Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial #118

PerezHz · 2017-08-30T03:02:06Z

This PR implements a solution for #116, and adds corresponding tests; tests are passing on my fork, thanks everyone for your feedback!

coveralls · 2017-08-30T03:18:41Z

Coverage increased (+0.3%) to 94.51% when pulling 2f6ae2e on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

PerezHz · 2017-08-30T04:53:53Z

PR tests are passing, if there is anything that I missed or that you think should be added, please let me know 😄

coveralls · 2017-08-30T05:37:13Z

Coverage increased (+0.3%) to 94.468% when pulling dd81b0c on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-08-30T05:44:04Z

Coverage increased (+0.3%) to 94.51% when pulling dd81b0c on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

blas-ko · 2017-08-31T03:33:42Z

if there is anything that I missed or that you think should be added, please let me know.

It would be a nice feature to take advantage of this PR to implement an evaluate method for an array of values. I'm thinking of something like

julia> using TaylorSeries
julia> import TaylorSeries: evaluate;
julia> function evaluate(p::Taylor1{T},x::Vector{S}) where {T<:Number,S<:Number}
    ll = length(x)
    p_eval = zeros(x)
    for (i,xi) in enumerate(x)
        @inbounds p_eval[i] = evaluate(p,xi)
    end
    return p_eval
end
julia> (p::Taylor1)(x) = evaluate(p,x) #this now works for numbers & arrays!!
julia> p = Taylor1([1,2,3,4])
 1 + 2 t + 3 t² + 4 t³ + 𝒪(t⁴)
julia> p(1.0)
 10.0
julia> p([1.0,0.0])
2-element Array{Float64,1}:
 10.0
  1.0

The analogous could be done for TaylorN but instead an NxM matrix should be passed as an argument where N: number of variables, M: number of values to be evaluated.

PerezHz · 2017-08-31T05:25:02Z

I agree that this functionality should be available for the cases you mention, @blas-ko! Granted, I didn't add the methods you are proposing; but actually, as the way it is now, such cases may already be handled via broadcasting:

#evaluating p at a matrix of Float64s:
julia> p.([1.0 0.0; -1.0 -2.0])
2×2 Array{Float64,2}:
 10.0    1.0
 -2.0  -23.0

#evaluating p at a 3x3x3 matrix of Float64s:
julia> p.(rand(3,3,3))
3×3×3 Array{Float64,3}:
[:, :, 1] =
 8.65957  1.17927  8.12569
 1.13276  2.57914  3.37285
 2.51999  5.42389  2.04953

[:, :, 2] =
 1.03394  1.19053  3.51668
 1.15536  9.98952  4.27719
 7.29441  2.3461   2.76938

[:, :, 3] =
 1.33343  1.11886  1.08465
 5.75461  1.47925  1.78689
 1.47734  2.19666  1.84005

and for TaylorNs:

julia> ξ1, ξ2 = set_variables("ξ", numvars=2, order=15);

julia> f = sin(ξ1+ξ1*ξ2); g = exp(-sin(ξ1)+ξ1*ξ2); h = [f, g];

#evaluating f. at a vector of evaluation points returns a vector of Float64 values:
julia> f.([rand(2),rand(2)])
2-element Array{Float64,1}:
 0.974375
 0.585455

#evaluating g. at a 2x2 matrix of evaluation points returns a 2x2 matrix of Float64 values:
julia> g.( map(x->rand(2), rand(2,2)) )
2×2 Array{Float64,2}:
 0.929124  0.932631
 0.825413  0.888743

#evaluating h=[f,g] at a 2x2 matrix of evaluation points returns a 2x2 matrix of Vector{Float64}(2) values:
julia> h.( map(x->rand(2), rand(2,2)) )
2×2 Array{Array{Float64,1},2}:
 [0.674398, 0.736717]  [0.991339, 0.994949]
 [0.865741, 0.959931]  [0.460701, 0.800402]

#and so on...
julia> h.( [rand(2),rand(2)] )
2-element Array{Array{Float64,1},1}:
 [0.748772, 0.728316]
 [0.165423, 0.964655]

julia> h.( map(x->rand(2), rand(3,2,2)) )
3×2×2 Array{Array{Float64,1},3}:
[:, :, 1] =
 [0.970154, 0.996443]  [0.952156, 0.628598]
 [0.434873, 0.979518]  [0.750666, 0.492932]
 [0.839201, 0.475184]  [0.151065, 0.894432]

[:, :, 2] =
 [0.966398, 0.597349]  [0.414589, 0.901062]
 [0.045531, 0.992213]  [0.58178, 0.701201] 
 [0.395325, 0.718587]  [0.951338, 0.66144]

I think this is, in a sense, more julian, but also more general; otherwise one would have to define a method for each particular case... The only caveat is that ~~this behavior is only supported by julia 0.6+~~

EDIT: Sorry for the mistake, just tried these examples on julia 0.5.2 and they worked too!

PerezHz · 2017-08-31T05:58:09Z

So, for the particular case case of Taylor1 it might be enough to define:

evaluate{T<:Number,S<:Number}(p::Taylor1{T},x::Vector{S}) = evaluate.(p,x)

Thus

julia> p = Taylor1(rand(10))

julia> vr = rand(5)

julia> p(vr) == p.(vr)
true

julia> p(vr) == evaluate.(p,vr)
true

I'm gonna push this extra method for Taylor1s and corresponding tests! Thanks @blas-ko for your suggestion! I'd like to use some similar broadcasting tricks for TaylorN, but then the second argument would have to be a Vector{Vector{S}}...

PerezHz · 2017-08-31T06:00:09Z

Is there an easy way to convert from a Vector{Vector{T}} to an Array{T,2}?

blas-ko · 2017-08-31T06:09:21Z

such cases may already be handled via broadcasting

You're absolutely right, my fault there!

Is there an easy way to convert from a Vector{Vector{T}} to an Array{T,2}?

Maybe hcat

julia> a = [[1,2,3],[4,5,6]];
julia> @time hcat(a...)
  0.000038 seconds (8 allocations: 384 bytes)
3×2 Array{Int64,2}:
 1  1
 1  1
 2  3

PerezHz · 2017-08-31T06:24:26Z

Many thanks, @blas-ko!

coveralls · 2017-08-31T06:35:57Z

Coverage increased (+0.3%) to 94.515% when pulling d7d5b71 on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

lbenet

I'm in favor of merging this.

I have two questions:

Is everything type stable? It seems to me that this is the case...
What about mixed-types, i.e. Taylor1{TaylorN{T}}, or TaylorN{Taylor1{T}} ?

PerezHz · 2017-08-31T21:13:12Z

Is everything type stable? It seems to me that this is the case...

Well, as this functionality is being proposed right now, the function-like behavior of Taylor1, etc., at the end of the day relies on evaluate, so in principle this new behavior should be as type-stable as evaluate is... Do you have any concrete cases in mind?

What about mixed-types, i.e. Taylor1{TaylorN{T}}, or TaylorN{Taylor1{T}} ?

I'm gonna add some tests for the mixtures! That's actually something important that I didn't add! 😅 sorry about that! Regarding the function-like behavior for mixtures, this again relies on evaluate, so there should be no problem, but I'm adding some tests which should check this

PerezHz · 2017-08-31T21:46:29Z

Thanks for all your comments @lbenet! I actually had to tweak a bit some parts of src/evaluate.jl for the mixtures, but now everything's working smoothly. Tests are passing locally on julia 0.5.2, 0.6.0 and 0.7.0-DEV.1486, but let's see what travis thinks... An important thing that I would like to note is that the tweaks in src/evaluate.jl proposed here are also consistent with TaylorIntegration.jl tests on latest master for julia 0.5.2, 0.6.0 and 0.7.0-DEV

coveralls · 2017-08-31T23:46:54Z

Coverage increased (+1.2%) to 95.385% when pulling 105efe6 on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-09-01T00:07:24Z

Coverage increased (+1.0%) to 95.176% when pulling b7605bf on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-09-01T00:07:24Z

Coverage increased (+1.0%) to 95.176% when pulling b7605bf on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-09-01T00:07:24Z

Coverage increased (+1.0%) to 95.176% when pulling b7605bf on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-09-01T02:01:36Z

Coverage increased (+1.4%) to 95.542% when pulling 105efe6 on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-09-01T02:01:36Z

Coverage increased (+1.4%) to 95.542% when pulling 105efe6 on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

coveralls · 2017-09-01T02:01:36Z

Coverage increased (+1.4%) to 95.542% when pulling 105efe6 on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

PerezHz · 2017-09-01T02:34:07Z

@lbenet @dpsanders there was a weird error on travis job#652.5, could you please help me restart it? otherwise, tests are passing

dpsanders · 2017-09-01T02:38:55Z

I restarted the job.

Actually, with the syntax t(3) to evaluate, is there now any need for the function called evaluate?

PerezHz · 2017-09-01T03:15:52Z

I restarted the job.

Thanks, David!

Actually, with the syntax t(3) to evaluate, is there now any need for the function called evaluate?

Well, currently t(3) is only an alternative syntax for evaluate(t,3) (is that what is called syntactic sugar?), i.e. t(3) == evaluate(t,3), where t is a Taylor1... But I agree, if done carefully, I think it would be possible to get rid completely of the evaluate function, if we substituted the code for the evaluate methods in the definition of the (p::Taylor1)(x) methods, etc. On the other hand, probably there still would be a need for the in-place version of evaluate (i.e., the evaluate! function).

PerezHz · 2017-09-01T07:29:54Z

The last commit addresses more mixture cases, such as evaluating a TaylorN{Taylor1{Float64}} or an Array{TaylorN{Taylor1{Float64}}} at an Array{Taylor1{Float64}}; I added the corresponding evaluate methods and tests... On travis, once again there was a job (travis job #653.5) with some weird errors which had nothing to do with TaylorSeries.jl; after restarting everything should be working fine... Locally, tests are passing in julia 0.5.2, 0.6.0 and 0.7.0-DEV.1599

lbenet · 2017-09-01T07:36:24Z

Actually, with the syntax t(3) to evaluate, is there now any need for the function called evaluate?

Probably we should keep evaluate for a while, and eventually not exporting it or simply deprecate it.

I just restarted one test that hung.

coveralls · 2017-09-01T08:02:17Z

Coverage increased (+1.8%) to 95.947% when pulling cc63849 on PerezHz:jp/functors into 2381ad4 on JuliaDiff:master.

PerezHz · 2017-09-01T17:11:00Z

Probably we should keep evaluate for a while, and eventually not exporting it or simply deprecate it.

I agree!

I just restarted one test that hung.

Many thanks, @lbenet!

coveralls · 2017-09-02T06:41:58Z

Coverage increased (+1.8%) to 95.947% when pulling 6ad8bc7 on PerezHz:jp/functors into 347fce1 on JuliaDiff:master.

PerezHz · 2017-09-03T04:28:13Z

Could you add something to the docs, and then we merge this?

Sure! I added some general details about this new behavior in the User's Guide section of the docs. I was also thinking that I should add some docstrings, but I was thinking whether I should add those in the evaluate docstrings, or in the docstrings for the constructors of Taylor1, HomogeneousPolynomial and TaylorN variables?

I'm asking this because, as I understood from JuliaDocs/Documenter.jl#228 and JuliaDocs/Documenter.jl#290, currently it is not possible to write docstrings for these kinds of methods, and the recommended approach mentioned there is to document within the type's docstring that objects of that type are callable and provide a usage example there. So, how would you recommend me to proceed?

coveralls · 2017-09-03T04:30:25Z

Coverage increased (+1.8%) to 95.947% when pulling 8c666f7 on PerezHz:jp/functors into 347fce1 on JuliaDiff:master.

coveralls · 2017-09-07T02:15:40Z

Coverage increased (+1.8%) to 95.967% when pulling 948936d on PerezHz:jp/functors into 347fce1 on JuliaDiff:master.

coveralls · 2017-09-07T04:04:51Z

Coverage increased (+1.8%) to 95.96% when pulling b34a836 on PerezHz:jp/functors into 347fce1 on JuliaDiff:master.

PerezHz · 2017-09-27T06:43:42Z

I've updated the docstrings for evaluate as well as the docstrings for the Taylor1, HomogeneousPolynomial and TaylorN constructors. That's the only change since last commit, so travis should give green lights. If there is anything that you think should be added, please let me know; otherwise, this should be ready to be merged...

PerezHz · 2017-09-27T06:55:38Z

Job #19.4 is failing on travis... While working with TaylorSeries.jl, I've seen this error is related to a test which fails from time to time (test/onevariable.jl, line 343) due to use of random variables, but if re-run, then it should pass

EDIT: Sorry, "job #19.4 on travis" refers to a travis job on my fork; tests are passing for this PR!

coveralls · 2017-09-27T07:01:17Z

Coverage increased (+1.8%) to 95.957% when pulling dad55f6 on PerezHz:jp/functors into 347fce1 on JuliaDiff:master.

PerezHz · 2017-09-27T07:15:04Z

Tests are now passing!

lbenet

While everyhting appears to be ok, I have some comments.

lbenet · 2017-09-28T03:02:27Z

src/evaluate.jl

@@ -88,8 +97,25 @@ function evaluate{T<:Number}(a::Taylor1{T}, x::Taylor1{T})
    end
    suma
 end
+function evaluate{T<:NumberNotSeries}(a::Taylor1{Taylor1{T}}, x::Taylor1{T})


NumberNotSeries here may be too restrictive; I'm thinking in cases such as Taylor1{Taylor1{...{T}...}. Would everything work if T<:Number?

Sure, it should work! Thanks!

lbenet · 2017-09-28T03:03:05Z

src/evaluate.jl

 evaluate{T<:Number}(a::TaylorN{T}) = a[1][1]

 function evaluate{T<:Number}(x::Array{TaylorN{T},1}, δx::Array{T,1})
    x0 = Array{T}( length(x) )
    evaluate!( x, δx, x0 )
    return x0
 end
+
+function evaluate{T<:NumberNotSeries}(x::Array{TaylorN{T},1}, δx::Array{Taylor1{T},1})


Again, I think the two following methods can be written as one, using T<:NumberNotSeriesN.

👌Great! Thanks!

PerezHz · 2017-09-29T04:43:59Z

src/evaluate.jl

@@ -100,6 +126,25 @@ function evaluate!{T<:Number}(x::Array{TaylorN{T},1}, δx::Array{T,1},
    end
    nothing
 end
+


Thanks @lbenet!

PerezHz · 2017-09-29T04:49:50Z

@lbenet: just pushed the changes you suggested; tests are passing locally on 0.5.2, 0.6.0, and 0.7.0-DEV and are running on travis right now. Again, many thanks!

coveralls · 2017-09-29T05:01:55Z

Coverage increased (+1.8%) to 95.934% when pulling b9bda83 on PerezHz:jp/functors into 347fce1 on JuliaDiff:master.

lbenet · 2017-09-29T20:06:53Z

Thanks a lot for your contribution! I am merging it right now!

blas-ko · 2017-09-29T20:06:56Z

I was just checking evaluation and it seems that broadcasting is pretty slow; check the following

julia> using TaylorSeries; import TaylorSeries: evaluate 

julia> function evaluate{T<:Number}(a::Taylor1{T},vals::Vector{T})
           ll = length(vals)
           sumas = zeros(T,ll)
           for i in 1:ll
               sumas[i] = evaluate(a,vals[i])
           end
           return sumas
       end
evaluate (generic function with 15 methods)

julia> function evaluate{T<:Number,S<:Number}(a::Taylor1{T},vals::Vector{S})
           ll = length(vals)
           R = promote_type(S,T)
           sumas = zeros(R,ll)
           for i in 1:ll
               sumas[i] = evaluate(a,vals[i])
           end
           return sumas
       end
evaluate (generic function with 16 methods)

julia> t = Taylor1(10); a = collect(0.:0.5:10);

julia> using BenchmarkTools

julia> @btime evaluate(t,a); @btime evaluate.(t,a);
  402.035 ns (1 allocation: 256 bytes)
  7.380 μs (26 allocations: 1.31 KiB)

I've not done this with the other cases, but in this particular case the difference is yuuuge. Maybe it's worth it to write the specific methods for evaluating in vectors or matrices.

lbenet · 2017-09-29T20:21:25Z

@blas-ko I just merged this PR, seemingly at the same time you wrote your comment, though I was a bit faster ;-).

You are right that broadcasting (here) incurs in some allocations that cost time, roughly a factor 18. Note that

julia> @which evaluate.(t,a)
broadcast(f, A, Bs...) in Base.Broadcast at broadcast.jl:434

so my guess is that internally broadcast calls evaluate(t,a[i]) with some internal evaluations, which are not as efficient as the explicit method. In other words, if there is a method that does broadcasting, use it.

@blas-ko

JuliaDiff#118) * Add function-like behavior for Taylor1 * Relocate new code * Add function-like behavior for TaylorN * Fix TaylorN functor methods * Add tests for Taylor1 * Add more Taylor1 tests * Add TaylorN tests; more Taylor1 tests; add missing evaluate methods * Add function-like behavior for HomogeneousPolynomial and corresponding tests * Add missing tests for HomogeneousPolynomial * Add another test for Taylor1s * Fix test * Add extra evaluate method for Taylor1 (suggested by @blas-ko) * Add an evaluate test for mixtures (more to come) * Add tests for mixtures; add/fix evaluate methods * A small fix * Add missing evaluate methods for mixtures and tests * Update docs * Add evaluate method and tests * Fix new method * Update docstrings * Changes suggested by @lbenet 's review

@blas-ko

JuliaDiff#118) * Add function-like behavior for Taylor1 * Relocate new code * Add function-like behavior for TaylorN * Fix TaylorN functor methods * Add tests for Taylor1 * Add more Taylor1 tests * Add TaylorN tests; more Taylor1 tests; add missing evaluate methods * Add function-like behavior for HomogeneousPolynomial and corresponding tests * Add missing tests for HomogeneousPolynomial * Add another test for Taylor1s * Fix test * Add extra evaluate method for Taylor1 (suggested by @blas-ko) * Add an evaluate test for mixtures (more to come) * Add tests for mixtures; add/fix evaluate methods * A small fix * Add missing evaluate methods for mixtures and tests * Update docs * Add evaluate method and tests * Fix new method * Update docstrings * Changes suggested by @lbenet 's review

@lbenet

* Added function and macro `taylor_expand` for expanding arbitraty functions. * Deleted macros and set order as keyword argument so methods doesnt clash `taylor_expand(f,x0::Int64)` and `taylor_expand(f,order)` clashed. * Added some tests for `taylor_expand`. * un-exported taylor_expand macros. * Updated taylor_expand tests. * Added taylor_expand method for TaylorN and warning if number of variables is changed. * Fix travis issue for taylor_expand (hopefully). * Added taylor_expand! and tests for Taylor1. Followed suggestion from @lbenet. * Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial (#118) * Add function-like behavior for Taylor1 * Relocate new code * Add function-like behavior for TaylorN * Fix TaylorN functor methods * Add tests for Taylor1 * Add more Taylor1 tests * Add TaylorN tests; more Taylor1 tests; add missing evaluate methods * Add function-like behavior for HomogeneousPolynomial and corresponding tests * Add missing tests for HomogeneousPolynomial * Add another test for Taylor1s * Fix test * Add extra evaluate method for Taylor1 (suggested by @blas-ko) * Add an evaluate test for mixtures (more to come) * Add tests for mixtures; add/fix evaluate methods * A small fix * Add missing evaluate methods for mixtures and tests * Update docs * Add evaluate method and tests * Fix new method * Update docstrings * Changes suggested by @lbenet 's review * Added method for evaluating a TaylorN with an array of TaylorNs. * Added taylor_expand! method for TaylorN * Added some test for taylor_expand! * Documentation for taylor_expand and taylor_expand! * Added function and macro `taylor_expand` for expanding arbitraty functions. * Deleted macros and set order as keyword argument so methods doesnt clash `taylor_expand(f,x0::Int64)` and `taylor_expand(f,order)` clashed. * Added some tests for `taylor_expand`. * un-exported taylor_expand macros. * Updated taylor_expand tests. * Added taylor_expand method for TaylorN and warning if number of variables is changed. * Fix travis issue for taylor_expand (hopefully). * Added taylor_expand! and tests for Taylor1. Followed suggestion from @lbenet. * Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial (#118) * Add function-like behavior for Taylor1 * Relocate new code * Add function-like behavior for TaylorN * Fix TaylorN functor methods * Add tests for Taylor1 * Add more Taylor1 tests * Add TaylorN tests; more Taylor1 tests; add missing evaluate methods * Add function-like behavior for HomogeneousPolynomial and corresponding tests * Add missing tests for HomogeneousPolynomial * Add another test for Taylor1s * Fix test * Add extra evaluate method for Taylor1 (suggested by @blas-ko) * Add an evaluate test for mixtures (more to come) * Add tests for mixtures; add/fix evaluate methods * A small fix * Add missing evaluate methods for mixtures and tests * Update docs * Add evaluate method and tests * Fix new method * Update docstrings * Changes suggested by @lbenet 's review * Added method for evaluating a TaylorN with an array of TaylorNs. * Added taylor_expand! method for TaylorN * Added some test for taylor_expand! * Documentation for taylor_expand and taylor_expand! * Corrected silly mistake from rebasing. * Rearanged taylor_expand tests to another place. They use set_variables internally. * called coeff_table directly so it doesn't make a copy. * changed docs for taylor_expand * Changed taylor_expand for TaylorN. * It doesn't use set_variables() anymore. * typeof(x0) is preserved if possible. * Changed taylor_expand! for update! * Added 1 more test... * Little performance and compatibility fix for taylor_expand

PerezHz changed the title ~~WIP: Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial~~ Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial Aug 30, 2017

PerezHz mentioned this pull request Aug 30, 2017

Add method for evaluating a TaylorN on a Vector{TaylorN} #119

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lbenet reviewed Aug 31, 2017

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PerezHz added 2 commits September 2, 2017 01:09

A small fix

547c3ce

Add missing evaluate methods for mixtures and tests

6ad8bc7

Update docs

8c666f7

PerezHz added 2 commits September 6, 2017 16:26

Add evaluate method and tests

948936d

Fix new method

b34a836

PerezHz mentioned this pull request Sep 16, 2017

Add root-finding methods PerezHz/TaylorIntegration.jl#38

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Update docstrings

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lbenet requested changes Sep 28, 2017

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Changes suggested by @lbenet 's review

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PerezHz commented Sep 29, 2017

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lbenet approved these changes Sep 29, 2017

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lbenet merged commit 3b68fb3 into JuliaDiff:master Sep 29, 2017

lbenet mentioned this pull request Sep 29, 2017

Add function-like behavior for Taylor1, HomogeneousPolynomial and TaylorN? #116

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Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial #118

Add function-like behavior for Taylor1, TaylorN, HomogeneousPolynomial #118

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