How to get Octave 4.4.0 for macOS with GUI

The macOS package manager Homebrew ships with Octave 4.4 but it links to Apple’s proprietary BLAS implementation, the QT graphical user interface is not supported and the ode15 solvers are broken due to Octave’s outdated sundials 2.x dependency. However, there are two alternatives:
If you prefer a quick and easy solution, then go to octave-app.org and download the disk image that is being put together by apjanke and me. On the other hand, if you want to compile it by yourself (including all necessary patches) then follow the instructions below and hope for the best…

#add openblas repository
brew tap dpo/openblas
brew tap-pin dpo/openblas
#download the new formula
curl https://raw.githubusercontent.com/schoeps/homebrew-openblas/master/octave.rb -o /usr/local/Homebrew/Library/Taps/dpo/homebrew-openblas/octave.rb
#compile
brew install octave --with-qt