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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 logtrick_sgd(sgd):
 r""" Log-Trick decorator for stochastic gradients. This decorator implements the "log trick" for optimizing positive bounded variables using SGD. It will apply this trick for any variables that correspond to a Positive() bound. Examples -------- Here is an example where we may want to enforce a particular parameter or parameters to be strictly greater than zero, Now let's enforce that the `w` are positive, Data Initial values array([ True, True], dtype=bool) Note ---- This decorator only works on unstructured optimizers. However, it can be use with structured_minimizer, so long as it is the inner wrapper. """

    @wraps(sgd)
    def new_sgd(fun, x0, data, bounds=None, eval_obj=False, **sgd_kwargs):

        if bounds is None:
            return sgd(fun, x0, data, bounds=bounds, eval_obj=eval_obj,
                       **sgd_kwargs)

        logx, expx, gradx, bounds = _logtrick_gen(bounds)

        if bool(eval_obj):
            def new_fun(x, *fargs, **fkwargs):
                o, g = fun(expx(x), *fargs, **fkwargs)
                return o, gradx(g, x)
        else:
            def new_fun(x, *fargs, **fkwargs):
                return gradx(fun(expx(x), *fargs, **fkwargs), x)

        # Transform the final result
        result = sgd(new_fun, logx(x0), data, bounds=bounds, eval_obj=eval_obj,
                     **sgd_kwargs)
        result['x'] = expx(result['x'])
        return result

    return new_sgd