integer Jac enforcement, bool to int function (for layout)

    bin_string = format(num, form)

    return [x == "1" for x in bin_string[::-1]], bin_string, form

def bool_list_to_int(bool_str, nSensorCandidate):

def bool_list_to_int(layout, nSensorCandidate):

    """

    takey a boolean layout (True=measured, False=unmeasured) and converts it 

    into the unique id generated from int_to_bool_list

    """

    # reverse the layout to comply with soar

    rev_layout = layout[8:] + layout[:8]  # Assuming layout is a list

    tlayout_np = np.array(rev_layout)

    rev_bin = [str(x) for x in tlayout_np[::-1].astype(int)]

    rev_bin_str = str.join("", rev_bin)

    int_layout = int(rev_bin_str, 2)

    return

    return int_layout

def jacnum(x0, fx, dx=1e-6):

    return bool_redundant

def observability_redundancy_labelling_rref(J, bool_measured,x0={}, debug=False, le_red_method=False):

def observability_redundancy_labelling_rref(J, bool_measured,x0={}, debug=False, le_red_method=False, enforce_integer =True):

    if len(x0) > 0:

        J = J.subs(x0)

    if enforce_integer and len(x0) > 0: 

        # convert to int matrix

        J = sy.Matrix(np.matrix(J).astype(int))

    bool_measured = np.array(bool_measured).astype(bool)

    Jm = J[:, list(np.where(bool_measured)[0])]

    Ju = J[:, list(np.where(~bool_measured)[0])]