field.py 19.6 KB
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from itertools import chain
import numpy as np
import sympy as sp
from sympy.core.cache import cacheit
from sympy.tensor import IndexedBase
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from pystencils.types import TypedSymbol, createType
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class Field(object):
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    """
    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.

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    Creating Fields:

        To create a field use one of the static create* members. There are two options:

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        1. create a kernel with fixed loop sizes i.e. the shape of the array is already known. This is usually the
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           case if just-in-time compilation directly from Python is done. (see :func:`Field.createFromNumpyArray`)
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        2. create a more general kernel that works for variable array sizes. This can be used to create kernels
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           beforehand for a library. (see :func:`Field.createGeneric`)
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    Dimensions:
        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 spatialDimensions is two or three,
        and indexDimensions equals N. If you want to store a matrix on each point in a two dimensional grid, there
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        are four dimensions, two spatial and two index dimensions: ``len(arr.shape) == spatialDims + indexDims``
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    Indexing:
        When accessing (indexing) a field the result is a FieldAccess which is derived from sympy Symbol.
        First specify the spatial offsets in [], then in case indexDimension>0 the indices in ()
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        e.g. ``f[-1,0,0](7)``
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    Example without index dimensions:
        >>> a = np.zeros([10, 10])
        >>> f = Field.createFromNumpyArray("f", a, indexDimensions=0)
        >>> jacobi = ( f[-1,0] + f[1,0] + f[0,-1] + f[0,1] ) / 4

    Example with index dimensions: LBM D2Q9 stream pull
        >>> stencil = np.array([[0,0], [0,1], [0,-1]])
        >>> src = Field.createGeneric("src", spatialDimensions=2, indexDimensions=1)
        >>> dst = Field.createGeneric("dst", spatialDimensions=2, indexDimensions=1)
        >>> for i, offset in enumerate(stencil):
        ...     sp.Eq(dst[0,0](i), src[-offset](i))
        Eq(dst_C^0, src_C^0)
        Eq(dst_C^1, src_S^1)
        Eq(dst_C^2, src_N^2)
    """
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    @staticmethod
    def createGeneric(fieldName, spatialDimensions, dtype=np.float64, indexDimensions=0, layout='numpy'):
        """
        Creates a generic field where the field size is not fixed i.e. can be called with arrays of different sizes

        :param fieldName: symbolic name for the field
        :param dtype: numpy data type of the array the kernel is called with later
        :param spatialDimensions: see documentation of Field
        :param indexDimensions: see documentation of Field
        :param 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 'reverseNumpy' (d, ..., 1, 0)
        """
        if isinstance(layout, str) and (layout == 'numpy' or layout.lower() == 'c'):
            layout = tuple(range(spatialDimensions))
        elif isinstance(layout, str) and (layout == 'reverseNumpy' or layout.lower() == 'f'):
            layout = tuple(reversed(range(spatialDimensions)))
        if len(layout) != spatialDimensions:
            raise ValueError("Layout")
        shapeSymbol = IndexedBase(TypedSymbol(Field.SHAPE_PREFIX + fieldName, Field.SHAPE_DTYPE), shape=(1,))
        strideSymbol = IndexedBase(TypedSymbol(Field.STRIDE_PREFIX + fieldName, Field.STRIDE_DTYPE), shape=(1,))
        totalDimensions = spatialDimensions + indexDimensions
        shape = tuple([shapeSymbol[i] for i in range(totalDimensions)])
        strides = tuple([strideSymbol[i] for i in range(totalDimensions)])
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        npDataType = np.dtype(dtype)
        if npDataType.fields is not None:
            if indexDimensions != 0:
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

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        return Field(fieldName, dtype, layout, shape, strides)

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    @staticmethod
    def createFromNumpyArray(fieldName, npArray, indexDimensions=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.
        :param fieldName: symbolic name for the field
        :param npArray: numpy array
        :param indexDimensions: see documentation of Field
        """
        spatialDimensions = len(npArray.shape) - indexDimensions
        if spatialDimensions < 1:
            raise ValueError("Too many index dimensions. At least one spatial dimension required")

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        fullLayout = getLayoutOfArray(npArray)
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        spatialLayout = tuple([i for i in fullLayout if i < spatialDimensions])
        assert len(spatialLayout) == spatialDimensions

        strides = tuple([s // np.dtype(npArray.dtype).itemsize for s in npArray.strides])
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        shape = tuple(int(s) for s in npArray.shape)
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        npDataType = np.dtype(npArray.dtype)
        if npDataType.fields is not None:
            if indexDimensions != 0:
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

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        return Field(fieldName, npArray.dtype, spatialLayout, shape, strides)

    @staticmethod
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    def createFixedSize(fieldName, shape, indexDimensions=0, dtype=np.float64, layout='numpy'):
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        """
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        Creates a field with fixed sizes i.e. can be called only wity arrays of the same size and layout
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        :param fieldName: symbolic name for the field
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        :param shape: overall shape of the array
        :param indexDimensions: how many of the trailing dimensions are interpreted as index (as opposed to spatial)
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        :param dtype: numpy data type of the array the kernel is called with later
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        :param layout: see createGeneric
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        """
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        spatialDimensions = len(shape) - indexDimensions
        assert spatialDimensions >= 1

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        if isinstance(layout, str) and (layout == 'numpy' or layout.lower() == 'c'):
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            layout = tuple(range(spatialDimensions))
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        elif isinstance(layout, str) and (layout == 'reverseNumpy' or layout.lower() == 'f'):
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            layout = tuple(reversed(range(spatialDimensions)))
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        shape = tuple(int(s) for s in shape)
        strides = computeStrides(shape, layout)
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        npDataType = np.dtype(dtype)
        if npDataType.fields is not None:
            if indexDimensions != 0:
                raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
            shape += (1,)
            strides += (1,)

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        return Field(fieldName, dtype, layout[:spatialDimensions], shape, strides)
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    def __init__(self, fieldName, dtype, layout, shape, strides):
        """Do not use directly. Use static create* methods"""
        self._fieldName = fieldName
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        self._dtype = createType(dtype)
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        self._layout = normalizeLayout(layout)
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        self.shape = shape
        self.strides = strides
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        # index fields are currently only used for boundary handling
        # the coordinates are not the loop counters in that case, but are read from this index field
        self.isIndexField = False
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    @property
    def spatialDimensions(self):
        return len(self._layout)

    @property
    def indexDimensions(self):
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        return len(self.shape) - len(self._layout)
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    @property
    def layout(self):
        return self._layout

    @property
    def name(self):
        return self._fieldName

    @property
    def spatialShape(self):
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        return self.shape[:self.spatialDimensions]
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    @property
    def hasFixedShape(self):
        try:
            [int(i) for i in self.shape]
            return True
        except TypeError:
            return False

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    @property
    def indexShape(self):
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        return self.shape[self.spatialDimensions:]
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    @property
    def spatialStrides(self):
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        return self.strides[:self.spatialDimensions]
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    @property
    def indexStrides(self):
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        return self.strides[self.spatialDimensions:]
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    @property
    def dtype(self):
        return self._dtype

    def __repr__(self):
        return self._fieldName

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    def neighbor(self, coordId, offset):
        offsetList = [0] * self.spatialDimensions
        offsetList[coordId] = offset
        return Field.Access(self, tuple(offsetList))

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    def __getitem__(self, offset):
        if type(offset) is np.ndarray:
            offset = tuple(offset)
        if type(offset) is str:
            offset = tuple(directionStringToOffset(offset, self.spatialDimensions))
        if type(offset) is not tuple:
            offset = (offset,)
        if len(offset) != self.spatialDimensions:
            raise ValueError("Wrong number of spatial indices: "
                             "Got %d, expected %d" % (len(offset), self.spatialDimensions))
        return Field.Access(self, offset)

    def __call__(self, *args, **kwargs):
        center = tuple([0]*self.spatialDimensions)
        return Field.Access(self, center)(*args, **kwargs)

    def __hash__(self):
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        return hash((self._layout, self.shape, self.strides, self._dtype, self._fieldName))
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    def __eq__(self, other):
        selfTuple = (self.shape, self.strides, self.name, self.dtype)
        otherTuple = (other.shape, other.strides, other.name, other.dtype)
        return selfTuple == otherTuple

    PREFIX = "f"
    STRIDE_PREFIX = PREFIX + "stride_"
    SHAPE_PREFIX = PREFIX + "shape_"
    STRIDE_DTYPE = "const int *"
    SHAPE_DTYPE = "const int *"
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    DATA_PREFIX = PREFIX + "d_"
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    class Access(sp.Symbol):
        def __new__(cls, name, *args, **kwargs):
            obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
            return obj

        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None):
            fieldName = field.name
            offsetsAndIndex = chain(offsets, idx) if idx is not None else offsets
            constantOffsets = not any([isinstance(o, sp.Basic) for o in offsetsAndIndex])

            if not idx:
                idx = tuple([0] * field.indexDimensions)

            if constantOffsets:
                offsetName = offsetToDirectionString(offsets)

                if field.indexDimensions == 0:
                    obj = super(Field.Access, self).__xnew__(self, fieldName + "_" + offsetName)
                elif field.indexDimensions == 1:
                    obj = super(Field.Access, self).__xnew__(self, fieldName + "_" + offsetName + "^" + str(idx[0]))
                else:
                    idxStr = ",".join([str(e) for e in idx])
                    obj = super(Field.Access, self).__xnew__(self, fieldName + "_" + offsetName + "^" + idxStr)

            else:
                offsetName = "%0.10X" % (abs(hash(tuple(offsetsAndIndex))))
                obj = super(Field.Access, self).__xnew__(self, fieldName + "_" + offsetName)

            obj._field = field
            obj._offsets = []
            for o in offsets:
                if isinstance(o, sp.Basic):
                    obj._offsets.append(o)
                else:
                    obj._offsets.append(int(o))
            obj._offsetName = offsetName
            obj._index = idx

            return obj

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        def __getnewargs__(self):
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            return self.field, self.offsets, self.index
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        __xnew__ = staticmethod(__new_stage2__)
        __xnew_cached_ = staticmethod(cacheit(__new_stage2__))

        def __call__(self, *idx):
            if self._index != tuple([0]*self.field.indexDimensions):
                print(self._index, tuple([0]*self.field.indexDimensions))
                raise ValueError("Indexing an already indexed Field.Access")

            idx = tuple(idx)
            if len(idx) != self.field.indexDimensions and idx != (0,):
                raise ValueError("Wrong number of indices: "
                                 "Got %d, expected %d" % (len(idx), self.field.indexDimensions))
            return Field.Access(self.field, self._offsets, idx)

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        def __getitem__(self, *idx):
            return self.__call__(*idx)

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        def __iter__(self):
            """This is necessary to work with parts of sympy that test if an object is iterable (e.g. simplify).
            The __getitem__ would make it iterable"""
            raise TypeError("Field access is not iterable")

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        @property
        def field(self):
            return self._field

        @property
        def offsets(self):
            return self._offsets

        @property
        def requiredGhostLayers(self):
            return int(np.max(np.abs(self._offsets)))

        @property
        def nrOfCoordinates(self):
            return len(self._offsets)

        @property
        def offsetName(self):
            return self._offsetName

        @property
        def index(self):
            return self._index

        def _hashable_content(self):
            superClassContents = list(super(Field.Access, self)._hashable_content())
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            t = tuple(superClassContents + [hash(self._field), self._index] + self._offsets)
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            return t
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def extractCommonSubexpressions(equations):
    """
    Uses sympy to find common subexpressions in equations and returns
    them in a topologically sorted order, ready for evaluation.
    Usually called before list of equations is passed to :func:`createKernel`
    """
    replacements, newEq = sp.cse(equations)
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    # Workaround for older sympy versions: here subexpressions (temporary = True) are extracted
    # which leads to problems in Piecewise functions which have to a default case indicated by True
    symbolsEqualToTrue = {r[0]: True for r in replacements if r[1] is sp.true}

    replacementEqs = [sp.Eq(*r) for r in replacements if r[1] is not sp.true]
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    equations = replacementEqs + newEq
    topologicallySortedPairs = sp.cse_main.reps_toposort([[e.lhs, e.rhs] for e in equations])
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    equations = [sp.Eq(a[0], a[1].subs(symbolsEqualToTrue)) for a in topologicallySortedPairs]
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    return equations


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def getLayoutOfArray(arr, indexDimensionIds=[]):
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    """
    Returns a list indicating the memory layout (linearization order) of the numpy array.
    Example:
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    >>> getLayoutOfArray(np.zeros([3,3,3]))
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    (0, 1, 2)
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    In this example the loop over the zeroth coordinate should be the outermost loop,
    followed by the first and second. Elements arr[x,y,0] and arr[x,y,1] are adjacent in memory.
    Normally constructed numpy arrays have this order, however by stride tricks or other frameworks, arrays
    with different memory layout can be created.
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    The indexDimensionIds parameter leaves specifies which coordinates should not be
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    """
    coordinates = list(range(len(arr.shape)))
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    relevantStrides = [stride for i, stride in enumerate(arr.strides) if i not in indexDimensionIds]
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    result = [x for (y, x) in sorted(zip(relevantStrides, coordinates), key=lambda pair: pair[0], reverse=True)]
    return normalizeLayout(result)


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def createNumpyArrayWithLayout(shape, layout):
    """
    Creates a numpy array with
    :param shape: shape of the resulting array
    :param layout: layout as tuple, where the coordinates are ordered from slow to fast
    >>> res = createNumpyArrayWithLayout(shape=(2, 3, 4, 5), layout=(3, 2, 0, 1))
    >>> res.shape
    (2, 3, 4, 5)
    >>> getLayoutOfArray(res)
    (3, 2, 0, 1)
    """
    assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
    currentLayout = list(range(len(shape)))
    swaps = []
    for i in range(len(layout)):
        if currentLayout[i] != layout[i]:
            indexToSwapWith = currentLayout.index(layout[i])
            swaps.append((i, indexToSwapWith))
            currentLayout[i], currentLayout[indexToSwapWith] = currentLayout[indexToSwapWith], currentLayout[i]
    assert tuple(currentLayout) == tuple(layout)

    shape = list(shape)
    for a, b in swaps:
        shape[a], shape[b] = shape[b], shape[a]

    res = np.empty(shape, order='c')
    for a, b in reversed(swaps):
        res = res.swapaxes(a, b)
    return res


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def normalizeLayout(layout):
    """Takes a layout tuple and subtracts the minimum from all entries"""
    minEntry = min(layout)
    return tuple(i - minEntry for i in layout)


def computeStrides(shape, layout):
    """
    Computes strides assuming no padding exists
    :param shape: shape (size) of array
    :param layout: layout specification as tuple
    :return: strides in elements, not in bytes
    """
    N = len(shape)
    assert len(layout) == N
    assert len(set(layout)) == N
    strides = [0] * N
    product = 1
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    for j in reversed(layout):
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        strides[j] = product
        product *= shape[j]
    return tuple(strides)
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def offsetComponentToDirectionString(coordinateId, value):
    """
    Translates numerical offset to string notation.
    x offsets are labeled with east 'E' and 'W',
    y offsets with north 'N' and 'S' and
    z offsets with top 'T' and bottom 'B'
    If the absolute value of the offset is bigger than 1, this number is prefixed.
    :param coordinateId: integer 0, 1 or 2 standing for x,y and z
    :param value: integer offset

    Example:
    >>> offsetComponentToDirectionString(0, 1)
    'E'
    >>> offsetComponentToDirectionString(1, 2)
    '2N'
    """
    nameComponents = (('W', 'E'),  # west, east
                      ('S', 'N'),  # south, north
                      ('B', 'T'),  # bottom, top
                      )
    if value == 0:
        result = ""
    elif value < 0:
        result = nameComponents[coordinateId][0]
    else:
        result = nameComponents[coordinateId][1]
    if abs(value) > 1:
        result = "%d%s" % (abs(value), result)
    return result


def offsetToDirectionString(offsetTuple):
    """
    Translates numerical offset to string notation.
    For details see :func:`offsetComponentToDirectionString`
    :param offsetTuple: 3-tuple with x,y,z offset

    Example:
    >>> offsetToDirectionString([1, -1, 0])
    'SE'
    >>> offsetToDirectionString(([-3, 0, -2]))
    '2B3W'
    """
    names = ["", "", ""]
    for i in range(len(offsetTuple)):
        names[i] = offsetComponentToDirectionString(i, offsetTuple[i])
    name = "".join(reversed(names))
    if name == "":
        name = "C"
    return name


def directionStringToOffset(directionStr, dim=3):
    """
    Reverse mapping of :func:`offsetToDirectionString`
    :param directionStr: string representation of offset
    :param dim: dimension of offset, i.e the length of the returned list

    >>> directionStringToOffset('NW', dim=3)
    array([-1,  1,  0])
    >>> directionStringToOffset('NW', dim=2)
    array([-1,  1])
    >>> directionStringToOffset(offsetToDirectionString([3,-2,1]))
    array([ 3, -2,  1])
    """
    offsetMap = {
        'C': np.array([0, 0, 0]),

        'W': np.array([-1, 0, 0]),
        'E': np.array([1, 0, 0]),

        'S': np.array([0, -1, 0]),
        'N': np.array([0, 1, 0]),

        'B': np.array([0, 0, -1]),
        'T': np.array([0, 0, 1]),
    }
    offset = np.array([0, 0, 0])

    while len(directionStr) > 0:
        factor = 1
        firstNonDigit = 0
        while directionStr[firstNonDigit].isdigit():
            firstNonDigit += 1
        if firstNonDigit > 0:
            factor = int(directionStr[:firstNonDigit])
            directionStr = directionStr[firstNonDigit:]
        curOffset = offsetMap[directionStr[0]]
        offset += factor * curOffset
        directionStr = directionStr[1:]
    return offset[:dim]