I had a similar goal, so I created a system with AMD APU (4 regular cores + 6 GPUs) and a discrete Nvidia graphics card. Sorry, it wasn’t easy to work, so I asked a question on the Ask Ubuntu forum, received no answers, experimented with installing hardware and software, and finally published my own answer to my question.
I will talk about my setup again - who knows what might happen to my answering machine to Ask Ubuntu ?
At first I had to turn on the integrated graphics hardware through the BIOS flag. This flag is called IGFX Multi-Monitor on my motherboard (ASUS A88X-PRO).
The second step was to find the right combination of a low-level graphics driver and a high-level OpenCL implementation. The low-level driver for AMD processors is called AMD Catalyst and has the file name fglrx . I did not install this driver from the Ubuntu software center - instead, I used version 15.302 directly downloaded from the AMD website. I had to install a significant number of prerequisites for this driver. Most importantly, I had to skip the aticonfig command after installing fglrx - this command actually configures the X server to use this driver for graphics output, and I didn’t want that.
Then I installed the AMD SDK Ver 3.0 (version 130.136, earlier versions did not work with my fglrx ) - this is AMD's OpenCL implementation. The clinfo team reports both the CPU and GPUs with the correct number of cores now.
So, I have an AMD hybrid processor supported by OpenCL, with all graphics output, supported by a discrete graphics card with an Nvidia processor.
Good luck
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