ITP method implementation

[yash2798]

Tackles this #184

[codecov]

Codecov Report

Merging #67 (6a1a40f) into main (b2a43e0) will decrease coverage by 89.05%.
The diff coverage is 0.00%.

@@            Coverage Diff             @@
##             main     #67       +/-   ##
==========================================
- Coverage   92.30%   3.25%   -89.05%     
==========================================
  Files          16      17        +1     
  Lines         819     859       +40     
==========================================
- Hits          756      28      -728     
- Misses         63     831      +768     

Impacted Files	Coverage Δ
src/SimpleNonlinearSolve.jl	33.33% <ø> (-60.01%)	⬇️
src/itp.jl	0.00% <0.00%> (ø)

... and 15 files with indirect coverage changes

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[yash2798]

@ChrisRackauckas I am kinda confused why such an error in only some test cases is happening. Do you have any inputs that might help? The code seems alright but maybe can you review it once?

[ChrisRackauckas]

How much has the solution converged?

[yash2798]

How much has the solution converged?

The solution (root of the function) has converged well upto the tolerance. This can be also be seen as the tests for this also pass. Just the AD tests fail only for a handful values for the parameter p.

[yash2798]

`g = function (p)
probN = IntervalNonlinearProblem{false}(f, typeof(p).(tspan), p)
sol = solve(probN, Itp())
return sol.u
end

for p in 1.1:0.1:100.0
@test g(p) ≈ sqrt(p)
@test ForwardDiff.derivative(g, p) ≈ 1 / (2 * sqrt(p))
end`

All these tests @test g(p) ≈ sqrt(p) pass.

[ChrisRackauckas]

How close to zero is the evaluation?

[ChrisRackauckas]

Try and recreate the derivative calculation in the REPL: https://github.com/SciML/SimpleNonlinearSolve.jl/blob/main/src/ad.jl#L2-L28

[yash2798]

okay i'll take a look

[yash2798]

@ChrisRackauckas I tried doing the derivative calc in the repl but nothing significant came up. Also, I am a little confused about what this function scalar_nlsolve_ad does? I can see that it is called in some dispatches written down after that but if I am not mistaken i don't see any dispatches that handle any algorithm except the Bisection one?

SimpleNonlinearSolve.jl/src/ad.jl

Line 51 in b2a43e0

for Alg in [Bisection]

[ChrisRackauckas]

It looks like there are test failures?

[oscardssmith]

The broad strokes of this look good.

[yash2798]

The broad strokes of this look good.

@oscardssmith you mean some scope for improvement still left?

[oscardssmith]

I just mean that all the tests seem to suggest that it is broken.