pystencils_tests/test_datahandling.py → tests/test_datahandling.py

@@ -6,8 +6,8 @@ import numpy as np
 
 import pystencils as ps
 from pystencils import create_data_handling, create_kernel
-from pystencils.datahandling.pycuda import PyCudaArrayHandler
-from pystencils.datahandling.pyopencl import PyOpenClArrayHandler
+from pystencils.gpu.gpu_array_handler import GPUArrayHandler
+from pystencils.enums import Target
 
 try:
     import pytest
@@ -15,6 +15,12 @@ except ImportError:
     import unittest.mock
     pytest = unittest.mock.MagicMock()
 
+try:
+    import cupy.cuda.runtime
+    device_numbers = range(cupy.cuda.runtime.getDeviceCount())
+except ImportError:
+    device_numbers = []
+
 SCRIPT_FOLDER = Path(__file__).parent.absolute()
 INPUT_FOLDER = SCRIPT_FOLDER / "test_data"
 
@@ -29,7 +35,7 @@ def basic_iteration(dh):
 
 
 def access_and_gather(dh, domain_size):
-    dh.add_array('f1', dtype=np.dtype(np.int32))
+    dh.add_array('f1', dtype=np.dtype(np.int8))
     dh.add_array_like('f2', 'f1')
     dh.add_array('v1', values_per_cell=3, dtype=np.int64, ghost_layers=2)
     dh.add_array_like('v2', 'v1')
@@ -40,7 +46,7 @@ def access_and_gather(dh, domain_size):
     # Check symbolic field properties
     assert dh.fields.f1.index_dimensions == 0
     assert dh.fields.f1.spatial_dimensions == len(domain_size)
-    assert dh.fields.f1.dtype.numpy_dtype == np.int32
+    assert dh.fields.f1.dtype.numpy_dtype == np.int8
 
     assert dh.fields.v1.index_dimensions == 1
     assert dh.fields.v1.spatial_dimensions == len(domain_size)
@@ -85,14 +91,10 @@ def access_and_gather(dh, domain_size):
 def synchronization(dh, test_gpu=False):
     field_name = 'comm_field_test'
     if test_gpu:
-        try:
-            from pycuda import driver
-            import pycuda.autoinit
-        except ImportError:
-            return
+        pytest.importorskip("cupy")
         field_name += 'Gpu'
 
-    dh.add_array(field_name, ghost_layers=1, dtype=np.int32, cpu=True, gpu=test_gpu)
+    dh.add_array(field_name, ghost_layers=1, dtype=np.int8, cpu=True, gpu=test_gpu)
 
     # initialize everything with 1
     for b in dh.iterate(ghost_layers=1):
@@ -102,8 +104,10 @@ def synchronization(dh, test_gpu=False):
 
     if test_gpu:
         dh.to_gpu(field_name)
+        dh.synchronization_function_gpu(field_name)()
+    else:
+        dh.synchronization_function_cpu(field_name)()
 
-    dh.synchronization_function(field_name, target='gpu' if test_gpu else 'cpu')()
 
     if test_gpu:
         dh.to_cpu(field_name)
@@ -114,7 +118,7 @@ def synchronization(dh, test_gpu=False):
 
 def kernel_execution_jacobi(dh, target):
 
-    test_gpu = target == 'gpu' or target == 'opencl'
+    test_gpu = target == Target.GPU
     dh.add_array('f', gpu=test_gpu)
     dh.add_array('tmp', gpu=test_gpu)
 
@@ -130,7 +134,7 @@ def kernel_execution_jacobi(dh, target):
     def jacobi():
         dh.fields.tmp.center @= sum(dh.fields.f.neighbors(stencil)) / len(stencil)
 
-    kernel = create_kernel(jacobi, target).compile()
+    kernel = create_kernel(jacobi, config=ps.CreateKernelConfig(target=target)).compile()
     for b in dh.iterate(ghost_layers=1):
         b['f'].fill(42)
     dh.run_kernel(kernel)
@@ -209,26 +213,22 @@ def test_kernel():
     for domain_shape in [(4, 5), (3, 4, 5)]:
         dh = create_data_handling(domain_size=domain_shape, periodicity=True)
         assert all(dh.periodicity)
-        kernel_execution_jacobi(dh, 'cpu')
+        kernel_execution_jacobi(dh, Target.CPU)
         reduction(dh)
 
         try:
-            import pycuda
+            import cupy
             dh = create_data_handling(domain_size=domain_shape, periodicity=True)
-            kernel_execution_jacobi(dh, 'gpu')
+            kernel_execution_jacobi(dh, Target.GPU)
         except ImportError:
             pass
 
 
-@pytest.mark.parametrize('target', ('cpu', 'gpu', 'opencl'))
+@pytest.mark.parametrize('target', (Target.CPU, Target.GPU))
 def test_kernel_param(target):
     for domain_shape in [(4, 5), (3, 4, 5)]:
-        if target == 'gpu':
-            pytest.importorskip('pycuda')
-        if target == 'opencl':
-            pytest.importorskip('pyopencl')
-            from pystencils.opencl.opencljit import init_globally
-            init_globally()
+        if target == Target.GPU:
+            pytest.importorskip('cupy')
 
         dh = create_data_handling(domain_size=domain_shape, periodicity=True, default_target=target)
         kernel_execution_jacobi(dh, target)
@@ -257,6 +257,20 @@ def test_add_arrays():
     assert y == dh.fields['y']
 
 
+@pytest.mark.parametrize('shape', [(17, 12), (7, 11, 18)])
+@pytest.mark.parametrize('layout', ['zyxf', 'fzyx'])
+def test_add_arrays_with_layout(shape, layout):
+    pytest.importorskip('cupy')
+
+    dh = create_data_handling(domain_size=shape, default_layout=layout, default_target=ps.Target.GPU)
+    f1 = dh.add_array("f1", values_per_cell=19)
+    dh.fill(f1.name, 1.0)
+
+    assert dh.cpu_arrays[f1.name].shape == dh.gpu_arrays[f1.name].shape
+    assert dh.cpu_arrays[f1.name].strides == dh.gpu_arrays[f1.name].strides
+    assert dh.cpu_arrays[f1.name].dtype == dh.gpu_arrays[f1.name].dtype
+
+
 def test_get_kwarg():
     domain_shape = (10, 10)
     field_description = 'src, dst'
@@ -267,7 +281,7 @@ def test_get_kwarg():
     dh.fill("dst", 0.0, ghost_layers=True)
 
     with pytest.raises(ValueError):
-        dh.add_array('src')
+        dh.add_array('src', values_per_cell=1)
 
     ur = ps.Assignment(src.center, dst.center)
     kernel = ps.create_kernel(ur).compile()
@@ -278,22 +292,20 @@ def test_get_kwarg():
 
 
 def test_add_custom_data():
-    pytest.importorskip('pycuda')
-
-    import pycuda.gpuarray as gpuarray
-    import pycuda.autoinit  # noqa
+    pytest.importorskip('cupy')
+    import cupy as cp
 
     def cpu_data_create_func():
         return np.ones((2, 2), dtype=np.float64)
 
     def gpu_data_create_func():
-        return gpuarray.zeros((2, 2), dtype=np.float64)
+        return cp.zeros((2, 2), dtype=np.float64)
 
     def cpu_to_gpu_transfer_func(gpuarr, cpuarray):
         gpuarr.set(cpuarray)
 
     def gpu_to_cpu_transfer_func(gpuarr, cpuarray):
-        gpuarr.get(cpuarray)
+        cpuarray[:] = gpuarr.get()
 
     dh = create_data_handling(domain_size=(10, 10))
     dh.add_custom_data('custom_data',
@@ -359,19 +371,11 @@ def test_load_data():
     assert np.all(dh.cpu_arrays['dst2']) == 0
 
 
-@pytest.mark.parametrize('target', ('gpu', 'opencl'))
-def test_array_handler(target):
+@pytest.mark.parametrize("device_number", device_numbers)
+def test_array_handler(device_number):
     size = (2, 2)
-    if target == 'gpu':
-        array_handler = PyCudaArrayHandler()
-    if target == 'opencl':
-        pytest.importorskip('pyopencl')
-        import pyopencl as cl
-        from pystencils.opencl.opencljit import init_globally
-        init_globally()
-        ctx = cl.create_some_context(0)
-        queue = cl.CommandQueue(ctx)
-        array_handler = PyOpenClArrayHandler(queue)
+    pytest.importorskip('cupy')
+    array_handler = GPUArrayHandler(device_number)
 
     zero_array = array_handler.zeros(size)
     cpu_array = np.empty(size)
@@ -385,8 +389,23 @@ def test_array_handler(target):
 
     empty = array_handler.empty(size)
     assert empty.strides == (16, 8)
-    empty = array_handler.empty(shape=size, layout=(1, 0))
+    empty = array_handler.empty(shape=size, order="F")
     assert empty.strides == (8, 16)
 
     random_array = array_handler.randn(size)
 
+    cpu_array = np.empty((20, 40), dtype=np.float64)
+    gpu_array = array_handler.to_gpu(cpu_array)
+
+    assert cpu_array.base is None
+    assert gpu_array.base is None
+    assert gpu_array.strides == cpu_array.strides
+
+    cpu_array2 = np.empty((20, 40), dtype=np.float64)
+    cpu_array2 = cpu_array2.swapaxes(0, 1)
+    gpu_array2 = array_handler.to_gpu(cpu_array2)
+
+    assert cpu_array2.base is not None
+    assert gpu_array2.base is not None
+    assert gpu_array2.strides == cpu_array2.strides
+

pystencils_tests/test_datahandling_parallel.py → tests/test_datahandling_parallel.py

 import numpy as np
 import waLBerla as wlb
+
+import pystencils
 from pystencils import make_slice
 
+from pathlib import Path
+
+from pystencils.boundaries import BoundaryHandling, Neumann
+from pystencils.slicing import slice_from_direction
+
 from pystencils.datahandling.parallel_datahandling import ParallelDataHandling
-from pystencils_tests.test_datahandling import (
+from pystencils.datahandling import create_data_handling
+from tests.test_datahandling import (
     access_and_gather, kernel_execution_jacobi, reduction, synchronization, vtk_output)
 
+SCRIPT_FOLDER = Path(__file__).parent.absolute()
+INPUT_FOLDER = SCRIPT_FOLDER / "test_data"
+
 try:
     import pytest
 except ImportError:
@@ -22,14 +33,12 @@ def test_access_and_gather():
     dh = ParallelDataHandling(blocks, default_ghost_layers=2)
     access_and_gather(dh, cells)
     synchronization(dh, test_gpu=False)
-    if hasattr(wlb, 'cuda'):
+    if hasattr(wlb, 'gpu'):
         synchronization(dh, test_gpu=True)
 
 
 def test_gpu():
-    if not hasattr(wlb, 'cuda'):
-        print("Skip GPU tests because walberla was built without CUDA")
-        return
+    pytest.importorskip('waLBerla.gpu')
 
     block_size = (4, 7, 1)
     num_blocks = (3, 2, 1)
@@ -47,24 +56,22 @@ def test_gpu():
         np.testing.assert_equal(b['v'], 42)
 
 
-def test_kernel():
+@pytest.mark.parametrize('target', (pystencils.Target.CPU, pystencils.Target.GPU))
+def test_kernel(target):
+    if target == pystencils.Target.GPU:
+        pytest.importorskip('waLBerla.gpu')
 
-    for gpu in (True, False):
-        if gpu and not hasattr(wlb, 'cuda'):
-            print("Skipping CUDA tests because walberla was built without GPU support")
-            continue
-
-        # 3D
-        blocks = wlb.createUniformBlockGrid(blocks=(3, 2, 4), cellsPerBlock=(3, 2, 5), oneBlockPerProcess=False)
-        dh = ParallelDataHandling(blocks)
-        kernel_execution_jacobi(dh, 'gpu')
-        reduction(dh)
+    # 3D
+    blocks = wlb.createUniformBlockGrid(blocks=(3, 2, 4), cellsPerBlock=(3, 2, 5), oneBlockPerProcess=False)
+    dh = ParallelDataHandling(blocks, default_target=target)
+    kernel_execution_jacobi(dh, target)
+    reduction(dh)
 
-        # 2D
-        blocks = wlb.createUniformBlockGrid(blocks=(3, 2, 1), cellsPerBlock=(3, 2, 1), oneBlockPerProcess=False)
-        dh = ParallelDataHandling(blocks, dim=2)
-        kernel_execution_jacobi(dh, 'gpu')
-        reduction(dh)
+    # 2D
+    blocks = wlb.createUniformBlockGrid(blocks=(3, 2, 1), cellsPerBlock=(3, 2, 1), oneBlockPerProcess=False)
+    dh = ParallelDataHandling(blocks, dim=2, default_target=target)
+    kernel_execution_jacobi(dh, target)
+    reduction(dh)
 
 
 def test_vtk_output():
@@ -78,7 +85,7 @@ def test_block_iteration():
     num_blocks = (2, 2, 2)
     blocks = wlb.createUniformBlockGrid(blocks=num_blocks, cellsPerBlock=block_size, oneBlockPerProcess=False)
     dh = ParallelDataHandling(blocks, default_ghost_layers=2)
-    dh.add_array('v', values_per_cell=1, dtype=np.int64, ghost_layers=2, gpu=True)
+    dh.add_array('v', values_per_cell=1, dtype=np.int64, ghost_layers=2)
 
     for b in dh.iterate():
         b['v'].fill(1)
@@ -101,10 +108,12 @@ def test_block_iteration():
 
 
 def test_getter_setter():
+    pytest.importorskip('waLBerla.gpu')
+
     block_size = (2, 2, 2)
     num_blocks = (2, 2, 2)
     blocks = wlb.createUniformBlockGrid(blocks=num_blocks, cellsPerBlock=block_size, oneBlockPerProcess=False)
-    dh = ParallelDataHandling(blocks, default_ghost_layers=2)
+    dh = ParallelDataHandling(blocks, default_ghost_layers=2, default_target=pystencils.Target.GPU)
     dh.add_array('v', values_per_cell=1, dtype=np.int64, ghost_layers=2, gpu=True)
 
     assert dh.shape == (4, 4, 4)
@@ -119,3 +128,72 @@ def test_getter_setter():
     dh.to_gpu('v')
     assert dh.is_on_gpu('v') is True
     dh.all_to_cpu()
+
+
+def test_parallel_datahandling_boundary_conditions():
+    pytest.importorskip('waLBerla.gpu')
+
+    dh = create_data_handling(domain_size=(7, 7), periodicity=True, parallel=True,
+                              default_target=pystencils.Target.GPU)
+
+    src = dh.add_array('src', values_per_cell=1)
+    dh.fill(src.name, 0.0, ghost_layers=True)
+    dh.fill(src.name, 1.0, ghost_layers=False)
+
+    src2 = dh.add_array('src2', values_per_cell=1)
+
+    src_cpu = dh.add_array('src_cpu', values_per_cell=1, gpu=False)
+    dh.fill(src_cpu.name, 0.0, ghost_layers=True)
+    dh.fill(src_cpu.name, 1.0, ghost_layers=False)
+
+    boundary_stencil = [(1, 0), (-1, 0), (0, 1), (0, -1)]
+    boundary_handling_cpu = BoundaryHandling(dh, src_cpu.name, boundary_stencil,
+                                             name="boundary_handling_cpu", target=pystencils.Target.CPU)
+
+    boundary_handling = BoundaryHandling(dh, src.name, boundary_stencil,
+                                         name="boundary_handling_gpu", target=pystencils.Target.GPU)
+
+    neumann = Neumann()
+    for d in ('N', 'S', 'W', 'E'):
+        boundary_handling.set_boundary(neumann, slice_from_direction(d, dim=2))
+        boundary_handling_cpu.set_boundary(neumann, slice_from_direction(d, dim=2))
+
+    boundary_handling.prepare()
+    boundary_handling_cpu.prepare()
+
+    boundary_handling_cpu()
+
+    dh.all_to_gpu()
+    boundary_handling()
+    dh.all_to_cpu()
+    for block in dh.iterate():
+        np.testing.assert_almost_equal(block[src_cpu.name], block[src.name])
+
+    assert dh.custom_data_names == ('boundary_handling_cpuIndexArrays', 'boundary_handling_gpuIndexArrays')
+    dh.swap(src.name, src2.name, gpu=True)
+
+
+def test_save_data():
+    domain_shape = (2, 2)
+
+    dh = create_data_handling(domain_size=domain_shape, default_ghost_layers=1, parallel=True)
+    dh.add_array("src", values_per_cell=9)
+    dh.fill("src", 1.0, ghost_layers=True)
+    dh.add_array("dst", values_per_cell=9)
+    dh.fill("dst", 1.0, ghost_layers=True)
+
+    dh.save_all(str(INPUT_FOLDER) + '/datahandling_parallel_save_test')
+
+
+def test_load_data():
+    domain_shape = (2, 2)
+
+    dh = create_data_handling(domain_size=domain_shape, default_ghost_layers=1, parallel=True)
+    dh.add_array("src", values_per_cell=9)
+    dh.fill("src", 0.0, ghost_layers=True)
+    dh.add_array("dst", values_per_cell=9)
+    dh.fill("dst", 0.0, ghost_layers=True)
+
+    dh.load_all(str(INPUT_FOLDER) + '/datahandling_parallel_load_test')
+    assert np.all(dh.gather_array('src')) == 1
+    assert np.all(dh.gather_array('src')) == 1

tests/test_dot_printer.ipynb

+%% Cell type:code id: tags:
+
+``` python
+from pystencils.session import *
+from pystencils.astnodes import Block, Conditional, SympyAssignment
+```
+
+%% Cell type:code id: tags:
+
+``` python
+src, dst = ps.fields("src, dst: double[2D]", layout='c')
+
+true_block = Block([SympyAssignment(dst[0, 0], src[-1, 0])])
+false_block = Block([SympyAssignment(dst[0, 0], src[1, 0])])
+ur = [true_block, Conditional(dst.center() > 0.0, true_block, false_block)]
+
+ast = ps.create_kernel(ur)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+ps.show_code(ast)
+```
+
+%% Output
+
+
+
+%% Cell type:code id: tags:
+
+``` python
+```

tests/test_dot_printer.py

+import pystencils as ps
+
+from pystencils.astnodes import Block, Conditional, SympyAssignment
+
+
+def test_dot_print():
+    src, dst = ps.fields("src, dst: double[2D]", layout='c')
+
+    true_block = Block([SympyAssignment(dst[0, 0], src[-1, 0])])
+    false_block = Block([SympyAssignment(dst[0, 0], src[1, 0])])
+    ur = [true_block, Conditional(dst.center() > 0.0, true_block, false_block)]
+
+    ast = ps.create_kernel(ur)

pystencils_tests/test_fast_approximation.py → tests/test_fast_approximation.py

+import pytest
 import sympy as sp
 
 import pystencils as ps
@@ -6,12 +7,13 @@ from pystencils.fast_approximation import (
 
 
 def test_fast_sqrt():
+    pytest.importorskip('cupy')
     f, g = ps.fields("f, g: double[2D]")
     expr = sp.sqrt(f[0, 0] + f[1, 0])
 
     assert len(insert_fast_sqrts(expr).atoms(fast_sqrt)) == 1
     assert len(insert_fast_sqrts([expr])[0].atoms(fast_sqrt)) == 1
-    ast_gpu = ps.create_kernel(ps.Assignment(g[0, 0], insert_fast_sqrts(expr)), target='gpu')
+    ast_gpu = ps.create_kernel(ps.Assignment(g[0, 0], insert_fast_sqrts(expr)), target=ps.Target.GPU)
     ast_gpu.compile()
     code_str = ps.get_code_str(ast_gpu)
     assert '__fsqrt_rn' in code_str
@@ -21,13 +23,14 @@ def test_fast_sqrt():
 
     ac = ps.AssignmentCollection([expr], [])
     assert len(insert_fast_sqrts(ac).main_assignments[0].atoms(fast_inv_sqrt)) == 1
-    ast_gpu = ps.create_kernel(insert_fast_sqrts(ac), target='gpu')
+    ast_gpu = ps.create_kernel(insert_fast_sqrts(ac), target=ps.Target.GPU)
     ast_gpu.compile()
     code_str = ps.get_code_str(ast_gpu)
     assert '__frsqrt_rn' in code_str
 
 
 def test_fast_divisions():
+    pytest.importorskip('cupy')
     f, g = ps.fields("f, g: double[2D]")
     expr = f[0, 0] / f[1, 0]
     assert len(insert_fast_divisions(expr).atoms(fast_division)) == 1
@@ -35,7 +38,7 @@ def test_fast_divisions():
     expr = 1 / f[0, 0] * 2 / f[0, 1]
     assert len(insert_fast_divisions(expr).atoms(fast_division)) == 1
 
-    ast = ps.create_kernel(ps.Assignment(g[0, 0], insert_fast_divisions(expr)), target='gpu')
+    ast = ps.create_kernel(ps.Assignment(g[0, 0], insert_fast_divisions(expr)), target=ps.Target.GPU)
     ast.compile()
     code_str = ps.get_code_str(ast)
     assert '__fdividef' in code_str

pystencils_tests/test_fd_derivation.ipynb → tests/test_fd_derivation.ipynb

 %% Cell type:code id: tags:
 
 ``` python
 from pystencils.session import *
 from pystencils.fd.derivation import *
 ```
 
 %% Cell type:markdown id: tags:
 
 # 2D standard stencils
 
 %% Cell type:code id: tags:
 
 ``` python
 stencil = [(-1, 0), (1, 0), (0, -1), (0, 1), (0, 0)]
 standard_2d_00 = FiniteDifferenceStencilDerivation((0,0), stencil)
 f = ps.fields("f: [2D]")
 standard_2d_00_res = standard_2d_00.get_stencil()
 res = standard_2d_00_res.apply(f.center)
 expected = f[-1, 0] - 2 * f[0, 0] + f[1, 0]
 assert res == expected
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 assert standard_2d_00_res.accuracy == 2
 assert not standard_2d_00_res.is_isotropic
 standard_2d_00_res
 ```
 
 %% Output
 
     Finite difference stencil of accuracy 2, isotropic error: False
 
 %% Cell type:code id: tags:
 
 ``` python
 standard_2d_00.get_stencil().as_array()
 ```
 
 %% Output
 
-
     $\displaystyle \left[\begin{matrix}0 & 0 & 0\\1 & -2 & 1\\0 & 0 & 0\end{matrix}\right]$
-    ⎡0  0   0⎤
-    ⎢        ⎥
-    ⎢1  -2  1⎥
-    ⎢        ⎥
-    ⎣0  0   0⎦
+    [[0, 0, 0], [1, -2, 1], [0, 0, 0]]
 
 %% Cell type:markdown id: tags:
 
 # 2D isotropic stencils
 
 ## second x-derivative
 
 %% Cell type:code id: tags:
 
 ``` python
 stencil = [(i, j) for i in (-1, 0, 1) for j in (-1, 0, 1)]
 isotropic_2d_00 = FiniteDifferenceStencilDerivation((0,0), stencil)
 isotropic_2d_00_res = isotropic_2d_00.get_stencil(isotropic=True)
 assert isotropic_2d_00_res.is_isotropic
 assert isotropic_2d_00_res.accuracy == 2
 isotropic_2d_00_res
 ```
 
 %% Output
 
     Finite difference stencil of accuracy 2, isotropic error: True
 
 %% Cell type:code id: tags:
 
 ``` python
 isotropic_2d_00_res.as_array()
 ```
 
 %% Output
 
-
     $\displaystyle \left[\begin{matrix}\frac{1}{12} & - \frac{1}{6} & \frac{1}{12}\\\frac{5}{6} & - \frac{5}{3} & \frac{5}{6}\\\frac{1}{12} & - \frac{1}{6} & \frac{1}{12}\end{matrix}\right]$
-    ⎡1/12  -1/6  1/12⎤
-    ⎢                ⎥
-    ⎢5/6   -5/3  5/6 ⎥
-    ⎢                ⎥
-    ⎣1/12  -1/6  1/12⎦
+    [[1/12, -1/6, 1/12], [5/6, -5/3, 5/6], [1/12, -1/6, 1/12]]
 
 %% Cell type:code id: tags:
 
 ``` python
 plt.figure(figsize=(2,2))
 isotropic_2d_00_res.visualize()
 ```
 
 %% Output
 
-
+
 
 %% Cell type:code id: tags:
 
 ``` python
 expected_result = sp.Array([[1, -2, 1], [10, -20, 10], [1, -2, 1]]) / 12
 assert expected_result == isotropic_2d_00_res.as_array()
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Isotropic laplacian
 
 %% Cell type:code id: tags:
 
 ``` python
 isotropic_2d_11 = FiniteDifferenceStencilDerivation((1,1), stencil)
 isotropic_2d_11_res = isotropic_2d_11.get_stencil(isotropic=True)
 iso_laplacian = isotropic_2d_00_res.as_array() + isotropic_2d_11_res.as_array()
 iso_laplacian
 ```
 
 %% Output
 
-
     $\displaystyle \left[\begin{matrix}\frac{1}{6} & \frac{2}{3} & \frac{1}{6}\\\frac{2}{3} & - \frac{10}{3} & \frac{2}{3}\\\frac{1}{6} & \frac{2}{3} & \frac{1}{6}\end{matrix}\right]$
-    ⎡1/6   2/3   1/6⎤
-    ⎢               ⎥
-    ⎢2/3  -10/3  2/3⎥
-    ⎢               ⎥
-    ⎣1/6   2/3   1/6⎦
+    [[1/6, 2/3, 1/6], [2/3, -10/3, 2/3], [1/6, 2/3, 1/6]]
 
 %% Cell type:code id: tags:
 
 ``` python
 expected_result = sp.Array([[1, 4, 1], [4, -20, 4], [1, 4, 1]]) / 6
 assert iso_laplacian == expected_result
 ```
 
 %% Cell type:markdown id: tags:
 
 # stencils for staggered fields
 
 %% Cell type:code id: tags:
 
 ``` python
 half = sp.Rational(1, 2)
 
 fd_points_ex = (
     (half, 0),
     (-half, 0),
     (half, 1),
     (half, -1),
     (-half, 1),
     (-half, -1)
 )
 assert set(fd_points_ex) == set(FiniteDifferenceStaggeredStencilDerivation("E", 2).stencil)
 
 fd_points_ey = (
     (0, half),
     (0, -half),
     (-1,-half),
     (-1, half),
     (1, -half),
     (1, half)
 )
 assert set(fd_points_ey) == set(FiniteDifferenceStaggeredStencilDerivation("N",2).stencil)
 
 fd_points_c = (
     (half, half),
     (-half, -half),
     (half, -half),
     (-half, half)
 )
 assert set(fd_points_c) ==  set(FiniteDifferenceStaggeredStencilDerivation("NE",2).stencil)
 
 assert len(FiniteDifferenceStaggeredStencilDerivation("E",3).points) == 10
 assert len(FiniteDifferenceStaggeredStencilDerivation("NE",3).points) == 12
 assert len(FiniteDifferenceStaggeredStencilDerivation("TNE",3).points) == 8
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 c = ps.fields("c: [2D]")
 c3 = ps.fields("c3: [3D]")
 
 assert FiniteDifferenceStaggeredStencilDerivation("E", 2, (0,)).apply(c.center) == c[1, 0] - c[0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("W", 2, (0,)).apply(c.center) == c[0, 0] - c[-1, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("N", 2, (1,)).apply(c.center) == c[0, 1] - c[0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("S", 2, (1,)).apply(c.center) == c[0, 0] - c[0, -1]
 
 assert FiniteDifferenceStaggeredStencilDerivation("E", 3, (0,)).apply(c3.center) == c3[1, 0, 0] - c3[0, 0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("W", 3, (0,)).apply(c3.center) == c3[0, 0, 0] - c3[-1, 0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("N", 3, (1,)).apply(c3.center) == c3[0, 1, 0] - c3[0, 0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("S", 3, (1,)).apply(c3.center) == c3[0, 0, 0] - c3[0, -1, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("T", 3, (2,)).apply(c3.center) == c3[0, 0, 1] - c3[0, 0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("B", 3, (2,)).apply(c3.center) == c3[0, 0, 0] - c3[0, 0, -1]
 
 assert FiniteDifferenceStaggeredStencilDerivation("S", 2, (0,)).apply(c.center) == \
        (c[1, 0] + c[1, -1] - c[-1, 0] - c[-1, -1])/4
 
 assert FiniteDifferenceStaggeredStencilDerivation("NE", 2, (0,)).apply(c.center) + \
        FiniteDifferenceStaggeredStencilDerivation("NE", 2, (1,)).apply(c.center) == c[1, 1] - c[0, 0]
 assert FiniteDifferenceStaggeredStencilDerivation("NE", 3, (0,)).apply(c3.center) + \
        FiniteDifferenceStaggeredStencilDerivation("NE", 3, (1,)).apply(c3.center) == c3[1, 1, 0] - c3[0, 0, 0]
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 d = FiniteDifferenceStaggeredStencilDerivation("NE", 2, (0, 1))
 assert d.apply(c.center) == c[0,0] + c[1,1] - c[1,0] - c[0,1]
 d.visualize()
 ```
 
 %% Output
 
-
+
 
 %% Cell type:code id: tags:
 
 ``` python
 v3 = ps.fields("v(3): [3D]")
 for i in range(*v3.index_shape):
     assert FiniteDifferenceStaggeredStencilDerivation("E", 3, (0,)).apply(v3.center_vector[i]) == \
            v3[1,0,0](i) - v3[0,0,0](i)
 ```

pystencils_tests/test_field.py → tests/test_field.py

@@ -3,35 +3,67 @@ import pytest
 import sympy as sp
 
 import pystencils as ps
-from pystencils.field import Field, FieldType, layout_string_to_tuple
+from pystencils import TypedSymbol
+from pystencils.typing import create_type
+from pystencils.field import Field, FieldType, layout_string_to_tuple, spatial_layout_string_to_tuple
 
 
 def test_field_basic():
-    f = Field.create_generic('f', spatial_dimensions=2)
+    f = Field.create_generic("f", spatial_dimensions=2)
     assert FieldType.is_generic(f)
-    assert f['E'] == f[1, 0]
-    assert f['N'] == f[0, 1]
-    assert '_' in f.center._latex('dummy')
-
-    f = Field.create_fixed_size('f', (10, 10), strides=(80, 8), dtype=np.float64)
+    assert f["E"] == f[1, 0]
+    assert f["N"] == f[0, 1]
+    assert "_" in f.center._latex("dummy")
+
+    assert (
+        f.index_to_physical(index_coordinates=sp.Matrix([0, 0]), staggered=False)[0]
+        == 0
+    )
+    assert (
+        f.index_to_physical(index_coordinates=sp.Matrix([0, 0]), staggered=False)[1]
+        == 0
+    )
+
+    assert (
+        f.physical_to_index(physical_coordinates=sp.Matrix([0, 0]), staggered=False)[0]
+        == 0
+    )
+    assert (
+        f.physical_to_index(physical_coordinates=sp.Matrix([0, 0]), staggered=False)[1]
+        == 0
+    )
+
+    f1 = f.new_field_with_different_name("f1")
+    assert f1.ndim == f.ndim
+    assert f1.values_per_cell() == f.values_per_cell()
+
+    fixed = ps.fields("f(5, 5) : double[20, 20]")
+    assert fixed.neighbor_vector((1, 1)).shape == (5, 5)
+
+    f = Field.create_fixed_size("f", (10, 10), strides=(80, 8), dtype=np.float64)
     assert f.spatial_strides == (10, 1)
     assert f.index_strides == ()
     assert f.center_vector == sp.Matrix([f.center])
 
-    f = Field.create_fixed_size('f', (8, 8, 2, 2), index_dimensions=2)
-    assert f.center_vector == sp.Matrix([[f(0, 0), f(0, 1)],
-                                         [f(1, 0), f(1, 1)]])
+    f1 = f.new_field_with_different_name("f1")
+    assert f1.ndim == f.ndim
+    assert f1.values_per_cell() == f.values_per_cell()
+
+    f = Field.create_fixed_size("f", (8, 8, 2, 2), index_dimensions=2)
+    assert f.center_vector == sp.Matrix([[f(0, 0), f(0, 1)], [f(1, 0), f(1, 1)]])
     field_access = f[1, 1]
     assert field_access.nr_of_coordinates == 2
-    assert field_access.offset_name == 'NE'
+    assert field_access.offset_name == "NE"
     neighbor = field_access.neighbor(coord_id=0, offset=-2)
     assert neighbor.offsets == (-1, 1)
-    assert '_' in neighbor._latex('dummy')
+    assert "_" in neighbor._latex("dummy")
 
-    f = Field.create_fixed_size('f', (8, 8, 2, 2, 2), index_dimensions=3)
-    assert f.center_vector == sp.Matrix([[[f(i, j, k) for k in range(2)] for j in range(2)] for i in range(2)])
+    f = Field.create_fixed_size("f", (8, 8, 2, 2, 2), index_dimensions=3)
+    assert f.center_vector == sp.Array(
+        [[[f(i, j, k) for k in range(2)] for j in range(2)] for i in range(2)]
+    )
 
-    f = Field.create_generic('f', spatial_dimensions=5, index_dimensions=2)
+    f = Field.create_generic("f", spatial_dimensions=5, index_dimensions=2)
     field_access = f[1, -1, 2, -3, 0](1, 0)
     assert field_access.offsets == (1, -1, 2, -3, 0)
     assert field_access.index == (1, 0)
@@ -41,61 +73,71 @@ def test_error_handling():
     struct_dtype = np.dtype([('a', np.int32), ('b', np.float64), ('c', np.uint32)])
     Field.create_generic('f', spatial_dimensions=2, index_dimensions=0, dtype=struct_dtype)
     with pytest.raises(ValueError) as e:
-        Field.create_generic('f', spatial_dimensions=2, index_dimensions=1, dtype=struct_dtype)
-    assert 'index dimension' in str(e.value)
+        Field.create_generic(
+            "f", spatial_dimensions=2, index_dimensions=1, dtype=struct_dtype
+        )
+    assert "index dimension" in str(e.value)
 
-    arr = np.array([[[(1,)*3, (2,)*3, (3,)*3]]*2], dtype=struct_dtype)
-    Field.create_from_numpy_array('f', arr, index_dimensions=0)
+    arr = np.array([[[(1,) * 3, (2,) * 3, (3,) * 3]] * 2], dtype=struct_dtype)
+    Field.create_from_numpy_array("f", arr, index_dimensions=0)
     with pytest.raises(ValueError) as e:
-        Field.create_from_numpy_array('f', arr, index_dimensions=1)
-    assert 'Structured arrays' in str(e.value)
+        Field.create_from_numpy_array("f", arr, index_dimensions=1)
+    assert "Structured arrays" in str(e.value)
 
     arr = np.zeros([3, 3, 3])
-    Field.create_from_numpy_array('f', arr, index_dimensions=2)
+    Field.create_from_numpy_array("f", arr, index_dimensions=2)
     with pytest.raises(ValueError) as e:
-        Field.create_from_numpy_array('f', arr, index_dimensions=3)
-    assert 'Too many' in str(e.value)
+        Field.create_from_numpy_array("f", arr, index_dimensions=3)
+    assert "Too many" in str(e.value)
 
-    Field.create_fixed_size('f', (3, 2, 4), index_dimensions=0, dtype=struct_dtype, layout='reverse_numpy')
+    Field.create_fixed_size(
+        "f", (3, 2, 4), index_dimensions=0, dtype=struct_dtype, layout="reverse_numpy"
+    )
     with pytest.raises(ValueError) as e:
-        Field.create_fixed_size('f', (3, 2, 4), index_dimensions=1, dtype=struct_dtype, layout='reverse_numpy')
-    assert 'Structured arrays' in str(e.value)
-
-    f = Field.create_fixed_size('f', (10, 10))
+        Field.create_fixed_size(
+            "f",
+            (3, 2, 4),
+            index_dimensions=1,
+            dtype=struct_dtype,
+            layout="reverse_numpy",
+        )
+    assert "Structured arrays" in str(e.value)
+
+    f = Field.create_fixed_size("f", (10, 10))
     with pytest.raises(ValueError) as e:
         f[1]
-    assert 'Wrong number of spatial indices' in str(e.value)
+    assert "Wrong number of spatial indices" in str(e.value)
 
-    f = Field.create_generic('f', spatial_dimensions=2, index_shape=(3,))
+    f = Field.create_generic("f", spatial_dimensions=2, index_shape=(3,))
     with pytest.raises(ValueError) as e:
         f(3)
-    assert 'out of bounds' in str(e.value)
+    assert "out of bounds" in str(e.value)
 
-    f = Field.create_fixed_size('f', (10, 10, 3, 4), index_dimensions=2)
+    f = Field.create_fixed_size("f", (10, 10, 3, 4), index_dimensions=2)
     with pytest.raises(ValueError) as e:
         f(3, 0)
-    assert 'out of bounds' in str(e.value)
+    assert "out of bounds" in str(e.value)
 
     with pytest.raises(ValueError) as e:
         f(1, 0)(1, 0)
-    assert 'Indexing an already indexed' in str(e.value)
+    assert "Indexing an already indexed" in str(e.value)
 
     with pytest.raises(ValueError) as e:
         f(1)
-    assert 'Wrong number of indices' in str(e.value)
+    assert "Wrong number of indices" in str(e.value)
 
     with pytest.raises(ValueError) as e:
-        Field.create_generic('f', spatial_dimensions=2, layout='wrong')
-    assert 'Unknown layout descriptor' in str(e.value)
+        Field.create_generic("f", spatial_dimensions=2, layout="wrong")
+    assert "Unknown layout descriptor" in str(e.value)
 
-    assert layout_string_to_tuple('fzyx', dim=4) == (3, 2, 1, 0)
+    assert layout_string_to_tuple("fzyx", dim=4) == (3, 2, 1, 0)
     with pytest.raises(ValueError) as e:
-        layout_string_to_tuple('wrong', dim=4)
-    assert 'Unknown layout descriptor' in str(e.value)
+        layout_string_to_tuple("wrong", dim=4)
+    assert "Unknown layout descriptor" in str(e.value)
 
 
 def test_decorator_scoping():
-    dst = ps.fields('dst : double[2D]')
+    dst = ps.fields("dst : double[2D]")
 
     def f1():
         a = sp.Symbol("a")
@@ -115,7 +157,7 @@ def test_decorator_scoping():
 
 
 def test_string_creation():
-    x, y, z = ps.fields('  x(4),    y(3,5) z : double[  3,  47]')
+    x, y, z = ps.fields("  x(4),    y(3,5) z : double[  3,  47]")
     assert x.index_shape == (4,)
     assert y.index_shape == (3, 5)
     assert z.spatial_shape == (3, 47)
@@ -123,51 +165,140 @@ def test_string_creation():
 
 def test_itemsize():
 
-    x = ps.fields('x: float32[1d]')
-    y = ps.fields('y:  float64[2d]')
-    i = ps.fields('i:  int16[1d]')
+    x = ps.fields("x: float32[1d]")
+    y = ps.fields("y:  float64[2d]")
+    i = ps.fields("i:  int16[1d]")
 
     assert x.itemsize == 4
     assert y.itemsize == 8
     assert i.itemsize == 2
 
 
+def test_spatial_memory_layout_descriptors():
+    assert (
+        spatial_layout_string_to_tuple("AoS", 3)
+        == spatial_layout_string_to_tuple("aos", 3)
+        == spatial_layout_string_to_tuple("ZYXF", 3)
+        == spatial_layout_string_to_tuple("zyxf", 3)
+        == (2, 1, 0)
+    )
+    assert (
+        spatial_layout_string_to_tuple("SoA", 3)
+        == spatial_layout_string_to_tuple("soa", 3)
+        == spatial_layout_string_to_tuple("FZYX", 3)
+        == spatial_layout_string_to_tuple("fzyx", 3)
+        == spatial_layout_string_to_tuple("f", 3)
+        == spatial_layout_string_to_tuple("F", 3)
+        == (2, 1, 0)
+    )
+    assert (
+        spatial_layout_string_to_tuple("c", 3)
+        == spatial_layout_string_to_tuple("C", 3)
+        == (0, 1, 2)
+    )
+
+    assert spatial_layout_string_to_tuple("C", 5) == (0, 1, 2, 3, 4)
+
+    with pytest.raises(ValueError):
+        spatial_layout_string_to_tuple("aos", -1)
+
+    with pytest.raises(ValueError):
+        spatial_layout_string_to_tuple("aos", 4)
+
+
+def test_memory_layout_descriptors():
+    assert (
+        layout_string_to_tuple("AoS", 4)
+        == layout_string_to_tuple("aos", 4)
+        == layout_string_to_tuple("ZYXF", 4)
+        == layout_string_to_tuple("zyxf", 4)
+        == (2, 1, 0, 3)
+    )
+    assert (
+        layout_string_to_tuple("SoA", 4)
+        == layout_string_to_tuple("soa", 4)
+        == layout_string_to_tuple("FZYX", 4)
+        == layout_string_to_tuple("fzyx", 4)
+        == layout_string_to_tuple("f", 4)
+        == layout_string_to_tuple("F", 4)
+        == (3, 2, 1, 0)
+    )
+    assert (
+        layout_string_to_tuple("c", 4)
+        == layout_string_to_tuple("C", 4)
+        == (0, 1, 2, 3)
+    )
+
+    assert layout_string_to_tuple("C", 5) == (0, 1, 2, 3, 4)
+
+    with pytest.raises(ValueError):
+        layout_string_to_tuple("aos", -1)
+
+    with pytest.raises(ValueError):
+        layout_string_to_tuple("aos", 5)
+
+
 def test_staggered():
 
     # D2Q5
-    j1, j2, j3 = ps.fields('j1(2), j2(2,2), j3(2,2,2) : double[2D]', field_type=FieldType.STAGGERED)
+    j1, j2, j3 = ps.fields(
+        "j1(2), j2(2,2), j3(2,2,2) : double[2D]", field_type=FieldType.STAGGERED
+    )
 
     assert j1[0, 1](1) == j1.staggered_access((0, sp.Rational(1, 2)))
+    assert j1[0, 1](1) == j1.staggered_access(np.array((0, sp.Rational(1, 2))))
     assert j1[1, 1](1) == j1.staggered_access((1, sp.Rational(1, 2)))
     assert j1[0, 2](1) == j1.staggered_access((0, sp.Rational(3, 2)))
     assert j1[0, 1](1) == j1.staggered_access("N")
     assert j1[0, 0](1) == j1.staggered_access("S")
     assert j1.staggered_vector_access("N") == sp.Matrix([j1.staggered_access("N")])
+    assert j1.staggered_stencil_name == "D2Q5"
+
+    assert j1.physical_coordinates[0] == TypedSymbol("ctr_0", create_type("int"), nonnegative=True)
+    assert j1.physical_coordinates[1] == TypedSymbol("ctr_1", create_type("int"), nonnegative=True)
+    assert j1.physical_coordinates_staggered[0] == TypedSymbol("ctr_0", create_type("int"), nonnegative=True) + 0.5
+    assert j1.physical_coordinates_staggered[1] == TypedSymbol("ctr_1", create_type("int"), nonnegative=True) + 0.5
+    assert j1.index_to_physical(index_coordinates=sp.Matrix([0, 0]), staggered=True)[0] == 0.5
+    assert j1.index_to_physical(index_coordinates=sp.Matrix([0, 0]), staggered=True)[1] == 0.5
+    assert j1.physical_to_index(physical_coordinates=sp.Matrix([0, 0]), staggered=True)[0] == -0.5
+    assert j1.physical_to_index(physical_coordinates=sp.Matrix([0, 0]), staggered=True)[1] == -0.5
 
     assert j2[0, 1](1, 1) == j2.staggered_access((0, sp.Rational(1, 2)), 1)
     assert j2[0, 1](1, 1) == j2.staggered_access("N", 1)
-    assert j2.staggered_vector_access("N") == sp.Matrix([j2.staggered_access("N", 0), j2.staggered_access("N", 1)])
+    assert j2.staggered_vector_access("N") == sp.Matrix(
+        [j2.staggered_access("N", 0), j2.staggered_access("N", 1)]
+    )
 
     assert j3[0, 1](1, 1, 1) == j3.staggered_access((0, sp.Rational(1, 2)), (1, 1))
     assert j3[0, 1](1, 1, 1) == j3.staggered_access("N", (1, 1))
-    assert j3.staggered_vector_access("N") == sp.Matrix([[j3.staggered_access("N", (i, j))
-                                                        for j in range(2)] for i in range(2)])
+    assert j3.staggered_vector_access("N") == sp.Matrix(
+        [[j3.staggered_access("N", (i, j)) for j in range(2)] for i in range(2)]
+    )
 
     # D2Q9
-    k1, k2 = ps.fields('k1(4), k2(2) : double[2D]', field_type=FieldType.STAGGERED)
+    k1, k2 = ps.fields("k1(4), k2(2) : double[2D]", field_type=FieldType.STAGGERED)
 
     assert k1[1, 1](2) == k1.staggered_access("NE")
     assert k1[0, 0](2) == k1.staggered_access("SW")
     assert k1[0, 0](3) == k1.staggered_access("NW")
-    
+
     a = k1.staggered_access("NE")
-    assert a._staggered_offset(a.offsets, a.index[0]) == [sp.Rational(1, 2), sp.Rational(1, 2)]
+    assert a._staggered_offset(a.offsets, a.index[0]) == [
+        sp.Rational(1, 2),
+        sp.Rational(1, 2),
+    ]
     a = k1.staggered_access("SW")
-    assert a._staggered_offset(a.offsets, a.index[0]) == [sp.Rational(-1, 2), sp.Rational(-1, 2)]
+    assert a._staggered_offset(a.offsets, a.index[0]) == [
+        sp.Rational(-1, 2),
+        sp.Rational(-1, 2),
+    ]
     a = k1.staggered_access("NW")
-    assert a._staggered_offset(a.offsets, a.index[0]) == [sp.Rational(-1, 2), sp.Rational(1, 2)]
+    assert a._staggered_offset(a.offsets, a.index[0]) == [
+        sp.Rational(-1, 2),
+        sp.Rational(1, 2),
+    ]
 
     # sign reversed when using as flux field
-    r = ps.fields('r(2) : double[2D]', field_type=FieldType.STAGGERED_FLUX)
+    r = ps.fields("r(2) : double[2D]", field_type=FieldType.STAGGERED_FLUX)
     assert r[0, 0](0) == r.staggered_access("W")
     assert -r[1, 0](0) == r.staggered_access("E")

pystencils_tests/test_field_access_poly.py → tests/test_field_access_poly.py

@@ -7,7 +7,7 @@
 
 """
 
-
+import pytest
 from pystencils.session import *
 
 from sympy import poly
@@ -22,8 +22,14 @@ def test_field_access_poly():
 
 
 def test_field_access_piecewise():
-    dh = ps.create_data_handling((20, 20))
-    ρ = dh.add_array('rho')
-    pw = sp.Piecewise((0, 1 < sp.Max(-0.5, ρ.center+0.5)), (1, True))
-    a = sp.simplify(pw)
-    print(a)
+    try:
+        a = sp.Piecewise((0, 1 < sp.Max(-0.5, sp.Symbol("test") + 0.5)), (1, True))
+        a.simplify()
+    except Exception as e:
+        pytest.skip(f"Bug in SymPy 1.10: {e}")
+    else:
+        dh = ps.create_data_handling((20, 20))
+        ρ = dh.add_array('rho')
+        pw = sp.Piecewise((0, 1 < sp.Max(-0.5, ρ.center+0.5)), (1, True))
+        a = sp.simplify(pw)
+        print(a)

pystencils_tests/test_field_equality.ipynb → tests/test_field_equality.ipynb

 %% Cell type:code id: tags:
 
 ``` python
 from pystencils.session import *
-from pystencils.data_types import cast_func
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Test field equality behaviour
 
 %% Cell type:markdown id: tags:
 
 Fields create with same parameters are equal
 
 %% Cell type:code id: tags:
 
 ``` python
 f1 = ps.Field.create_generic('f', spatial_dimensions=2, index_dimensions=0)
 f2 = ps.Field.create_generic('f', spatial_dimensions=2, index_dimensions=0)
 
 assert f1 == f2
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 print("Field ids equal in accesses: ", id(f1.center._field) == id(f2.center._field))
 print("Field accesses equal: ", f1.center == f2.center)
 ```
 
 %% Output
 
     Field ids equal in accesses:  True
     Field accesses equal:  True
 
 %% Cell type:code id: tags:
 
 ``` python
 f1 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0)
 f2 = ps.Field.create_generic('f', spatial_dimensions=2, index_dimensions=0)
 assert f1 != f2
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 f1 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0)
 f2 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0, dtype=np.float32)
 assert f1 != f2
 ```
 
 %% Cell type:markdown id: tags:
 
 Properties of fields:
 - `field_type`: enum distinguishing normal from index or buffer fields
 - `_dtype`: data type of field elements
 - `_layout`: tuple indicating the memory linearization order
 - `shape`: size of field for each dimension
 - `strides`: number of elements to jump over to increase coordinate of this dimension by one
 - `latex_name`: optional display name when field is printed as latex
 
 Equality compare of fields:
 - field has `__eq__` and ``__hash__`` overridden
 - all parameter but `latex_name` are considered for equality
 
 %% Cell type:markdown id: tags:
 
 ## Test field access equality behaviour
 
 %% Cell type:code id: tags:
 
 ``` python
 f1 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0)
 f2 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0)
 assert f1.center == f2.center
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 f1 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0)
 f2 = ps.Field.create_generic('f', spatial_dimensions=1, index_dimensions=0, dtype=np.float32)
 assert f1.center != f2.center
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 def print_field_accesses_debug(expr):
     from pystencils import Field
     fas = list(expr.atoms(Field.Access))
     fields = list({e.field for e in fas})
     print("Field Accesses:")
     for fa in fas:
         print(f"   - {fa}, hash {hash(fa)}, offsets {fa._offsets}, index {fa._index}, {fa._hashable_content()}")
     print("")
     for i in range(len(fas)):
         for j in range(len(fas)):
             if not i < j:
                 continue
             print( f"   -> {i},{j}  {fas[i]} == {fas[j]}: {fas[i] == {fas[j]}}")
 
     print("Fields")
     for f in fields:
         print(f"  - {f}, {id(f)}, shape {f.shape}, strides {f.strides}, {f._dtype}, {f.field_type}, layout {f.layout}")
     print("")
     for i in range(len(fields)):
         for j in range(len(fields)):
             if not i < j:
                 continue
             print(f"  - {fields[i]} == {fields[j]}: {fields[i] == fields[j]}, ids equal {id(fields[i])==id(fields[j])}, hash equal {hash(fields[i])==hash(fields[j])}")
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 print_field_accesses_debug(f1.center * f2.center)
 ```
 
 %% Output
 
     Field Accesses:
-       - f[0], hash -3276894289571194847, offsets (0,), index (), (('f_C', ('commutative', True)), ((0,), (_size_f_0,), (_stride_f_0,), 3146377891102027609, <FieldType.GENERIC: 0>, 'f', None), 0)
-       - f[0], hash -1516451775709390846, offsets (0,), index (), (('f_C', ('commutative', True)), ((0,), (_size_f_0,), (_stride_f_0,), -1421177580377734245, <FieldType.GENERIC: 0>, 'f', None), 0)
+       - f[0], hash -8859424145258271267, offsets (0,), index (), ((('f_C', ('commutative', True), ('complex', True), ('extended_real', True), ('finite', True), ('hermitian', True), ('imaginary', False), ('infinite', False), ('real', True)), 2305067722319023373), ((0,), (_size_f_0,), (_stride_f_0,), <FieldType.GENERIC: 0>, 'f', None, double), 0)
+       - f[0], hash -6454673863007224785, offsets (0,), index (), ((('f_C', ('commutative', True), ('complex', True), ('extended_real', True), ('finite', True), ('hermitian', True), ('imaginary', False), ('infinite', False), ('real', True)), 4093629613697528859), ((0,), (_size_f_0,), (_stride_f_0,), <FieldType.GENERIC: 0>, 'f', None, float), 0)
     
        -> 0,1  f[0] == f[0]: False
     Fields
-      - f, 140548694371968, shape (_size_f_0,), strides (_stride_f_0,), double, FieldType.GENERIC, layout (0,)
-      - f, 140548693963104, shape (_size_f_0,), strides (_stride_f_0,), float, FieldType.GENERIC, layout (0,)
+      - f, 4881406800, shape (_size_f_0,), strides (_stride_f_0,), double, FieldType.GENERIC, layout (0,)
+      - f, 4881445024, shape (_size_f_0,), strides (_stride_f_0,), float, FieldType.GENERIC, layout (0,)
     
       - f == f: False, ids equal False, hash equal False

pystencils_tests/test_finite_differences.py → tests/test_finite_differences.py

@@ -4,7 +4,8 @@ import pytest
 import pystencils as ps
 from pystencils.astnodes import LoopOverCoordinate
 from pystencils.fd import diff, diffusion, Discretization2ndOrder
-from pystencils.fd.spatial import discretize_spatial, fd_stencils_isotropic, fd_stencils_standard
+from pystencils.fd.spatial import discretize_spatial, fd_stencils_isotropic, fd_stencils_standard, \
+    fd_stencils_forth_order_isotropic
 
 
 def test_spatial_2d_unit_sum():
@@ -18,7 +19,7 @@ def test_spatial_2d_unit_sum():
              diff(f, 1, 1),
              diff(f, 0, 0) + diff(f, 1, 1)]
 
-    schemes = [fd_stencils_standard, fd_stencils_isotropic]
+    schemes = [fd_stencils_standard, fd_stencils_isotropic, 'standard', 'isotropic']
 
     for term in terms:
         for scheme in schemes:
@@ -34,7 +35,7 @@ def test_spatial_1d_unit_sum():
     terms = [diff(f, 0),
              diff(f, 0, 0)]
 
-    schemes = [fd_stencils_standard, fd_stencils_isotropic]
+    schemes = [fd_stencils_standard, fd_stencils_isotropic, 'standard', 'isotropic']
 
     for term in terms:
         for scheme in schemes:
@@ -43,6 +44,17 @@ def test_spatial_1d_unit_sum():
             assert sum(coefficients) == 0
 
 
+def test_fd_stencils_forth_order_isotropic():
+    f = ps.fields("f: double[2D]")
+    a = fd_stencils_forth_order_isotropic([0], 1, f[0, 0](0))
+    sten, coefficients = ps.stencil.coefficients(a)
+    assert sum(coefficients) == 0
+
+    for i, direction in enumerate(sten):
+        counterpart = sten.index((direction[0] * -1, direction[1] * -1))
+        assert coefficients[i] + coefficients[counterpart] == 0
+
+
 def test_staggered_laplacian():
     f = ps.fields("f : double[2D]")
     a, dx = sp.symbols("a, dx")