コード例 #1
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ファイル: test_wigner.py プロジェクト: MichalKononenko/qutip
def test_wigner_fock():
    "wigner: test wigner function calculation for Fock states"

    xvec = np.linspace(-5.0, 5.0, 100)
    yvec = xvec

    X, Y = np.meshgrid(xvec, yvec)

    a = X + 1j * Y  # consistent with g=2 option to wigner function

    dx = xvec[1] - xvec[0]
    dy = yvec[1] - yvec[0]

    N = 15

    for n in [2, 3, 4, 5, 6]:

        psi = fock(N, n)

        # calculate the wigner function using qutip and analytic formula
        W_qutip = wigner(psi, xvec, yvec, g=2)
        W_qutip_cl = wigner(psi, xvec, yvec, g=2, method='clenshaw')
        W_analytic = 2 / np.pi * (-1) ** n * \
            np.exp(-2 * abs(a) ** 2) * np.polyval(laguerre(n), 4 * abs(a) ** 2)

        # check difference
        assert_(np.sum(abs(W_qutip - W_analytic)) < 1e-4)
        assert_(np.sum(abs(W_qutip_cl - W_analytic)) < 1e-4)

        # check normalization
        assert_(np.sum(W_qutip) * dx * dy - 1.0 < 1e-8)
        assert_(np.sum(W_qutip_cl) * dx * dy - 1.0 < 1e-8)
        assert_(np.sum(W_analytic) * dx * dy - 1.0 < 1e-8)
コード例 #2
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ファイル: test_wigner.py プロジェクト: JonathanUlm/qutip
def test_wigner_compare_methods_ket():
    "wigner: compare wigner methods for random state vectors"

    xvec = np.linspace(-5.0, 5.0, 100)
    yvec = xvec

    X, Y = np.meshgrid(xvec, yvec)

    # a = X + 1j * Y  # consistent with g=2 option to wigner function

    dx = xvec[1] - xvec[0]
    dy = yvec[1] - yvec[0]

    N = 15

    for n in range(10):
        # try ten different random density matrices

        psi = rand_ket(N, 0.5 + rand() / 2)

        # calculate the wigner function using qutip and analytic formula
        W_qutip1 = wigner(psi, xvec, yvec, g=2)
        W_qutip2 = wigner(psi, xvec, yvec, g=2, method='laguerre')

        # check difference
        assert_(np.sum(abs(W_qutip1 - W_qutip1)) < 1e-4)

        # check normalization
        assert_(np.sum(W_qutip1) * dx * dy - 1.0 < 1e-8)
        assert_(np.sum(W_qutip2) * dx * dy - 1.0 < 1e-8)
コード例 #3
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ファイル: test_wigner.py プロジェクト: dweigand/qutip
def test_wigner_compare_methods_ket():
    "wigner: compare wigner methods for random state vectors"

    xvec = np.linspace(-5.0, 5.0, 100)
    yvec = xvec

    X, Y = np.meshgrid(xvec, yvec)

    # a = X + 1j * Y  # consistent with g=2 option to wigner function

    dx = xvec[1] - xvec[0]
    dy = yvec[1] - yvec[0]

    N = 15

    for n in range(10):
        # try ten different random density matrices

        psi = rand_ket(N, 0.5 + rand() / 2)

        # calculate the wigner function using qutip and analytic formula
        W_qutip1 = wigner(psi, xvec, yvec, g=2)
        W_qutip2 = wigner(psi, xvec, yvec, g=2, sparse=True)

        # check difference
        assert_(np.sum(abs(W_qutip1 - W_qutip2)) < 1e-4)

        # check normalization
        assert_(np.sum(W_qutip1) * dx * dy - 1.0 < 1e-8)
        assert_(np.sum(W_qutip2) * dx * dy - 1.0 < 1e-8)
コード例 #4
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ファイル: test_wigner.py プロジェクト: MichalKononenko/qutip
def test_wigner_coherent():
    "wigner: test wigner function calculation for coherent states"
    xvec = np.linspace(-5.0, 5.0, 100)
    yvec = xvec

    X, Y = np.meshgrid(xvec, yvec)

    a = X + 1j * Y  # consistent with g=2 option to wigner function

    dx = xvec[1] - xvec[0]
    dy = yvec[1] - yvec[0]

    N = 20
    beta = rand() + rand() * 1.0j
    psi = coherent(N, beta)

    # calculate the wigner function using qutip and analytic formula
    W_qutip = wigner(psi, xvec, yvec, g=2)
    W_qutip_cl = wigner(psi, xvec, yvec, g=2, method='clenshaw')
    W_analytic = 2 / np.pi * np.exp(-2 * abs(a - beta) ** 2)

    # check difference
    assert_(np.sum(abs(W_qutip - W_analytic) ** 2) < 1e-4)
    assert_(np.sum(abs(W_qutip_cl - W_analytic) ** 2) < 1e-4)

    # check normalization
    assert_(np.sum(W_qutip) * dx * dy - 1.0 < 1e-8)
    assert_(np.sum(W_qutip_cl) * dx * dy - 1.0 < 1e-8)
    assert_(np.sum(W_analytic) * dx * dy - 1.0 < 1e-8)
コード例 #5
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ファイル: test_wigner.py プロジェクト: dweigand/qutip
def test_wigner_coherent():
    "wigner: test wigner function calculation for coherent states"
    xvec = np.linspace(-5.0, 5.0, 100)
    yvec = xvec

    X, Y = np.meshgrid(xvec, yvec)

    a = X + 1j * Y  # consistent with g=2 option to wigner function

    dx = xvec[1] - xvec[0]
    dy = yvec[1] - yvec[0]

    N = 20
    beta = rand() + rand() * 1.0j
    psi = coherent(N, beta)

    # calculate the wigner function using qutip and analytic formula
    W_qutip = wigner(psi, xvec, yvec, g=2)
    W_qutip_cl = wigner(psi, xvec, yvec, g=2, method='clenshaw')
    W_analytic = 2 / np.pi * np.exp(-2 * abs(a - beta)**2)

    # check difference
    assert_(np.sum(abs(W_qutip - W_analytic)**2) < 1e-4)
    assert_(np.sum(abs(W_qutip_cl - W_analytic)**2) < 1e-4)

    # check normalization
    assert_(np.sum(W_qutip) * dx * dy - 1.0 < 1e-8)
    assert_(np.sum(W_qutip_cl) * dx * dy - 1.0 < 1e-8)
    assert_(np.sum(W_analytic) * dx * dy - 1.0 < 1e-8)
コード例 #6
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ファイル: test_wigner.py プロジェクト: JonathanUlm/qutip
def test_wigner_fft_comparse_dm():
    "Wigner: Compare Wigner fft and iterative for rand. dm"
    N = 20
    xvec = np.linspace(-10, 10, 128)
    for i in range(3):
        rho = rand_dm(N)

        Wfft, yvec = wigner(rho, xvec, xvec, method='fft')
        W = wigner(rho, xvec, yvec, method='iterative')

        Wdiff = abs(W - Wfft)
        assert_equal(np.sum(abs(Wdiff)) < 1e-7, True)
コード例 #7
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ファイル: test_wigner.py プロジェクト: qutip/qutip
def test_wigner_clenshaw_sp_iter_dm():
    "Wigner: Compare Wigner sparse clenshaw and iterative for rand. dm"
    N = 20
    xvec = np.linspace(-10, 10, 128)
    for i in range(3):
        rho = rand_dm(N)

        Wclen = wigner(rho, xvec, xvec, method='clenshaw', sparse=True)
        W = wigner(rho, xvec, xvec, method='iterative')

        Wdiff = abs(W - Wclen)
        assert_equal(np.sum(abs(Wdiff)) < 1e-7, True)
コード例 #8
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ファイル: test_wigner.py プロジェクト: dweigand/qutip
def test_wigner_clenshaw_sp_iter_dm():
    "Wigner: Compare Wigner sparse clenshaw and iterative for rand. dm"
    N = 20
    xvec = np.linspace(-10, 10, 128)
    for i in range(3):
        rho = rand_dm(N)

        Wclen = wigner(rho, xvec, xvec, method='clenshaw', sparse=True)
        W = wigner(rho, xvec, xvec, method='iterative')

        Wdiff = abs(W - Wclen)
        assert_equal(np.sum(abs(Wdiff)) < 1e-7, True)
コード例 #9
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ファイル: test_wigner.py プロジェクト: dweigand/qutip
def test_wigner_fft_comparse_dm():
    "Wigner: Compare Wigner fft and iterative for rand. dm"
    N = 20
    xvec = np.linspace(-10, 10, 128)
    for i in range(3):
        rho = rand_dm(N)

        Wfft, yvec = wigner(rho, xvec, xvec, method='fft')
        W = wigner(rho, xvec, yvec, method='iterative')

        Wdiff = abs(W - Wfft)
        assert_equal(np.sum(abs(Wdiff)) < 1e-7, True)
コード例 #10
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def test_wigner_fock():
    "wigner: test wigner function calculation for Fock states"

    xvec = np.linspace(-5.0, 5.0, 100)
    yvec = xvec

    X, Y = np.meshgrid(xvec, yvec)

    a = X + 1j * Y  # consistent with g=2 option to wigner function

    dx = xvec[1] - xvec[0]
    dy = yvec[1] - yvec[0]

    N = 15

    for n in [2, 3, 4, 5, 6]:

        psi = fock(N, n)

        # calculate the wigner function using qutip and analytic formula
        W_qutip = wigner(psi, xvec, yvec, g=2)
        W_analytic = 2 / np.pi * (-1) ** n * \
            np.exp(-2 * abs(a) ** 2) * np.polyval(laguerre(n), 4 * abs(a) ** 2)

        # check difference
        assert_(np.sum(abs(W_qutip - W_analytic)) < 1e-4)

        # check normalization
        assert_(np.sum(W_qutip) * dx * dy - 1.0 < 1e-8)
        assert_(np.sum(W_analytic) * dx * dy - 1.0 < 1e-8)
コード例 #11
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    def update(self, rho):

        self.data = wigner(rho, self.xvecs[0], self.xvecs[1])
コード例 #12
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ファイル: distributions.py プロジェクト: Marata459/qutip
    def update(self, rho):

        self.data = wigner(rho, self.xvecs[0], self.xvecs[1])
コード例 #13
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ファイル: visualization.py プロジェクト: Marata459/qutip
def plot_wigner(rho, fig=None, ax=None, figsize=(8, 4),
                cmap=None, alpha_max=7.5, colorbar=False,
                method='iterative', projection='2d'):
    """
    Plot the the Wigner function for a density matrix (or ket) that describes
    an oscillator mode.

    Parameters
    ----------
    rho : :class:`qutip.qobj.Qobj`
        The density matrix (or ket) of the state to visualize.

    fig : a matplotlib Figure instance
        The Figure canvas in which the plot will be drawn.

    ax : a matplotlib axes instance
        The axes context in which the plot will be drawn.

    figsize : (width, height)
        The size of the matplotlib figure (in inches) if it is to be created
        (that is, if no 'fig' and 'ax' arguments are passed).

    cmap : a matplotlib cmap instance
        The colormap.

    alpha_max : float
        The span of the x and y coordinates (both [-alpha_max, alpha_max]).

    colorbar : bool
        Whether (True) or not (False) a colorbar should be attached to the
        Wigner function graph.

    method : string {'iterative', 'laguerre', 'fft'}
        The method used for calculating the wigner function. See the
        documentation for qutip.wigner for details.

    projection: string {'2d', '3d'}
        Specify whether the Wigner function is to be plotted as a
        contour graph ('2d') or surface plot ('3d').

    Returns
    -------
    fig, ax : tuple
        A tuple of the matplotlib figure and axes instances used to produce
        the figure.
    """

    if not fig and not ax:
        if projection == '2d':
            fig, ax = plt.subplots(1, 1, figsize=figsize)
        elif projection == '3d':
            fig = plt.figure(figsize=figsize)
            ax = fig.add_subplot(1, 1, 1, projection='3d')
        else:
            raise ValueError('Unexpected value of projection keyword argument')

    if isket(rho):
        rho = ket2dm(rho)

    xvec = np.linspace(-alpha_max, alpha_max, 200)
    W0 = wigner(rho, xvec, xvec, method=method)

    W, yvec = W0 if type(W0) is tuple else (W0, xvec)

    wlim = abs(W).max()

    if cmap is None:
        cmap = cm.get_cmap('RdBu')

    if projection == '2d':
        cf = ax.contourf(xvec, yvec, W, 100,
                         norm=mpl.colors.Normalize(-wlim, wlim), cmap=cmap)
    elif projection == '3d':
        X, Y = np.meshgrid(xvec, xvec)
        cf = ax.plot_surface(X, Y, W0, rstride=5, cstride=5, linewidth=0.5,
                             norm=mpl.colors.Normalize(-wlim, wlim), cmap=cmap)
    else:
        raise ValueError('Unexpected value of projection keyword argument.')

    if xvec is not yvec:
        ax.set_ylim(xvec.min(), xvec.max())

    ax.set_xlabel(r'$\rm{Re}(\alpha)$', fontsize=12)
    ax.set_ylabel(r'$\rm{Im}(\alpha)$', fontsize=12)

    if colorbar:
        cb = fig.colorbar(cf, ax=ax)

    ax.set_title("Wigner function", fontsize=12)

    return fig, ax
コード例 #14
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ファイル: visualization.py プロジェクト: perkaer/qutip
def wigner_fock_distribution(rho, fig=None, axes=None, figsize=(8, 4), cmap=None, alpha_max=7.5, colorbar=False):
    """
    Plot the Fock distribution and the Wigner function for a density matrix
    (or ket) that describes an oscillator mode.

    Parameters
    ----------
    rho : :class:`qutip.qobj.Qobj`
        The density matrix (or ket) of the state to visualize.

    fig : a matplotlib Figure instance
        The Figure canvas in which the plot will be drawn.

    axes : a list of two matplotlib axes instances
        The axes context in which the plot will be drawn.

    figsize : (width, height)
        The size of the matplotlib figure (in inches) if it is to be created
        (that is, if no 'fig' and 'ax' arguments are passed).

    cmap : a matplotlib cmap instance
        The colormap.

    alpha_max : float
        The span of the x and y coordinates (both [-alpha_max, alpha_max]).

    colorbar : bool
        Whether (True) or not (False) a colorbar should be attached to the
        Wigner function graph.

    Returns
    -------
    fig, ax : tuple
        A tuple of the matplotlib figure and axes instances used to produce
        the figure.
    """

    if not fig and not axes:
        fig, axes = plt.subplots(1, 2, figsize=figsize)

    if isket(rho):
        rho = ket2dm(rho)

    fock_distribution(rho, fig=fig, ax=axes[0])

    xvec = linspace(-alpha_max, alpha_max, 200)
    W = wigner(rho, xvec, xvec)
    wlim = abs(W).max()

    if cmap is None:
        cmap = get_cmap("RdBu")
        # cmap = wigner_cmap(W)

    cf = axes[1].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-wlim, wlim), cmap=cmap)

    axes[1].set_xlabel(r"$\rm{Re}(\alpha)$", fontsize=12)
    axes[1].set_ylabel(r"$\rm{Im}(\alpha)$", fontsize=12)

    if colorbar:
        cb = fig.colorbar(cf, ax=axes[1])

    axes[0].set_title("Fock distribution", fontsize=12)
    axes[1].set_title("Wigner function", fontsize=12)

    return fig, axes
コード例 #15
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def wigner_fock_distribution(rho, fig=None, ax=None, figsize=(8, 4),
                             cmap=None, alpha_max=7.5, colorbar=False):
    """
    Plot the Fock distribution and the Wigner function for a density matrix
    (or ket) that describes an oscillator mode.

    Parameters
    ----------
    rho : :class:`qutip.qobj.Qobj`
        The density matrix (or ket) of the state to visualize.

    fig : a matplotlib Figure instance
        The Figure canvas in which the plot will be drawn.

    ax : a matplotlib axes instance
        The axes context in which the plot will be drawn.

    figsize : (width, height)
        The size of the matplotlib figure (in inches) if it is to be created
        (that is, if no 'fig' and 'ax' arguments are passed).

    cmap : a matplotlib cmap instance
        The colormap.

    alpha_max : float
        The span of the x and y coordinates (both [-alpha_max, alpha_max]).

    colorbar : bool
        Whether (True) or not (False) a colorbar should be attached to the
        Wigner function graph.

    Returns
    -------

        A tuple of matplotlib figure and axes instances.

    """

    if not fig and not ax:
        fig, axes = plt.subplots(1, 2, figsize=figsize)

    if isket(rho):
        rho = ket2dm(rho)

    fock_distribution(rho, fig=fig, ax=axes[0])

    xvec = linspace(-alpha_max, alpha_max, 200)
    W = wigner(rho, xvec, xvec)
    wlim = abs(W).max()

    if cmap is None:
        cmap = get_cmap('RdBu')
        # cmap = wigner_cmap(W)

    cf = axes[1].contourf(xvec, xvec, W, 100,
                          norm=mpl.colors.Normalize(-wlim, wlim), cmap=cmap)

    axes[1].set_xlabel(r'$\rm{Re}(\alpha)$', fontsize=12)
    axes[1].set_ylabel(r'$\rm{Im}(\alpha)$', fontsize=12)

    if colorbar:
        cb = fig.colorbar(cf, ax=axes[1])

    axes[0].set_title("Fock distribution", fontsize=12)
    axes[1].set_title("Wigner function", fontsize=12)

    return fig, ax
コード例 #16
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ファイル: visualization.py プロジェクト: tacruc/qutip
def plot_wigner(rho,
                fig=None,
                ax=None,
                figsize=(6, 6),
                cmap=None,
                alpha_max=7.5,
                colorbar=False,
                method='clenshaw',
                projection='2d'):
    """
    Plot the the Wigner function for a density matrix (or ket) that describes
    an oscillator mode.

    Parameters
    ----------
    rho : :class:`qutip.qobj.Qobj`
        The density matrix (or ket) of the state to visualize.

    fig : a matplotlib Figure instance
        The Figure canvas in which the plot will be drawn.

    ax : a matplotlib axes instance
        The axes context in which the plot will be drawn.

    figsize : (width, height)
        The size of the matplotlib figure (in inches) if it is to be created
        (that is, if no 'fig' and 'ax' arguments are passed).

    cmap : a matplotlib cmap instance
        The colormap.

    alpha_max : float
        The span of the x and y coordinates (both [-alpha_max, alpha_max]).

    colorbar : bool
        Whether (True) or not (False) a colorbar should be attached to the
        Wigner function graph.

    method : string {'clenshaw', 'iterative', 'laguerre', 'fft'}
        The method used for calculating the wigner function. See the
        documentation for qutip.wigner for details.

    projection: string {'2d', '3d'}
        Specify whether the Wigner function is to be plotted as a
        contour graph ('2d') or surface plot ('3d').

    Returns
    -------
    fig, ax : tuple
        A tuple of the matplotlib figure and axes instances used to produce
        the figure.
    """

    if not fig and not ax:
        if projection == '2d':
            fig, ax = plt.subplots(1, 1, figsize=figsize)
        elif projection == '3d':
            fig = plt.figure(figsize=figsize)
            ax = fig.add_subplot(1, 1, 1, projection='3d')
        else:
            raise ValueError('Unexpected value of projection keyword argument')

    if isket(rho):
        rho = ket2dm(rho)

    xvec = np.linspace(-alpha_max, alpha_max, 200)
    W0 = wigner(rho, xvec, xvec, method=method)

    W, yvec = W0 if type(W0) is tuple else (W0, xvec)

    wlim = abs(W).max()

    if cmap is None:
        cmap = cm.get_cmap('RdBu')

    if projection == '2d':
        cf = ax.contourf(xvec,
                         yvec,
                         W,
                         100,
                         norm=mpl.colors.Normalize(-wlim, wlim),
                         cmap=cmap)
    elif projection == '3d':
        X, Y = np.meshgrid(xvec, xvec)
        cf = ax.plot_surface(X,
                             Y,
                             W0,
                             rstride=5,
                             cstride=5,
                             linewidth=0.5,
                             norm=mpl.colors.Normalize(-wlim, wlim),
                             cmap=cmap)
    else:
        raise ValueError('Unexpected value of projection keyword argument.')

    if xvec is not yvec:
        ax.set_ylim(xvec.min(), xvec.max())

    ax.set_xlabel(r'$\rm{Re}(\alpha)$', fontsize=12)
    ax.set_ylabel(r'$\rm{Im}(\alpha)$', fontsize=12)

    if colorbar:
        fig.colorbar(cf, ax=ax)

    ax.set_title("Wigner function", fontsize=12)

    return fig, ax