def reshape(expr: Variable, new_shape: tuple): ''' This function reshapes the input into a new shape. Parameters ---------- expr: Variable The Variable which you want to reshape new_shape: tuple[int] A tuple of ints specifying the new shape desired ''' if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out = Variable() out.shape = new_shape out.add_dependency_node(expr) out.build = lambda: ReshapeComp( shape=expr.shape, in_name=expr.name, out_name=out.name, new_shape=out.shape, val=expr.val, ) return out
def sum(*summands: List[Variable], axes=None): ''' This function can compute an elementwise or axiswise sum of a single or multiple inputs. Parameters ---------- summands: Variable(s) The Variable(s) over which to take the sum axes: tuple[int] The axes along which the sum will be taken over ''' out = Variable() for expr in summands: if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out.add_dependency_node(expr) if axes == None: if len(summands) == 1: out.build = lambda: SingleTensorSumComp( in_name=summands[0].name, shape=summands[0].shape, out_name=out.name, val=summands[0].val, ) else: out.shape = expr.shape out.build = lambda: MultipleTensorSumComp( in_names=[expr.name for expr in summands], shape=expr.shape, out_name=out.name, vals=[expr.val for expr in summands], ) else: output_shape = np.delete(expr.shape, axes) out.shape = tuple(output_shape) if len(summands) == 1: out.build = lambda: SingleTensorSumComp( in_name=expr.name, shape=expr.shape, out_name=out.name, out_shape=out.shape, axes=axes, val=summands[0].val, ) else: out.build = lambda: MultipleTensorSumComp( in_names=[expr.name for expr in summands], shape=expr.shape, out_name=out.name, out_shape=out.shape, axes=axes, vals=[expr.val for expr in summands], ) return out
def rotmat(expr: Variable, axis: str): ''' This function creates a rotation matrix depending on the input value and the axis. Parameters ---------- expr: Variable The value which determines by how much the rotation matrix axis: str The axis along which the rotation matrix should rotate. Can we specified with: 'x' , 'y' , or 'z'. ''' if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out = Variable() out.add_dependency_node(expr) if expr.shape == (1, ): out.shape = (3, 3) else: out.shape = expr.shape + (3, 3) out.build = lambda: RotationMatrixComp( shape=expr.shape, in_name=expr.name, out_name=out.name, axis=axis, val=expr.val, ) return out
def matvec(mat1, vec1): ''' This function can compute a matrix-vector multiplication, similar to the numpy counterpart. Parameters ---------- mat1: Variable The matrix needed for the matrix-vector multiplication vec1: Variable The vector needed for the matrix-vector multiplication ''' if not (isinstance(mat1, Variable) and isinstance(vec1, Variable)): raise TypeError("Arguments must both be Variable objects") out = Variable() out.add_dependency_node(mat1) out.add_dependency_node(vec1) if mat1.shape[1] == vec1.shape[0] and len(vec1.shape) == 1: out.shape = (mat1.shape[0], ) out.build = lambda: MatVecComp( in_names=[mat1.name, vec1.name], out_name=out.name, in_shapes=[mat1.shape, vec1.shape], in_vals=[mat1.val, vec1.val], ) else: raise Exception("Cannot multiply: ", mat1.shape, "by", vec1.shape) return out
def reorder_axes(expr: Variable, operation: str): ''' The function reorders the axes of the input. Parameters ---------- expr: Variable The Variable that will have its axes reordered. operation: str Specifies the subscripts for reordering as comma separated list of subscript labels. Ex: 'ijk->kij' ''' if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out = Variable() out.add_dependency_node(expr) # Computing out_shape new_axes_locations = compute_new_axes_locations(expr.shape, operation) out.shape = tuple(expr.shape[i] for i in new_axes_locations) out.build = lambda: ReorderAxesComp( in_name=expr.name, in_shape=expr.shape, out_name=out.name, out_shape=out.shape, operation=operation, new_axes_locations=new_axes_locations, val=expr.val, ) return out
def expand(expr: Variable, shape: tuple, indices=None): if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") if indices is not None: if not isinstance(indices, str): raise TypeError(indices, " is not a str or None") if '->' not in indices: raise ValueError(indices, " is invalid") if indices is not None: in_indices, out_indices = indices.split('->') expand_indices = [] for i in range(len(out_indices)): index = out_indices[i] if index not in in_indices: expand_indices.append(i) out = Variable() out.shape = shape out.add_dependency_node(expr) if not expr.shape == (1, ): if indices is None: raise ValueError('If expanding something other than a scalar ' + 'indices must be given') ( _, _, _, in_shape, _, _, ) = decompose_shape_tuple(shape, expand_indices) if in_shape != expr.shape: raise ValueError('Shape or indices is invalid') out.build = lambda: ArrayExpansionComp( shape=shape, expand_indices=expand_indices, in_name=expr.name, out_name=out.name, val=expr.val, ) else: out.build = lambda: ScalarExpansionComp( shape=shape, in_name=expr.name, out_name=out.name, ) return out
def einsum_new_api(*operands: List[Variable], operation: List[tuple], partial_format='dense'): ''' The Einstein Summation function performs the equivalent of numpy.einsum using a new api Parameters ---------- operands: Variables(s) The Variable(s) which you would like to perform an einsum with. subscripts: list[tuple] Specifies the subscripts for summation as a list of tuples partial_format: str Denotes whether to compute 'dense' partials or 'sparse' partials ''' out = Variable() for expr in operands: if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out.add_dependency_node(expr) scalar_output = False if len(operands) == len(operation): scalar_output = True operation_aslist, operation_string = new_einsum_subscripts_to_string_and_list( operation, scalar_output=scalar_output) shape = compute_einsum_shape(operation_aslist, [expr.shape for expr in operands]) out.shape = shape if partial_format == 'dense': out.build = lambda: EinsumComp( in_names=[expr.name for expr in operands], in_shapes=[expr.shape for expr in operands], out_name=out.name, operation=operation_string, out_shape=shape, in_vals=[expr.val for expr in operands], ) elif partial_format == 'sparse': out.build = lambda: SparsePartialEinsumComp( in_names=[expr.name for expr in operands], in_shapes=[expr.shape for expr in operands], out_name=out.name, operation=operation_string, out_shape=shape, in_vals=[expr.val for expr in operands], ) else: raise Exception('partial_format should be either dense or sparse') return out
def dot(expr1: Variable, expr2: Variable, axis=None): ''' This can the dot product between two inputs. Parameters ---------- expr1: Variable The first input for the dot product. expr2: Variable The second input for the dot product. axis: int The axis along which the dot product is taken. The axis must have an axis of 3. ''' if not (isinstance(expr1, Variable) and isinstance(expr2, Variable)): raise TypeError("Arguments must both be Variable objects") out = Variable() out.add_dependency_node(expr1) out.add_dependency_node(expr2) if expr1.shape != expr2.shape: raise Exception("The shapes of the inputs must match!") print(len(expr1.shape)) print(len(expr2.shape)) if len(expr1.shape) == 1: out.build = lambda: VectorInnerProductComp( in_names=[expr1.name, expr2.name], out_name=out.name, in_shape=expr1.shape[0], in_vals=[expr1.val, expr2.val], ) else: if expr1.shape[axis] != 3: raise Exception( "The specified axis must correspond to the value of 3 in shape" ) else: out.shape = tuple(np.delete(list(expr1.shape), axis)) out.build = lambda: TensorDotProductComp( in_names=[expr1.name, expr2.name], out_name=out.name, in_shape=expr1.shape, axis=axis, out_shape=out.shape, in_vals=[expr1.val, expr2.val], ) return out
def sinh(expr): if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out = Variable() out.shape = expr.shape out.add_dependency_node(expr) out.build = lambda: SinhComp( shape=expr.shape, in_name=expr.name, out_name=out.name, val=expr.val, ) return out
def pnorm(expr, pnorm_type=2, axis=None): ''' This function computes the pnorm Parameters ---------- expr: Variable The Variable(s) over which to take the minimum pnorm_type: int This specifies what pnorm to compute. Values must be nonzero positive and even. axis: int Specifies the axis over which to take the pnorm ''' if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") if axis is not None: if not isinstance(axis, int) and not isinstance(axis, tuple): raise TypeError("axis must be an integer or tuple of integers") out = Variable() out.add_dependency_node(expr) if pnorm_type % 2 != 0 or pnorm_type <= 0: raise Exception(pnorm_type, " is not positive OR is not even") else: if axis == None: out.build = lambda: VectorizedPnormComp( shape=expr.shape, in_name=expr.name, out_name=out.name, pnorm_type=pnorm_type, val=expr.val, ) else: output_shape = np.delete(expr.shape, axis) out.shape = tuple(output_shape) out.build = lambda: VectorizedAxisWisePnormComp( shape=expr.shape, in_name=expr.name, out_shape=out.shape, out_name=out.name, pnorm_type=pnorm_type, axis=axis if isinstance(axis, tuple) else (axis, ), val=expr.val, ) return out
def replace_output_leaf_nodes( root: Output, node: Variable, leaf: Input, ): """ Replace ``Output`` objects that are used before they are defined with ``Input`` objects with same data. """ for dependency in node.dependencies: if dependency is root: # replace dependency reference with Input node node.remove_dependency_node(dependency) node.add_dependency_node(leaf) replace_output_leaf_nodes(root, dependency, leaf)
def einsum(*operands: List[Variable], subscripts: str, partial_format='dense'): ''' The Einstein Summation function performs the equivalent of numpy.einsum Parameters ---------- operands: Variable(s) The Variable(s) which you would like to perform an einsum with. subscripts: str Specifies the subscripts for summation as comma separated list of subscript labels partial_format: str Denotes whether to compute 'dense' partials or 'sparse' partials ''' out = Variable() for expr in operands: if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out.add_dependency_node(expr) operation_aslist = einsum_subscripts_tolist(subscripts) shape = compute_einsum_shape(operation_aslist, [expr.shape for expr in operands]) out.shape = shape if partial_format == 'dense': out.build = lambda: EinsumComp( in_names=[expr.name for expr in operands], in_shapes=[expr.shape for expr in operands], out_name=out.name, operation=subscripts, out_shape=shape, in_vals=[expr.val for expr in operands], ) elif partial_format == 'sparse': out.build = lambda: SparsePartialEinsumComp( in_names=[expr.name for expr in operands], in_shapes=[expr.shape for expr in operands], out_name=out.name, operation=subscripts, out_shape=shape, in_vals=[expr.val for expr in operands], ) else: raise Exception('partial_format should be either dense or sparse') return out
def matmat(mat1, mat2): ''' This function can compute a matrix-matrix multiplication, similar to the numpy counterpart. Parameters ---------- mat1: Variable The first input for the matrix-matrix multiplication mat2: Variable The second input for the matrix-matrix multiplication ''' if not (isinstance(mat1, Variable) and isinstance(mat2, Variable)): raise TypeError("Arguments must both be Variable objects") out = Variable() out.add_dependency_node(mat1) out.add_dependency_node(mat2) if mat1.shape[1] == mat2.shape[0] and len(mat2.shape) == 2: # Compute the output shape if both inputs are matrices out.shape = (mat1.shape[0], mat2.shape[1]) out.build = lambda: MatMatComp( in_names=[mat1.name, mat2.name], out_name=out.name, in_shapes=[mat1.shape, mat2.shape], in_vals=[mat1.val, mat2.val], ) elif mat1.shape[1] == mat2.shape[0] and len(mat2.shape) == 1: out.shape = (mat1.shape[0], 1) mat2_shape = (mat2.shape[0], 1) out.build = lambda: MatMatComp( in_names=[mat1.name, mat2.name], out_name=out.name, in_shapes=[mat1.shape, mat2_shape], in_vals=[mat1.val, mat2.val.reshape(mat2_shape)], ) else: raise Exception("Cannot multiply: ", mat1.shape, "by", mat2.shape) return out
def cross(in1, in2, axis: int): ''' This can the cross product between two inputs. Parameters ---------- in1: Variable The first input for the cross product. in2: Variable The second input for the cross product. axis: int The axis along which the cross product is taken. The axis specified must have a value of 3. ''' if not (isinstance(in1, Variable) and isinstance(in2, Variable)): raise TypeError("Arguments must both be Variable objects") out = Variable() out.add_dependency_node(in1) out.add_dependency_node(in2) if in1.shape != in2.shape: raise Exception("The shapes of the inputs must match!") else: out.shape = in1.shape if in1.shape[axis] != 3: raise Exception( "The specified axis must correspond to the value of 3 in shape") out.build = lambda: CrossProductComp( shape=in1.shape, in1_name=in1.name, in2_name=in2.name, out_name=out.name, axis=axis, in1_val=in1.val, in2_val=in2.val, ) return out
def outer(expr1: Variable, expr2: Variable): ''' This can the outer product between two inputs. Parameters ---------- expr1: Variable The first input for the outer product. expr2: Variable The second input for the outer product. ''' if not isinstance(expr1, Variable): raise TypeError(expr1, " is not an Variable object") elif not isinstance(expr2, Variable): raise TypeError(expr2, " is not an Variable object") out = Variable() out.add_dependency_node(expr1) out.add_dependency_node(expr2) if len(expr1.shape) == 1 and len(expr2.shape) == 1: out.shape = tuple(list(expr1.shape) + list(expr2.shape)) out.build = lambda: VectorOuterProductComp( in_names=[expr1.name, expr2.name], out_name=out.name, in_shapes=[expr1.shape[0], expr2.shape[0]], in_vals=[expr1.val, expr2.val], ) else: out.shape = tuple(list(expr1.shape) + list(expr2.shape)) out.build = lambda: TensorOuterProductComp( in_names=[expr1.name, expr2.name], out_name=out.name, in_shapes=[expr1.shape, expr2.shape], in_vals=[expr1.val, expr2.val], ) return out
def if_else( condition: Variable, expr_true: Variable, expr_false: Variable, ): if expr_true.shape != expr_false.shape: raise ValueError( "Variable shapes must be the same for Variable objects for both branches of execution" ) out = Variable() out.add_dependency_node(condition) out.add_dependency_node(expr_true) out.add_dependency_node(expr_false) out.build = lambda: ConditionalComponent( out_name=out.name, condition=condition, expr_true=expr_true, expr_false=expr_false, ) return out
def transpose(expr: Variable): ''' This function can perform the transpose of an input Parameters ---------- expr: Variable The input which will be transposed ''' if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out = Variable() out.add_dependency_node(expr) out.shape = expr.shape[::-1] out.build = lambda: TransposeComp( in_name=expr.name, in_shape=expr.shape, out_name=out.name, out_shape=out.shape, val=expr.val, ) return out
def replace_input_leaf_nodes( node: Variable, leaves: Dict[str, Input], ): """ Replace ``Input`` objects that depend on previous subsystems with ``Input`` objects that do not. This is required for defining graphs for residuals so that ``ImplicitComponent`` objects do not include subsystems. """ for dependency in node.dependencies: if isinstance(dependency, Input): if len(dependency.dependencies) > 0: node.remove_dependency_node(dependency) if dependency._id in leaves.keys(): node.add_dependency_node(leaves[dependency._id]) else: leaf = Input(dependency.name, shape=dependency.shape, val=dependency.val) leaf._id = dependency._id node.add_dependency_node(leaf) leaves[dependency._id] = leaf replace_input_leaf_nodes(dependency, leaves)
def max(*exprs, axis=None, rho=20.): ''' This function can compute an elementwise or axiswise maximum of a single or multiple inputs. Parameters ---------- exprs: Variable(s) The Variable(s) over which to take the maximum axis: int The axis along which the maximum will be taken over rho: float This is a smoothing parameter, which dictates how smooth or sharp the maximum is ''' out = Variable() for expr in exprs: if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out.add_dependency_node(expr) if len(exprs) == 1 and axis != None: output_shape = np.delete(expr.shape, axis) out.shape = tuple(output_shape) out.build = lambda: AxisMaxComp( shape=exprs[0].shape, in_name=exprs[0].name, axis=axis, out_name=out.name, rho=rho, val=exprs[0].val, ) elif len(exprs) > 1 and axis == None: shape = exprs[0].shape for expr in exprs: if shape != expr.shape: raise Exception("The shapes of the inputs must match!") out.shape = expr.shape out.build = lambda: ElementwiseMaxComp( shape=expr.shape, in_names=[expr.name for expr in exprs], out_name=out.name, rho=rho, vals=[expr.val for expr in exprs], ) elif len(exprs) == 1 and axis == None: out.build = lambda: ScalarExtremumComp( shape=exprs[0].shape, in_name=exprs[0].name, out_name=out.name, rho=rho, lower_flag=False, val=exprs[0].val, ) else: raise Exception("Do not give multiple inputs and an axis") return out
class Group(OMGroup, metaclass=_ComponentBuilder): """ The ``omtools.Group`` class builds ``openmdao.Component`` objects from Python-like expressions and adds their corresponding subsystems by constructing stock ``openmdao.Component`` objects. In ``self.setup``, first, the user declares inputs, writes expressions, and registers outputs. After ``self.setup`` runs, ``self`` builds a Directed Acyclic Graph (DAG) from registered outputs, analyzes the DAG to determine execution order, and adds the appropriate subsystems. In addition to supporting an expression-based style of defining a subsystem, ``omtools.Group`` also supports adding a subystem defined using a subclass of ``omtools.Group`` or ``openmdao.System``. The ``omtools.Group`` class only allows for expressions that define explicit relationships. For defining models that use implicit relationships and defining residuals, see ``omtools.ImplicitGroup``. """ def __init__(self, **kwargs): super().__init__(**kwargs) self.nodes: dict = {} self.input_vals: dict = {} self.sorted_builders = [] self.reverse_branch_sorting: bool = False self._root = Variable() self._most_recently_added_subsystem: Subsystem = None self.res_out_map: Dict[str, str] = dict() self.brackets_map = None self.out_vals = dict() def initialize(self, *args, **kwargs): """ User defined method to set options """ pass def setup(self): pass def declare_input( self, name: str, shape: Tuple[int] = (1, ), val=1, # units=None, ) -> Input: """ Declare an input to use in an expression. An input can be an output of a child ``System``. If the user declares an input that is computed by a child ``System``, then the call to ``self.declare_input`` must appear after the call to ``self.add_subsystem``. Parameters ---------- name: str Name of variable in OpenMDAO to be used as an input in generated ``Component`` objects shape: Tuple[int] Shape of variable val: Number or ndarray Default value for variable Returns ------- Input An object to use in expressions """ inp = Input( name, shape=shape, val=val, # units=units, ) if self._most_recently_added_subsystem is not None: inp.add_dependency_node(self._most_recently_added_subsystem) return inp def create_indep_var( self, name: str, shape: Tuple[int] = (1, ), val=1, # units=None, dv: bool = False, ) -> Indep: """ Create a value that is constant during model evaluation Parameters ---------- name: str Name of variable in OpenMDAO to be computed by ``ExplicitComponent`` objects connected in a cycle, or by an ``ExplicitComponent`` that concatenates variables shape: Tuple[int] Shape of variable val: Number or ndarray Value for variable during first model evaluation dv: bool Flag to set design variable Returns ------- Indep An object to use in expressions """ indep = Indep(name, shape=shape, val=val, dv=dv) # Ensure that independent variables are always at the top of n2 # diagram if self._most_recently_added_subsystem is not None: self._most_recently_added_subsystem.add_dependency_node(indep) # NOTE: We choose to always include IndepVarComp objects, even # if they are not used by other Component objects self.register_output(name, indep) return indep def create_output( self, name: str, shape: Tuple[int] = (1, ), val=1, ) -> ExplicitOutput: """ Create a value that is computed explicitly Parameters ---------- name: str Name of variable in OpenMDAO to be computed by ``ExplicitComponent`` objects connected in a cycle, or by an ``ExplicitComponent`` that concatenates variables shape: Tuple[int] Shape of variable Returns ------- ExplicitOutput An object to use in expressions """ ex = ExplicitOutput( name, shape=shape, val=val, ) self._root.add_dependency_node(ex) return ex def create_implicit_output( self, name: str, shape: Tuple[int] = (1, ), val=1, ) -> ImplicitOutput: """ Create a value that is computed implicitly Parameters ---------- name: str Name of variable in OpenMDAO to be computed by an ``ImplicitComponent`` shape: Tuple[int] Shape of variable Returns ------- ImplicitOutput An object to use in expressions """ im = ImplicitOutput( self, name, shape=shape, val=val, ) # self._root.add_dependency_node(im) return im def register_output(self, name: str, expr: ExplicitOutput) -> ExplicitOutput: """ Register ``expr`` as an output of the ``Group``. When adding subsystems, each of the subsystem's inputs requires a call to ``register_output`` prior to the call to ``add_subsystem``. Parameters ---------- name: str Name of variable in OpenMDAO expr: Variable Variable that computes output Returns ------- Variable Variable that computes output """ if isinstance(expr, Input): raise TypeError("Cannot register input " + expr + " as an output") if expr in self._root.dependencies: raise ValueError( "Cannot register output twice; attempting to register " + expr.name + " as " + name) expr.name = name self._root.add_dependency_node(expr) return expr def add_subsystem( self, name: str, subsys: System, promotes: Iterable = None, promotes_inputs: Iterable = None, promotes_outputs: Iterable = None, ): """ Add a subsystem to the ``Group``. ``self.add_subsystem`` call must be preceded by a call to ``self.register_output`` for each of the subsystem's inputs, and followed by ``self.declare_input`` for each of the subsystem's outputs. Parameters ---------- name: str Name of subsystem subsys: System Subsystem to add to `Group` promotes: Iterable Variables to promote promotes_inputs: Iterable Inputs to promote promotes_outputs: Iterable Outputs to promote Returns ------- System Subsystem to add to `Group` """ self._most_recently_added_subsystem = Subsystem( name, subsys, promotes=promotes, promotes_inputs=promotes_inputs, promotes_outputs=promotes_outputs, ) for dependency in self._root.dependencies: self._most_recently_added_subsystem.add_dependency_node(dependency) # Add subystem to DAG self._root.add_dependency_node(self._most_recently_added_subsystem) return subsys @contextmanager def create_group(self, name: str): """ Create a ``Group`` object and add as a subsystem, promoting all inputs and outputs. For use in ``with`` contexts. NOTE: Only use if planning to promote all varaibales within child ``Group`` object. Parameters ---------- name: str Name of new child ``Group`` object Returns ------- Group Child ``Group`` object whosevariables are all promoted """ try: group = Group() self.add_subsystem(name, group, promotes=['*']) yield group finally: group.setup() pass
def average(*operands: List[Variable], axes=None): ''' This function can compute the average of a single input, multiple inputs, or along an axis. Parameters ---------- operands: Variables The Variable(s) over which to take the average axes: tuple[int] Axes along which to take the average, default value is None ''' out = Variable() for expr in operands: if not isinstance(expr, Variable): raise TypeError(expr, " is not an Variable object") out.add_dependency_node(expr) if axes == None: if len(operands) == 1: out.build = lambda: SingleTensorAverageComp( in_name=operands[0].name, shape=operands[0].shape, out_name=out.name, val=operands[0].val, ) else: out.shape = expr.shape out.build = lambda: MultipleTensorAverageComp( in_names=[expr.name for expr in operands], shape=expr.shape, out_name=out.name, vals=[expr.val for expr in operands], ) else: output_shape = np.delete(expr.shape, axes) out.shape = tuple(output_shape) if len(operands) == 1: out.build = lambda: SingleTensorAverageComp( in_name=operands[0].name, shape=operands[0].shape, out_name=out.name, out_shape=out.shape, axes=axes, val=operands[0].val, ) else: out.build = lambda: MultipleTensorAverageComp( in_names=[expr.name for expr in operands], shape=expr.shape, out_name=out.name, out_shape=out.shape, axes=axes, vals=[expr.val for expr in operands], ) return out