Laravel Homestead not working database connect

I have installed laravel homestead and run it.

But I can't run migration locally and in vagrant.

If I try to run the migration inside vagrant

cd ~/code/project/
php artisan migrate

I got an error

could not connect to server: Connection refused
Is the server running on host "127.0.0.1" and accepting TCP/IP connections on port 54320?"

If I try to run the migration locally I got a another error

PDOException::("could not find driver")

my .env file contains the same code as written in doc

DB_CONNECTION=pgsql
DB_HOST=127.0.0.1
DB_PORT=54320
DB_DATABASE=homestead
DB_USERNAME=homestead
DB_PASSWORD=secret

Maybe something I do not understand but do I need posgresql locally and inside my vagrant? Where I have to work with database locally or with vagrant?

via Chebli Mohamed