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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 update(self):
 """ Update this `~photutils.isophote.EllipseSample` instance. This method calls the :meth:`~photutils.isophote.EllipseSample.extract` method to get the values that match the current ``geometry`` attribute, and then computes the the mean intensity, local gradient, and other associated quantities. """


        step = self.geometry.astep

        # Update the mean value first, using extraction from main sample.
        s = self.extract()
        self.mean = np.mean(s[2])

        # Get sample with same geometry but at a different distance from
        # center. Estimate gradient from there.
        gradient, gradient_error = self._get_gradient(step)

        # Check for meaningful gradient. If no meaningful gradient, try
        # another sample, this time using larger radius. Meaningful
        # gradient means something  shallower, but still close to within
        # a factor 3 from previous gradient estimate. If no previous
        # estimate is available, guess it.
        previous_gradient = self.gradient
        if not previous_gradient:
            previous_gradient = -0.05    # good enough, based on usage

        if gradient >= (previous_gradient / 3.):   # gradient is negative!
            gradient, gradient_error = self._get_gradient(2 * step)

        # If still no meaningful gradient can be measured, try with
        # previous one, slightly shallower. A factor 0.8 is not too far
        # from what is expected from geometrical sampling steps of 10-20%
        # and a deVaucouleurs law or an exponential disk (at least at its
        # inner parts, r <~ 5 req). Gradient error is meaningless in this
        # case.
        if gradient >= (previous_gradient / 3.):
            gradient = previous_gradient * 0.8
            gradient_error = None

        self.gradient = gradient
        self.gradient_error = gradient_error
        if gradient_error:
            self.gradient_relative_error = gradient_error / np.abs(gradient)
        else:
            self.gradient_relative_error = None