Vehicle-cpp/hkpc/software/sympy/physics/quantum/tests/test_represent.py

from sympy.core.numbers import (Float, I, Integer)
from sympy.matrices.dense import Matrix
from sympy.external import import_module
from sympy.testing.pytest import skip

from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.represent import (represent, rep_innerproduct,
                                             rep_expectation, enumerate_states)
from sympy.physics.quantum.state import Bra, Ket
from sympy.physics.quantum.operator import Operator, OuterProduct
from sympy.physics.quantum.tensorproduct import TensorProduct
from sympy.physics.quantum.tensorproduct import matrix_tensor_product
from sympy.physics.quantum.commutator import Commutator
from sympy.physics.quantum.anticommutator import AntiCommutator
from sympy.physics.quantum.innerproduct import InnerProduct
from sympy.physics.quantum.matrixutils import (numpy_ndarray,
                                               scipy_sparse_matrix, to_numpy,
                                               to_scipy_sparse, to_sympy)
from sympy.physics.quantum.cartesian import XKet, XOp, XBra
from sympy.physics.quantum.qapply import qapply
from sympy.physics.quantum.operatorset import operators_to_state

Amat = Matrix([[1, I], [-I, 1]])
Bmat = Matrix([[1, 2], [3, 4]])
Avec = Matrix([[1], [I]])


class AKet(Ket):

    @classmethod
    def dual_class(self):
        return ABra

    def _represent_default_basis(self, **options):
        return self._represent_AOp(None, **options)

    def _represent_AOp(self, basis, **options):
        return Avec


class ABra(Bra):

    @classmethod
    def dual_class(self):
        return AKet


class AOp(Operator):

    def _represent_default_basis(self, **options):
        return self._represent_AOp(None, **options)

    def _represent_AOp(self, basis, **options):
        return Amat


class BOp(Operator):

    def _represent_default_basis(self, **options):
        return self._represent_AOp(None, **options)

    def _represent_AOp(self, basis, **options):
        return Bmat


k = AKet('a')
b = ABra('a')
A = AOp('A')
B = BOp('B')

_tests = [
    # Bra
    (b, Dagger(Avec)),
    (Dagger(b), Avec),
    # Ket
    (k, Avec),
    (Dagger(k), Dagger(Avec)),
    # Operator
    (A, Amat),
    (Dagger(A), Dagger(Amat)),
    # OuterProduct
    (OuterProduct(k, b), Avec*Avec.H),
    # TensorProduct
    (TensorProduct(A, B), matrix_tensor_product(Amat, Bmat)),
    # Pow
    (A**2, Amat**2),
    # Add/Mul
    (A*B + 2*A, Amat*Bmat + 2*Amat),
    # Commutator
    (Commutator(A, B), Amat*Bmat - Bmat*Amat),
    # AntiCommutator
    (AntiCommutator(A, B), Amat*Bmat + Bmat*Amat),
    # InnerProduct
    (InnerProduct(b, k), (Avec.H*Avec)[0])
]


def test_format_sympy():
    for test in _tests:
        lhs = represent(test[0], basis=A, format='sympy')
        rhs = to_sympy(test[1])
        assert lhs == rhs


def test_scalar_sympy():
    assert represent(Integer(1)) == Integer(1)
    assert represent(Float(1.0)) == Float(1.0)
    assert represent(1.0 + I) == 1.0 + I


np = import_module('numpy')


def test_format_numpy():
    if not np:
        skip("numpy not installed.")

    for test in _tests:
        lhs = represent(test[0], basis=A, format='numpy')
        rhs = to_numpy(test[1])
        if isinstance(lhs, numpy_ndarray):
            assert (lhs == rhs).all()
        else:
            assert lhs == rhs


def test_scalar_numpy():
    if not np:
        skip("numpy not installed.")

    assert represent(Integer(1), format='numpy') == 1
    assert represent(Float(1.0), format='numpy') == 1.0
    assert represent(1.0 + I, format='numpy') == 1.0 + 1.0j


scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})


def test_format_scipy_sparse():
    if not np:
        skip("numpy not installed.")
    if not scipy:
        skip("scipy not installed.")

    for test in _tests:
        lhs = represent(test[0], basis=A, format='scipy.sparse')
        rhs = to_scipy_sparse(test[1])
        if isinstance(lhs, scipy_sparse_matrix):
            assert np.linalg.norm((lhs - rhs).todense()) == 0.0
        else:
            assert lhs == rhs


def test_scalar_scipy_sparse():
    if not np:
        skip("numpy not installed.")
    if not scipy:
        skip("scipy not installed.")

    assert represent(Integer(1), format='scipy.sparse') == 1
    assert represent(Float(1.0), format='scipy.sparse') == 1.0
    assert represent(1.0 + I, format='scipy.sparse') == 1.0 + 1.0j

x_ket = XKet('x')
x_bra = XBra('x')
x_op = XOp('X')


def test_innerprod_represent():
    assert rep_innerproduct(x_ket) == InnerProduct(XBra("x_1"), x_ket).doit()
    assert rep_innerproduct(x_bra) == InnerProduct(x_bra, XKet("x_1")).doit()

    try:
        rep_innerproduct(x_op)
    except TypeError:
        return True


def test_operator_represent():
    basis_kets = enumerate_states(operators_to_state(x_op), 1, 2)
    assert rep_expectation(
        x_op) == qapply(basis_kets[1].dual*x_op*basis_kets[0])


def test_enumerate_states():
    test = XKet("foo")
    assert enumerate_states(test, 1, 1) == [XKet("foo_1")]
    assert enumerate_states(
        test, [1, 2, 4]) == [XKet("foo_1"), XKet("foo_2"), XKet("foo_4")]