perf: speed up time loop in processed var init sens

[martinjrobins]

Description

Speeds up initial sensitivitiy calculation in ProcessedVariable. The diagcat and vertcat is done once instead of every timestep

I did a simple test using the DFN model and one input paramter (current), before the change the timings were (over 10 runs)

(env-pybammsolvers) ➜  PyBaMM git:(develop) ✗ python test.py
Time taken to compute sensitivities: 0.05452 seconds
Time taken to compute sensitivities: 0.04619 seconds
Time taken to compute sensitivities: 0.04333 seconds
Time taken to compute sensitivities: 0.04116 seconds
Time taken to compute sensitivities: 0.04146 seconds
Time taken to compute sensitivities: 0.04142 seconds
Time taken to compute sensitivities: 0.04156 seconds
Time taken to compute sensitivities: 0.04135 seconds
Time taken to compute sensitivities: 0.04133 seconds
Time taken to compute sensitivities: 0.04186 seconds

After the change the timings were:

(env-pybammsolvers) ➜  PyBaMM git:(develop) ✗ python test.py
Time taken to compute sensitivities: 0.02355 seconds
Time taken to compute sensitivities: 0.02262 seconds
Time taken to compute sensitivities: 0.02266 seconds
Time taken to compute sensitivities: 0.02286 seconds
Time taken to compute sensitivities: 0.02309 seconds
Time taken to compute sensitivities: 0.02277 seconds
Time taken to compute sensitivities: 0.02158 seconds
Time taken to compute sensitivities: 0.01918 seconds
Time taken to compute sensitivities: 0.01988 seconds
Time taken to compute sensitivities: 0.02149 seconds

Type of change

Important checks:

Please confirm the following before marking the PR as ready for review:

• No style issues: nox -s pre-commit
• All tests pass: nox -s tests
• The documentation builds: nox -s doctests
• Code is commented for hard-to-understand areas
• Tests added that prove fix is effective or that feature works

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.57%. Comparing base (dce8938) to head (baf332c).
⚠️ Report is 117 commits behind head on develop.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #5000      +/-   ##
===========================================
- Coverage    98.57%   98.57%   -0.01%     
===========================================
  Files          304      304              
  Lines        23652    23645       -7     
===========================================
- Hits         23316    23309       -7     
  Misses         336      336              

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[MarcBerliner]

Great speedup, thanks!

[kratman]

@martinjrobins I re-triggered the CI, looks like a link check failure