
+    z = dh.add_array('z', values_per_cell=1, dtype=dtype)
+    dh.fill("z", 2.0, ghost_layers=True)
+
+    config = ps.CreateKernelConfig(target=target)
+
+    # test sp.Max with one argument
+    up = ps.Assignment(x.center, func(y.center, z.center))
+    ast = ps.create_kernel(up, config=config)
+    code = ps.get_code_str(ast)
+    if dtype == 'float32':
+        assert func.__name__.lower() in code
+    kernel = ast.compile()
+
+    dh.all_to_gpu()
+    dh.run_kernel(kernel)
+    dh.all_to_cpu()
+
+    np.testing.assert_allclose(dh.gather_array("x")[0, 0], float(func(1.0, 2.0).evalf()),
+                               13 if dtype == 'float64' else 5)
+
+
+@pytest.mark.parametrize('dtype', ["float64", "float32"])
+@pytest.mark.parametrize('func', [sp.sin, sp.cos, sp.sinh, sp.cosh, sp.atan, sp.floor, sp.ceiling])
+@pytest.mark.parametrize('target', [ps.Target.CPU, ps.Target.GPU])
+def test_single_arguments(dtype, func, target):
+    if target == ps.Target.GPU:
+        pytest.importorskip("cupy")
+    dh = ps.create_data_handling(domain_size=(10, 10), periodicity=True, default_target=target)
+
+    x = dh.add_array('x', values_per_cell=1, dtype=dtype)
+    dh.fill("x", 0.0, ghost_layers=True)
+    y = dh.add_array('y', values_per_cell=1, dtype=dtype)
+    dh.fill("y", 1.0, ghost_layers=True)
+
+    config = ps.CreateKernelConfig(target=target)
+
+    # test sp.Max with one argument
+    up = ps.Assignment(x.center, func(y.center))
+    ast = ps.create_kernel(up, config=config)
+    code = ps.get_code_str(ast)
+    if dtype == 'float32':
+        func_name = func.__name__.lower() if func is not sp.ceiling else "ceil"
+        assert func_name in code
+    kernel = ast.compile()
+
+    dh.all_to_gpu()
+    dh.run_kernel(kernel)
+    dh.all_to_cpu()
+
+    np.testing.assert_allclose(dh.gather_array("x")[0, 0], float(func(1.0).evalf()),
+                               rtol=10**-3 if dtype == 'float32' else 10**-5)
+
+
+@pytest.mark.parametrize('a', [sp.Symbol('a'), ps.fields('a:  float64[2d]').center])
+def test_avoid_pow(a):
+    x = ps.fields('x:  float64[2d]')
+
+    up = ps.Assignment(x.center_vector[0], 2 * a ** 2 / 3)
+    ast = ps.create_kernel(up)
+
+    code = ps.get_code_str(ast)
+
+    assert "pow" not in code
+
+
+def test_avoid_pow_fast_div():
+    x = ps.fields('x:  float64[2d]')
+    a = ps.fields('a:  float64[2d]').center
+
+    up = ps.Assignment(x.center_vector[0], fast_division(1, (a**2)))
+    ast = ps.create_kernel(up, config=ps.CreateKernelConfig(target=ps.Target.GPU))
+    # ps.show_code(ast)
+
+    code = ps.get_code_str(ast)
+
+    assert "pow" not in code
+
+
+def test_avoid_pow_move_constants():
+    # At the end of the kernel creation the function move_constants_before_loop will be called
+    # This function additionally contains substitutions for symbols with the same value
+    # Thus it simplifies the equations again
+    x = ps.fields('x:  float64[2d]')
+    a, b, c = sp.symbols("a, b, c")
+
+    up = [ps.Assignment(a, 0.0),
+          ps.Assignment(b, 0.0),
+          ps.Assignment(c, 0.0),
+          ps.Assignment(x.center_vector[0], a**2/18 - a*b/6 - a/18 + b**2/18 + b/18 - c**2/36)]
+    ast = ps.create_kernel(up)
+
+    code = ps.get_code_str(ast)
+    ps.show_code(ast)
+
+    assert "pow" not in code

tests/test_modulo.py

+import pytest
+
+import numpy as np
+import sympy as sp
+import pystencils as ps
+from pystencils.astnodes import LoopOverCoordinate, Conditional, Block, SympyAssignment
+
+SLICE_LIST = [False,
+              ps.make_slice[1:-1:2, 1:-1:2],
+              ps.make_slice[2:-1:2, 4:-1:7],
+              ps.make_slice[4:-1:2, 5:-1:2],
+              ps.make_slice[3:-1:4, 7:-1:3]]
+
+
+@pytest.mark.parametrize('target', [ps.Target.CPU, ps.Target.GPU])
+@pytest.mark.parametrize('iteration_slice', SLICE_LIST)
+def test_mod(target, iteration_slice):
+    if target == ps.Target.GPU:
+        pytest.importorskip("cupy")
+    dh = ps.create_data_handling(domain_size=(51, 51), periodicity=True, default_target=target)
+
+    loop_ctrs = [LoopOverCoordinate.get_loop_counter_symbol(i) for i in range(dh.dim)]
+    cond = [sp.Eq(sp.Mod(loop_ctrs[i], 2), 1) for i in range(dh.dim)]
+
+    field = dh.add_array("a", values_per_cell=1)
+
+    eq_list = [SympyAssignment(field.center, 1.0)]
+
+    if iteration_slice:
+        config = ps.CreateKernelConfig(target=dh.default_target, iteration_slice=iteration_slice)
+        assign = eq_list
+    else:
+        assign = [Conditional(sp.And(*cond), Block(eq_list))]
+        config = ps.CreateKernelConfig(target=dh.default_target)
+
+    kernel = ps.create_kernel(assign, config=config).compile()
+
+    dh.fill(field.name, 0, ghost_layers=True)
+
+    if config.target == ps.enums.Target.GPU:
+        dh.to_gpu(field.name)
+
+    dh.run_kernel(kernel)
+
+    if config.target == ps.enums.Target.GPU:
+        dh.to_cpu(field.name)
+
+    result = dh.gather_array(field.name, ghost_layers=True)
+
+    assert np.all(result[iteration_slice] == 1.0)
+

pystencils_tests/test_move_constant_before_loop.py → tests/test_move_constant_before_loop.py

-import pystencils as ps
 import numpy as np
-from pystencils.astnodes import LoopOverCoordinate, Block, SympyAssignment, TypedSymbol
+
+import pystencils as ps
+from pystencils.astnodes import Block, LoopOverCoordinate, SympyAssignment, TypedSymbol
 from pystencils.transformations import move_constants_before_loop
 
 
@@ -24,7 +25,40 @@ def test_symbol_renaming():
 
     loops = block.atoms(LoopOverCoordinate)
     assert len(loops) == 2
+    assert len(block.args[1].body.args) == 1
+    assert len(block.args[3].body.args) == 2
+
     for loop in loops:
-        assert len(loop.body.args) == 1
         assert len(loop.parent.args) == 4  # 2 loops + 2 subexpressions
-        assert loop.parent.args[0].lhs.name != loop.parent.args[1].lhs.name
+        assert loop.parent.args[0].lhs.name != loop.parent.args[2].lhs.name
+
+
+def test_keep_order_of_accesses():
+    f = ps.fields("f: [1D]")
+    x = TypedSymbol("x", np.float64)
+    n = 5
+
+    loop = LoopOverCoordinate(Block([SympyAssignment(x, f[0]),
+                                     SympyAssignment(f[1], 2 * x)]),
+                              0, 0, n)
+    block = Block([loop])
+
+    ps.transformations.resolve_field_accesses(block)
+    new_loops = ps.transformations.cut_loop(loop, [n - 1])
+    ps.transformations.move_constants_before_loop(new_loops.args[1])
+
+    kernel_func = ps.astnodes.KernelFunction(
+        block, ps.Target.CPU, ps.Backend.C, ps.cpu.cpujit.make_python_function, None
+    )
+    kernel = kernel_func.compile()
+
+    print(ps.show_code(kernel_func))
+
+    f_arr = np.ones(n + 1)
+    kernel(f=f_arr)
+
+    print(f_arr)
+
+    assert np.allclose(f_arr, np.array([
+        1, 2, 4, 8, 16, 32
+    ]))

tests/test_nodecollection.py

+import sympy as sp
+
+from pystencils import AssignmentCollection, Assignment
+from pystencils.node_collection import NodeCollection
+from pystencils.astnodes import SympyAssignment
+
+
+def test_node_collection_from_assignment_collection():
+    x = sp.symbols('x')
+    assignment_collection = AssignmentCollection([Assignment(x, 2)])
+    node_collection = NodeCollection.from_assignment_collection(assignment_collection)
+
+    assert node_collection.all_assignments[0] == SympyAssignment(x, 2)

pystencils_tests/test_parameterstudy.py → tests/test_parameterstudy.py

 import io
 import json
-from http.server import HTTPServer, BaseHTTPRequestHandler
+from http.server import BaseHTTPRequestHandler, HTTPServer
 from tempfile import TemporaryDirectory
+
 from pystencils.runhelper import ParameterStudy
 
 

tests/test_phasefield_dentritic_3D.ipynb

+%% Cell type:code id: tags:
+
+``` python
+import pytest
+pytest.importorskip('cupy')
+```
+
+%% Output
+
+    <module 'cupy' from '/home/markus/Python311/lib/python3.11/site-packages/cupy/__init__.py'>
+
+%% Cell type:code id: tags:
+
+``` python
+from pystencils.session import *
+sp.init_printing()
+frac = sp.Rational
+```
+
+%% Cell type:markdown id: tags:
+
+# Phase-field simulation of dentritic solidification in 3D
+
+This notebook tests the model presented in the dentritic growth tutorial in 3D.
+
+%% Cell type:code id: tags:
+
+``` python
+target = ps.Target.GPU
+gpu = target == ps.Target.GPU
+domain_size = (25, 25, 25) if 'is_test_run' in globals() else (300, 300, 300)
+
+dh = ps.create_data_handling(domain_size=domain_size, periodicity=True, default_target=target)
+φ_field = dh.add_array('phi', latex_name='φ')
+φ_field_tmp = dh.add_array('phi_tmp', latex_name='φ_tmp')
+φ_delta_field = dh.add_array('phidelta', latex_name='φ_D')
+t_field = dh.add_array('T')
+t_field_tmp = dh.add_array('T_tmp')
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ε, m, δ, j, θzero, α, γ, Teq, κ, τ = sp.symbols("ε m δ j θ_0 α γ T_eq κ τ")
+εb = sp.Symbol("\\bar{\\epsilon}")
+discretize = ps.fd.Discretization2ndOrder(dx=0.03, dt=1e-5)
+
+φ = φ_field.center
+T = t_field.center
+d = ps.fd.Diff
+
+def f(φ, m):
+    return φ**4 / 4 - (frac(1, 2) - m/3) * φ**3 + (frac(1,4)-m/2)*φ**2
+
+
+
+bulk_free_energy_density = f(φ, m)
+interface_free_energy_density = ε ** 2 / 2 * (d(φ, 0) ** 2 + d(φ, 1) ** 2 + d(φ, 2) ** 2)
+```
+
+%% Cell type:markdown id: tags:
+
+Here comes the major change, that has to be made for the 3D model: $\epsilon$ depends on the interface normal, which can not be computed simply as atan() as in the 2D case
+
+%% Cell type:code id: tags:
+
+``` python
+n = sp.Matrix([d(φ, i) for i in range(3)])
+nLen = sp.sqrt(sum(n_i**2 for n_i in n))
+n = n / nLen
+nVal = sum(n_i**4 for n_i in n)
+σ = δ * nVal
+
+εVal = εb * (1 + σ)
+εVal
+```
+
+%% Output
+
+    $\displaystyle \bar{\epsilon} \left(δ \left(\frac{{\partial_{0} {φ}_{(0,0,0)}}^{4}}{\left({\partial_{0} {φ}_{(0,0,0)}}^{2} + {\partial_{1} {φ}_{(0,0,0)}}^{2} + {\partial_{2} {φ}_{(0,0,0)}}^{2}\right)^{2}} + \frac{{\partial_{1} {φ}_{(0,0,0)}}^{4}}{\left({\partial_{0} {φ}_{(0,0,0)}}^{2} + {\partial_{1} {φ}_{(0,0,0)}}^{2} + {\partial_{2} {φ}_{(0,0,0)}}^{2}\right)^{2}} + \frac{{\partial_{2} {φ}_{(0,0,0)}}^{4}}{\left({\partial_{0} {φ}_{(0,0,0)}}^{2} + {\partial_{1} {φ}_{(0,0,0)}}^{2} + {\partial_{2} {φ}_{(0,0,0)}}^{2}\right)^{2}}\right) + 1\right)$
+                   ⎛  ⎛                            4
+                   ⎜  ⎜                 D(φ[0,0,0])
+    \bar{\epsilon}⋅⎜δ⋅⎜───────────────────────────────────────────── + ───────────
+                   ⎜  ⎜                                            2
+                   ⎜  ⎜⎛           2              2              2⎞    ⎛
+                   ⎝  ⎝⎝D(φ[0,0,0])  + D(φ[0,0,0])  + D(φ[0,0,0]) ⎠    ⎝D(φ[0,0,0]
+    
+                     4                                               4
+          D(φ[0,0,0])                                     D(φ[0,0,0])
+    ────────────────────────────────── + ─────────────────────────────────────────
+                                     2
+     2              2              2⎞    ⎛           2              2
+    )  + D(φ[0,0,0])  + D(φ[0,0,0]) ⎠    ⎝D(φ[0,0,0])  + D(φ[0,0,0])  + D(φ[0,0,0]
+    
+        ⎞    ⎞
+        ⎟    ⎟
+    ────⎟ + 1⎟
+       2⎟    ⎟
+     2⎞ ⎟    ⎟
+    ) ⎠ ⎠    ⎠
+
+%% Cell type:code id: tags:
+
+``` python
+def m_func(temperature):
+    return (α / sp.pi) * sp.atan(γ * (Teq - temperature))
+```
+
+%% Cell type:code id: tags:
+
+``` python
+substitutions = {m: m_func(T),
+                 ε: εVal}
+
+fe_i = interface_free_energy_density.subs(substitutions)
+fe_b = bulk_free_energy_density.subs(substitutions)
+
+μ_if = ps.fd.expand_diff_full(ps.fd.functional_derivative(fe_i, φ), functions=[φ])
+μ_b = ps.fd.expand_diff_full(ps.fd.functional_derivative(fe_b, φ), functions=[φ])
+```
+
+%% Cell type:code id: tags:
+
+``` python
+dF_dφ = μ_b + sp.Piecewise((μ_if, nLen**2 > 1e-10), (0, True))
+```
+
+%% Cell type:code id: tags:
+
+``` python
+parameters = {
+    τ: 0.0003,
+    κ: 1.8,
+    εb: 0.01,
+    δ: 0.3,
+    γ: 10,
+    j: 6,
+    α: 0.9,
+    Teq: 1.0,
+    θzero: 0.2,
+    sp.pi: sp.pi.evalf()
+}
+parameters
+```
+
+%% Output
+
+
+    $\displaystyle \left\{ \pi : 3.14159265358979, \  T_{eq} : 1.0, \  \bar{\epsilon} : 0.01, \  j : 6, \  α : 0.9, \  γ : 10, \  δ : 0.3, \  θ_{0} : 0.2, \  κ : 1.8, \  τ : 0.0003\right\}$
+    {π: 3.14159265358979, T_eq: 1.0, \bar{\epsilon}: 0.01, j: 6, α: 0.9, γ: 10, δ:
+     0.3, θ₀: 0.2, κ: 1.8, τ: 0.0003}
+
+%% Cell type:code id: tags:
+
+``` python
+dφ_dt = - dF_dφ / τ
+assignments = [
+    ps.Assignment(φ_delta_field.center, discretize(dφ_dt.subs(parameters))),
+]
+φEqs = ps.simp.sympy_cse_on_assignment_list(assignments)
+φEqs.append(ps.Assignment(φ_field_tmp.center, discretize(ps.fd.transient(φ) - φ_delta_field.center)))
+
+
+temperatureEvolution = -ps.fd.transient(T) + ps.fd.diffusion(T, 1) + κ * φ_delta_field.center
+temperatureEqs = [
+    ps.Assignment(t_field_tmp.center, discretize(temperatureEvolution.subs(parameters)))
+]
+```
+
+%% Cell type:code id: tags:
+
+``` python
+φ_kernel = ps.create_kernel(φEqs, cpu_openmp=4, target=target).compile()
+temperatureKernel = ps.create_kernel(temperatureEqs, cpu_openmp=4, target=target).compile()
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def time_loop(steps):
+    φ_sync = dh.synchronization_function(['phi'], target=target)
+    temperature_sync = dh.synchronization_function(['T'], target=target)
+    dh.all_to_gpu()
+    for t in range(steps):
+        φ_sync()
+        dh.run_kernel(φ_kernel)
+        temperature_sync()
+        dh.run_kernel(temperatureKernel)
+        dh.swap(φ_field.name, φ_field_tmp.name)
+        dh.swap(t_field.name, t_field_tmp.name)
+    dh.all_to_cpu()
+
+
+def init(nucleus_size=np.sqrt(5)):
+    for b in dh.iterate():
+        x, y, z = b.cell_index_arrays
+        x, y, z = x - b.shape[0] // 2, y - b.shape[1] // 2, z - b.shape[2] // 2
+        b['phi'].fill(0)
+        b['phi'][(x ** 2 + y ** 2 + z ** 2) < nucleus_size ** 2] = 1.0
+        b['T'].fill(0.0)
+
+
+def plot(slice_obj=ps.make_slice[:, :, 0.5]):
+    plt.subplot(1, 3, 1)
+    plt.scalar_field(dh.gather_array('phi', slice_obj).squeeze())
+    plt.title("φ")
+    plt.colorbar()
+    plt.subplot(1, 3, 2)
+    plt.title("T")
+    plt.scalar_field(dh.gather_array('T', slice_obj).squeeze())
+    plt.colorbar()
+    plt.subplot(1, 3, 3)
+    plt.title("∂φ")
+    plt.scalar_field(dh.gather_array('phidelta', slice_obj).squeeze())
+    plt.colorbar()
+```
+
+%% Cell type:code id: tags:
+
+``` python
+init()
+plot()
+print(dh)
+```
+
+%% Output
+
+        Name|      Inner (min/max)|     WithGl (min/max)
+    ----------------------------------------------------
+           T|            (  0,  0)|            (  0,  0)
+       T_tmp|            (  0,  0)|            (  0,  0)
+         phi|            (  0,  1)|            (  0,  1)
+     phi_tmp|            (  0,  0)|            (  0,  0)
+    phidelta|            (  0,  0)|            (  0,  0)
+    
+
+
+
+%% Cell type:code id: tags:
+
+``` python
+if 'is_test_run' in globals():
+    time_loop(2)
+    assert np.isfinite(dh.max('phi'))
+    assert np.isfinite(dh.max('T'))
+    assert np.isfinite(dh.max('phidelta'))
+else:
+    from time import perf_counter
+    vtk_writer = dh.create_vtk_writer('dentritic_growth_large', ['phi'])
+    last = perf_counter()
+    for i in range(4):
+        time_loop(100)
+        vtk_writer(i)
+        print("Step ", i, perf_counter() - last, dh.max('phi'))
+        last = perf_counter()
+```
+
+%% Output
+
+    Step  0 19.713090835999992 1.0
+    Step  1 19.673075279000045 1.0
+    Step  2 19.696444219 1.0
+    Step  3 19.752472744999977 1.0

pystencils_tests/test_pickle_support.py → tests/test_pickle_support.py

-from pystencils import Field, TypedSymbol
 from copy import copy, deepcopy
 
+from pystencils.field import Field
+from pystencils.typing import TypedSymbol
+
 
 def test_field_access():
     field = Field.create_generic('some_field', spatial_dimensions=2, index_dimensions=0)