# 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
from qiskit.circuit.exceptions import CircuitError
from qiskit.utils import optionals as _optionals
# 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]
[ドキュメント]class ParameterExpression:
"""ParameterExpression class to enable creating expressions of Parameters."""
__slots__ = ["_parameter_symbols", "_parameters", "_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.
"""
self._parameter_symbols = symbol_map
self._parameters = set(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._parameters
@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._parameters}
return self._name_map
[ドキュメント] def conjugate(self) -> "ParameterExpression":
"""Return the conjugate."""
if _optionals.HAS_SYMENGINE:
import symengine
conjugated = ParameterExpression(
self._parameter_symbols, symengine.conjugate(self._symbol_expr)
)
else:
conjugated = ParameterExpression(self._parameter_symbols, self._symbol_expr.conjugate())
return conjugated
[ドキュメント] 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})
[ドキュメント] 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 parameter in self._parameters:
param_expr = self._parameter_symbols[parameter]
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)
[ドキュメント] 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
}
if _optionals.HAS_SYMENGINE:
import symengine
symbol_type = symengine.Symbol
else:
from sympy import Symbol
symbol_type = 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_param in self._parameters:
symbol_map[self._parameter_symbols[old_param]] = 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
[ドキュメント] 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]
if _optionals.HAS_SYMENGINE:
import symengine
expr_grad = symengine.Derivative(self._symbol_expr, key)
else:
# TODO enable nth derivative
from sympy import Derivative
expr_grad = Derivative(self._symbol_expr, key).doit()
# 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 _call(self, ufunc):
return ParameterExpression(self._parameter_symbols, ufunc(self._symbol_expr))
[ドキュメント] def sin(self):
"""Sine of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.sin)
else:
from sympy import sin as _sin
return self._call(_sin)
[ドキュメント] def cos(self):
"""Cosine of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.cos)
else:
from sympy import cos as _cos
return self._call(_cos)
[ドキュメント] def tan(self):
"""Tangent of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.tan)
else:
from sympy import tan as _tan
return self._call(_tan)
[ドキュメント] def arcsin(self):
"""Arcsin of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.asin)
else:
from sympy import asin as _asin
return self._call(_asin)
[ドキュメント] def arccos(self):
"""Arccos of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.acos)
else:
from sympy import acos as _acos
return self._call(_acos)
[ドキュメント] def arctan(self):
"""Arctan of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.atan)
else:
from sympy import atan as _atan
return self._call(_atan)
[ドキュメント] def exp(self):
"""Exponential of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.exp)
else:
from sympy import exp as _exp
return self._call(_exp)
[ドキュメント] def log(self):
"""Logarithm of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.log)
else:
from sympy import log as _log
return self._call(_log)
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
try:
# 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
except TypeError:
pass
raise TypeError("could not cast expression to float") from exc
def __int__(self):
try:
return int(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 an int.".format(self.parameters)
) from None
raise TypeError("could not cast expression to int") from exc
def __hash__(self):
return hash((frozenset(self._parameter_symbols), self._symbol_expr))
def __copy__(self):
return self
def __deepcopy__(self, memo=None):
return self
def __abs__(self):
"""Absolute of a ParameterExpression"""
if _optionals.HAS_SYMENGINE:
import symengine
return self._call(symengine.Abs)
else:
from sympy import Abs as _abs
return self._call(_abs)
[ドキュメント] 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
if _optionals.HAS_SYMENGINE:
from sympy import sympify
return sympify(self._symbol_expr).equals(sympify(other._symbol_expr))
else:
return self._symbol_expr.equals(other._symbol_expr)
elif isinstance(other, numbers.Number):
return len(self.parameters) == 0 and complex(self._symbol_expr) == other
return False
[ドキュメント] def is_real(self):
"""Return whether the expression is real"""
# workaround for symengine behavior that const * (0 + 1 * I) is not real
# see https://github.com/symengine/symengine.py/issues/414
if _optionals.HAS_SYMENGINE and self._symbol_expr.is_real is None:
symbol_expr = self._symbol_expr.evalf()
else:
symbol_expr = self._symbol_expr
if not symbol_expr.is_real and 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 _optionals.HAS_SYMENGINE:
if symbol_expr.imag == 0.0:
return True
return False
return symbol_expr.is_real
[ドキュメント] 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. Qiskit will not accept or work with raw Sympy or
Symegine expressions in its parameters, because they do not contain the tracking
information used in circuit-parameter binding and assignment.
"""
return self._symbol_expr
# Redefine the type so external imports get an evaluated reference; Sphinx needs this to understand
# the type hints.
ParameterValueType = Union[ParameterExpression, float]