from typing import Union, Dict, Tuple, Any, Sequence, Optional, Callable
from numbers import Number
from types import CodeType
import warnings
import functools
import builtins
import math
import sympy
import numpy
try:
from sympy.printing.numpy import NumPyPrinter
except ImportError:
# sympy moved NumPyPrinter in release 1.8
from sympy.printing.pycode import NumPyPrinter
warnings.warn("Please update sympy.", DeprecationWarning)
try:
import scipy.special as _special_functions
except ImportError:
_special_functions = {fname: numpy.vectorize(fobject)
for fname, fobject in math.__dict__.items()
if callable(fobject) and not fname.startswith('_') and fname not in numpy.__dict__}
warnings.warn('scipy is not installed. This reduces the set of available functions to those present in numpy + '
'manually vectorized functions in math.')
__all__ = ["sympify", "substitute_with_eval", "to_numpy", "get_variables", "get_free_symbols", "recursive_substitution",
"evaluate_lambdified", "get_most_simple_representation"]
_lru_cache = functools.lru_cache(maxsize=2048, typed=True)
Sympifyable = Union[str, Number, sympy.Expr, numpy.str_]
SYMPY_DURATION_ERROR_MARGIN = 1e-15 # error margin when checking sympy expression durations
class IndexedBasedFinder(dict):
"""Acts as a symbol lookup and determines which symbols in an expression a subscripted."""
def __init__(self):
super().__init__()
self.symbols = set()
self.indexed_base = set()
self.indices = set()
class SubscriptionChecker(sympy.Symbol):
"""A symbol stand-in which detects whether the symbol is subscripted."""
def __getitem__(s, k):
self.indexed_base.add(str(s))
self.indices.add(k)
if isinstance(k, SubscriptionChecker):
k = sympy.Symbol(str(k))
return sympy.IndexedBase(str(s))[k]
self.SubscriptionChecker = SubscriptionChecker
def unimplementded(*args, **kwargs):
raise NotImplementedError("Not a full dict")
for m in vars(dict).keys():
if not m.startswith('_') and (m not in ('pop',)):
setattr(self, m, unimplementded)
def __getitem__(self, k) -> sympy.Expr:
"""Return an instance of the internal SubscriptionChecker class for each symbol to determine which symbols are
indexed/subscripted.
__getitem__ is (apparently) called by symbol for each token and gets either symbol names or type names such as
'Integer', 'Float', etc. We have to take care of returning correct types for symbols (-> SubscriptionChecker)
and the base types (-> Integer, Float, etc).
"""
if not k:
raise KeyError(k)
if hasattr(sympy, k): # if k is a sympy base type identifier, return the base type
return getattr(sympy, k)
# otherwise track the symbol name and return a SubscriptionChecker instance
self.symbols.add(k)
return self.SubscriptionChecker(k)
def pop(self, key, *args, **kwargs):
# this is a workaround for some sympy 1.9 code
if args:
default, = args
elif kwargs:
default, = kwargs.values()
else:
raise KeyError(key)
return default
def __setitem__(self, key, value):
raise NotImplementedError("Not a full dict")
def __delitem__(self, key):
raise NotImplementedError("Not a full dict")
def __contains__(self, k) -> bool:
return bool(k)
class Broadcast(sympy.Function):
"""Broadcast x to the specified shape using numpy.broadcast_to. The shape must not be symbolic.
Examples:
>>> bc = Broadcast('a', (3,))
>>> assert bc.subs({'a': 2}) == sympy.Array([2, 2, 2])
>>> assert bc.subs({'a': (1, 2, 3)}) == sympy.Array([1, 2, 3])
"""
nargs = (2,)
@classmethod
def eval(cls, x, shape: Tuple[int]) -> Optional[sympy.Array]:
shape = _parse_broadcast_shape(shape, user=cls)
if shape is None:
return None
if hasattr(x, '__len__') or not x.free_symbols:
return sympy.Array(numpy.broadcast_to(x, shape))
def __getitem__(self, item: Union):
return IndexedBroadcast(*self.args, item)
# Not iterable. If not set to None __getitem__ would be used for iterating
__iter__ = None
def _eval_Integral(self, *symbols, **assumptions):
x, shape = self.args
return Broadcast(sympy.Integral(x, *symbols, **assumptions), shape)
def _eval_derivative(self, sym):
x, shape = self.args
return Broadcast(sympy.diff(x, sym), shape)
def _numpycode(self, printer, **kwargs):
x, shape = map(functools.partial(printer._print, **kwargs), self.args)
return f'broadcast_to({x}, {shape})'
class IndexedBroadcast(sympy.Function):
"""Broadcast x to the specified shape using numpy.broadcast_to and index in the result."""
nargs = (3,)
@classmethod
def eval(cls, x, shape: Tuple[int], idx: int) -> Optional[sympy.Expr]:
shape = _parse_broadcast_shape(shape, user=cls)
idx = _parse_broadcast_index(idx, user=cls)
if shape is None or idx is None:
return None
if hasattr(x, '__len__') or not x.free_symbols:
return sympy.Array(numpy.broadcast_to(x, shape))[idx]
def _eval_Integral(self, *symbols, **assumptions):
x, shape, idx = self.args
return IndexedBroadcast(sympy.Integral(x, *symbols, **assumptions), shape, idx)
def _eval_derivative(self, sym):
x, shape, idx = self.args
return IndexedBroadcast(sympy.diff(x, sym), shape, idx)
def _eval_is_commutative(self):
x, shape, idx = self.args
result = self.eval(*self.args)
if result is None:
return x.is_commutative
else:
return result.is_commutative
def _numpycode(self, printer, **kwargs):
x, shape, idx = map(functools.partial(printer._print, **kwargs), self.args)
return f'broadcast_to({x}, {shape})[{idx}]'
class Len(sympy.Function):
nargs = 1
@classmethod
def eval(cls, arg) -> Optional[sympy.Integer]:
if hasattr(arg, '__len__'):
return sympy.Integer(len(arg))
is_Integer = True
Len.__name__ = 'len'
sympify_namespace = {'len': Len,
'Len': Len,
'Broadcast': Broadcast,
'IndexedBroadcast': IndexedBroadcast}
def numpy_compatible_mul(*args) -> Union[sympy.Mul, sympy.Array]:
if any(isinstance(a, sympy.NDimArray) for a in args):
result = 1
for a in args:
result = result * (numpy.array(a.tolist()) if isinstance(a, sympy.NDimArray) else a)
return sympy.Array(result)
else:
return sympy.Mul(*args)
def numpy_compatible_add(*args) -> Union[sympy.Add, sympy.Array]:
if any(isinstance(a, sympy.NDimArray) for a in args):
result = 0
for a in args:
result = result + (numpy.array(a.tolist()) if isinstance(a, sympy.NDimArray) else a)
return sympy.Array(result)
else:
return sympy.Add(*args)
_NUMPY_COMPATIBLE = {
sympy.Add: numpy_compatible_add,
sympy.Mul: numpy_compatible_mul
}
def _float_arr_to_int_arr(float_arr):
"""Try to cast array to int64. Return original array if data is not representable."""
int_arr = float_arr.astype(numpy.int64)
if numpy.any(int_arr != float_arr):
# we either have a float that is too large or NaN
return float_arr
else:
return int_arr
def numpy_compatible_ceiling(input_value: Any) -> Any:
if isinstance(input_value, numpy.ndarray):
return _float_arr_to_int_arr(numpy.ceil(input_value))
else:
return sympy.ceiling(input_value)
def _floor_to_int(input_value: Any) -> Any:
if isinstance(input_value, numpy.ndarray):
return _float_arr_to_int_arr(numpy.floor(input_value))
else:
return sympy.floor(input_value)
[docs]def to_numpy(sympy_array: sympy.NDimArray) -> numpy.ndarray:
if isinstance(sympy_array, sympy.DenseNDimArray):
if len(sympy_array.shape) == 2:
return numpy.asarray(sympy_array.tomatrix())
elif len(sympy_array.shape) == 1:
return numpy.asarray(sympy_array)
return numpy.array(sympy_array.tolist())
def get_subscripted_symbols(expression: str) -> set:
# track all symbols that are subscipted in here
indexed_base_finder = IndexedBasedFinder()
sympy.sympify(expression, locals=indexed_base_finder)
return indexed_base_finder.indexed_base
[docs]def sympify(expr: Union[str, Number, sympy.Expr, numpy.str_], **kwargs) -> sympy.Expr:
if isinstance(expr, numpy.str_):
# putting numpy.str_ in sympy.sympify behaves unexpected in version 1.1.1
# It seems to ignore the locals argument
expr = str(expr)
if isinstance(expr, (tuple, list)):
expr = numpy.array(expr)
try:
return sympy.sympify(expr, **kwargs, locals=sympify_namespace)
except TypeError as err:
if True:#err.args[0] == "'Symbol' object is not subscriptable":
indexed_base = get_subscripted_symbols(expr)
return sympy.sympify(expr, **kwargs, locals={**{k: k if isinstance(k, Broadcast) else sympy.IndexedBase(k)
for k in indexed_base},
**sympify_namespace})
else:
raise
[docs]def get_most_simple_representation(expression: sympy.Expr) -> Union[str, int, float]:
if expression.free_symbols:
return str(expression)
elif expression.is_Integer:
return int(expression)
elif expression.is_Float:
return float(expression)
else:
return str(expression)
[docs]def get_free_symbols(expression: sympy.Expr) -> Sequence[sympy.Symbol]:
return tuple(symbol
for symbol in expression.free_symbols
if not isinstance(symbol, sympy.Indexed))
[docs]def get_variables(expression: sympy.Expr) -> Sequence[str]:
return tuple(map(str, get_free_symbols(expression)))
[docs]def substitute_with_eval(expression: sympy.Expr,
substitutions: Dict[str, Union[sympy.Expr, numpy.ndarray, str]]) -> sympy.Expr:
"""Substitutes only sympy.Symbols. Workaround for numpy like array behaviour. ~Factor 3 slower compared to subs"""
warnings.warn("substitute_with_eval does not handle dummy symbols correctly and is planned to be removed",
FutureWarning)
substitutions = {k: v if isinstance(v, sympy.Expr) else sympify(v)
for k, v in substitutions.items()}
for symbol in get_free_symbols(expression):
symbol_name = str(symbol)
if symbol_name not in substitutions:
substitutions[symbol_name] = symbol
string_representation = sympy.srepr(expression)
return eval(string_representation, sympy.__dict__, {'Symbol': substitutions.__getitem__,
'Mul': numpy_compatible_mul,
'Add': numpy_compatible_add})
get_free_symbols_cache = _lru_cache(get_free_symbols)
def _recursive_substitution(expression: sympy.Expr,
substitutions: Dict[sympy.Symbol, sympy.Expr]) -> sympy.Expr:
if not expression.free_symbols:
return expression
elif expression.func in (sympy.Symbol, sympy.Dummy):
return substitutions.get(expression, expression)
func = _NUMPY_COMPATIBLE.get(expression.func, expression.func)
substitutions = {s: substitutions.get(s, s) for s in get_free_symbols_cache(expression)}
operands = (_recursive_substitution(arg, substitutions) for arg in expression.args)
return func(*operands)
_cached_sympify = _lru_cache(sympify)
def sympify_cache(value):
"""Cache sympify result for all hashable types"""
if getattr(value, '__hash__', None) is not None:
try:
return _cached_sympify(value)
except TypeError:
pass
# type is either not hashable or the sympification failed for another reason
return sympify(value)
[docs]def recursive_substitution(expression: sympy.Expr,
substitutions: Dict[str, Union[sympy.Expr, numpy.ndarray, str]]) -> sympy.Expr:
substitutions = {k if isinstance(k, (sympy.Symbol, sympy.Dummy)) else sympy.Symbol(k): sympify_cache(v)
for k, v in substitutions.items()}
for s in get_free_symbols(expression):
substitutions.setdefault(s, s)
return _recursive_substitution(expression, substitutions)
_base_environment = {'builtins': builtins, '__builtins__': builtins, 'math': math}
_math_environment = {**_base_environment, **math.__dict__}
_numpy_environment = {**_base_environment, **numpy.__dict__}
_sympy_environment = {**_base_environment, **sympy.__dict__}
_lambdify_modules = [{'ceiling': numpy_compatible_ceiling, 'floor': _floor_to_int,
'Broadcast': numpy.broadcast_to}, 'numpy', _special_functions]
def evaluate_compiled(expression: sympy.Expr,
parameters: Dict[str, Union[numpy.ndarray, Number]],
compiled: CodeType=None, mode=None) -> Tuple[any, CodeType]:
if compiled is None:
compiled = compile(sympy.printing.lambdarepr.lambdarepr(expression),
'<string>', 'eval')
if mode == 'numeric' or mode is None:
result = eval(compiled, parameters.copy(), _numpy_environment)
elif mode == 'exact':
result = eval(compiled, parameters.copy(), _sympy_environment)
else:
raise ValueError("Unknown mode: '{}'".format(mode))
return result, compiled
[docs]def evaluate_lambdified(expression: Union[sympy.Expr, numpy.ndarray],
variables: Sequence[str],
parameters: Dict[str, Union[numpy.ndarray, Number]],
lambdified: Optional[Callable]) -> Tuple[Any, Any]:
lambdified = lambdified or sympy.lambdify(variables, expression, _lambdify_modules)
return lambdified(**parameters), lambdified
class HighPrecPrinter(NumPyPrinter):
"""Custom printer that translates sympy.Rational into TimeType"""
def _print_Rational(self, expr):
return f'TimeType.from_fraction({expr.p}, {expr.q})'
@classmethod
def make(cls, expr, modules, use_imps=True):
"""This is basically the printer creation code from sympy 1.6 lambdify"""
namespaces = []
if use_imps:
raise NotImplementedError('this is copied from lambdify printer creation but _imp_namespace is not puplic')
# Check for dict before iterating
namespaces += list(modules)
user_functions = {}
for m in _lambdify_modules[::-1]:
if isinstance(m, dict):
for k in m:
user_functions[k] = k
return cls({'fully_qualified_modules': False, 'inline': True,
'allow_unknown_functions': True,
'user_functions': user_functions})
def evaluate_lamdified_exact_rational(expression: sympy.Expr,
variables: Sequence[str],
parameters: Dict[str, Union[numpy.ndarray, Number]],
lambdified: Optional[Callable]) -> Tuple[Any, Any]:
"""Evaluates Rational as TimeType. Only supports scalar expressions"""
from qupulse.utils.types import TimeType
_lambdify_modules[0]['TimeType'] = TimeType
printer = HighPrecPrinter.make(expression, _lambdify_modules, use_imps=False)
lambdified = lambdified or sympy.lambdify(variables, expression, _lambdify_modules, printer=printer)
return lambdified(**parameters), lambdified
def almost_equal(lhs: sympy.Expr, rhs: sympy.Expr, epsilon: Optional[float]=None) -> Optional[bool]:
"""Returns True (or False) if the two expressions are almost equal (or not). Returns None if this cannot be
determined."""
if epsilon is None:
epsilon = SYMPY_DURATION_ERROR_MARGIN
relation = sympy.simplify(sympy.Abs(lhs - rhs) <= epsilon)
if relation is sympy.true:
return True
elif relation is sympy.false:
return False
else:
return None
class UnsupportedBroadcastArgumentWarning(RuntimeWarning):
pass
def _parse_broadcast_shape(shape: Tuple[int], user: type) -> Optional[Tuple[int]]:
try:
return tuple(map(int, shape))
except TypeError as err:
warnings.warn(f"The shape passed to {user.__module__}.{user.__name__} is not convertible to a tuple of integers: {err}\n"
"Be aware that using a symbolic shape can lead to unexpected behaviour.",
category=UnsupportedBroadcastArgumentWarning,
# probably sympy version dependent what is most useful here...
stacklevel=7)
return None
def _parse_broadcast_index(idx: int, user: type) -> Optional[int]:
try:
return int(idx)
except TypeError as err:
warnings.warn(f"The index passed to {user.__module__}.{user.__name__} is not convertible to an integer: {err}\n"
"Be aware that using a symbolic index can lead to unexpected behaviour.",
category=UnsupportedBroadcastArgumentWarning,
# probably sympy version dependent what is most useful here...
stacklevel=7)
return None