Document Color Matrix Math Better

[reedbn]

In https://docs.microsoft.com/en-us/dotnet/api/system.drawing.imaging.colormatrix?view=netframework-4.8 (which is not exactly the API being used, but also appears to be functionally the same), we're given the image:

This shows a row-vector being multiplied by the matrix, and above it, there's an explanation for the vector components.

As such, I'd recommend adding something to the config to indicate this operation style, since many references online prefer column vector notation. A possible comment:

# Given color matrix M, and
# given an input pixel p = [r g b a w], where r is red, g is green, b is blue, a is alpha, w is offset,
# then to calculate output pixel color d, the following multiplication is performed:
#   p*M = d
# Many papers use column vector multiplication, which is written as M*p = d, so if you
# find that a color matrix doesn't seem to be behaving correctly, it could be that your
# matrix assumes a column vector instead of a row vector. Try transposing the matrix,
# and you may discover the problem is fixed.

[mlaily]

Hey!

(Sorry about the delayed answer)

You are right, it's a problem I and others have already faced before with NegativeScreen, and I should document it somewhere else than in the comments of NegativeScreen's web page...

A lot of things could be improved regarding NegativeScreen, and I hope I will be able to do that as well soon(ish).
In the meantime, I will keep this issue open if it can be useful to someone.

[mlaily]

I still haven't updated the docs, sorry!

As a follow up, here is another suggestion to improve the documentation about the maths that someone sent me by email:

# Let the color matrix M have the entries:
# {           R1,          G1,         B1,          A1,         C1}
# {           R2,          G2,         B2,          A2,         C2}
# {           R3,          G3,         B3,          A3,         C3}
# {           R4,          G4,         B4,          A4,         C4}
# {           R5,          G5,         B5,          A5,         C5}
#
# If you multiply it with a color-vector [r, g, b, a, 1], the resulting [r, g, b, a, c] vector has entries:
# r = R1*r             + R2*g  + R3*b  + R4*a  + R5
# g = G1*r           + G2*g  + G3*b + G4*a  + G5
# b = B1*r            + B2*g  + B3*b  + B4*a  + B5
# a = A1*r            + A2*g  + A3*b  + A4*a  + A5
# c = C1*r            + C2*g  + C3*b  + C4*a  + C5
#
# Note that the resulting "c" component has no effect on the vector, and thus, the entries C1 to C5 are effectively meaningless.