Reinterpret Vector of TaylorScalars as Matrix

[YichengDWu]

By reinterpreting Vector of TaylorScalars as Matrix we can take advantage of matrix multiplication.

Also relax the type annotation so that we can use TaylorDiff on gpu.

[YichengDWu]

The test failure does not look related to this PR.

[tansongchen]

Hi Yicheng, sorry for the late reply. Yes, it is definitely reasonable to relax the restrictions on types of x and l. The test failure is due to a mismatch of Julia version (1.8 on buildkite, 1.9 on my local develop env). I just fixed this. Could you rebase to the latest commit of main branch, update this PR and let the CIs run again?

[codecov]

Codecov Report

Patch coverage: 100.00% and project coverage change: -0.48% ⚠️

Comparison is base (45d95b6) 86.30% compared to head (bd895e6) 85.83%.

❗ Current head bd895e6 differs from pull request most recent head 1193331. Consider uploading reports for the commit 1193331 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #39      +/-   ##
==========================================
- Coverage   86.30%   85.83%   -0.48%     
==========================================
  Files           6        6              
  Lines         241      240       -1     
==========================================
- Hits          208      206       -2     
- Misses         33       34       +1     

Files Changed	Coverage Δ
src/chainrules.jl	70.14% <100.00%> (-2.16%)	⬇️
src/derivative.jl	100.00% <100.00%> (ø)

... and 2 files with indirect coverage changes

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[tansongchen]

There were some conflicts, just fixed by squashing and merged.