can variables be used in regular expressions?

[foxgab]

i want to change the redirect location URI protocol to https if that is
using, so i tried to configure like this:

  proxy_redirect      ~*^http://$host(/.*)?$ $scheme://$host$1;

but that didn't work, so i change it to:

  proxy_redirect      http://$http_host $scheme://$http_host;

then, it works. I suspect that the variable in regular expressions is treat
as a string, hence my former directive failed, am I right?
Is there any way to make variables effect in regular expressions?

Posted at Nginx Forum: https://forum.nginx.org/read.php?2,275675,275675#msg-275675