コード例 #1
0
    def get_eqn_matrix(expressions, varList):
        """ Return A and B matrices for expression with x as varList """

        exprs = []
        for expr in expressions.split('&&'):
            if '==' in expr:
                eq = expr.split('==')
                exprs.append(sympy.sympify(eq[0] + '<=' + eq[1]))
                exprs.append(sympy.sympify(eq[0] + '>=' + eq[1]))
            else:
                sym_expr = sympy.sympify(expr)
                if sym_expr.func == sympy.StrictLessThan:
                    sym_expr = sympy.LessThan(sym_expr.lhs, sym_expr.rhs)
                elif sym_expr.func == sympy.StrictGreaterThan:
                    sym_expr = sympy.GreaterThan(sym_expr.lhs, sym_expr.rhs)
                exprs.append(sym_expr)
        aMatrix = [[0 for v in varList] for expr in exprs]
        bMatrix = [0 for expr in exprs]
        eqMatrix = []
        for i, expr in enumerate(exprs):
            eqMatrix.append([expr.rel_op])
            expr = expr.lhs - expr.rhs
            expr *= SymEq.get_factor(expr)
            for v in expr.free_symbols:
                aMatrix[i][varList.index(
                    str(v))] = expr.as_coefficients_dict()[v]
                bMatrix[i] = [
                    -expr.as_coefficients_dict()[sympy.numbers.One()]
                ]
        return [aMatrix, bMatrix, eqMatrix]
コード例 #2
0
 def construct_invariant(guard):
     inv_eqn = []
     for eqn in guard.expr:
         print('Eqn is: ' + str(eqn))
         if eqn.func == sympy.LessThan:
             inv = sympy.GreaterThan(*eqn.args)
         elif eqn.func == sympy.GreaterThan:
             inv = sympy.LessThan(*eqn.args)
         elif eqn.func == sympy.StrictLessThan:
             inv = sympy.StrictGreaterThan(*eqn.args)
         elif eqn.func == sympy.StrictGreaterThan:
             inv = sympy.StrictLessThan(*eqn.args)
         inv_eqn.append(inv)
     inv_eqn = [str(inv) for inv in inv_eqn]
     return Invariant('||'.join(inv_eqn))
コード例 #3
0
ファイル: process_latex.py プロジェクト: HuyLafa/MathTutor
def convert_relation(rel):
    if rel.expr():
        return convert_expr(rel.expr())

    lh = convert_relation(rel.relation(0))
    rh = convert_relation(rel.relation(1))
    if rel.LT():
        return sympy.StrictLessThan(lh, rh)
    elif rel.LTE():
        return sympy.LessThan(lh, rh)
    elif rel.GT():
        return sympy.StrictGreaterThan(lh, rh)
    elif rel.GTE():
        return sympy.GreaterThan(lh, rh)
    elif rel.EQUAL():
        return sympy.Eq(lh, rh)
コード例 #4
0
ファイル: parse.py プロジェクト: mattpaletta/latexpr
    def __convert_relation(rel: PSParser.RelationContext):
        if rel.expr():
            return Math.__convert_expr(rel.expr())

        lh = Math.__convert_relation(rel.relation(0))
        rh = Math.__convert_relation(rel.relation(1))
        if rel.LT():
            return sympy.StrictLessThan(lh, rh)
        elif rel.LTE():
            return sympy.LessThan(lh, rh)
        elif rel.GT():
            return sympy.StrictGreaterThan(lh, rh)
        elif rel.GTE():
            return sympy.GreaterThan(lh, rh)
        elif rel.EQUAL():
            return sympy.Eq(lh, rh)
        else:
            raise NotImplementedError("Function implemented")
コード例 #5
0
def convert_relation(rel):
    if rel.expr():
        return convert_expr(rel.expr())

    lh = convert_relation(rel.relation(0))
    rh = convert_relation(rel.relation(1))
    if rel.LT():
        return sympy.StrictLessThan(lh, rh, evaluate=False)
    elif rel.LTE():
        return sympy.LessThan(lh, rh, evaluate=False)
    elif rel.GT():
        return sympy.StrictGreaterThan(lh, rh, evaluate=False)
    elif rel.GTE():
        return sympy.GreaterThan(lh, rh, evaluate=False)
    elif rel.EQUAL():
        return sympy.Eq(lh, rh, evaluate=False)
    elif rel.ASSIGNMENT():
        # !Use Global variances
        variances[lh] = rh
        var[str(lh)] = rh
        return rh
    elif rel.UNEQUAL():
        return sympy.Ne(lh, rh, evaluate=False)
コード例 #6
0
    def calculate_cache_access(self):
        # FIXME handle multiple datatypes
        element_size = self.kernel.datatypes_size[self.kernel.datatype]

        results = {'dimensions': {}}

        def sympy_compare(a, b):
            c = 0
            for i in range(min(len(a), len(b))):
                s = a[i] - b[i]
                if sympy.simplify(s > 0):
                    c = -1
                elif sympy.simplify(s == 0):
                    c = 0
                else:
                    c = 1
                if c != 0: break
            return c

        accesses = defaultdict(list)
        sympy_accesses = defaultdict(list)
        for var_name in self.kernel.variables:
            for r in self.kernel._sources.get(var_name, []):
                if r is None: continue
                accesses[var_name].append(r)
                sympy_accesses[var_name].append(
                    self.kernel.access_to_sympy(var_name, r))
            for w in self.kernel._destinations.get(var_name, []):
                if w is None: continue
                accesses[var_name].append(w)
                sympy_accesses[var_name].append(
                    self.kernel.access_to_sympy(var_name, w))
            # order accesses by increasing order
            accesses[var_name].sort(
                key=cmp_to_key(sympy_compare))  #cmp=sympy_compare)

        results['accesses'] = accesses
        results['sympy_accesses'] = sympy_accesses

        # For each dimension (1D, 2D, 3D ... nD)
        for dimension in range(1, len(list(self.kernel.get_loop_stack())) + 1):
            results['dimensions'][dimension] = {}

            slices = defaultdict(list)
            slices_accesses = defaultdict(list)
            for var_name in accesses:
                for a in accesses[var_name]:
                    # slices are identified by the tuple of indices of higher dimensions
                    slice_id = tuple([var_name, tuple(a[:-dimension])])
                    slices[slice_id].append(a)
                    slices_accesses[slice_id].append(
                        self.kernel.access_to_sympy(var_name, a))
            results['dimensions'][dimension]['slices'] = slices
            results['dimensions'][dimension][
                'slices_accesses'] = slices_accesses

            slices_distances = defaultdict(list)
            for k, v in slices_accesses.items():
                for i in range(1, len(v)):
                    slices_distances[k].append((v[i - 1] - v[i]).simplify())
            results['dimensions'][dimension][
                'slices_distances'] = slices_distances

            # Check that distances contain only free_symbols based on constants
            for dist in chain(*slices_distances.values()):
                if any([
                        s not in self.kernel.constants.keys()
                        for s in dist.free_symbols
                ]):
                    raise ValueError(
                        "Some distances are not based on non-constants: " +
                        str(dist))

            # Sum of lengths between relative distances
            slices_sum = sum(
                [sum(dists) for dists in slices_distances.values()])
            results['dimensions'][dimension]['slices_sum'] = slices_sum

            # Max of lengths between relative distances
            # Work-around, the arguments with the most symbols get to stay
            # FIXME, may not be correct in all cases. e.g., N+M vs. N*M
            def FuckedUpMax(*args):
                if len(args) == 1:
                    return args[0]
                # expand all expressions:
                args = [a.expand() for a in args]
                # Filter expressions with less than the maximum number of symbols
                max_symbols = max([len(a.free_symbols) for a in args])
                args = list(
                    filter(lambda a: len(a.free_symbols) == max_symbols, args))
                if max_symbols == 0:
                    return sympy.Max(*args)
                # Filter symbols with lower exponent
                max_coeffs = 0
                for a in args:
                    for s in a.free_symbols:
                        max_coeffs = max(max_coeffs,
                                         len(sympy.Poly(a, s).all_coeffs()))

                def coeff_filter(a):
                    return max(
                        0, 0, *[
                            len(sympy.Poly(a, s).all_coeffs())
                            for s in a.free_symbols
                        ]) == max_coeffs

                args = list(filter(coeff_filter, args))

                m = sympy.Max(*args)
                #if m.is_Function:
                #    raise ValueError("Could not resolve {} to maximum.".format(m))
                return m

            slices_max = FuckedUpMax(
                *[FuckedUpMax(*dists) for dists in slices_distances.values()])
            results['dimensions'][dimension]['slices_sum'] = slices_sum

            # Nmber of slices
            slices_count = len(slices_accesses)
            results['dimensions'][dimension]['slices_count'] = slices_count

            # Cache requirement expression
            cache_requirement_bytes = (
                slices_sum + slices_max * slices_count) * element_size
            results['dimensions'][dimension][
                'cache_requirement_bytes'] = cache_requirement_bytes

            # Apply to all cache sizes
            csim = self.machine.get_cachesim()
            results['dimensions'][dimension]['caches'] = {}
            for cl in csim.levels(with_mem=False):
                cache_equation = sympy.Eq(cache_requirement_bytes, cl.size())
                if len(self.kernel.constants.keys()) <= 1:
                    inequality = sympy.solve(
                        sympy.LessThan(cache_requirement_bytes, cl.size()),
                        *self.kernel.constants.keys())
                else:
                    # Sympy does not solve for multiple constants
                    inequality = sympy.LessThan(cache_requirement_bytes,
                                                cl.size())
                results['dimensions'][dimension]['caches'][cl.name] = {
                    'cache_size':
                    cl.size(),
                    'equation':
                    cache_equation,
                    'lt':
                    inequality,
                    'eq':
                    sympy.solve(cache_equation,
                                *self.kernel.constants.keys(),
                                dict=True)
                }

        return results
コード例 #7
0
def _class_resolver_dictionary() -> Dict[str, ObjectFactory]:
    import cirq
    from cirq.ops import raw_types
    import pandas as pd
    import numpy as np
    from cirq.devices.noise_model import _NoNoiseModel
    from cirq.experiments import CrossEntropyResult, CrossEntropyResultDict, GridInteractionLayer
    from cirq.experiments.grid_parallel_two_qubit_xeb import GridParallelXEBMetadata

    def _boolean_hamiltonian_gate_op(qubit_map, boolean_strs, theta):
        return cirq.BooleanHamiltonianGate(parameter_names=list(
            qubit_map.keys()),
                                           boolean_strs=boolean_strs,
                                           theta=theta).on(*qubit_map.values())

    def _identity_operation_from_dict(qubits, **kwargs):
        return cirq.identity_each(*qubits)

    def single_qubit_matrix_gate(matrix):
        if not isinstance(matrix, np.ndarray):
            matrix = np.array(matrix, dtype=np.complex128)
        return cirq.MatrixGate(matrix, qid_shape=(matrix.shape[0], ))

    def two_qubit_matrix_gate(matrix):
        if not isinstance(matrix, np.ndarray):
            matrix = np.array(matrix, dtype=np.complex128)
        return cirq.MatrixGate(matrix, qid_shape=(2, 2))

    def _parallel_gate_op(gate, qubits):
        return cirq.parallel_gate_op(gate, *qubits)

    def _datetime(timestamp: float) -> datetime.datetime:
        # As part of our serialization logic, we make sure we only serialize "aware"
        # datetimes with the UTC timezone, so we implicitly add back in the UTC timezone here.
        #
        # Please note: even if the assumption is somehow violated, the fact that we use
        # unix timestamps should mean that the deserialized datetime should refer to the
        # same point in time but may not satisfy o = read_json(to_json(o)) because the actual
        # timezones, and hour fields will not be identical.
        return datetime.datetime.fromtimestamp(timestamp,
                                               tz=datetime.timezone.utc)

    def _symmetricalqidpair(qids):
        return frozenset(qids)

    import sympy

    return {
        'AmplitudeDampingChannel': cirq.AmplitudeDampingChannel,
        'AnyIntegerPowerGateFamily': cirq.AnyIntegerPowerGateFamily,
        'AnyUnitaryGateFamily': cirq.AnyUnitaryGateFamily,
        'AsymmetricDepolarizingChannel': cirq.AsymmetricDepolarizingChannel,
        'BitFlipChannel': cirq.BitFlipChannel,
        'BitstringAccumulator': cirq.work.BitstringAccumulator,
        'BooleanHamiltonianGate': cirq.BooleanHamiltonianGate,
        'CCNotPowGate': cirq.CCNotPowGate,
        'CCXPowGate': cirq.CCXPowGate,
        'CCZPowGate': cirq.CCZPowGate,
        'Circuit': cirq.Circuit,
        'CircuitOperation': cirq.CircuitOperation,
        'ClassicallyControlledOperation': cirq.ClassicallyControlledOperation,
        'ClassicalDataDictionaryStore': cirq.ClassicalDataDictionaryStore,
        'CliffordGate': cirq.CliffordGate,
        'CliffordState': cirq.CliffordState,
        'CliffordTableau': cirq.CliffordTableau,
        'CNotPowGate': cirq.CNotPowGate,
        'ConstantQubitNoiseModel': cirq.ConstantQubitNoiseModel,
        'ControlledGate': cirq.ControlledGate,
        'ControlledOperation': cirq.ControlledOperation,
        'CrossEntropyResult': CrossEntropyResult,
        'CrossEntropyResultDict': CrossEntropyResultDict,
        'CSwapGate': cirq.CSwapGate,
        'CXPowGate': cirq.CXPowGate,
        'CZPowGate': cirq.CZPowGate,
        'CZTargetGateset': cirq.CZTargetGateset,
        'DiagonalGate': cirq.DiagonalGate,
        'DensePauliString': cirq.DensePauliString,
        'DepolarizingChannel': cirq.DepolarizingChannel,
        'DeviceMetadata': cirq.DeviceMetadata,
        'Duration': cirq.Duration,
        'FrozenCircuit': cirq.FrozenCircuit,
        'FSimGate': cirq.FSimGate,
        'GateFamily': cirq.GateFamily,
        'GateOperation': cirq.GateOperation,
        'Gateset': cirq.Gateset,
        'GeneralizedAmplitudeDampingChannel':
        cirq.GeneralizedAmplitudeDampingChannel,
        'GlobalPhaseGate': cirq.GlobalPhaseGate,
        'GlobalPhaseOperation': cirq.GlobalPhaseOperation,
        'GridDeviceMetadata': cirq.GridDeviceMetadata,
        'GridInteractionLayer': GridInteractionLayer,
        'GridParallelXEBMetadata': GridParallelXEBMetadata,
        'GridQid': cirq.GridQid,
        'GridQubit': cirq.GridQubit,
        'HPowGate': cirq.HPowGate,
        'ISwapPowGate': cirq.ISwapPowGate,
        'IdentityGate': cirq.IdentityGate,
        'InitObsSetting': cirq.work.InitObsSetting,
        'KeyCondition': cirq.KeyCondition,
        'KrausChannel': cirq.KrausChannel,
        'LinearDict': cirq.LinearDict,
        'LineQubit': cirq.LineQubit,
        'LineQid': cirq.LineQid,
        'LineTopology': cirq.LineTopology,
        'MatrixGate': cirq.MatrixGate,
        'MixedUnitaryChannel': cirq.MixedUnitaryChannel,
        'MeasurementKey': cirq.MeasurementKey,
        'MeasurementGate': cirq.MeasurementGate,
        'MeasurementType': cirq.MeasurementType,
        '_MeasurementSpec': cirq.work._MeasurementSpec,
        'Moment': cirq.Moment,
        'MutableDensePauliString': cirq.MutableDensePauliString,
        'MutablePauliString': cirq.MutablePauliString,
        '_NoNoiseModel': _NoNoiseModel,
        'NamedQubit': cirq.NamedQubit,
        'NamedQid': cirq.NamedQid,
        'NoIdentifierQubit': cirq.testing.NoIdentifierQubit,
        'ObservableMeasuredResult': cirq.work.ObservableMeasuredResult,
        'OpIdentifier': cirq.OpIdentifier,
        'ParamResolver': cirq.ParamResolver,
        'ParallelGate': cirq.ParallelGate,
        'ParallelGateFamily': cirq.ParallelGateFamily,
        'PauliInteractionGate': cirq.PauliInteractionGate,
        'PauliMeasurementGate': cirq.PauliMeasurementGate,
        'PauliString': cirq.PauliString,
        'PauliStringPhasor': cirq.PauliStringPhasor,
        'PauliStringPhasorGate': cirq.PauliStringPhasorGate,
        'PauliSum': cirq.PauliSum,
        '_PauliX': cirq.ops.pauli_gates._PauliX,
        '_PauliY': cirq.ops.pauli_gates._PauliY,
        '_PauliZ': cirq.ops.pauli_gates._PauliZ,
        'PhaseDampingChannel': cirq.PhaseDampingChannel,
        'PhaseFlipChannel': cirq.PhaseFlipChannel,
        'PhaseGradientGate': cirq.PhaseGradientGate,
        'PhasedFSimGate': cirq.PhasedFSimGate,
        'PhasedISwapPowGate': cirq.PhasedISwapPowGate,
        'PhasedXPowGate': cirq.PhasedXPowGate,
        'PhasedXZGate': cirq.PhasedXZGate,
        'ProductState': cirq.ProductState,
        'ProjectorString': cirq.ProjectorString,
        'ProjectorSum': cirq.ProjectorSum,
        'QasmUGate': cirq.circuits.qasm_output.QasmUGate,
        '_QubitAsQid': raw_types._QubitAsQid,
        'QuantumFourierTransformGate': cirq.QuantumFourierTransformGate,
        'QubitPermutationGate': cirq.QubitPermutationGate,
        'RandomGateChannel': cirq.RandomGateChannel,
        'RepetitionsStoppingCriteria': cirq.work.RepetitionsStoppingCriteria,
        'ResetChannel': cirq.ResetChannel,
        'Result': cirq.ResultDict,  # Keep support for Cirq < 0.14.
        'ResultDict': cirq.ResultDict,
        'Rx': cirq.Rx,
        'Ry': cirq.Ry,
        'Rz': cirq.Rz,
        'SingleQubitCliffordGate': cirq.SingleQubitCliffordGate,
        'SingleQubitPauliStringGateOperation':
        cirq.SingleQubitPauliStringGateOperation,
        'SingleQubitReadoutCalibrationResult':
        cirq.experiments.SingleQubitReadoutCalibrationResult,
        'SqrtIswapTargetGateset': cirq.SqrtIswapTargetGateset,
        'StabilizerStateChForm': cirq.StabilizerStateChForm,
        'StatePreparationChannel': cirq.StatePreparationChannel,
        'SwapPowGate': cirq.SwapPowGate,
        'SympyCondition': cirq.SympyCondition,
        'TaggedOperation': cirq.TaggedOperation,
        'TensoredConfusionMatrices': cirq.TensoredConfusionMatrices,
        'TiltedSquareLattice': cirq.TiltedSquareLattice,
        'ThreeQubitDiagonalGate': cirq.ThreeQubitDiagonalGate,
        'TrialResult': cirq.ResultDict,  # keep support for Cirq < 0.11.
        'TwoQubitDiagonalGate': cirq.TwoQubitDiagonalGate,
        'TwoQubitGateTabulation': cirq.TwoQubitGateTabulation,
        '_UnconstrainedDevice':
        cirq.devices.unconstrained_device._UnconstrainedDevice,
        'VarianceStoppingCriteria': cirq.work.VarianceStoppingCriteria,
        'VirtualTag': cirq.VirtualTag,
        'WaitGate': cirq.WaitGate,
        # The formatter keeps putting this back
        # pylint: disable=line-too-long
        'XEBPhasedFSimCharacterizationOptions':
        cirq.experiments.XEBPhasedFSimCharacterizationOptions,
        # pylint: enable=line-too-long
        '_XEigenState': cirq.value.product_state._XEigenState,  # type: ignore
        'XPowGate': cirq.XPowGate,
        'XXPowGate': cirq.XXPowGate,
        '_YEigenState': cirq.value.product_state._YEigenState,  # type: ignore
        'YPowGate': cirq.YPowGate,
        'YYPowGate': cirq.YYPowGate,
        '_ZEigenState': cirq.value.product_state._ZEigenState,  # type: ignore
        'ZPowGate': cirq.ZPowGate,
        'ZZPowGate': cirq.ZZPowGate,
        # Old types, only supported for backwards-compatibility
        'BooleanHamiltonian': _boolean_hamiltonian_gate_op,  # Removed in v0.15
        'IdentityOperation': _identity_operation_from_dict,
        'ParallelGateOperation': _parallel_gate_op,  # Removed in v0.14
        'SingleQubitMatrixGate': single_qubit_matrix_gate,
        'SymmetricalQidPair': _symmetricalqidpair,  # Removed in v0.15
        'TwoQubitMatrixGate': two_qubit_matrix_gate,
        # not a cirq class, but treated as one:
        'pandas.DataFrame': pd.DataFrame,
        'pandas.Index': pd.Index,
        'pandas.MultiIndex': pd.MultiIndex.from_tuples,
        'sympy.Symbol': sympy.Symbol,
        'sympy.Add': lambda args: sympy.Add(*args),
        'sympy.Mul': lambda args: sympy.Mul(*args),
        'sympy.Pow': lambda args: sympy.Pow(*args),
        'sympy.GreaterThan': lambda args: sympy.GreaterThan(*args),
        'sympy.StrictGreaterThan': lambda args: sympy.StrictGreaterThan(*args),
        'sympy.LessThan': lambda args: sympy.LessThan(*args),
        'sympy.StrictLessThan': lambda args: sympy.StrictLessThan(*args),
        'sympy.Equality': lambda args: sympy.Equality(*args),
        'sympy.Unequality': lambda args: sympy.Unequality(*args),
        'sympy.Float': lambda approx: sympy.Float(approx),
        'sympy.Integer': sympy.Integer,
        'sympy.Rational': sympy.Rational,
        'sympy.pi': lambda: sympy.pi,
        'sympy.E': lambda: sympy.E,
        'sympy.EulerGamma': lambda: sympy.EulerGamma,
        'complex': complex,
        'datetime.datetime': _datetime,
    }
コード例 #8
0
def approx_eq(val: Any, other: Any, *, atol: Union[int, float] = 1e-8) -> bool:
    """Approximately compares two objects.

    If `val` implements SupportsApproxEquality protocol then it is invoked and
    takes precedence over all other checks:
     - For primitive numeric types `int` and `float` approximate equality is
       delegated to math.isclose().
     - For complex primitive type the real and imaginary parts are treated
       independently and compared using math.isclose().
     - For `val` and `other` both iterable of the same length, consecutive
       elements are compared recursively. Types of `val` and `other` does not
       necessarily needs to match each other. They just need to be iterable and
       have the same structure.

    Args:
        val: Source object for approximate comparison.
        other: Target object for approximate comparison.
        atol: The minimum absolute tolerance. See np.isclose() documentation for
              details. Defaults to 1e-8 which matches np.isclose() default
              absolute tolerance.

    Returns:
        True if objects are approximately equal, False otherwise.
    """

    # Check if val defines approximate equality via _approx_eq_. This takes
    # precedence over all other overloads.
    approx_eq_getter = getattr(val, '_approx_eq_', None)
    if approx_eq_getter is not None:
        result = approx_eq_getter(other, atol)
        if result is not NotImplemented:
            return result

    # The same for other to make approx_eq symmetric.
    other_approx_eq_getter = getattr(other, '_approx_eq_', None)
    if other_approx_eq_getter is not None:
        result = other_approx_eq_getter(val, atol)
        if result is not NotImplemented:
            return result

    # Compare primitive types directly.
    if isinstance(val, numbers.Number):
        if not isinstance(other, numbers.Number):
            return False
        result = _isclose(val, other, atol=atol)
        if result is not NotImplemented:
            return result

    if isinstance(val, str):
        return val == other

    if isinstance(val, sympy.Basic) or isinstance(other, sympy.Basic):
        delta = sympy.Abs(other - val).simplify()
        if not delta.is_number:
            raise AttributeError('Insufficient information to decide whether '
                                 'expressions are approximately equal '
                                 f'[{val}] vs [{other}]')
        return sympy.LessThan(delta, atol) == sympy.true

    # If the values are iterable, try comparing recursively on items.
    if isinstance(val, Iterable) and isinstance(other, Iterable):
        return _approx_eq_iterables(val, other, atol=atol)

    # Last resort: exact equality.
    return val == other
コード例 #9
0
print('## str, repr')
display(str(expr))
display(repr(expr))

# In[10]:

display((expr.lhs, expr.rhs))  # left-hand side, # right-hand side
display((expr.lts, expr.gts))  # less-than side, # greater-than side
# Sympy rewrites inequalities so that the left-hand side is the less-than-side:
assert expr.lhs == expr.lts
assert expr.rhs == expr.gts

# In[11]:

expr = sympy.solve(x <= 10)
expr2 = sympy.LessThan(x, 10)
expr3 = (x <= 10)
expr4 = (10 >= x)
display(expr, expr2, expr3, expr4)
assert expr == expr2 == expr3 == expr4
# Sympy rewrites inequalities so that the left-hand side is the less-than-side:
assert (expr.lhs, expr.rhs) == (expr.lts, expr.gts)
assert (expr4.lhs, expr4.rhs) == (expr4.lts, expr4.gts)
display((expr2.lts, expr2.gts))
display((expr3.lts, expr3.gts))
display((expr4.lts, expr4.gts))

# In[12]:

expr.rel_op
コード例 #10
0
ファイル: test.py プロジェクト: Udaptive/latex2sympy
 ("x_0", sympy.Symbol('x_{0}')), ("x_{1}", sympy.Symbol('x_{1}')),
 ("x_a", sympy.Symbol('x_{a}')), ("x_{b}", sympy.Symbol('x_{b}')),
 ("h_\\theta", sympy.Symbol('h_{theta}')),
 ("h_{\\theta}", sympy.Symbol('h_{theta}')),
 ("h_{\\theta}(x_0, x_1)",
  sympy.Symbol('h_{theta}')(sympy.Symbol('x_{0}'), sympy.Symbol('x_{1}'))),
 ("x!", _factorial(x)), ("100!", _factorial(100)),
 ("\\theta!", _factorial(theta)), ("(x + 1)!", _factorial(_Add(x, 1))),
 ("(x!)!", _factorial(_factorial(x))),
 ("x!!!", _factorial(_factorial(_factorial(x)))),
 ("5!7!", _Mul(_factorial(5), _factorial(7))), ("\\sqrt{x}", sympy.sqrt(x)),
 ("\\sqrt{x + b}", sympy.sqrt(_Add(x, b))),
 ("\\sqrt[3]{\\sin x}", sympy.root(sympy.sin(x), 3)),
 ("\\sqrt[y]{\\sin x}", sympy.root(sympy.sin(x), y)),
 ("\\sqrt[\\theta]{\\sin x}", sympy.root(sympy.sin(x), theta)),
 ("x < y", sympy.StrictLessThan(x, y)), ("x \\leq y", sympy.LessThan(x, y)),
 ("x > y", sympy.StrictGreaterThan(x, y)),
 ("x \\geq y", sympy.GreaterThan(x, y)), ("\\mathit{x}", sympy.Symbol('x')),
 ("\\mathit{test}", sympy.Symbol('test')),
 ("\\mathit{TEST}", sympy.Symbol('TEST')),
 ("\\mathit{HELLO world}", sympy.Symbol('HELLO world')),
 ("\\sum_{k = 1}^{3} c", sympy.Sum(c, (k, 1, 3))),
 ("\\sum_{k = 1}^3 c", sympy.Sum(c, (k, 1, 3))),
 ("\\sum^{3}_{k = 1} c", sympy.Sum(c, (k, 1, 3))),
 ("\\sum^3_{k = 1} c", sympy.Sum(c, (k, 1, 3))),
 ("\\sum_{k = 1}^{10} k^2", sympy.Sum(k**2, (k, 1, 10))),
 ("\\sum_{n = 0}^{\\infty} \\frac{1}{n!}",
  sympy.Sum(_Pow(_factorial(n), -1), (n, 0, sympy.oo))),
 ("\\prod_{a = b}^{c} x", sympy.Product(x, (a, b, c))),
 ("\\prod_{a = b}^c x", sympy.Product(x, (a, b, c))),
 ("\\prod^{c}_{a = b} x", sympy.Product(x, (a, b, c))),
コード例 #11
0
def _class_resolver_dictionary() -> Dict[str, ObjectFactory]:
    import cirq
    from cirq.ops import raw_types
    import pandas as pd
    import numpy as np
    from cirq.devices.noise_model import _NoNoiseModel
    from cirq.experiments import CrossEntropyResult, CrossEntropyResultDict, GridInteractionLayer
    from cirq.experiments.grid_parallel_two_qubit_xeb import GridParallelXEBMetadata

    def _identity_operation_from_dict(qubits, **kwargs):
        return cirq.identity_each(*qubits)

    def single_qubit_matrix_gate(matrix):
        if not isinstance(matrix, np.ndarray):
            matrix = np.array(matrix, dtype=np.complex128)
        return cirq.MatrixGate(matrix, qid_shape=(matrix.shape[0], ))

    def two_qubit_matrix_gate(matrix):
        if not isinstance(matrix, np.ndarray):
            matrix = np.array(matrix, dtype=np.complex128)
        return cirq.MatrixGate(matrix, qid_shape=(2, 2))

    def _parallel_gate_op(gate, qubits):
        return cirq.parallel_gate_op(gate, *qubits)

    import sympy

    return {
        'AmplitudeDampingChannel': cirq.AmplitudeDampingChannel,
        'AnyIntegerPowerGateFamily': cirq.AnyIntegerPowerGateFamily,
        'AnyUnitaryGateFamily': cirq.AnyUnitaryGateFamily,
        'AsymmetricDepolarizingChannel': cirq.AsymmetricDepolarizingChannel,
        'BitFlipChannel': cirq.BitFlipChannel,
        'BitstringAccumulator': cirq.work.BitstringAccumulator,
        'BooleanHamiltonian': cirq.BooleanHamiltonian,
        'CCNotPowGate': cirq.CCNotPowGate,
        'CCXPowGate': cirq.CCXPowGate,
        'CCZPowGate': cirq.CCZPowGate,
        'Circuit': cirq.Circuit,
        'CircuitOperation': cirq.CircuitOperation,
        'ClassicallyControlledOperation': cirq.ClassicallyControlledOperation,
        'CliffordState': cirq.CliffordState,
        'CliffordTableau': cirq.CliffordTableau,
        'CNotPowGate': cirq.CNotPowGate,
        'ConstantQubitNoiseModel': cirq.ConstantQubitNoiseModel,
        'ControlledGate': cirq.ControlledGate,
        'ControlledOperation': cirq.ControlledOperation,
        'CrossEntropyResult': CrossEntropyResult,
        'CrossEntropyResultDict': CrossEntropyResultDict,
        'CSwapGate': cirq.CSwapGate,
        'CXPowGate': cirq.CXPowGate,
        'CZPowGate': cirq.CZPowGate,
        'DensePauliString': cirq.DensePauliString,
        'DepolarizingChannel': cirq.DepolarizingChannel,
        'DeviceMetadata': cirq.DeviceMetadata,
        'Duration': cirq.Duration,
        'FrozenCircuit': cirq.FrozenCircuit,
        'FSimGate': cirq.FSimGate,
        'GateFamily': cirq.GateFamily,
        'GateOperation': cirq.GateOperation,
        'Gateset': cirq.Gateset,
        'GeneralizedAmplitudeDampingChannel':
        cirq.GeneralizedAmplitudeDampingChannel,
        'GlobalPhaseGate': cirq.GlobalPhaseGate,
        'GlobalPhaseOperation': cirq.GlobalPhaseOperation,
        'GridDeviceMetadata': cirq.GridDeviceMetadata,
        'GridInteractionLayer': GridInteractionLayer,
        'GridParallelXEBMetadata': GridParallelXEBMetadata,
        'GridQid': cirq.GridQid,
        'GridQubit': cirq.GridQubit,
        'HPowGate': cirq.HPowGate,
        'ISwapPowGate': cirq.ISwapPowGate,
        'IdentityGate': cirq.IdentityGate,
        'InitObsSetting': cirq.work.InitObsSetting,
        'KeyCondition': cirq.KeyCondition,
        'KrausChannel': cirq.KrausChannel,
        'LinearDict': cirq.LinearDict,
        'LineQubit': cirq.LineQubit,
        'LineQid': cirq.LineQid,
        'LineTopology': cirq.LineTopology,
        'MatrixGate': cirq.MatrixGate,
        'MixedUnitaryChannel': cirq.MixedUnitaryChannel,
        'MeasurementKey': cirq.MeasurementKey,
        'MeasurementGate': cirq.MeasurementGate,
        '_MeasurementSpec': cirq.work._MeasurementSpec,
        'Moment': cirq.Moment,
        'MutableDensePauliString': cirq.MutableDensePauliString,
        'MutablePauliString': cirq.MutablePauliString,
        '_NoNoiseModel': _NoNoiseModel,
        'NamedQubit': cirq.NamedQubit,
        'NamedQid': cirq.NamedQid,
        'NoIdentifierQubit': cirq.testing.NoIdentifierQubit,
        'ObservableMeasuredResult': cirq.work.ObservableMeasuredResult,
        'OpIdentifier': cirq.OpIdentifier,
        'ParamResolver': cirq.ParamResolver,
        'ParallelGate': cirq.ParallelGate,
        'ParallelGateFamily': cirq.ParallelGateFamily,
        'PauliMeasurementGate': cirq.PauliMeasurementGate,
        'PauliString': cirq.PauliString,
        'PauliStringPhasor': cirq.PauliStringPhasor,
        'PauliStringPhasorGate': cirq.PauliStringPhasorGate,
        '_PauliX': cirq.ops.pauli_gates._PauliX,
        '_PauliY': cirq.ops.pauli_gates._PauliY,
        '_PauliZ': cirq.ops.pauli_gates._PauliZ,
        'PhaseDampingChannel': cirq.PhaseDampingChannel,
        'PhaseFlipChannel': cirq.PhaseFlipChannel,
        'PhaseGradientGate': cirq.PhaseGradientGate,
        'PhasedFSimGate': cirq.PhasedFSimGate,
        'PhasedISwapPowGate': cirq.PhasedISwapPowGate,
        'PhasedXPowGate': cirq.PhasedXPowGate,
        'PhasedXZGate': cirq.PhasedXZGate,
        'ProductState': cirq.ProductState,
        'ProjectorString': cirq.ProjectorString,
        'ProjectorSum': cirq.ProjectorSum,
        'QasmUGate': cirq.circuits.qasm_output.QasmUGate,
        '_QubitAsQid': raw_types._QubitAsQid,
        'QuantumFourierTransformGate': cirq.QuantumFourierTransformGate,
        'RandomGateChannel': cirq.RandomGateChannel,
        'RepetitionsStoppingCriteria': cirq.work.RepetitionsStoppingCriteria,
        'ResetChannel': cirq.ResetChannel,
        'Result': cirq.Result,
        'Rx': cirq.Rx,
        'Ry': cirq.Ry,
        'Rz': cirq.Rz,
        'SingleQubitCliffordGate': cirq.SingleQubitCliffordGate,
        'SingleQubitPauliStringGateOperation':
        cirq.SingleQubitPauliStringGateOperation,
        'SingleQubitReadoutCalibrationResult':
        cirq.experiments.SingleQubitReadoutCalibrationResult,
        'StabilizerStateChForm': cirq.StabilizerStateChForm,
        'StatePreparationChannel': cirq.StatePreparationChannel,
        'SwapPowGate': cirq.SwapPowGate,
        'SymmetricalQidPair': cirq.SymmetricalQidPair,
        'SympyCondition': cirq.SympyCondition,
        'TaggedOperation': cirq.TaggedOperation,
        'TiltedSquareLattice': cirq.TiltedSquareLattice,
        'TrialResult': cirq.Result,  # keep support for Cirq < 0.11.
        'TwoQubitGateTabulation': cirq.TwoQubitGateTabulation,
        '_UnconstrainedDevice':
        cirq.devices.unconstrained_device._UnconstrainedDevice,
        'VarianceStoppingCriteria': cirq.work.VarianceStoppingCriteria,
        'VirtualTag': cirq.VirtualTag,
        'WaitGate': cirq.WaitGate,
        # The formatter keeps putting this back
        # pylint: disable=line-too-long
        'XEBPhasedFSimCharacterizationOptions':
        cirq.experiments.XEBPhasedFSimCharacterizationOptions,
        # pylint: enable=line-too-long
        '_XEigenState': cirq.value.product_state._XEigenState,  # type: ignore
        'XPowGate': cirq.XPowGate,
        'XXPowGate': cirq.XXPowGate,
        '_YEigenState': cirq.value.product_state._YEigenState,  # type: ignore
        'YPowGate': cirq.YPowGate,
        'YYPowGate': cirq.YYPowGate,
        '_ZEigenState': cirq.value.product_state._ZEigenState,  # type: ignore
        'ZPowGate': cirq.ZPowGate,
        'ZZPowGate': cirq.ZZPowGate,
        # Old types, only supported for backwards-compatibility
        'IdentityOperation': _identity_operation_from_dict,
        'ParallelGateOperation': _parallel_gate_op,  # Removed in v0.14
        'SingleQubitMatrixGate': single_qubit_matrix_gate,
        'TwoQubitMatrixGate': two_qubit_matrix_gate,
        # not a cirq class, but treated as one:
        'pandas.DataFrame': pd.DataFrame,
        'pandas.Index': pd.Index,
        'pandas.MultiIndex': pd.MultiIndex.from_tuples,
        'sympy.Symbol': sympy.Symbol,
        'sympy.Add': lambda args: sympy.Add(*args),
        'sympy.Mul': lambda args: sympy.Mul(*args),
        'sympy.Pow': lambda args: sympy.Pow(*args),
        'sympy.GreaterThan': lambda args: sympy.GreaterThan(*args),
        'sympy.StrictGreaterThan': lambda args: sympy.StrictGreaterThan(*args),
        'sympy.LessThan': lambda args: sympy.LessThan(*args),
        'sympy.StrictLessThan': lambda args: sympy.StrictLessThan(*args),
        'sympy.Equality': lambda args: sympy.Equality(*args),
        'sympy.Unequality': lambda args: sympy.Unequality(*args),
        'sympy.Float': lambda approx: sympy.Float(approx),
        'sympy.Integer': sympy.Integer,
        'sympy.Rational': sympy.Rational,
        'sympy.pi': lambda: sympy.pi,
        'sympy.E': lambda: sympy.E,
        'sympy.EulerGamma': lambda: sympy.EulerGamma,
        'complex': complex,
    }