class Field(field_name, field_type, dtype, layout, shape, strides)

With fields one can formulate stencil-like update rules on structured grids. This Field class knows about the dimension, memory layout (strides) and optionally about the size of an array.

Creating Fields:

The preferred method to create fields is the fields function. Alternatively one can use one of the static functions Field.create_generic, Field.create_from_numpy_array and Field.create_fixed_size. Don’t instantiate the Field directly! Fields can be created with known or unknown shapes:

  1. If you want to create a kernel with fixed loop sizes i.e. the shape of the array is already known. This is usually the case if just-in-time compilation directly from Python is done. (see Field.create_from_numpy_array

  2. create a more general kernel that works for variable array sizes. This can be used to create kernels beforehand for a library. (see Field.create_generic)

Dimensions and Indexing:

A field has spatial and index dimensions, where the spatial dimensions come first. The interpretation is that the field has multiple cells in (usually) two or three dimensional space which are looped over. Additionally N values are stored per cell. In this case spatial_dimensions is two or three, and index_dimensions equals N. If you want to store a matrix on each point in a two dimensional grid, there are four dimensions, two spatial and two index dimensions: len(arr.shape) == spatial_dims + index_dims

The shape of the index dimension does not have to be specified. Just use the ‘index_dimensions’ parameter. However, it is good practice to define the shape, since out of bounds accesses can be directly detected in this case. The shape can be passed with the ‘index_shape’ parameter of the field creation functions.

When accessing (indexing) a field the result is a Field.Access which is derived from sympy Symbol. First specify the spatial offsets in [], then in case index_dimension>0 the indices in () e.g. f[-1,0,0](7)

Staggered Fields:

Staggered fields are used to store a value on a second grid shifted by half a cell with respect to the usual grid.

The first index dimension is used to specify the position on the staggered grid (e.g. 0 means half-way to the eastern neighbor, 1 is half-way to the northern neighbor, etc.), while additional indices can be used to store multiple values at each position.

Example using no index dimensions:
>>> a = np.zeros([10, 10])
>>> f = Field.create_from_numpy_array("f", a, index_dimensions=0)
>>> jacobi = (f[-1,0] + f[1,0] + f[0,-1] + f[0,1]) / 4
Examples for index dimensions to create LB field and implement stream pull:
>>> from pystencils import Assignment
>>> stencil = np.array([[0,0], [0,1], [0,-1]])
>>> src, dst = fields("src(3), dst(3) : double[2D]")
>>> assignments = [Assignment(dst[0,0](i), src[-offset](i)) for i, offset in enumerate(stencil)];
static create_generic(field_name, spatial_dimensions, dtype=<class 'numpy.float64'>, index_dimensions=0, layout='numpy', index_shape=None, field_type=<FieldType.GENERIC: 0>)

Creates a generic field where the field size is not fixed i.e. can be called with arrays of different sizes

  • field_name – symbolic name for the field

  • dtype – numpy data type of the array the kernel is called with later

  • spatial_dimensions – see documentation of Field

  • index_dimensions – see documentation of Field

  • layout – tuple specifying the loop ordering of the spatial dimensions e.g. (2, 1, 0 ) means that the outer loop loops over dimension 2, the second outer over dimension 1, and the inner loop over dimension 0. Also allowed: the strings ‘numpy’ (0,1,..d) or ‘reverse_numpy’ (d, …, 1, 0)

  • index_shape – optional shape of the index dimensions i.e. maximum values allowed for each index dimension, has to be a list or tuple

  • field_type – besides the normal GENERIC fields, there are INDEXED fields that store indices of the domain that should be iterated over, BUFFER fields that are used to generate communication packing/unpacking kernels, and STAGGERED fields, which store values half-way to the next cell

Return type


static create_from_numpy_array(field_name, array, index_dimensions=0, field_type=<FieldType.GENERIC: 0>)

Creates a field based on the layout, data type, and shape of a given numpy array.

Kernels created for these kind of fields can only be called with arrays of the same layout, shape and type.

  • field_name (str) – symbolic name for the field

  • array (ndarray) – numpy array

  • index_dimensions (int) – see documentation of Field

  • field_type – kind of field

Return type


static create_fixed_size(field_name, shape, index_dimensions=0, dtype=<class 'numpy.float64'>, layout='numpy', strides=None, field_type=<FieldType.GENERIC: 0>)

Creates a field with fixed sizes i.e. can be called only with arrays of the same size and layout

  • field_name (str) – symbolic name for the field

  • shape (Tuple[int, …]) – overall shape of the array

  • index_dimensions (int) – how many of the trailing dimensions are interpreted as index (as opposed to spatial)

  • dtype – numpy data type of the array the kernel is called with later

  • layout (str) – full layout of array, not only spatial dimensions

  • strides (Optional[Sequence[int]]) – strides in bytes or None to automatically compute them from shape (assuming no padding)

  • field_type – kind of field

Return type



Like neighbor, but returns the entire vector/tensor stored at offset.

interpolated_access(offset, interpolation_mode='linear', address_mode='BORDER', allow_textures=True)

Provides access to field values at non-integer positions

interpolated_access is similar to Field.absolute_access() except that it allows non-integer offsets and automatic handling of out-of-bound accesses.

  • offset (Tuple) – Tuple of spatial coordinates (can be floats)

  • interpolation_mode – One of pystencils.interpolation_astnodes.InterpolationMode

  • address_mode – How boundaries are handled can be ‘border’, ‘wrap’, ‘mirror’, ‘clamp’

  • allow_textures – Allow implementation by texture accesses on GPUs

staggered_access(offset, index=None)

If this field is a staggered field, it can be accessed using half-integer offsets. For example, an offset of (0, sp.Rational(1,2)) or "E" corresponds to the staggered point to the east of the cell center, i.e. half-way to the eastern-next cell. If the field stores more than one value per staggered point (e.g. a vector or a tensor), the index (integer or tuple of integers) refers to which of these values to access.


Like staggered_access, but returns the entire vector/tensor stored at offset.

class Access(name, *args, **kwargs)

Class representing a relative access into a Field.

This class behaves like a normal sympy Symbol, it is actually derived from it. One can built up sympy expressions using field accesses, solve for them, etc.


>>> vector_field_2d = fields("v(2): double[2D]")  # create a 2D vector field
>>> northern_neighbor_y_component = vector_field_2d[0, 1](1)
>>> northern_neighbor_y_component
>>> central_y_component = vector_field_2d(1)
>>> central_y_component
>>> central_y_component.get_shifted(1, 0)  # move the existing access
>>> central_y_component.at_index(0)  # change component
property field

Field that the Access points to

Return type


property offsets

Spatial offset as tuple

Return type


property required_ghost_layers

Largest spatial distance that is accessed.

Return type


property nr_of_coordinates
property offset_name

Spatial offset as string, East-West for x, North-South for y and Top-Bottom for z coordinate.


>>> f = fields("f: double[2D]")
>>> f[1, 1].offset_name  # north-east
Return type


property index

Value of index coordinates as tuple.

neighbor(coord_id, offset)

Returns a new Access with changed spatial coordinates.

  • coord_id (int) – index of the coordinate to change (0 for x, 1 for y,…)

  • offset (int) – incremental change of this coordinate


>>> f = fields('f: [2D]')
>>> f[0,0].neighbor(coord_id=1, offset=-1)
Return type



Returns a new Access with changed spatial coordinates


>>> f = fields("f: [2D]")
>>> f[0,0].get_shifted(1, 1)
Return type



Returns new Access with changed index.


>>> f = fields("f(9): [2D]")
>>> f(0).at_index(8)
Return type


property is_absolute_access

Indicates if a field access is relative to the loop counters (this is the default) or absolute

Return type


property indirect_addressing_fields

Returns a set of fields that the access depends on.

e.g. f[index_field[1, 0]], the outer access to f depends on index_field

Return type


fields(description=None, index_dimensions=0, layout=None, field_type=<FieldType.GENERIC: 0>, **kwargs)

Creates pystencils fields from a string description.


Create a 2D scalar and vector field:
>>> s, v = fields("s, v(2): double[2D]")
>>> assert s.spatial_dimensions == 2 and s.index_dimensions == 0
>>> assert (v.spatial_dimensions, v.index_dimensions, v.index_shape) == (2, 1, (2,))
Create an integer field of shape (10, 20):
>>> f = fields("f : int32[10, 20]")
>>> f.has_fixed_shape, f.shape
(True, (10, 20))
Numpy arrays can be used as template for shape and data type of field:
>>> arr_s, arr_v = np.zeros([20, 20]), np.zeros([20, 20, 2])
>>> s, v = fields("s, v(2)", s=arr_s, v=arr_v)
>>> assert s.index_dimensions == 0 and s.dtype.numpy_dtype == arr_s.dtype
>>> assert v.index_shape == (2,)
Format string can be left out, field names are taken from keyword arguments.
>>> fields(f1=arr_s, f2=arr_s)
[f1: double[20,20], f2: double[20,20]]
The keyword names index_dimension and layout have special meaning, don’t use them for field names
>>> f = fields(f=arr_v, index_dimensions=1)
>>> assert f.index_dimensions == 1
>>> f = fields("pdfs(19) : float32[3D]", layout='fzyx')
>>> f.layout
(2, 1, 0)
class FieldType(value)

An enumeration.