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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2019.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","\"\"\"","ParameterExpression Class to enable creating simple expressions of Parameters.","\"\"\"","","from __future__ import annotations","from typing import Callable, Union","","import numbers","import operator","","import numpy","import symengine","","from qiskit.circuit.exceptions import CircuitError","","# This type is redefined at the bottom to insert the full reference to \"ParameterExpression\", so it","# can safely be used by runtime type-checkers like Sphinx. Mypy does not need this because it","# handles the references by static analysis.","ParameterValueType = Union[\"ParameterExpression\", float]","","","class ParameterExpression:"," \"\"\"ParameterExpression class to enable creating expressions of Parameters.\"\"\"",""," __slots__ = [\"_parameter_symbols\", \"_parameter_keys\", \"_symbol_expr\", \"_name_map\"]",""," def __init__(self, symbol_map: dict, expr):"," \"\"\"Create a new :class:`ParameterExpression`.",""," Not intended to be called directly, but to be instantiated via operations"," on other :class:`Parameter` or :class:`ParameterExpression` objects.",""," Args:"," symbol_map (Dict[Parameter, [ParameterExpression, float, or int]]):"," Mapping of :class:`Parameter` instances to the :class:`sympy.Symbol`"," serving as their placeholder in expr."," expr (sympy.Expr): Expression of :class:`sympy.Symbol` s."," \"\"\""," # NOTE: `Parameter.__init__` does not call up to this method, since this method is dependent"," # on `Parameter` instances already being initialised enough to be hashable. If changing"," # this method, check that `Parameter.__init__` and `__setstate__` are still valid."," self._parameter_symbols = symbol_map"," self._parameter_keys = frozenset(p._hash_key() for p in self._parameter_symbols)"," self._symbol_expr = expr"," self._name_map: dict | None = None",""," @property"," def parameters(self) -> set:"," \"\"\"Returns a set of the unbound Parameters in the expression.\"\"\""," return self._parameter_symbols.keys()",""," @property"," def _names(self) -> dict:"," \"\"\"Returns a mapping of parameter names to Parameters in the expression.\"\"\""," if self._name_map is None:"," self._name_map = {p.name: p for p in self._parameter_symbols}"," return self._name_map",""," def conjugate(self) -> \"ParameterExpression\":"," \"\"\"Return the conjugate.\"\"\""," conjugated = ParameterExpression("," self._parameter_symbols, symengine.conjugate(self._symbol_expr)"," )"," return conjugated",""," def assign(self, parameter, value: ParameterValueType) -> \"ParameterExpression\":"," \"\"\""," Assign one parameter to a value, which can either be numeric or another parameter"," expression.",""," Args:"," parameter (Parameter): A parameter in this expression whose value will be updated."," value: The new value to bind to.",""," Returns:"," A new expression parameterized by any parameters which were not bound by assignment."," \"\"\""," if isinstance(value, ParameterExpression):"," return self.subs({parameter: value})"," return self.bind({parameter: value})",""," def bind("," self, parameter_values: dict, allow_unknown_parameters: bool = False"," ) -> \"ParameterExpression\":"," \"\"\"Binds the provided set of parameters to their corresponding values.",""," Args:"," parameter_values: Mapping of Parameter instances to the numeric value to which"," they will be bound."," allow_unknown_parameters: If ``False``, raises an error if ``parameter_values``"," contains Parameters in the keys outside those present in the expression."," If ``True``, any such parameters are simply ignored.",""," Raises:"," CircuitError:"," - If parameter_values contains Parameters outside those in self."," - If a non-numeric value is passed in parameter_values."," ZeroDivisionError:"," - If binding the provided values requires division by zero.",""," Returns:"," A new expression parameterized by any parameters which were not bound by"," parameter_values."," \"\"\""," if not allow_unknown_parameters:"," self._raise_if_passed_unknown_parameters(parameter_values.keys())"," self._raise_if_passed_nan(parameter_values)",""," symbol_values = {}"," for parameter, value in parameter_values.items():"," if (param_expr := self._parameter_symbols.get(parameter)) is not None:"," symbol_values[param_expr] = value",""," bound_symbol_expr = self._symbol_expr.subs(symbol_values)",""," # Don't use sympy.free_symbols to count remaining parameters here."," # sympy will in some cases reduce the expression and remove even"," # unbound symbols."," # e.g. (sympy.Symbol('s') * 0).free_symbols == set()",""," free_parameters = self.parameters - parameter_values.keys()"," free_parameter_symbols = {"," p: s for p, s in self._parameter_symbols.items() if p in free_parameters"," }",""," if ("," hasattr(bound_symbol_expr, \"is_infinite\") and bound_symbol_expr.is_infinite"," ) or bound_symbol_expr == float(\"inf\"):"," raise ZeroDivisionError("," \"Binding provided for expression \""," \"results in division by zero \""," \"(Expression: {}, Bindings: {}).\".format(self, parameter_values)"," )",""," return ParameterExpression(free_parameter_symbols, bound_symbol_expr)",""," def subs("," self, parameter_map: dict, allow_unknown_parameters: bool = False"," ) -> \"ParameterExpression\":"," \"\"\"Returns a new Expression with replacement Parameters.",""," Args:"," parameter_map: Mapping from Parameters in self to the ParameterExpression"," instances with which they should be replaced."," allow_unknown_parameters: If ``False``, raises an error if ``parameter_map``"," contains Parameters in the keys outside those present in the expression."," If ``True``, any such parameters are simply ignored.",""," Raises:"," CircuitError:"," - If parameter_map contains Parameters outside those in self."," - If the replacement Parameters in parameter_map would result in"," a name conflict in the generated expression.",""," Returns:"," A new expression with the specified parameters replaced."," \"\"\""," if not allow_unknown_parameters:"," self._raise_if_passed_unknown_parameters(parameter_map.keys())",""," inbound_names = {"," p.name: p"," for replacement_expr in parameter_map.values()"," for p in replacement_expr.parameters"," }"," self._raise_if_parameter_names_conflict(inbound_names, parameter_map.keys())",""," # Include existing parameters in self not set to be replaced."," new_parameter_symbols = {"," p: s for p, s in self._parameter_symbols.items() if p not in parameter_map"," }"," symbol_type = symengine.Symbol",""," # If new_param is an expr, we'll need to construct a matching sympy expr"," # but with our sympy symbols instead of theirs."," symbol_map = {}"," for old_param, new_param in parameter_map.items():"," if (old_symbol := self._parameter_symbols.get(old_param)) is not None:"," symbol_map[old_symbol] = new_param._symbol_expr"," for p in new_param.parameters:"," new_parameter_symbols[p] = symbol_type(p.name)",""," substituted_symbol_expr = self._symbol_expr.subs(symbol_map)",""," return ParameterExpression(new_parameter_symbols, substituted_symbol_expr)",""," def _raise_if_passed_unknown_parameters(self, parameters):"," unknown_parameters = parameters - self.parameters"," if unknown_parameters:"," raise CircuitError("," \"Cannot bind Parameters ({}) not present in \""," \"expression.\".format([str(p) for p in unknown_parameters])"," )",""," def _raise_if_passed_nan(self, parameter_values):"," nan_parameter_values = {"," p: v for p, v in parameter_values.items() if not isinstance(v, numbers.Number)"," }"," if nan_parameter_values:"," raise CircuitError("," f\"Expression cannot bind non-numeric values ({nan_parameter_values})\""," )",""," def _raise_if_parameter_names_conflict(self, inbound_parameters, outbound_parameters=None):"," if outbound_parameters is None:"," outbound_parameters = set()"," outbound_names = {}"," else:"," outbound_names = {p.name: p for p in outbound_parameters}",""," inbound_names = inbound_parameters"," conflicting_names = []"," for name, param in inbound_names.items():"," if name in self._names and name not in outbound_names:"," if param != self._names[name]:"," conflicting_names.append(name)"," if conflicting_names:"," raise CircuitError("," f\"Name conflict applying operation for parameters: {conflicting_names}\""," )",""," def _apply_operation("," self, operation: Callable, other: ParameterValueType, reflected: bool = False"," ) -> \"ParameterExpression\":"," \"\"\"Base method implementing math operations between Parameters and"," either a constant or a second ParameterExpression.",""," Args:"," operation: One of operator.{add,sub,mul,truediv}."," other: The second argument to be used with self in operation."," reflected: Optional - The default ordering is \"self operator other\"."," If reflected is True, this is switched to \"other operator self\"."," For use in e.g. __radd__, ...",""," Raises:"," CircuitError:"," - If parameter_map contains Parameters outside those in self."," - If the replacement Parameters in parameter_map would result in"," a name conflict in the generated expression.",""," Returns:"," A new expression describing the result of the operation."," \"\"\""," self_expr = self._symbol_expr",""," if isinstance(other, ParameterExpression):"," self._raise_if_parameter_names_conflict(other._names)"," parameter_symbols = {**self._parameter_symbols, **other._parameter_symbols}"," other_expr = other._symbol_expr"," elif isinstance(other, numbers.Number) and numpy.isfinite(other):"," parameter_symbols = self._parameter_symbols.copy()"," other_expr = other"," else:"," return NotImplemented",""," if reflected:"," expr = operation(other_expr, self_expr)"," else:"," expr = operation(self_expr, other_expr)",""," out_expr = ParameterExpression(parameter_symbols, expr)"," out_expr._name_map = self._names.copy()"," if isinstance(other, ParameterExpression):"," out_expr._names.update(other._names.copy())",""," return out_expr",""," def gradient(self, param) -> Union[\"ParameterExpression\", complex]:"," \"\"\"Get the derivative of a parameter expression w.r.t. a specified parameter expression.",""," Args:"," param (Parameter): Parameter w.r.t. which we want to take the derivative",""," Returns:"," ParameterExpression representing the gradient of param_expr w.r.t. param"," or complex or float number"," \"\"\""," # Check if the parameter is contained in the parameter expression"," if param not in self._parameter_symbols.keys():"," # If it is not contained then return 0"," return 0.0",""," # Compute the gradient of the parameter expression w.r.t. param"," key = self._parameter_symbols[param]"," expr_grad = symengine.Derivative(self._symbol_expr, key)",""," # generate the new dictionary of symbols"," # this needs to be done since in the derivative some symbols might disappear (e.g."," # when deriving linear expression)"," parameter_symbols = {}"," for parameter, symbol in self._parameter_symbols.items():"," if symbol in expr_grad.free_symbols:"," parameter_symbols[parameter] = symbol"," # If the gradient corresponds to a parameter expression then return the new expression."," if len(parameter_symbols) > 0:"," return ParameterExpression(parameter_symbols, expr=expr_grad)"," # If no free symbols left, return a complex or float gradient"," expr_grad_cplx = complex(expr_grad)"," if expr_grad_cplx.imag != 0:"," return expr_grad_cplx"," else:"," return float(expr_grad)",""," def __add__(self, other):"," return self._apply_operation(operator.add, other)",""," def __radd__(self, other):"," return self._apply_operation(operator.add, other, reflected=True)",""," def __sub__(self, other):"," return self._apply_operation(operator.sub, other)",""," def __rsub__(self, other):"," return self._apply_operation(operator.sub, other, reflected=True)",""," def __mul__(self, other):"," return self._apply_operation(operator.mul, other)",""," def __neg__(self):"," return self._apply_operation(operator.mul, -1.0)",""," def __rmul__(self, other):"," return self._apply_operation(operator.mul, other, reflected=True)",""," def __truediv__(self, other):"," if other == 0:"," raise ZeroDivisionError(\"Division of a ParameterExpression by zero.\")"," return self._apply_operation(operator.truediv, other)",""," def __rtruediv__(self, other):"," return self._apply_operation(operator.truediv, other, reflected=True)",""," def __pow__(self, other):"," return self._apply_operation(pow, other)",""," def __rpow__(self, other):"," return self._apply_operation(pow, other, reflected=True)",""," def _call(self, ufunc):"," return ParameterExpression(self._parameter_symbols, ufunc(self._symbol_expr))",""," def sin(self):"," \"\"\"Sine of a ParameterExpression\"\"\""," return self._call(symengine.sin)",""," def cos(self):"," \"\"\"Cosine of a ParameterExpression\"\"\""," return self._call(symengine.cos)",""," def tan(self):"," \"\"\"Tangent of a ParameterExpression\"\"\""," return self._call(symengine.tan)",""," def arcsin(self):"," \"\"\"Arcsin of a ParameterExpression\"\"\""," return self._call(symengine.asin)",""," def arccos(self):"," \"\"\"Arccos of a ParameterExpression\"\"\""," return self._call(symengine.acos)",""," def arctan(self):"," \"\"\"Arctan of a ParameterExpression\"\"\""," return self._call(symengine.atan)",""," def exp(self):"," \"\"\"Exponential of a ParameterExpression\"\"\""," return self._call(symengine.exp)",""," def log(self):"," \"\"\"Logarithm of a ParameterExpression\"\"\""," return self._call(symengine.log)",""," def sign(self):"," \"\"\"Sign of a ParameterExpression\"\"\""," return self._call(symengine.sign)",""," def __repr__(self):"," return f\"{self.__class__.__name__}({str(self)})\"",""," def __str__(self):"," from sympy import sympify, sstr",""," return sstr(sympify(self._symbol_expr), full_prec=False)",""," def __complex__(self):"," try:"," return complex(self._symbol_expr)"," # TypeError is for sympy, RuntimeError for symengine"," except (TypeError, RuntimeError) as exc:"," if self.parameters:"," raise TypeError("," \"ParameterExpression with unbound parameters ({}) \""," \"cannot be cast to a complex.\".format(self.parameters)"," ) from None"," raise TypeError(\"could not cast expression to complex\") from exc",""," def __float__(self):"," try:"," return float(self._symbol_expr)"," # TypeError is for sympy, RuntimeError for symengine"," except (TypeError, RuntimeError) as exc:"," if self.parameters:"," raise TypeError("," \"ParameterExpression with unbound parameters ({}) \""," \"cannot be cast to a float.\".format(self.parameters)"," ) from None"," # In symengine, if an expression was complex at any time, its type is likely to have"," # stayed \"complex\" even when the imaginary part symbolically (i.e. exactly)"," # cancelled out. Sympy tends to more aggressively recognise these as symbolically"," # real. This second attempt at a cast is a way of unifying the behaviour to the"," # more expected form for our users."," cval = complex(self)"," if cval.imag == 0.0:"," return cval.real"," raise TypeError(\"could not cast expression to float\") from exc",""," def __int__(self):"," try:"," return int(self._symbol_expr)"," # TypeError is for backwards compatibility, RuntimeError is raised by symengine"," except RuntimeError as exc:"," if self.parameters:"," raise TypeError("," \"ParameterExpression with unbound parameters ({}) \""," \"cannot be cast to an int.\".format(self.parameters)"," ) from None"," raise TypeError(\"could not cast expression to int\") from exc",""," def __hash__(self):"," return hash((self._parameter_keys, self._symbol_expr))",""," def __copy__(self):"," return self",""," def __deepcopy__(self, memo=None):"," return self",""," def __abs__(self):"," \"\"\"Absolute of a ParameterExpression\"\"\""," return self._call(symengine.Abs)",""," def abs(self):"," \"\"\"Absolute of a ParameterExpression\"\"\""," return self.__abs__()",""," def __eq__(self, other):"," \"\"\"Check if this parameter expression is equal to another parameter expression"," or a fixed value (only if this is a bound expression)."," Args:"," other (ParameterExpression or a number):"," Parameter expression or numeric constant used for comparison"," Returns:"," bool: result of the comparison"," \"\"\""," if isinstance(other, ParameterExpression):"," if self.parameters != other.parameters:"," return False"," from sympy import sympify",""," return sympify(self._symbol_expr).equals(sympify(other._symbol_expr))"," elif isinstance(other, numbers.Number):"," return len(self.parameters) == 0 and complex(self._symbol_expr) == other"," return False",""," def is_real(self):"," \"\"\"Return whether the expression is real\"\"\""," if not self._symbol_expr.is_real and self._symbol_expr.is_real is not None:"," # Symengine returns false for is_real on the expression if"," # there is a imaginary component (even if that component is 0),"," # but the parameter will evaluate as real. Check that if the"," # expression's is_real attribute returns false that we have a"," # non-zero imaginary"," if self._symbol_expr.imag == 0.0:"," return True"," return False"," return self._symbol_expr.is_real",""," def numeric(self) -> int | float | complex:"," \"\"\"Return a Python number representing this object, using the most restrictive of"," :class:`int`, :class:`float` and :class:`complex` that is valid for this object.",""," In general, an :class:`int` is only returned if the expression only involved symbolic"," integers. If floating-point values were used during the evaluation, the return value will"," be a :class:`float` regardless of whether the represented value is an integer. This is"," because floating-point values \"infect\" symbolic computations by their inexact nature, and"," symbolic libraries will use inexact floating-point semantics not exact real-number semantics"," when they are involved. If you want to assert that all floating-point calculations *were*"," carried out at infinite precision (i.e. :class:`float` could represent every intermediate"," value exactly), you can use :meth:`float.is_integer` to check if the return float represents"," an integer and cast it using :class:`int` if so. This would be an unusual pattern;"," typically one requires this by only ever using explicitly :class:`~numbers.Rational` objects"," while working with symbolic expressions.",""," This is more reliable and performant than using :meth:`is_real` followed by calling"," :class:`float` or :class:`complex`, as in some cases :meth:`is_real` needs to force a"," floating-point evaluation to determine an accurate result to work around bugs in the"," upstream symbolic libraries.",""," Returns:"," A Python number representing the object.",""," Raises:"," TypeError: if there are unbound parameters."," \"\"\""," if self._parameter_symbols:"," raise TypeError("," f\"Expression with unbound parameters '{self.parameters}' is not numeric\""," )"," if self._symbol_expr.is_integer:"," # Integer evaluation is reliable, as far as we know."," return int(self._symbol_expr)"," # We've come across several ways in which symengine's general-purpose evaluators"," # introduce spurious imaginary components can get involved in the output. The most"," # reliable strategy \"try it and see\" while forcing real floating-point evaluation."," try:"," real_expr = self._symbol_expr.evalf(real=True)"," except RuntimeError:"," # Symengine returns `complex` if any imaginary floating-point enters at all, even if"," # the result is zero. The best we can do is detect that and decay to a float."," out = complex(self._symbol_expr)"," return out.real if out.imag == 0.0 else out"," return float(real_expr)",""," def sympify(self):"," \"\"\"Return symbolic expression as a raw Sympy or Symengine object.",""," Symengine is used preferentially; if both are available, the result will always be a"," ``symengine`` object. Symengine is a separate library but has integration with Sympy.",""," .. note::",""," This is for interoperability only. 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