Python sympy.sign() Examples

The following are 5 code examples of sympy.sign(). You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may also want to check out all available functions/classes of the module sympy , or try the search function .
Example #1
Source File: test_sympy_conv.py    From symengine.py with MIT License 5 votes vote down vote up 
def test_sign():
    x = Symbol("x")
    e1 = sympy.sign(sympy.Symbol("x"))
    e2 = sign(x)
    assert sympify(e1) == e2
    assert e2._sympy_() == e1
Example #2
Source File: convert_to_sqrt_iswap.py    From Cirq with Apache License 2.0 5 votes vote down vote up 
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)
Example #3
Source File: symbolic.py    From simupy with BSD 2-Clause "Simplified" License 5 votes vote down vote up 
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))
    ])
Example #4
Source File: operators.py    From devito with MIT License 5 votes vote down vote up 
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'])
Example #5
Source File: convert_to_sqrt_iswap.py    From Cirq with Apache License 2.0 4 votes vote down vote up 
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))