<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def approx(x, y, xout, method='linear', rule=1, f=0, yleft=None, yright=None, ties='mean'):
 """Linearly interpolate points. Return a list of points which (linearly) interpolate given data points, or a function performing the linear (or constant) interpolation. Parameters x : array-like, shape=(n_samples,) Numeric vector giving the coordinates of the points to be interpolated. y : array-like, shape=(n_samples,) Numeric vector giving the coordinates of the points to be interpolated. xout : int, float or iterable A scalar or iterable of numeric values specifying where interpolation is to take place. method : str, optional (default='linear') Specifies the interpolation method to be used. Choices are "linear" or "constant". rule : int, optional (default=1) An integer describing how interpolation is to take place outside the interval ``[min(x), max(x)]``. If ``rule`` is 1 then np.nans are returned for such points and if it is 2, the value at the closest data extreme is used. f : int, optional (default=0) For ``method`` = "constant" a number between 0 and 1 inclusive, indicating a compromise between left- and right-continuous step functions. If y0 and y1 are the values to the left and right of the point then the value is y0 if f == 0, y1 if f == 1, and y0*(1-f)+y1*f for intermediate values. In this way the result is right-continuous for f == 0 and left-continuous for f == 1, even for non-finite ``y`` values. yleft : float, optional (default=None) The value to be returned when input ``x`` values are less than ``min(x)``. The default is defined by the value of rule given below. yright : float, optional (default=None) The value to be returned when input ``x`` values are greater than ``max(x)``. The default is defined by the value of rule given below. ties : str, optional (default='mean') Handling of tied ``x`` values. Choices are "mean" or "ordered". """

    if method not in VALID_APPROX:
        raise ValueError('method must be one of %r' % VALID_APPROX)

    # make sure xout is an array
    xout = c(xout).astype(np.float64)  # ensure double

    # check method
    method_key = method

    # not a callable, actually, but serves the purpose..
    method = get_callable(method_key, VALID_APPROX)

    # copy/regularize vectors
    x, y = _regularize(x, y, ties)
    nx = x.shape[0]

    # if len 1? (we've already handled where the size is 0, since we check that
    # in the _regularize function when we call c1d)
    if nx == 1:
        if method_key == 'linear':
            raise ValueError('need at least two points to '
                             'linearly interpolate')

    # get yleft, yright
    if yleft is None:
        yleft = y[0] if rule != 1 else np.nan
    if yright is None:
        yright = y[-1] if rule != 1 else np.nan

    # call the C subroutine
    yout = C_Approx(x, y, xout, method, f, yleft, yright)  # MemoryView
    return xout, np.asarray(yout)