import re import numpy import cupy import cupy._core._routines_manipulation as _manipulation from cupy._core._dtype import get_dtype, _raise_if_invalid_cast from cupy._core import internal # Signature parsing code and dimension accessing has been borrowed # from dask # https://github.com/dask/dask/blob/61b578f5a3ad88cbc6a8b9a73ce08c551bd969fa/dask/array/gufunc.py#L12-L55 _DIMENSION_NAME = r'\w+\?*' _CORE_DIMENSION_LIST = '(?:{0:}(?:,{0:})*,?)?'.format(_DIMENSION_NAME) _ARGUMENT = r'\({}\)'.format(_CORE_DIMENSION_LIST) _INPUT_ARGUMENTS = '(?:{0:}(?:,{0:})*,?)?'.format(_ARGUMENT) _OUTPUT_ARGUMENTS = '{0:}(?:,{0:})*'.format( _ARGUMENT ) # Use `'{0:}(?:,{0:})*,?'` if gufunc- # signature should be allowed for length 1 tuple returns _SIGNATURE = '^{0:}->{1:}$'.format(_INPUT_ARGUMENTS, _OUTPUT_ARGUMENTS) def _parse_gufunc_signature(signature): # The code has been modified from dask to support optional dimensions if not isinstance(signature, str): raise TypeError('Signature is not a string') if signature == '' or signature is None: raise ValueError('Signature cannot be empty') signature = signature.replace(' ', '') if not re.match(_SIGNATURE, signature): raise ValueError('Not a valid gufunc signature: {}'.format(signature)) in_txt, out_txt = signature.split('->') ins = [tuple(x.split(',')) if x != '' else () for x in in_txt[1:-1].split('),(')] outs = [tuple(y.split(',')) if y != '' else () for y in out_txt[1:-1].split('),(')] # TODO(ecastill) multiple output support if len(outs) > 1: raise ValueError('Currently more than 1 output is not supported') return ins, outs def _validate_normalize_axes( axes, axis, keepdims, input_coredimss, output_coredimss ): # This code credit goes to Dask # https://github.com/dask/dask/blob/61b578f5a3ad88cbc6a8b9a73ce08c551bd969fa/dask/array/gufunc.py#L58-L172 nin = len(input_coredimss) nout = ( 1 if not isinstance(output_coredimss, list) else len(output_coredimss) ) if axes is not None and axis is not None: raise ValueError( 'Only one of `axis` or `axes` keyword arguments should be given') if axes and not isinstance(axes, list): raise ValueError('`axes` has to be of type list') # output_coredimss = output_coredimss if nout > 1 else [output_coredimss] filtered_core_dims = list(filter(len, input_coredimss)) nr_outputs_with_coredims = len( [True for x in output_coredimss if len(x) > 0]) if keepdims: if nr_outputs_with_coredims > 0: raise ValueError('`keepdims` can only be used for scalar outputs') output_coredimss = len(output_coredimss) * [filtered_core_dims[0]] core_dims = input_coredimss + output_coredimss if axis is not None: if not isinstance(axis, int): raise ValueError('`axis` argument has to be an integer value') if filtered_core_dims: cd0 = filtered_core_dims[0] if len(cd0) != 1: raise ValueError( '`axis` can be used only, if one core dimension is present' ) for cd in filtered_core_dims: if cd0 != cd: raise ValueError( 'To use `axis`, all core dimensions have to be equal' ) # Expand defaults or axis if axes is None: if axis is not None: axes = [(axis,) if cd else tuple() for cd in core_dims] else: axes = [tuple(range(-len(icd), 0)) for icd in core_dims] axes = [(a,) if isinstance(a, int) else a for a in axes] if ( (nr_outputs_with_coredims == 0) and (nin != len(axes)) and (nin + nout != len(axes)) ) or ((nr_outputs_with_coredims > 0) and (nin + nout != len(axes))): raise ValueError( 'The number of `axes` entries is not equal the number' ' of input and output arguments') # Treat outputs output_axes = axes[nin:] output_axes = ( output_axes if output_axes else [tuple(range(-len(ocd), 0)) for ocd in output_coredimss] ) input_axes = axes[:nin] # Assert we have as many axes as output core dimensions for idx, (iax, icd) in enumerate(zip(input_axes, input_coredimss)): if len(iax) != len(icd): raise ValueError( f'The number of `axes` entries for argument #{idx}' ' is not equal the number of respective input core' ' dimensions in signature') if not keepdims: for idx, (oax, ocd) in enumerate(zip(output_axes, output_coredimss)): if len(oax) != len(ocd): raise ValueError( f'The number of `axes` entries for argument #{idx}' ' is not equal the number of respective output core' ' dimensions in signature') else: if input_coredimss: icd0 = input_coredimss[0] for icd in input_coredimss: if icd0 != icd: raise ValueError( 'To use `keepdims`, all core dimensions' ' have to be equal') iax0 = input_axes[0] output_axes = [iax0 for _ in output_coredimss] return input_axes, output_axes class _OpsRegister: ''' Holds the ops for each dtypes signature like ('ff->f', func1) and allows to do look ups for these ''' class _Op: def __init__(self, in_types, out_types, func): self.func = func self.in_types = tuple(numpy.dtype(i) for i in in_types) self.out_types = tuple(numpy.dtype(o) for o in out_types) self.sig_str = (''.join( in_t.char for in_t in self.in_types) + '->' + ''.join( out_t.char for out_t in self.out_types)) def __init__(self, signatures, default_func, nin, nout, name): self._default_func = default_func self._nin = nin self._nout = nout self._ops = self._process_signatures(signatures) self._name = name def _sig_str_to_tuple(self, sig): sig = sig.replace(' ', '') toks = sig.split('->') if len(toks) != 2: raise ValueError(f'signature {sig} for dtypes is invalid') else: ins, outs = toks return ins, outs def _process_signatures(self, signatures): ops = [] for sig in signatures: if isinstance(sig, tuple): sig, op = sig else: op = self._default_func ins, outs = self._sig_str_to_tuple(sig) # Check the number of inputs and outputs matches the gufunc sig if len(ins) != self._nin: raise ValueError( f'signature {sig} for dtypes is invalid number of inputs ' 'is not consistent with general signature') if len(outs) != self._nout: raise ValueError( f'signature {sig} for dtypes is invalid number of inputs ' 'is not consistent with general signature') ops.append(_OpsRegister._Op(ins, outs, op)) return ops def _determine_from_args(self, args, casting): n = len(args) in_types = tuple(arg.dtype for arg in args) for op in self._ops: op_types = op.in_types for i in range(n): it = in_types[i] ot = op_types[i] if not numpy.can_cast(it, ot, casting=casting): break else: return op return None def _determine_from_dtype(self, dtype): for op in self._ops: op_types = op.out_types for t in op_types: if t != dtype: break else: return op return None def _determine_from_signature(self, signature): # Lets convert the signature as it can be a tuple of tuples # or a string if isinstance(signature, tuple): # create a string to do a look-up on the ops if len(signature) == 1: raise TypeError( 'The use of a length 1 tuple for the ufunc `signature` is' ' not allowed. Use `dtype` or fill the tuple with' ' `None`s.') nin = self._nin nout = self._nout if len(signature) != (nin + nout): raise TypeError( 'A type-tuple must be specified of length 1 or 3 for ufunc' f' {self._name}') signature = ''.join( numpy.dtype(t).char for t in signature[:nin]) + '->' + ''.join( numpy.dtype(t).char for t in signature[nin:nin+nout]) if isinstance(signature, str): is_out = len(signature) == 1 for op in self._ops: if is_out: for t in op.out_types: if t.char != signature: break else: return op else: if op.sig_str == signature: return op raise TypeError('No loop matching the specified signature and' f' casting was found for ufunc {self._name}') def determine_dtype(self, args, dtype, casting, signature): ret_dtype = None func = self._default_func if signature is not None: # TODO(ecastill) use an externally provided signature to # find the typecasting rules op = self._determine_from_signature(signature) elif dtype is not None: if isinstance(dtype, tuple): # TODO(ecastill) support dtype tuples raise RuntimeError('dtype with tuple is not yet supported') op = self._determine_from_dtype(dtype) else: op = self._determine_from_args(args, casting) if op is None: # Should we allow op to be none? if dtype is None: dtype = args[0].dtype for arg in args: ret_dtype = numpy.promote_types(dtype, arg.dtype) else: ret_dtype = get_dtype(dtype) else: # Convert args to the op specified in_types n_args = [] def argname(): return f'ufunc {self._name} input {i}' for i, (arg, in_type) in enumerate(zip(args, op.in_types)): _raise_if_invalid_cast(arg.dtype, in_type, casting, argname) n_args.append(arg.astype(in_type, copy=False)) args = n_args ret_dtype = op.out_types[0] func = op.func return args, ret_dtype, func class _GUFunc: ''' Creates a Generalized Universal Function by wrapping a user provided function with the signature. ``signature`` determines if the function consumes or produces core dimensions. The remaining dimensions in given input arrays (``*args``) are considered loop dimensions and are required to broadcast naturally against each other. Args: func (callable): Function to call like ``func(*args, **kwargs)`` on input arrays (``*args``) that returns an array or tuple of arrays. If multiple arguments with non-matching dimensions are supplied, this function is expected to vectorize (broadcast) over axes of positional arguments in the style of NumPy universal functions. signature (string): Specifies what core dimensions are consumed and produced by ``func``. According to the specification of numpy.gufunc signature. supports_batched (bool, optional): If the wrapped function supports to pass the complete input array with the loop and the core dimensions. Defaults to `False`. Dimensions will be iterated in the `GUFunc` processing code. supports_out (bool, optional): If the wrapped function supports out as one of its kwargs. Defaults to `False`. signatures (list of tuple of str): Contains strings in the form of 'ii->i' with i being the char of a dtype. Each element of the list is a tuple with the string and a alternative function to `func` to be executed when the inputs of the function can be casted as described by this function. name (str, optional): Name for the GUFunc object. If not specified, ``func``'s name is used. doc (str, optional): Docstring for the GUFunc object. If not specified, ``func.__doc__`` is used. ''' def __init__(self, func, signature, **kwargs): # We would like to create gufuncs from cupy regular ufuncs # so we can avoid most of the __call__ stuff self._func = func self._signature = signature self.__name__ = kwargs.pop('name', func.__name__) self.__doc__ = kwargs.pop('doc', func.__doc__) # The following are attributes to avoid applying certain steps # when wrapping cupy functions that do some of the gufunc # stuff internally due to CUDA libraries requirements self._supports_batched = kwargs.pop('supports_batched', False) self._supports_out = kwargs.pop('supports_out', False) signatures = kwargs.pop('signatures', []) if kwargs: raise TypeError( 'got unexpected keyword arguments: ' + ', '.join([repr(k) for k in kwargs]) ) # Preprocess the signature here input_coredimss, output_coredimss = _parse_gufunc_signature( self._signature) self._input_coredimss = input_coredimss self._output_coredimss = output_coredimss # This is pre-calculated to later check the minimum number of # dimensions required per input self._min_dims = [0] * len(input_coredimss) for i, inp in enumerate(input_coredimss): for d in inp: if d[-1] != '?': self._min_dims[i] += 1 # Determine nout: nout = None for functions of one # direct return; nout = int for return tuples self._nout = ( 0 if not isinstance(output_coredimss, list) else len(output_coredimss) ) self._nin = ( 0 if not isinstance(input_coredimss, list) else len(input_coredimss) ) # Determines the function that will be run depending on the datatypes # Pass a list of signatures that are either the types in format # ii->o or a tuple with the string and a function other than func to be # executed for those types # For some reason _nout is a tuple and now we get it with 0s self._ops_register = _OpsRegister( signatures, self._func, self._nin, self._nout, self.__name__) def _apply_func_to_inputs(self, func, dim, sizes, dims, args, outs): # Apply function # The resulting array is loop_output_dims+the specified dims # Some functions have batching logic inside due to highly # optimized CUDA libraries so we just call them if self._supports_batched or dim == len(dims): # Check if the function supports out, order and other args if self._supports_out and outs is not None: outs = outs[0] if len(outs) == 1 else outs func(*args, out=outs) else: fouts = func(*args) # TODO(ecastill) improve this check if isinstance(fouts, cupy.ndarray): fouts = (fouts,) for o, fo in zip(outs, fouts): cupy._core.elementwise_copy(fo, o) else: dim_size = sizes[dims[dim]][0] for i in range(dim_size): n_args = [a[i] for a in args] if outs is not None: n_outs = [o[i] for o in outs] self._apply_func_to_inputs( func, dim + 1, sizes, dims, n_args, n_outs) def _transpose_element(self, arg, iax, shape): iax = tuple(a if a < 0 else a - len(shape) for a in iax) tidc = ( tuple(i for i in range( -len(shape) + 0, 0) if i not in iax) + iax ) return arg.transpose(tidc) def _get_args_transposed(self, args, input_axes, outs, output_axes): # This code credit goes to Dask # https://github.com/dask/dask/blob/61b578f5a3ad88cbc6a8b9a73ce08c551bd969fa/dask/array/gufunc.py#L349-L377 # modifications have been done to support arguments broadcast # out argument, and optional core dims. transposed_args = [] # This is used when reshaping the outputs so that we can delete # dims that were not specified in the input missing_dims = set() for i, (arg, iax, input_coredims, md) in enumerate(zip( args, input_axes, self._input_coredimss, self._min_dims)): shape = arg.shape nds = len(shape) # For the inputs that has missing dimensions we need to reshape if nds < md: raise ValueError(f'Input operand {i} does not have enough' f' dimensions (has {nds}, gufunc core with' f' signature {self._signature} requires {md}') optionals = len(input_coredims) - nds if optionals > 0: # Look for optional dimensions # We only allow the first or the last dimensions to be optional if input_coredims[0][-1] == '?': shape = (1,) * optionals + shape missing_dims.update(set(input_coredims[:optionals])) else: shape = shape + (1,) * optionals missing_dims.update( set(input_coredims[min(0, len(shape)-1):])) arg = arg.reshape(shape) transposed_args.append(self._transpose_element(arg, iax, shape)) args = transposed_args if outs is not None: transposed_outs = [] # outs should be transposed to the intermediate form before # copying all results for out, iox, coredims in zip( outs, output_axes, self._output_coredimss): transposed_outs.append(self._transpose_element( out, iox, out.shape)) # check that outs has been correctly transposed # if the function returns a scalar, outs will be ignored if len(transposed_outs) == len(outs): outs = transposed_outs # we can't directly broadcast arrays together since their core dims # might differ. Only the loop dimensions are broadcastable shape = internal._broadcast_shapes( [a.shape[:-len(self._input_coredimss)] for a in args]) args = [_manipulation.broadcast_to( a, shape + a.shape[-len(self._input_coredimss):]) for a in args] # Assess input args for loop dims input_shapes = [a.shape for a in args] num_loopdims = [ len(s) - len(cd) for s, cd in zip( input_shapes, self._input_coredimss) ] max_loopdims = max(num_loopdims) if num_loopdims else None core_input_shapes = [ dict(zip(icd, s[n:])) for s, n, icd in zip( input_shapes, num_loopdims, self._input_coredimss) ] core_shapes = {} for d in core_input_shapes: core_shapes.update(d) loop_input_dimss = [ tuple( '__loopdim%d__' % d for d in range( max_loopdims - n, max_loopdims) ) for n in num_loopdims ] input_dimss = [li + c for li, c in zip( loop_input_dimss, self._input_coredimss)] loop_output_dims = max(loop_input_dimss, key=len, default=()) # Assess input args for same size and chunk sizes # Collect sizes and chunksizes of all dims in all arrays dimsizess = {} for dims, shape in zip(input_dimss, input_shapes): for dim, size in zip(dims, shape): dimsizes = dimsizess.get(dim, []) dimsizes.append(size) dimsizess[dim] = dimsizes # Assert correct partitioning, for case: for dim, sizes in dimsizess.items(): if set(sizes).union({1}) != {1, max(sizes)}: raise ValueError( f'Dimension {dim} with different lengths in arrays' ) return args, dimsizess, loop_output_dims, outs, missing_dims def _determine_order(self, args, order): if order.upper() in ('C', 'K'): # Order is determined to be C to allocate the out array # but we will change the strides of the out array # to be K later in __call__ return 'C' elif order.upper() == 'A': # order is F if all arrays are strictly F order = ('F' if all([a.flags.f_contiguous and not a.flags.c_contiguous for a in args]) else 'C') return order elif order.upper() == 'F': return 'F' else: raise RuntimeError(f'Unknown order {order}') def __call__(self, *args, **kwargs): ''' Apply a generalized ufunc. Args: args: Input arguments. Each of them can be a :class:`cupy.ndarray` object or a scalar. The output arguments can be omitted or be specified by the ``out`` argument. axes (List of tuples of int, optional): A list of tuples with indices of axes a generalized ufunc should operate on. For instance, for a signature of ``'(i,j),(j,k)->(i,k)'`` appropriate for matrix multiplication, the base elements are two-dimensional matrices and these are taken to be stored in the two last axes of each argument. The corresponding axes keyword would be ``[(-2, -1), (-2, -1), (-2, -1)]``. For simplicity, for generalized ufuncs that operate on 1-dimensional arrays (vectors), a single integer is accepted instead of a single-element tuple, and for generalized ufuncs for which all outputs are scalars, the output tuples can be omitted. axis (int, optional): A single axis over which a generalized ufunc should operate. This is a short-cut for ufuncs that operate over a single, shared core dimension, equivalent to passing in axes with entries of (axis,) for each single-core-dimension argument and ``()`` for all others. For instance, for a signature ``'(i),(i)->()'``, it is equivalent to passing in ``axes=[(axis,), (axis,), ()]``. keepdims (bool, optional): If this is set to True, axes which are reduced over will be left in the result as a dimension with size one, so that the result will broadcast correctly against the inputs. This option can only be used for generalized ufuncs that operate on inputs that all have the same number of core dimensions and with outputs that have no core dimensions , i.e., with signatures like ``'(i),(i)->()'`` or ``'(m,m)->()'``. If used, the location of the dimensions in the output can be controlled with axes and axis. casting (str, optional): Provides a policy for what kind of casting is permitted. Defaults to ``'same_kind'`` dtype (dtype, optional): Overrides the dtype of the calculation and output arrays. Similar to signature. signature (str or tuple of dtype, optional): Either a data-type, a tuple of data-types, or a special signature string indicating the input and output types of a ufunc. This argument allows you to provide a specific signature for the function to be used if registered in the ``signatures`` kwarg of the ``__init__`` method. If the loop specified does not exist for the ufunc, then a TypeError is raised. Normally, a suitable loop is found automatically by comparing the input types with what is available and searching for a loop with data-types to which all inputs can be cast safely. This keyword argument lets you bypass that search and choose a particular loop. order (str, optional): Specifies the memory layout of the output array. Defaults to ``'K'``.``'C'`` means the output should be C-contiguous, ``'F'`` means F-contiguous, ``'A'`` means F-contiguous if the inputs are F-contiguous and not also not C-contiguous, C-contiguous otherwise, and ``'K'`` means to match the element ordering of the inputs as closely as possible. out (cupy.ndarray): Output array. It outputs to new arrays default. Returns: Output array or a tuple of output arrays. ''' # This argument cannot be used for generalized ufuncs # as those take non-scalar input. # where = kwargs.pop('where', None) outs = kwargs.pop('out', None) axes = kwargs.pop('axes', None) axis = kwargs.pop('axis', None) order = kwargs.pop('order', 'K') dtype = kwargs.pop('dtype', None) keepdims = kwargs.pop('keepdims', False) signature = kwargs.pop('signature', None) casting = kwargs.pop('casting', 'same_kind') if len(kwargs) > 0: raise RuntimeError( 'Unknown kwargs {}'.format(' '.join(kwargs.keys()))) ret_dtype = None func = self._func # this will cast the inputs appropriately args, ret_dtype, func = self._ops_register.determine_dtype( args, dtype, casting, signature) if not isinstance(self._signature, str): raise TypeError('`signature` has to be of type string') if outs is not None and not isinstance(outs, tuple): if isinstance(outs, cupy.ndarray): outs = (outs,) else: raise TypeError('`outs` must be a tuple or `cupy.ndarray`') filter_order = self._determine_order(args, order) input_coredimss = self._input_coredimss output_coredimss = self._output_coredimss if outs is not None and not isinstance(outs, tuple): raise TypeError('`outs` must be a tuple') # Axes input_axes, output_axes = _validate_normalize_axes( axes, axis, keepdims, input_coredimss, output_coredimss ) if len(input_coredimss) != len(args): ValueError( 'According to `signature`, `func` requires %d arguments,' ' but %s given' % (len(input_coredimss), len(args))) args, dimsizess, loop_output_dims, outs, m_dims = self._get_args_transposed( # NOQA args, input_axes, outs, output_axes) # The output shape varies depending on optional dims or not # TODO(ecastill) this only works for one out argument out_shape = [dimsizess[od][0] for od in loop_output_dims] if self._nout > 0: out_shape += [dimsizess[od][0] for od in output_coredimss[0]] out_shape = tuple(out_shape) if outs is None: outs = cupy.empty(out_shape, dtype=ret_dtype, order=filter_order) if order == 'K': strides = internal._get_strides_for_order_K( outs, ret_dtype, out_shape) outs._set_shape_and_strides(out_shape, strides, True, True) outs = (outs,) else: if outs[0].shape != out_shape: raise ValueError(f'Invalid shape for out {outs[0].shape}' f' needs {out_shape}') _raise_if_invalid_cast( ret_dtype, outs[0].dtype, casting, "out dtype") self._apply_func_to_inputs( func, 0, dimsizess, loop_output_dims, args, outs) # This code credit goes to Dask # https://github.com/dask/dask/blob/61b578f5a3ad88cbc6a8b9a73ce08c551bd969fa/dask/array/gufunc.py#L462-L503 # Treat direct output if self._nout == 0: output_coredimss = [output_coredimss] # Split output # tmp might be a tuple of outs # we changed the way we apply the function compared to dask # we have added support for optional dims leaf_arrs = [] for tmp in outs: for i, (ocd, oax) in enumerate(zip(output_coredimss, output_axes)): leaf_arr = tmp # Axes: if keepdims: slices = (len(leaf_arr.shape) * (slice(None),) + len(oax) * (numpy.newaxis,)) leaf_arr = leaf_arr[slices] tidcs = [None] * len(leaf_arr.shape) for i, oa in zip(range(-len(oax), 0), oax): tidcs[oa] = i j = 0 for i in range(len(tidcs)): if tidcs[i] is None: tidcs[i] = j j += 1 leaf_arr = leaf_arr.transpose(tidcs) # Delete the dims that were optionals after the input expansion if len(m_dims) > 0: shape = leaf_arr.shape # This line deletes the dimensions that were not present # in the input core_shape = shape[-len(ocd):] core_shape = tuple([ d for d, n in zip(core_shape, ocd) if n not in m_dims]) shape = shape[:-len(ocd)] + core_shape leaf_arr = leaf_arr.reshape(shape) # leaf_arrs.append(leaf_arr.astype(leaf_arr.dtype, order=order)) # NOQA leaf_arrs.append(leaf_arr) return tuple(leaf_arrs) if self._nout > 1 else leaf_arrs[0]