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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def tam_danielson_window(ray_trafo, smoothing_width=0.05, n_pi=1):
 """Create Tam-Danielson window from a `RayTransform`. The Tam-Danielson window is an indicator function on the minimal set of data needed to reconstruct a volume from given data. It is useful in analytic reconstruction methods such as FBP to give a more accurate reconstruction. See [TAM1998] for more informationon the window. See [PKGT2000] for information on the ``n_pi`` parameter. Parameters ray_trafo : `RayTransform` The ray transform for which to compute the window. smoothing_width : positive float, optional Width of the smoothing applied to the window's edges given as a fraction of the width of the full window. n_pi : odd int, optional Total number of half rotations to include in the window. Values larger than 1 should be used if the pitch is much smaller than the detector height. Returns ------- tam_danielson_window : ``ray_trafo.range`` element See Also -------- fbp_op : Filtered back-projection operator from `RayTransform` tam_danielson_window : Weighting for short scan data odl.tomo.geometry.conebeam.ConeFlatGeometry : Primary use case for this window function. References [TSS1998] Tam, K C, Samarasekera, S and Sauer, F. *Exact cone beam CT with a spiral scan*. Physics in Medicine & Biology 4 (1998), p 1015. https://dx.doi.org/10.1088/0031-9155/43/4/028 [PKGT2000] Proksa R, Köhler T, Grass M, Timmer J. *The n-PI-method for helical cone-beam CT* IEEE Trans Med Imaging. 2000 Sep;19(9):
848-63. https://www.ncbi.nlm.nih.gov/pubmed/11127600 """

    # Extract parameters
    src_radius = ray_trafo.geometry.src_radius
    det_radius = ray_trafo.geometry.det_radius
    pitch = ray_trafo.geometry.pitch

    if pitch == 0:
        raise ValueError('Tam-Danielson window is only defined with '
                         '`pitch!=0`')

    smoothing_width = float(smoothing_width)
    if smoothing_width < 0:
        raise ValueError('`smoothing_width` should be a positive float')

    if n_pi % 2 != 1:
        raise ValueError('`n_pi` must be odd, got {}'.format(n_pi))

    # Find projection of axis on detector
    axis_proj = _axis_in_detector(ray_trafo.geometry)
    rot_dir = _rotation_direction_in_detector(ray_trafo.geometry)

    # Find distance from projection of rotation axis for each pixel
    dx = (rot_dir[0] * ray_trafo.range.meshgrid[1]
          + rot_dir[1] * ray_trafo.range.meshgrid[2])

    dx_axis = dx * src_radius / (src_radius + det_radius)

    def Vn(u):
        return (pitch / (2 * np.pi)
                * (1 + (u / src_radius) ** 2)
                * (n_pi * np.pi / 2.0 - np.arctan(u / src_radius)))

    lower_proj_axis = -Vn(dx_axis)
    upper_proj_axis = Vn(-dx_axis)

    lower_proj = lower_proj_axis * (src_radius + det_radius) / src_radius
    upper_proj = upper_proj_axis * (src_radius + det_radius) / src_radius

    # Compute a smoothed width
    interval = (upper_proj - lower_proj)
    width = interval * smoothing_width / np.sqrt(2)

    # Create window function
    def window_fcn(x):
        # Lazy import to improve `import odl` time
        import scipy.special

        x_along_axis = axis_proj[0] * x[1] + axis_proj[1] * x[2]
        if smoothing_width != 0:
            lower_wndw = 0.5 * (
                1 + scipy.special.erf((x_along_axis - lower_proj) / width))
            upper_wndw = 0.5 * (
                1 + scipy.special.erf((upper_proj - x_along_axis) / width))
        else:
            lower_wndw = (x_along_axis >= lower_proj)
            upper_wndw = (x_along_axis <= upper_proj)

        return lower_wndw * upper_wndw

    return ray_trafo.range.element(window_fcn) / n_pi