`==`(x,y) is true when only partials(y) have NaNs

[magerton]

When x and y are duals and have equal values, but the partials differ in that some are NaNs, the statement x==y evaluates to true, even though partials(x) == partials(y) is not true. I'm guessing that this is not the intended behavior, but I'm not sure where the fix would go. The problem doesn't seem to hold for Partials

using ForwardDiff: Dual, Partials, partials
Dual(0.0, (1.0, 0.0)) == Dual(0.0, (1.0, NaN)) # true... should be false?
Dual(0.0, (1.0, 0.0)) == Dual(0.0, (NaN, NaN)) # true... should be false?
Dual(0.0, (1.0, 0.0)) == Dual(NaN, (1.0, 0.0)) # false

Partials((0.0, 1.0)) == Partials((0.0, 1.0)) # true
Partials((0.0, 1.0)) == Partials((NaN, 1.0)) # false

partials(Dual(0.0, (1.0, 0.0))) == partials(Dual(0.0, (1.0, 0.0))) # true
partials(Dual(0.0, (1.0, 0.0))) == partials(Dual(0.0, (1.0, NaN))) # false
partials(Dual(0.0, (1.0, 0.0))) == partials(Dual(0.0, (NaN, NaN))) # false

[mcabbott]

On master, which now includes #481, these tests are as you desire:

julia> Dual(0.0, (1.0, 0.0)) == Dual(0.0, (1.0, NaN)) # true... should be false?
false

julia> Dual(0.0, (1.0, 0.0)) == Dual(0.0, (NaN, NaN)) # true... should be false?
false

julia> Dual(0.0, (1.0, 0.0)) == Dual(NaN, (1.0, 0.0)) # false
false

That change was not driven by NaN concerns. Can you say why you prefer these, what the application is?

[magerton]

Hi @mcabbott , thanks for the quick response.

I'm not sure what you mean by the "tests are as you desire." What was strange (and undesirable to me) was that x==y evaluated to true even though the dual parts (Partials) were not equal. If this is fixed in master, we should close this issue.

To answer your question, I noticed this when testing a backslash (\) method I'm writing to handle a sparse matrix of duals (a derivative of #363). For my small test case, the dense version of \ returned a vector of duals with partials equal to zero, while the sparse version of the function returned NaNs. The fact that Msparse\b == Mdense\b when the partials were different (eg, one had NaNs) is problematic for verifying that my function is returning the same result for dense and sparse matrices.

https://github.com/magerton/ForwardDiffMatrixTools.jl/blob/eb56f763abc6fc87ea4f58b6e29fdec5f9f13ae6/src/ForwardDiffMatrixTools.jl#L66-L106

[magerton]

In case helpful, I'm using

[f6369f11] ForwardDiff v0.10.32

[mcabbott]

Ok, good. So your test Msparse\b == Mdense\b will (soon) detect the presence of NaNs, although presumably the final calculation once it all works will not contain them.

v0.10.32 is without this PR. My results above are with ] add ForwardDiff#master, which includes it.

[magerton]

Perfect. Thank you!!

Closed by #481