Python sympy.sign方法代碼示例

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import sign [as 別名]
def test_sign():
    x = Symbol("x")
    e1 = sympy.sign(sympy.Symbol("x"))
    e2 = sign(x)
    assert sympify(e1) == e2
    assert e2._sympy_() == e1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import sign [as 別名]
def cphase_symbols_to_sqrt_iswap(a, b, turns):
    """Version of cphase_to_sqrt_iswap that works with symbols.

    Note that the formulae contained below will need to be flattened
    into a sweep before serializing.
    """
    theta = sympy.Mod(turns, 2.0) * sympy.pi

    # -1 if theta > pi.  Adds a hacky fudge factor so theta=pi is not 0
    sign = sympy.sign(sympy.pi - theta + 1e-9)

    # For sign = 1: theta. For sign = -1, 2pi-theta
    theta_prime = (sympy.pi - sign * sympy.pi) + sign * theta

    phi = sympy.asin(np.sqrt(2) * sympy.sin(theta_prime / 4))
    xi = sympy.atan(sympy.tan(phi) / np.sqrt(2))

    yield ops.rz(sign * 0.5 * theta_prime).on(a)
    yield ops.rz(sign * 0.5 * theta_prime).on(b)
    yield ops.rx(xi).on(a)
    yield ops.X(b)**(-sign * 0.5)
    yield SQRT_ISWAP_INV(a, b)
    yield ops.rx(-2 * phi).on(a)
    yield SQRT_ISWAP(a, b)
    yield ops.rx(xi).on(a)
    yield ops.X(b)**(sign * 0.5) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import sign [as 別名]
def grad(f, basis, for_numerical=True):
    """
    Compute the symbolic gradient of a vector-valued function with respect to a
    basis.

    Parameters
    ----------
    f : 1D array_like of sympy Expressions
        The vector-valued function to compute the gradient of.
    basis : 1D array_like of sympy symbols
        The basis symbols to compute the gradient with respect to.
    for_numerical : bool, optional
        A placeholder for the option of numerically computing the gradient.

    Returns
    -------
    grad : 2D array_like of sympy Expressions
        The symbolic gradient.
    """
    if hasattr(f, '__len__'):  # as of version 1.1.1, Array isn't supported
        f = sp.Matrix(f)

    return f.__class__([
        [
            sp.diff(f[x], basis[y])
            if not for_numerical or not f[x].has(sp.sign(basis[y])) else 0
            for y in range(len(basis))
        ] for x in range(len(f))
    ]) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import sign [as 別名]
def freesurface(model, eq):
    """
    Generate the stencil that mirrors the field as a free surface modeling for
    the acoustic wave equation.

    Parameters
    ----------
    model : Model
        Physical model.
    eq : Eq
        Time-stepping stencil (time update) to mirror at the freesurface.
    """
    lhs, rhs = eq.evaluate.args
    # Get vertical dimension and corresponding subdimension
    zfs = model.grid.subdomains['fsdomain'].dimensions[-1]
    z = zfs.parent

    # Functions present in the stencil
    funcs = retrieve_functions(rhs)
    mapper = {}
    # Antisymmetric mirror at negative indices
    # TODO: Make a proper "mirror_indices" tool function
    for f in funcs:
        zind = f.indices[-1]
        if (zind - z).as_coeff_Mul()[0] < 0:
            s = sign(zind.subs({z: zfs, z.spacing: 1}))
            mapper.update({f: s * f.subs({zind: INT(abs(zind))})})
    return Eq(lhs, rhs.subs(mapper), subdomain=model.grid.subdomains['fsdomain']) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import sign [as 別名]
def cphase_to_sqrt_iswap(a, b, turns):
    """Implement a C-Phase gate using two sqrt ISWAP gates and single-qubit
    operations. The circuit is equivalent to cirq.CZPowGate(exponent=turns).

    Output unitary:
    [1   0   0   0],
    [0   1   0   0],
    [0   0   1   0],
    [0   0   0   e^{i turns pi}].

    Args:
        a: the first qubit
        b: the second qubit
        turns: Exponent specifying the evolution time in number of rotations.
    """
    theta = (turns % 2) * np.pi
    if 0 <= theta <= np.pi:
        sign = 1.
        theta_prime = theta
    elif np.pi < theta < 2 * np.pi:
        sign = -1.
        theta_prime = 2 * np.pi - theta

    if np.isclose(theta, np.pi):
        # If we are close to pi, just set values manually to avoid possible
        # numerical errors with arcsin of greater than 1.0 (Ahem, Windows).
        phi = np.pi / 2
        xi = np.pi / 2
    else:
        phi = np.arcsin(np.sqrt(2) * np.sin(theta_prime / 4))
        xi = np.arctan(np.tan(phi) / np.sqrt(2))

    yield ops.rz(sign * 0.5 * theta_prime).on(a)
    yield ops.rz(sign * 0.5 * theta_prime).on(b)
    yield ops.rx(xi).on(a)
    yield ops.X(b)**(-sign * 0.5)
    yield SQRT_ISWAP_INV(a, b)
    yield ops.rx(-2 * phi).on(a)
    yield SQRT_ISWAP(a, b)

    yield ops.rx(xi).on(a)
    yield ops.X(b)**(sign * 0.5)
    # Corrects global phase
    yield ops.GlobalPhaseOperation(np.exp(sign * theta_prime * 0.25j))