Revise calculation of bound check

[bennibolm]

Before, only the bounds' deviation of the last stage of the current time step was printed to the txt file. Now, it is the maximum deviations since the last export.

[github-actions]

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[bennibolm]

the maximum deviations at the end of the simulations are equal in the old and new version:

────────────────────────────────────────────────────────────────────────────────────────────────────
Maximum deviation from bounds:
────────────────────────────────────────────────────────────────────────────────────────────────────
rho1:
- positivity: 2.220446049250313e-16
rho2:
- positivity: 3.122502256758253e-17
────────────────────────────────────────────────────────────────────────────────────────────────────

[bennibolm]

Runtime comparison: (interval=100)

Before:
check_bounds 417 2.41ms 3.8% 5.78μs 216KiB 8.7% 531B

Now:
check_bounds 417 2.52ms 4.0% 6.04μs 210KiB 8.5% 517B

I think the small difference are acceptable

[bennibolm]

Another analysis: Looking at the deviation of every stage; 3 time steps in total

1. Print deviation of every stage (manually implemented; no setting for this)
2. Print deviation not for every stage but interval=1
3. Print deviation not for every stage but interval=2

Before:

# iter, simu_time, rho1_min, rho2_min
1, 0.0, 0.0, 0.0
1, 0.0, 0.0, 0.0
1, 0.0, 0.0, 0.0
2, 7.25234339269239e-5, 0.0, 0.0
2, 7.25234339269239e-5, 6.938893903907228e-18, 0.0
2, 7.25234339269239e-5, 0.0, 0.0
3, 0.00014385709817375206, 0.0, 0.0
3, 0.00014385709817375206, 4.5102810375396984e-17, 0.0
3, 0.00014385709817375206, 0.0, 0.0

# iter, simu_time, rho1_min, rho2_min
1, 0.0, 0.0, 0.0
2, 7.25234339269239e-5, 0.0, 0.0
3, 0.00014385709817375206, 0.0, 0.0

# iter, simu_time, rho1_min, rho2_min
1, 0.0, 0.0, 0.0
3, 0.00014385709817375206, 0.0, 0.0

Now:

# iter, simu_time, rho1_min, rho2_min
1, 0.0, 0.0, 0.0
1, 0.0, 0.0, 0.0
1, 0.0, 0.0, 0.0
2, 7.25234339269239e-5, 0.0, 0.0
2, 7.25234339269239e-5, 6.938893903907228e-18, 0.0
2, 7.25234339269239e-5, 0.0, 0.0
3, 0.00014385709817375206, 0.0, 0.0
3, 0.00014385709817375206, 4.5102810375396984e-17, 0.0
3, 0.00014385709817375206, 0.0, 0.0

# iter, simu_time, rho1_min, rho2_min
1, 0.0, 0.0, 0.0
2, 7.25234339269239e-5, 6.938893903907228e-18, 0.0
3, 0.00014385709817375206, 4.5102810375396984e-17, 0.0

# iter, simu_time, rho1_min, rho2_min
1, 0.0, 0.0, 0.0
3, 0.00014385709817375206, 4.5102810375396984e-17, 0.0

Looks good to me. Before, all errors disappeared. Now, we got all of them.

[bennibolm]

Replacing Symbol("$(v)_min") by Symbol(string(v), "_min") decreases the allocations.
Here for example monitored for the bounds checking routine
check_bounds 417 2.38ms 3.9% 5.70μs 98.9KiB 4.4% 243B