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from __future__ import annotations
from dataclasses import dataclass
from typing import Any, Callable, Mapping
import numpy as np
from .expression import (
Aggregate,
Binary,
Expression,
Function,
GroupedParameter,
Indexed,
Number,
Parameter,
Reduction,
RelationLift,
Symbol,
Unary,
)
from .tree import children, iter_preorder
@dataclass(slots=True)
class _RelationScope:
name: str
table: np.ndarray
indices: tuple[str, ...]
@property
def bindings(self) -> dict[str, np.ndarray]:
return {name: self.table[:, column] for column, name in enumerate(self.indices)}
class _ExpressionEvaluator:
"""NumPy expression-tree evaluator."""
def __init__(
self,
values: Mapping[str, Any] | None,
parameters: Mapping[str, Any] | None,
time: Any,
delay_resolver: Callable[..., Any] | None,
expression: Expression,
num_nodes: int | None = None,
):
self.values = dict(values or {})
self.parameters = dict(parameters or {})
self.time = None if time is None else np.asarray(time, dtype=float)
self.delay_resolver = delay_resolver
self.parameter_defaults = self._parameter_defaults(expression)
self.num_nodes = num_nodes
def __call__(self, expression: Expression) -> Any:
if any(isinstance(node, Indexed) for node in walk(expression)):
from .indexed_evaluation import IndexedEvaluator
return IndexedEvaluator(
self.values,
self.parameters,
self.parameter_defaults,
self.num_nodes,
self.time,
self.delay_resolver,
)(expression)
return self._eval(expression, None)
def _eval(self, node: Expression, scope: _RelationScope | None) -> Any:
if isinstance(node, Number):
return np.asarray(node.value)
if isinstance(node, Symbol):
if node.name in self.values:
return np.asarray(self.values[node.name])
if node.value is not None:
return np.asarray(node.value)
raise KeyError(f"No value was provided for symbol {node.name!r}.")
if isinstance(node, Parameter):
value = self.parameters.get(node.name, self.parameter_defaults.get(node.name))
if value is None:
raise ValueError(
f"Parameter {node.name!r} has no value. Fit it or provide "
f"parameters[{node.name!r}]."
)
return np.asarray(value, dtype=float)
if isinstance(node, GroupedParameter):
labels = np.asarray(self._eval(node.by, scope), dtype=object)
key = grouped_parameter_key(node)
fitted = self.parameters.get(key, node.value)
fitted = {} if fitted is None else dict(fitted)
default = node.default
missing = [label for label in _unique(labels) if label not in fitted]
if missing and default is None:
raise ValueError(
f"Grouped parameter {key!r} has no values for categories "
f"{missing!r}. Fit it first."
)
result = np.asarray(
[fitted.get(label, default) for label in labels.reshape(-1)], dtype=float
)
return result.reshape(labels.shape)
if isinstance(node, Unary):
value = self._eval(node.operand, scope)
return -value
if isinstance(node, Binary):
left, right = _align(self._eval(node.left, scope), self._eval(node.right, scope))
with np.errstate(all="ignore"):
return {
"+": np.add,
"-": np.subtract,
"*": np.multiply,
"/": np.divide,
"**": np.power,
}[node.operator](left, right)
if isinstance(node, Function):
return self._function(node, scope)
if isinstance(node, Indexed):
return self._indexed(node, scope)
if isinstance(node, Reduction):
return self._reduction(node)
if isinstance(node, Aggregate):
return self._aggregate(node)
if isinstance(node, RelationLift):
return self._relation_lift(node, scope)
raise TypeError(f"Cannot evaluate {type(node).__name__}.")
def _function(self, node: Function, scope: _RelationScope | None) -> Any:
arguments = [self._eval(argument, scope) for argument in node.arguments]
if node.name == "delay":
return self._delay(arguments[0], arguments[1])
functions = {
"abs": np.abs,
"arccos": np.arccos,
"arcsin": np.arcsin,
"arctan": np.arctan,
"cos": np.cos,
"cosh": np.cosh,
"cot": lambda value: 1.0 / np.tan(value),
"csc": lambda value: 1.0 / np.sin(value),
"exp": np.exp,
"inv": lambda value: 1.0 / value,
"log": np.log,
"log10": np.log10,
"log2": np.log2,
"max": np.maximum,
"min": np.minimum,
"pow2": lambda value: value**2,
"pow3": lambda value: value**3,
"sec": lambda value: 1.0 / np.cos(value),
"sech": lambda value: 1.0 / np.cosh(value),
"sin": np.sin,
"sinh": np.sinh,
"sign": np.sign,
"sqrt": np.sqrt,
"tan": np.tan,
"tanh": np.tanh,
"sigmoid": lambda value: 1.0 / (1.0 + np.exp(-value)),
}
with np.errstate(all="ignore"):
return functions[node.name](*arguments)
def _indexed(self, node: Indexed, scope: _RelationScope | None) -> Any:
value = np.asarray(self._eval(node.base, None))
names = tuple(index.name for index in node.indices)
if scope is not None and len(names) > 1:
if names != scope.indices:
raise ValueError(
f"Relation fields must use bound indices {scope.indices}, not {names}."
)
if isinstance(node.base, Symbol) and node.base.name == scope.name:
return np.ones(len(scope.table), dtype=float)
edge_count = len(scope.table)
if value.ndim == 1 and value.shape[0] == edge_count:
return value
if value.ndim > 1 and value.shape[-1] == edge_count:
return np.moveaxis(value, -1, 0)
raise ValueError(
f"Relation field {node.base!s} must have an edge axis of length "
f"{edge_count} in its last dimension."
)
if scope is not None and len(names) == 1 and names[0] in scope.bindings:
return value[scope.bindings[names[0]]]
if len(names) > value.ndim:
raise ValueError(
f"{len(names)} symbolic indices were applied to a {value.ndim}-dimensional value."
)
# A free index names an existing leading axis; it does not slice it.
return value
def _reduction(self, node: Reduction) -> Any:
scope = self._relation_scope(node.relation) if node.relation is not None else None
value = np.asarray(self._eval(node.operand, scope))
reduced = {index.name for index in node.indices}
if scope is None:
if self._find_relation_scope(node.operand) is not None:
raise ValueError(
"Pass the relation separately, for example "
"sum[j](A[i, j], expression)."
)
return np.sum(value, axis=tuple(range(min(len(reduced), value.ndim))))
unknown = reduced - set(scope.indices)
if unknown:
raise ValueError(
f"Indices {sorted(unknown)!r} are not bound by relation {scope.name!r}."
)
free = [name for name in scope.indices if name not in reduced]
if not free:
return np.sum(value, axis=0)
coordinates = tuple(scope.bindings[name] for name in free)
sizes = tuple(
self._index_size(node.operand, name, coordinate)
for name, coordinate in zip(free, coordinates)
)
result = np.zeros(sizes + value.shape[1:], dtype=np.result_type(value, float))
np.add.at(result, coordinates[0] if len(coordinates) == 1 else coordinates, value)
return result
def _relation_scope(self, relation: Expression) -> _RelationScope:
if not isinstance(relation, Indexed) or not isinstance(relation.base, Symbol):
raise ValueError("A reduction relation must be indexed, such as A[i, j].")
name, table = self._relation(relation.base)
indices = tuple(index.name for index in relation.indices)
if table.shape[1] != len(indices):
raise ValueError(
f"Relation {name!r} has {table.shape[1]} columns but "
f"{len(indices)} indices were supplied."
)
return _RelationScope(name, table, indices)
def _aggregate(self, node: Aggregate) -> Any:
relation_name, table = self._relation(node.relation)
if table.shape[1] != 2:
raise ValueError("aggr currently expects a two-column edge list.")
scope = _RelationScope(relation_name, table, ("source", "target"))
value = np.asarray(self._eval(node.operand, scope))
target = table[:, 1]
fallback = int(target.max()) + 1 if target.size else 0
size = self._leading_size(node.operand, fallback=fallback)
result = np.zeros((size,) + value.shape[1:], dtype=np.result_type(value, float))
np.add.at(result, target, value)
return result
def _relation_lift(self, node: RelationLift, scope: _RelationScope | None) -> Any:
if node.relation is not None:
name, table = self._relation(node.relation)
scope = _RelationScope(name, table, ("source", "target"))
if scope is None:
raise ValueError(f"{node.role} requires a relation argument or an enclosing aggr(...).")
column = 1 if node.role == "target" else 0
return np.asarray(self._eval(node.operand, None))[scope.table[:, column]]
def _delay(self, value: Any, lag: Any) -> Any:
value = np.asarray(value, dtype=float)
lag = np.asarray(lag, dtype=float)
if self.delay_resolver is not None:
return np.asarray(self.delay_resolver(value, lag, self.time))
if value.ndim == 0:
return value
time = np.arange(value.shape[0], dtype=float) if self.time is None else self.time
if time.shape != (value.shape[0],):
raise ValueError("time must be one-dimensional and match the leading data axis.")
query = time - lag
try:
query = np.broadcast_to(query, (value.shape[0],))
except ValueError as error:
raise ValueError(
"delay delta must be scalar or match the leading data axis."
) from error
flat = value.reshape(value.shape[0], -1)
delayed = np.column_stack([
np.interp(query, time, column, left=np.nan, right=np.nan) for column in flat.T
])
return delayed.reshape(value.shape)
def _find_relation_scope(self, node: Expression) -> _RelationScope | None:
relations: dict[str, tuple[np.ndarray, tuple[str, ...]]] = {}
for item in walk(node):
if not isinstance(item, Indexed) or not isinstance(item.base, Symbol):
continue
if item.base.name not in self.values:
continue
value = np.asarray(self.values[item.base.name])
if value.ndim != 2 or value.shape[1] != len(item.indices) or len(item.indices) < 2:
continue
if value.dtype.kind not in "iu":
continue
relations[item.base.name] = (
value.astype(int, copy=False),
tuple(index.name for index in item.indices),
)
if not relations:
return None
if len(relations) > 1:
raise ValueError(
"One reduction cannot currently combine multiple relations: "
f"{sorted(relations)}."
)
name, (table, indices) = next(iter(relations.items()))
if np.any(table < 0):
raise ValueError("Relation indices must be non-negative integers.")
return _RelationScope(name, table, indices)
def _relation(self, node: Expression) -> tuple[str, np.ndarray]:
value = np.asarray(self._eval(node, None))
if value.ndim != 2 or value.dtype.kind not in "iu" or value.shape[1] < 2:
raise ValueError("A relation must be an integer array shaped (relations, arity).")
name = node.name if isinstance(node, Symbol) else "<relation>"
return name, value.astype(int, copy=False)
def _index_size(self, node: Expression, index: str, coordinate: np.ndarray) -> int:
sizes = []
for item in walk(node):
if not isinstance(item, Indexed) or len(item.indices) != 1:
continue
if not isinstance(item.base, Symbol):
continue
if item.base.name in self.values:
value = np.asarray(self.values[item.base.name])
# Every singly-indexed node field belongs to the same node domain
# inside one relation contraction, even when this particular free
# index does not occur on that field (for example A[i,j] with x[j]).
if value.ndim:
sizes.append(value.shape[0])
fallback = int(coordinate.max()) + 1 if coordinate.size else 0
return max(sizes, default=fallback)
def _leading_size(self, node: Expression, fallback: int) -> int:
sizes = []
for item in walk(node):
if isinstance(item, Symbol) and item.name in self.values:
value = np.asarray(self.values[item.name])
is_edge_list = (
value.ndim == 2 and value.dtype.kind in "iu" and value.shape[1] == 2
)
if value.ndim and not is_edge_list:
sizes.append(value.shape[0])
return max(sizes, default=fallback)
@staticmethod
def _parameter_defaults(expression: Expression) -> dict[str, float | None]:
defaults: dict[str, float | None] = {}
for node in walk(expression):
if not isinstance(node, Parameter):
continue
previous = defaults.get(node.name)
if previous is not None and node.value is not None and previous != node.value:
raise ValueError(f"Conflicting initial values for parameter {node.name!r}.")
if node.value is not None or node.name not in defaults:
defaults[node.name] = node.value
return defaults
def _align(left: Any, right: Any) -> tuple[np.ndarray, np.ndarray]:
left, right = np.asarray(left), np.asarray(right)
if left.ndim == 1 and right.ndim > 1 and left.shape[0] == right.shape[0]:
left = left.reshape((left.shape[0],) + (1,) * (right.ndim - 1))
if right.ndim == 1 and left.ndim > 1 and right.shape[0] == left.shape[0]:
right = right.reshape((right.shape[0],) + (1,) * (left.ndim - 1))
return left, right
def _unique(values: np.ndarray) -> list[Any]:
result = []
for value in values.reshape(-1):
value = value.item() if isinstance(value, np.generic) else value
if value not in result:
result.append(value)
return result
def grouped_parameter_key(node: GroupedParameter) -> str:
"""Return the storage key for a grouped parameter.
Args:
node: Grouped parameter to identify.
Returns:
Its explicit name or a stable name derived from the grouping symbol.
"""
if node.name:
return node.name
if isinstance(node.by, Symbol):
return f"grouped:{node.by.name}"
return f"grouped:{node.by}"
def walk(node: Expression):
"""Iterate over an expression tree in preorder.
Args:
node: Expression or syntax-tree node.
Yields:
Expression nodes in parent-before-children order.
"""
yield from iter_preorder(node)
def evaluate(
expression: Expression,
values: Mapping[str, Any] | None = None,
*,
parameters: Mapping[str, Any] | None = None,
time: Any = None,
delay_resolver: Callable[..., Any] | None = None,
num_nodes: int | None = None,
) -> Any:
"""Evaluate an expression without executing arbitrary Python code.
Args:
expression: Symbolic expression to process.
values: Values keyed by symbol name.
parameters: Fitted parameter values keyed by parameter name.
time: Optional sample times.
delay_resolver: Optional callback that resolves delayed values.
num_nodes: Explicit node count for indexed expressions.
Returns:
The evaluated scalar or NumPy array.
"""
return _ExpressionEvaluator(values, parameters, time, delay_resolver, expression, num_nodes)(expression)
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