Make shear operation area preserving

[pedrofreire]

This PR handles issue #1185.

PR #1371 attempted to fix this, but noticed the issue that the formula did not give the same shear direction - the reason for this is that the formulas in #1185 used a different sign for the shear.

So, to fix the problem, we just have to replace the signs of shear_x and shear_y in the matrix formula from #1185.

I verified the formula by hand, and by the following sympy code:

from sympy import Matrix, cos, sin, tan, simplify
from sympy.abc import x, y, phi

Xs = Matrix(
        [[1, -tan(x)],
         [0, 1]]
        )

Ys = Matrix(
        [[1, 0],
         [-tan(y), 1]]
        )

R = Matrix(
        [[cos(phi), -sin(phi)],
         [sin(phi), cos(phi)]]
        )

RSS = Matrix(
        [[cos(phi - y)/cos(y), -cos(phi - y)*tan(x)/cos(y) - sin(phi)],
         [sin(phi - y)/cos(y), -sin(phi - y)*tan(x)/cos(y) + cos(phi)]])

print(simplify(R * Ys * Xs - RSS))
# Matrix([[0, 0], [0, 0]])

(One thing I'm uncertain is whether there is really a gain of performance by avoiding to calculate the explicit matrices and inverses, since the matrices are small and numpy can be quite efficient - I might run some time comparisons to check.)

[fmassa]

Thanks a lot for the PR!

I only really have one ask, which is to use np.matmul instead of @, because @ is not present in Python2. Apart from that, the rest is good to go, I only have minor comments.

[fmassa]

nit: Any reason to use numpy's functions instead of those from math?

[pedrofreire]

No strong reason here - my reason for this import was not much of whether to use math or numpy, but more that I felt this type of code is very error prone, and it was worth it to import the names directly and make the formulae more readable. And then for importing from numpy instead of math, it was just because the numpy functions are a superset of the math ones in terms of behavior (i.e. np.sin works for normal numbers and for np.array while math won't work for np.array), in case the functions are needed for np.arrays in the future.

[codecov-io]

Codecov Report

Merging #1529 into master will increase coverage by 0.03%.
The diff coverage is 88.88%.

@@            Coverage Diff             @@
##           master    #1529      +/-   ##
==========================================
+ Coverage    64.4%   64.44%   +0.03%     
==========================================
  Files          87       87              
  Lines        6746     6750       +4     
  Branches     1038     1038              
==========================================
+ Hits         4345     4350       +5     
+ Misses       2099     2097       -2     
- Partials      302      303       +1

Impacted Files	Coverage Δ
torchvision/transforms/functional.py	71.67% <88.88%> (+0.61%)	⬆️

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[fmassa]

Thanks a lot!