human
Complete the below
def linear_cg(fn, params, tol=0.001, max_iters=1000, floatX=None):

    ''''Minimizes a POSITIVE DEFINITE quadratic function via linear conjugate
    gradient using the R operator to avoid explicitly representing the Hessian.
    If you have several variables, this is cheaper than Newton\'s method, which
    would need to invert the Hessian. It is also cheaper than standard linear
    conjugate gradient, which works with an explicit representation of the
    Hessian. It is also cheaper than nonlinear conjugate gradient which does a
    line search by repeatedly evaluating f.
    For more information about linear conjugate gradient, you may look at
    http://en.wikipedia.org/wiki/Conjugate_gradient_method .
    (This reference describes linear CG but not converting it to use
    the R operator instead of an explicit representation of the Hessian)
    Parameters
    params : WRITEME
    f : theano_like
    A theano expression which is quadratic with POSITIVE DEFINITE hessian
    in x
    x : list
    List of theano shared variables that influence f
    tol : float
    Minimization halts when the norm of the gradient is smaller than tol
    Returns
    rval : theano_like
    The solution in form of a symbolic expression (or list of
    symbolic expressions)'
    '''
assistant
#Here is the Python program you requested.
    provided_as_list = True
    if (not isinstance(params, (list, tuple))):
        params = [params]
        provided_as_list = False
    n_params = len(params)
    def loop(rsold, *args):
        ps = args[:n_params]
        rs = args[n_params:(2 * n_params)]
        xs = args[(2 * n_params):]
        Aps = []
        for param in params:
            rval = tensor.Rop(tensor.grad(fn, param), params, ps)
            if isinstance(rval, (list, tuple)):
                Aps.append(rval[0])
            else:
                Aps.append(rval)
        alpha = (rsold / sum(((x * y).sum() for (x, y) in zip(Aps, ps))))
        xs = [(x - (alpha * p)) for (x, p) in zip(xs, ps)]
        rs = [(r - (alpha * Ap)) for (r, Ap) in zip(rs, Aps)]
        rsnew = sum(((r * r).sum() for r in rs))
        ps = [(r + ((rsnew / rsold) * p)) for (r, p) in zip(rs, ps)]
        return (((([rsnew] + ps) + rs) + xs), theano.scan_module.until((rsnew < tol)))
    r0s = tensor.grad(fn, params)
    if (not isinstance(r0s, (list, tuple))):
        r0s = [r0s]
    p0s = [x for x in r0s]
    x0s = params
    rsold = sum(((r * r).sum() for r in r0s))
    (outs, updates) = theano.scan(loop, outputs_info=((([rsold] + p0s) + r0s) + x0s), n_steps=max_iters, name='linear_conjugate_gradient')
    fxs = outs[(1 + (2 * n_params)):]
    fxs = [ifelse((rsold < tol), x0, x[(-1)]) for (x0, x) in zip(x0s, fxs)]
    if (not provided_as_list):
        return fxs[0]
    else:
        return fxs