Simplify some functions #19

KristofferC · 2017-03-12T11:16:05Z

TODO:

fix more functions
benchmark

fredrikekre · 2017-03-12T11:20:57Z

src/tensor_products.jl

-        @inbounds return $TensorType($expr)
-    end
+@inline function otimes{dim}(S1::SecondOrderTensor{dim}, S2::SecondOrderTensor{dim})
+    TensorType = getreturntype(otimes, get_base(typeof(S1)), get_base(typeof(S2)))


This will only be fast if getreturntype is @pure
Edit: Should have kept scrolling.

KristofferC · 2017-03-12T11:27:42Z

We could perhaps have some "reduce" function to simplify other things

fredrikekre · 2017-03-12T11:27:59Z

src/math_ops.jl

+    Tt = get_base(typeof(S))
+    tr = trace(S) / 3
+    Tt(
+        @inline function(i, j)


This function will return different eltype for Int tensors.

julia> Tensor{2, 3}((i, j)-> i == j ? 1 : 1.0) ERROR: MethodError: Cannot `convert` an object of type Tuple{Int64,Float64,Float64,Float64,Int64,Float64,Float64,Float64,Int64} to an object of type Tensors.Tensor{2,3,T<:Real,M} This may have arisen from a call to the constructor Tensors.Tensor{2,3,T<:Real,M}(...), since type constructors fall back to convert methods. in Tensors.Tensor{2,3,T<:Real,M}(::Tuple{Int64,Float64,Float64,Float64,Int64,Float64,Float64,Float64,Int64}) at ./sysimg.jl:53 in macro expansion at /home/fredrik/Dropbox/Programming/Tensors.jl/src/constructors.jl:15 [inlined] in Tensors.Tensor{2,3,T<:Real,M}(::##1#2) at /home/fredrik/Dropbox/Programming/Tensors.jl/src/constructors.jl:5

Yep. I tried:

@inline function dev(S::SecondOrderTensor) Tt = get_base(typeof(S)) tr = trace(S) / 3 T = typeof(one(eltype(S)) / 3) Tt( @inline function(i, j) @inbounds if i == j return T(S[i,j] - tr) else return T(S[i,j]) end end ) end

but it is slow for some reason.

Could do this:

@inline function dev{dim, T}(S::SecondOrderTensor{dim, T}) Tt = get_base(typeof(S)) tr = trace(S) / 3 R = promote_type(T, typeof(tr)) Tt( @inline function(i, j) @inbounds if i == j return R(S[i,j] - tr) else return R(S[i,j]) end end ) end

Edit, yea its really slow.

Looks like Tt is not inferred..

It doesn't work on master either so

julia> A = rand(Tensor{2, 3, Int}); julia> dev(A) ERROR: MethodError: Cannot `convert` an object of type Tuple{Float64,Int64,Int64,Int64,Float64,Int64,Int64,Int64,Float64} to an object of type Tensors.Tensor{2,3,T<:Real,M} This may have arisen from a call to the constructor Tensors.Tensor{2,3,T<:Real,M}(...), since type constructors fall back to convert methods. in macro expansion at /home/fredrik/Dropbox/Programming/Tensors.jl/src/math_ops.jl:275 [inlined] in dev(::Tensors.Tensor{2,3,Int64,9}) at /home/fredrik/Dropbox/Programming/Tensors.jl/src/math_ops.jl:267

I put it back since it fails on master

We could perhaps limit eltype for this method to AbstractFloat?

Ideally it should just promote but I dunno why it gets slow then...

fredrikekre · 2017-03-12T15:10:39Z

src/transpose.jl

-        $(Expr(:meta, :inline))
-        @inbounds return Tensor{4, dim}($expr)
-    end
+@inline function majortranspose{dim}(S::Tensor{4, dim})


This method should have S::FourthOrderTensor{dim} as input but always return Tensor{4, dim} so just change the input type signature.

KristofferC · 2017-03-12T19:28:49Z

Did some more functions.. Using the function stuff is really powerful.

KristofferC · 2017-03-12T19:45:43Z

Jesus we have a lot of benchmarks...

fredrikekre · 2017-03-12T19:55:27Z

src/transpose.jl

-        @inbounds return Tensor{2, dim}($expr)
-    end
+@inline function Base.transpose{dim}(S::Tensor{2, dim})
+    Tensor{2, dim}(@inline function(i, j) @inbounds v = S[j,i]; v; end)


@inboundsret ?

fredrikekre · 2017-03-12T19:57:06Z

This is great!

Jesus we have a lot of benchmarks...

Yea, better safe than sorry :p

KristofferC · 2017-03-12T20:06:53Z

Benchmarks here: https://gist.github.com/KristofferC/8f423c6d4b2c1f614b3ff7f03fa7c394

I did not find any difference in the generated code for anything that looked like it could be real regressions.

fredrikekre · 2017-03-12T20:27:30Z

I tested some cases too, didn't see any difference. Benchmarks really are weird...

codecov-io · 2017-03-13T00:05:57Z

Codecov Report

Merging #19 into master will decrease coverage by 0.18%.
The diff coverage is 96.96%.

@@            Coverage Diff             @@
##           master      #19      +/-   ##
==========================================
- Coverage   97.62%   97.44%   -0.19%     
==========================================
  Files          14       14              
  Lines         970      899      -71     
==========================================
- Hits          947      876      -71     
  Misses         23       23

Impacted Files	Coverage Δ
src/constructors.jl	`97.53% <100%> (+1.14%)`	⬆️
src/tensor_ops_errors.jl	`100% <100%> (ø)`	⬆️
src/math_ops.jl	`100% <100%> (ø)`	⬆️
src/tensor_products.jl	`100% <100%> (ø)`	⬆️
src/transpose.jl	`100% <100%> (ø)`	⬆️
src/symmetric.jl	`100% <100%> (ø)`	⬆️
src/basic_operations.jl	`92.85% <66.66%> (-7.15%)`	⬇️
src/utilities.jl	`98.27% <95%> (+0.09%)`	⬆️

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 7728952...ed841b0. Read the comment docs.

KristofferC · 2017-03-13T06:35:35Z

Pfft 36 min on Travis 0.6. Is this due to a change in Base or this PR?

fredrikekre · 2017-03-13T07:47:50Z

Locally on v06:

278.792679 seconds (1.01 G allocations: 21.509 GiB, 2.43% gc time) # master
479.304849 seconds (3.57 G allocations: 63.570 GiB, 3.17% gc time) # PR

KristofferC · 2017-03-13T08:22:12Z

Yuck... hmm.

fredrikekre · 2017-03-13T08:44:38Z

JuliaLang/julia#18077 ? But upgraded to 0.6 from 0.5 :)

KristofferC · 2017-03-18T12:08:13Z

 Section               ncalls     time   %tot     avg     alloc   %tot      avg
 ──────────────────────────────────────────────────────────────────────────────
 tensor ops                 1     923s  57.6%    923s    131GiB  61.9%   131GiB
   symmetric/skew-s...      9     665s  41.5%   73.9s    101GiB  47.5%  11.2GiB
   transpose                9     159s  9.93%   17.7s   22.4GiB  10.5%  2.49GiB
   outer product            9    73.6s  4.59%   8.18s   7.26GiB  3.42%   826MiB
   double contraction       9    21.9s  1.37%   2.43s    779MiB  0.36%  86.6MiB
   dot products             9    1.82s  0.11%   202ms   55.1MiB  0.03%  6.12MiB
   special                  9    1.12s  0.07%   124ms   36.7MiB  0.02%  4.08MiB
   cross product            9    186ms  0.01%  20.7ms   3.96MiB  0.00%   450KiB
   rotation                 9    362μs  0.00%  40.2μs   40.6KiB  0.00%  4.52KiB
 constrct Arr               1     281s  17.5%    281s   41.8GiB  19.7%  41.8GiB
 AD                         1     149s  9.30%    149s   11.9GiB  5.61%  11.9GiB
   dim 3                    1     129s  8.06%    129s   11.1GiB  5.25%  11.1GiB
     hessian                2    70.2s  4.38%   35.1s   6.79GiB  3.20%  3.39GiB
     2nd tensor grad        2    23.3s  1.45%   11.6s   1.60GiB  0.75%   817MiB
     scalar grad            2    2.05s  0.13%   1.03s    113MiB  0.05%  56.4MiB
   dim 2                    1    14.3s  0.89%   14.3s    625MiB  0.29%   625MiB
     hessian                2    6.39s  0.40%   3.19s    293MiB  0.13%   147MiB
     2nd tensor grad        2    3.39s  0.21%   1.69s    132MiB  0.06%  65.8MiB
     scalar grad            2    1.15s  0.07%   573ms   41.2MiB  0.02%  20.6MiB
   dim 1                    1    5.53s  0.34%   5.53s    163MiB  0.07%   163MiB
     hessian                2    2.65s  0.17%   1.33s   81.9MiB  0.04%  40.9MiB
     2nd tensor grad        2    1.09s  0.07%   543ms   24.8MiB  0.01%  12.4MiB
     scalar grad            2    549ms  0.03%   274ms   16.0MiB  0.01%  8.00MiB
 indexing                   1     136s  8.47%    136s   20.9GiB  9.84%  20.9GiB
 tensor identities          1    44.9s  2.80%   44.9s   3.85GiB  1.81%  3.85GiB
 constructors               1    22.8s  1.42%   22.8s    700MiB  0.32%   700MiB
 simple math                1    17.1s  1.07%   17.1s    724MiB  0.33%   724MiB
 norm, trace, det, ...      1    13.0s  0.81%   13.0s    484MiB  0.22%   484MiB
 promotion/conversion       1    7.32s  0.46%   7.32s    301MiB  0.14%   301MiB
 base vectors               1    3.66s  0.23%   3.66s    137MiB  0.06%   137MiB
 diagm, one                 1    3.41s  0.21%   3.41s   93.9MiB  0.04%  93.9MiB
 constrct func              1    2.64s  0.16%   2.64s   96.5MiB  0.04%  96.5MiB
 exceptions                 1   2.14ms  0.00%  2.14ms   7.89KiB  0.00%  7.89KiB
 ──────────────────────────────────────────────────────────────────────────────

symmetric /skew symmetric 600 seconds!, one master, 3.52 seconds.

construct from array: 13.8s -> 281s

fredrikekre · 2017-03-18T12:27:26Z

Seems to be extremely hard on inference with this method...

KristofferC · 2017-03-18T12:28:05Z

I don't get it though.. on 0.5.1:

<< using Tensors

<< a  = rand(Tensor{4,3});

<< @time symmetric(a);
 51.641367 seconds (68.55 M allocations: 1.077 GB, 0.48% gc time)

so why is it fast when doing the tests?

fredrikekre · 2017-03-18T12:31:29Z

That time is just ridiculous LOL

fredrikekre · 2017-03-18T12:39:15Z

I tried typeasserting the functions but didn’t make a difference.

KristofferC · 2017-03-18T12:43:01Z

This is fast though:

immutable Tensor{order, dim, T <: Real, M}
    data::NTuple{M, T}
end

@generated function gg{order, dim}((S::Type{Tensor{order, dim}}), f::Function)
    exp = Expr(:tuple, [:(f($i,$j,$k,$l)) for i=1:dim, j=1:dim, k = 1:dim, l = 1:dim]...)
    return quote
        return $exp
    end
end

gg(Tensor{4,3}, (i,j,k,l) -> i+j+k+l)

KristofferC · 2017-03-19T11:31:16Z

With JuliaLang/julia#21085 tests on this branch are slightly faster than on master.

KristofferC · 2017-03-19T14:11:30Z

It seems that we can generally avoid using the compute_index stuff to avoid the indexing because the compiler does it by itself.
For example:

@generated function dcontract_muladd{dim}(S1::Tensor{2, dim}, S2::Tensor{2, dim})
    ex1 = Expr[:(S1[$i, $j]) for i in 1:dim, j in 1:dim][:]
    ex2 = Expr[:(S2[$i, $j]) for i in 1:dim, j in 1:dim][:]
    exp = reducer(ex1, ex2, true)
    return quote
        $(Expr(:meta, :inline))
        @inbounds return $exp
    end
end

produces just as good code as the one with compute_index.

fredrikekre · 2017-03-19T14:26:01Z

Yea, but for SymmetricTensor we can not do that

KristofferC · 2017-03-19T14:28:19Z

Why not?

fredrikekre · 2017-03-19T14:29:00Z

the for i in 1:dim, j in 1:dim-loop I mean.

KristofferC · 2017-03-19T14:34:03Z

Ah, no. This also seems to be more expensive for compilation...

fredrikekre · 2017-03-20T07:45:57Z

src/constructors.jl

-        @inbounds return $TensorType($expr)
-    end
-end
+Base.fill{T <: AbstractTensor}(el::Number, S::Type{T}) = apply_all(get_base(T), i -> el)


This became really neat.

fredrikekre · 2017-03-20T07:46:59Z

src/math_ops.jl

-    end
+@inline Base.det(t::SecondOrderTensor{1}) = @inboundsret t[1,1]
+@inline Base.det(t::SecondOrderTensor{2}) = @inboundsret (t[1,1] * t[2,2] - t[1,2] * t[2,1])
+@inline function Base.det(t::SecondOrderTensor{3})


Will this give the same code even for SymmetricTensor?

Appear so, yes.

fredrikekre · 2017-03-20T07:48:42Z

src/tensor_products.jl

-    end
+@inline function otimes{dim}(S1::SecondOrderTensor{dim}, S2::SecondOrderTensor{dim})
+    TensorType = getreturntype(otimes, get_base(typeof(S1)), get_base(typeof(S2)))
+    TensorType(@inline function(i,j,k,l) @inboundsret S1[i,j] * S2[k,l]; end)


Same here; results in the same code for SymmetricTensor?

I'm pretty sure checked that but can check again.

As long as compute_index via getindex is elided for Tensor, no reason it shouldn't for SymmetricTensor as well. Just making sure.

Yes, exact same code

fredrikekre · 2017-03-20T07:53:51Z

test/test_ops.jl

@@ -7,7 +7,7 @@ end

 @testsection "tensor ops" begin
 for T in (Float32, Float64, F64), dim in (1,2,3)
-
+println("T = $T, dim = $dim")


Perhaps this should be removed? It was included in #23

It is there because sometimes there were time outs for this section because nothing got printed for 10 minutes. I think maybe when Travis is extra slow. So good to have something that prints maybe?

But #23 results in prints just as often?

There is no printing there from what I can see?

Ah, right. It was removed in #23 :) https://github.com/KristofferC/Tensors.jl/pull/23/files#diff-78a3de5eaf1c4bcf42b32436cba105ceL8

KristofferC · 2017-03-20T08:05:55Z

Good to go?

fredrikekre

Nice code deletion!

fredrikekre · 2017-03-20T23:33:17Z

I tried this #19 (comment) for all functions. Test time (eg compilation time) went from 120s to 750. It really helps the compiler to compute the linear index by ourselves. Sadly, cause it led to some nice code deletion

KristofferC · 2017-03-21T06:38:29Z

Perhaps we can make an issue about it...

fredrikekre reviewed Mar 12, 2017

View reviewed changes

merge

48b5acf

KristofferC force-pushed the kc/simplify branch from b76a616 to ad54bed Compare March 18, 2017 11:02

fixup

aa4e141

KristofferC force-pushed the kc/simplify branch from ad54bed to aa4e141 Compare March 18, 2017 11:04

KristofferC mentioned this pull request Mar 18, 2017

60+ seconds to compile a function JuliaLang/julia#21081

Closed

fredrikekre mentioned this pull request Mar 18, 2017

Explicit simd for ad #17

Closed

some stuff

ed841b0

KristofferC closed this Mar 20, 2017

KristofferC reopened this Mar 20, 2017

fredrikekre reviewed Mar 20, 2017

View reviewed changes

fredrikekre approved these changes Mar 20, 2017

View reviewed changes

fredrikekre changed the title ~~WIP: simplify some functions~~ Simplify some functions Mar 20, 2017

KristofferC merged commit d01ee37 into master Mar 20, 2017

KristofferC deleted the kc/simplify branch March 20, 2017 08:13

KristofferC mentioned this pull request Mar 22, 2017

avoid stackoverflow in promotion #29

Merged

fredrikekre mentioned this pull request Apr 4, 2017

Lots of stuff... Ferrite-FEM/Ferrite.jl#125

Merged

Simplify some functions #19

Simplify some functions #19

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