I watched that one already (think you or someone else posted it yesterday or so).
A general understanding isn’t my problem. I ran into a weird default configuration thing in GIMP (weird as in: why did they do this this way!) that threw me off for a moment. @age explained it nicely and now the numbers add and subtract again (literally).
I’m actually trying out channel mixer and still learning a lot about.
My edit is based mostly on @anon41087856 's Auto-filmic style. In my opinion your “heaviness” (darkness) comes mostly from underexposure. As soon as you increase the exposure by roughly 2 EV and reconstruct the highlights using Filmic, you get much “lighter” (and pinker) cherry flowers (left side). With channel mixer you can then add a bit of green to blue channel and blue to red channel (right side).
DSC_8833_02.NEF.xmp (10,1 KB)Right side is best. Only a tiny, tiny adjustment in the channel mixer… and a mask! And that seems to be the key to succes, because the channel mixer would otherwise change the whole image, and this could be a problem. Thank you for your input……
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Nice idea, though, I prefer old version.
Your description helps to orientate in the colour space, but it gives the impression that there are more than 3 basic colours, and distracts from the fact that cyan, magenta and yellow are only combinations (with the corresponding ratio) of red, green and blue.
I would like to give a short demonstration of how channel mixers could be used to remove color cast.
The photo I use for this is in this post:
This is what the photo looks like unprocessed. We have a strong yellowish tint in the room caused by the lighting. Also in the windows you can see purple coloration:
I suppose the light in the opposite room was white and I will first use the window area for white balance:
Now it has been corrected for the purple color cast and we can try to use the channel mixer to correct the yellow color cast as much as possible.
With color picker we first look for a place in the room where we know that it had to be grey but is illuminated by the yellow light. The surface of the white chair behind the girl, seems to be a good choice. We select it with the color picker and add the values to the list below:
Now we can read the color values there:
R = 163
G = 153
B = 86
We know from our color wheel…
… that yellow is a combination of red and green in the absence of blue which is confirmed in the values; red and green have similar values (163, 153) and the value for blue is very low (86).
That means, to remove yellow color cast, we have to increase the blue color channel by some amount of red and green.
Let’s start with red.
In the channel mixer we select blue as the destination and increase the red part of the blue channel. At the same time, we **reduce the blue part of the blue channel approximately ** by the amount we increased with red:
As you can see, the color has already improved. Now we increase the green part of the blue channel, but not as much as the red part, because it was originally also lower:
Now we have to make a few adjustments to adjust the ratio between red and green.
We choose green channel as destination and increase the red and green part of the green channel very subtly, so that the ratio stays about the same:
Now we go back to the blue channel and reduce the blue part of the blue channel very subtly to prevent that the yellow in the photo disappears completely:
Here is the result from before and after:
A note: In the picture there is another light source with purple light which illuminates the face of the woman and the girl. This can also be corrected with a new instance of the channel mixer. First these purple areas have to be masked
Here is the result after further processing steps:
Looks really interesting…… I will examine your edits closely.
Thank you…
I suppose you edited the original raf file that is still available. Could you please upload your xmp?
20180922_FUJ8679.raf.xmp (11,7 KB)
Thank you for the xmp but Darktable stops working when I try to load the file. Maybe it’s not compatible with 3.0.1?
Ah! That may be. I use developer’s version . 
Hi’ @s7habo
thank you for your explanations…….
I have had very little time to look at darktable recently but now I have successfully followed the steps you have shown. I have a few questions and observations……
!
If anybody want to follow the steps shown in the post it’s possible to download the raw file from the thread mentioned above. Be sure to start editing with the same history (no base curve and white balance) and have the color wheel handy……
The settings of red, green and blue should ideally add up to 1 for every destination to produce correct grey? But this not completely the case in your edits.
What do you mean by “so the ration stays the same”?
The final further steps have a great effect. Could you please shortly explain these steps?
Selection with color picker (seat of the chair) as reference should be grey (all three color values should be equal as much as possible):
First I had to remove purple color cast (second light source from the face and skin of woman and girl):
This could be done with a color mixer, but I found it much easier with Color look up table module:
Then I added a little saturation with Velvia:
Final color adjustment with Color Balance Module (that the colors look more vivid):
And finally, removed purple color cast from the windows (with the drawn mask). For this I used Color Zones module:
I forgot to answer this question
No. This is about adjusting the colors locally because there is a color cast. Here is the selection with the color picker important. It should serve as a reference in this case.
By the way, there is no color distortion here because the white balance does not work, but is caused by two different light sources, which makes the photo aesthetically unattractive. The task is actually more of an artistic one - to make the color impression more pleasant.
I haven’t seen an example and explanation of how to get red in the sky and grass image that I think explains it well enough, so I thought I would offer this:
At least someone’s got it. 
That’s definitely a start. 
I’ve played around with all kinds of combinations, and I could never get red at the top of the image to 255, and I could never get rid of a small amount of green, I did get it very low by zeroing green, but then the grass was red.
How do you improve on this?
You can’t do this without a mask, because the sky is not only blue, but has the proportions of green. Also the grass is yellow, which means a combination of red and green. So if you remove green, the yellow part of the grass will be red.
Okay. I thought the challenge was to do it without a mask. My bad. Thanks for your reply.
In fact, it was intended that way, and you actually did it. That the sky isn’t 100% red doesn’t matter. More important was understanding the logic of how the channel mixer works. You understood that, which fulfilled the purpose of the game. 
I forgot to say that if you understand the logic, you can put it into practice and do corrections quite well. For example, if this photo was taken early in the evening at sunset and I had the impression that there was still too much blue in the sky, I could use the channel mixer to make the sky a little more “reddish”.
I may be a little late here, but I had written up something similar a while back on a similar question for RawTherapee. My GIMP example was here (maybe it can help in some way?):
