How show sub menu only using wp_nav_menu()

I am using this code to show the custom menu subpages if you are on the parent page. But what this code also shows is a parent page on a page that has no sub menu, which I would like hidden. Basically only use this code if we are on a page that has a sub page,

class Selective_Walker extends Walker_Nav_Menu
{
    function walk( $elements, $max_depth) {

        $args = array_slice(func_get_args(), 2);
        $output = '';

        if ($max_depth < -1) //invalid parameter
            return $output;

        if (empty($elements)) //nothing to walk
            return $output;

        $id_field = $this->db_fields['id'];
        $parent_field = $this->db_fields['parent'];

        // flat display
        if ( -1 == $max_depth ) {
            $empty_array = array();
            foreach ( $elements as $e )
                $this->display_element( $e, $empty_array, 1, 0, $args, $output );
            return $output;
        }

        /*
         * need to display in hierarchical order
         * separate elements into two buckets: top level and children elements
         * children_elements is two dimensional array, eg.
         * children_elements[10][] contains all sub-elements whose parent is 10.
         */
        $top_level_elements = array();
        $children_elements  = array();
        foreach ( $elements as $e) {
            if ( 0 == $e->$parent_field )
                $top_level_elements[] = $e;
            else
                $children_elements[ $e->$parent_field ][] = $e;
        }

        /*
         * when none of the elements is top level
         * assume the first one must be root of the sub elements
         */
        if ( empty($top_level_elements) ) {

            $first = array_slice( $elements, 0, 1 );
            $root = $first[0];

            $top_level_elements = array();
            $children_elements  = array();
            foreach ( $elements as $e) {
                if ( $root->$parent_field == $e->$parent_field )
                    $top_level_elements[] = $e;
                else
                    $children_elements[ $e->$parent_field ][] = $e;
            }
        }

        $current_element_markers = array( 'current-menu-item', 'current-menu-parent', 'current-menu-ancestor' );  //added by continent7
        foreach ( $top_level_elements as $e ){  //changed by continent7
            // descend only on current tree
            $descend_test = array_intersect( $current_element_markers, $e->classes );
            if ( !empty( $descend_test ) ) 
                $this->display_element( $e, $children_elements, 2, 0, $args, $output );
        }

        /*
         * if we are displaying all levels, and remaining children_elements is not empty,
         * then we got orphans, which should be displayed regardless
         */
         /* removed by continent7
        if ( ( $max_depth == 0 ) && count( $children_elements ) > 0 ) {
            $empty_array = array();
            foreach ( $children_elements as $orphans )
                foreach( $orphans as $op )
                    $this->display_element( $op, $empty_array, 1, 0, $args, $output );
         }
        */
         return $output;
    }
}

in the template using:

wp_nav_menu( 
   array(
       'theme_location'=>'primary', 
       'walker'=>new Selective_Walker() 
   )
);