How to show all posts in all categories custom post type?

I need to show all posts in all categories (custom post type)? Below code works with normal post only, but I think it can be change to works with custom post type. Can you give me an example? Thank you.

Output look like this:

custom post type cat 1
+ post a
+ post b
custom post type cat 2
+ post c
+ … etc

<?php
        //for each category, show all posts
        $cat_args=array(
          'orderby' => 'name',
          'order' => 'ASC',
           );
        $categories=wp_list_categories($cat_args);
          foreach($categories as $category) {
            $args=array(
              'showposts' => -1,
              'category__in' => array($category->term_id),
              'caller_get_posts'=>1
            );
            $posts=get_posts($args);
              if ($posts) {
                echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
                foreach($posts as $post) {
                  setup_postdata($post); ?>

    <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>">
  <?php the_title(); ?>
  </a></p>
    <?php
                } // foreach($posts
              } // if ($posts
            } // foreach($categories
        ?>