Considering the fact that an user can type into the browser address my domain address as any one of the following:

mydomain.com
www.mydomain.com
http://www.mydomain.com
https://mydomain.com
https://www.mydomain.com

How can I always redirect instantly to https://www.mydomain.com ?
This becomes somewhat important as https:// and https://www show different font sizes of a default install of Elgg. (why this is so?)
Also sometimes such redirection gives login error : login from different domain not allowed (what to do to avoid this?)

I am trying the following but not getting desired results uniformly

RewriteEngine On
RewriteCond %{HTTP_HOST} ^yourdomain.com [NC]
RewriteRule ^(.*)$ http://www.yourdomain.com/$1 [L,R=301]
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]