3-Tensor Operations and Constructors #415

zjwegert · 2020-10-07T22:44:39Z

Added functionality to compute

a_ij = b_kij*c_k
a_i = b_ijk*c_jk

Added functionality to compute ``` a_ij = b_kij*c_k a_i = b_ijk*c_jk ```

codecov-io · 2020-10-07T23:13:57Z

Codecov Report

Merging #415 into master will increase coverage by 0.05%.
The diff coverage is 93.50%.

@@            Coverage Diff             @@
##           master     #415      +/-   ##
==========================================
+ Coverage   87.26%   87.32%   +0.05%     
==========================================
  Files         158      158              
  Lines       11094    11170      +76     
==========================================
+ Hits         9681     9754      +73     
- Misses       1413     1416       +3

Impacted Files	Coverage Δ
src/TensorValues/TensorValues.jl	`100.00% <ø> (ø)`
src/TensorValues/ThirdOrderTensorValueTypes.jl	`52.77% <16.66%> (-7.23%)`	⬇️
src/TensorValues/Operations.jl	`87.24% <100.00%> (+4.13%)`	⬆️
src/TensorValues/VectorValueTypes.jl	`79.54% <0.00%> (-2.28%)`	⬇️
src/ReferenceFEs/CLagrangianRefFEs.jl	`94.52% <0.00%> (-0.31%)`	⬇️
src/TensorValues/Indexing.jl	`84.61% <0.00%> (+9.61%)`	⬆️

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fverdugo

@Omega-xyZac thanks for your PR.

I have added some coments to be addressed (see inline).

In addition:

Please, add some test for the new functionality in test/TensorValuesTests/OperationsTests.jl
Before merging this, please clarify what is causing the you reported in issue 3-tensor contractions with 2-tensor and 1-tensor #414

src/TensorValues/Operations.jl

zjwegert · 2020-10-08T22:53:08Z

Bug reported in #414 is due to not using @law for part of the weak form. Unrelated to new functionality.

Forgot to switch inner and outer for loop

- This new functionality calculates `a_ijpm = b_ijkl*c_jkpm` and also provides testing. - I have re-enabled use of `:` operator since this is the most suitable.

zjwegert · 2020-10-09T10:46:20Z

I guess we need a new symbol instead of : @fverdugo.

fverdugo · 2020-10-09T11:08:01Z

I guess we need a new symbol instead of : @fverdugo.

Sure @Omega-xyZac ! Perhaps we can use ⊡ (\boxdot)

In addition, try to respect our convention in which the indices that are contracted are the ones that are in "contact". That is:

a = b ⊡ c # a_ijkl = b_ijab*c_abkl

This convention is important since products with tensors are not always commutative.

zjwegert · 2020-10-09T11:15:42Z

I guess we need a new symbol instead of : @fverdugo.

Sure @Omega-xyZac ! Perhaps we can use ⊡ (\boxdot)

In addition, try to respect our convention in which the indices that are contracted are the ones that are in "contact". That is:
a = b ⊡ c # a_ijkl = b_ijab*c_abkl
This convention is important since products with tensors are not always commutative.

Ah yes sorry! That was actually a typo in the comment. The new \boxdot functionality adheres to that.

- Also changed comment to correctly reflect computation

santiagobadia · 2020-10-09T11:43:25Z

Why do we introduce a new symbol for the double contraction of tensors? There is a standard symbol for this and it is : . I would keep : unless there is a very compelling reason.

zjwegert · 2020-10-09T11:44:47Z

Why do we introduce a new symbol for the double contraction of tensors? There is a standard symbol for this and it is : . I would keep : unless there is a very compelling reason.

I agree but there seems to be issues with :? Perhaps @fverdugo can explain this more.

fverdugo · 2020-10-09T11:55:34Z

@santiagobadia the symbol : has a very concrete meaning in julia (range). I find very confusing to give it another meaning.

santiagobadia · 2020-10-09T12:31:27Z

There is not going to be any clash between these two cases. The problem is that the precedence of : vs +,- is different between these two cases. Probably, this cannot be fixed. That is a compelling reason. So 👍 with the new symbol.

zjwegert · 2020-10-09T22:32:02Z

Hi all,
I have some other contractions that I would like to add. One of these will break the convention a_ijmp = b_kij*c_kmp. I don't see any nice way around this. I can just leave this one out and use it in my personal code.

The others are

# a_ilm = b_ijk*c_jklm
# a_ilm = b_ij*c_jlm
# a_il = b_ijk*c_jkl
# a_il = b_ij*c_jl

santiagobadia · 2020-10-10T02:05:09Z

The last operations are single and double contractions. You can add them and use the agreed symbols. I would not include the one that breaks the rules in Gridap. I don't think this is standard enough. You can define them in your part.

santiagobadia · 2020-10-10T02:27:58Z

We could probably consider also this notation...

⋅¹,⋅²,⋅³,⋅⁴,... # n-contractions
⋅¹ == ⋅
⋅² == ⊡

I guess we will need 4-contractions of 4-tensors, which are usually expressed as :: or 3-contractions, etc.

What do you think @fverdugo @Omega-xyZac ?

zjwegert · 2020-10-10T03:45:26Z

This is probably the best solution to the problem of higher order contractions.

santiagobadia · 2020-10-10T05:38:25Z

src/TensorValues/Operations.jl

@@ -220,8 +246,40 @@ function inner(a::SymFourthOrderTensorValue{D},b::MultiValue{Tuple{D,D}}) where
  inner(a,symmetric_part(b))
 end

+# a_i = b_ijk*c_jk
+@generated function inner(a::A, b::B) where {A<:MultiValue{Tuple{D1,D2,D3}},B<:MultiValue{Tuple{D2,D3}}} where {D1,D2,D3}


This is not an inner product. This is a double contraction, isn't it?

Yes. I was trying to follow the convention that has been used in the rest of the file. I'll update these with the above notation

santiagobadia · 2020-10-10T05:39:32Z

src/TensorValues/Operations.jl

+###############################################################
+
+# a_ijpm = b_ijkl*c_klpm
+@generated function ⊡(a::A, b::B) where {A<:SymFourthOrderTensorValue{D},B<:SymFourthOrderTensorValue{D}} where D


I would give a name to this method, e.g., double_contraction and then define the symbol, as we do, e.g., for dot.

Added ``` # a_ilm = b_ijk*c_jklm # a_ilm = b_ij*c_jlm # a_il = b_ijk*c_jkl # a_il = b_ij*c_jl ``` Implemented notation per S. Badia: ``` ⋅¹,⋅²,⋅³,⋅⁴,... # n-contractions ⋅¹ == ⋅ ⋅² == ⊡ ```

Remove ⊡ from op

zjwegert · 2020-10-10T06:34:44Z

Noticed this in the build doc

$ julia --check-bounds=yes --color=yes -e "if VERSION < v\"0.7.0-DEV.5183\"; Pkg.test(\"${JL_PKG}\", coverage=true); else using Pkg; Pkg.test(coverage=true); end"

   Testing Gridap

 Resolving package versions...

WARNING: Method definition dot(A<:(Gridap.TensorValues.MultiValue{Tuple{D1, D2}, T, N, L} where L where N where T), B<:(Gridap.TensorValues.MultiValue{Tuple{D2, D3}, T, N, L} where L where N where T)) where {D1, D2, D3, A<:(Gridap.TensorValues.MultiValue{Tuple{D1, D2}, T, N, L} where L where N where T), B<:(Gridap.TensorValues.MultiValue{Tuple{D2, D3}, T, N, L} where L where N where T)} in module TensorValues at /home/travis/build/gridap/Gridap.jl/src/TensorValues/Operations.jl:158 overwritten at /home/travis/build/gridap/Gridap.jl/src/TensorValues/Operations.jl:212.

  ** incremental compilation may be fatally broken for this module **

WARNING: Method definition dot(Gridap.Helpers.GridapType, Gridap.Helpers.GridapType) in module Helpers at /home/travis/build/gridap/Gridap.jl/src/Helpers/GridapTypes.jl:41 overwritten in module TensorValues at /home/travis/build/gridap/Gridap.jl/src/TensorValues/Operations.jl:600.

  ** incremental compilation may be fatally broken for this module **

I think this is due to lines 339,340, and 598-606. Is this the correct way to be doing this? Perhaps ⋅¹ should not be in like 598.

Removed `⋅¹` from line 598. Changed `\odot` to `\cdot\^2` in testing for double contraction (L487).

src/TensorValues/Operations.jl

fverdugo · 2020-10-10T07:44:13Z

We could probably consider also this notation...
⋅¹,⋅²,⋅³,⋅⁴,... # n-contractions
⋅¹ == ⋅
⋅² == ⊡
I guess we will need 4-contractions of 4-tensors, which are usually expressed as :: or 3-contractions, etc.

What do you think @fverdugo @Omega-xyZac ?

I dont know if these names are going to be interpreted as operators by the julia compiler

zjwegert · 2020-10-10T07:45:02Z

We could probably consider also this notation...
⋅¹,⋅²,⋅³,⋅⁴,... # n-contractions
⋅¹ == ⋅
⋅² == ⊡
I guess we will need 4-contractions of 4-tensors, which are usually expressed as :: or 3-contractions, etc.
What do you think @fverdugo @Omega-xyZac ?
I dont know if these names are going to be interpreted as operators by the julia compiler

This seems to be working so far in my testing and other code.

zjwegert · 2020-10-12T01:52:00Z

#416 addressed here.

fverdugo

I have added some more comments (see inline)

Note that ⋅² and ⊡ are the same. I would only keep one version, perhaps ⋅². On the other hand, having double_contraction is fine since it is the plain asci version.

fverdugo · 2020-10-13T12:39:19Z

src/TensorValues/Operations.jl

+# a_ijpm = b_ijkl*c_klpm
+@generated function double_contraction(a::A, b::B) where {A<:SymFourthOrderTensorValue{D},B<:SymFourthOrderTensorValue{D}} where D
+
+  Sym4TensorIndexing = [1111, 1121, 1131, 1122, 1132, 1133, 2111, 2121, 2131, 2122, 2132, 2133,


This is particular for 3D. Can you implement it in general?
If for performance reasons, you want to keep the 3D specialization then use the signature

function double_contraction(a::A, b::B) where {A<:SymFourthOrderTensorValue{3},B<:SymFourthOrderTensorValue{3}}

Okay, perhaps ⋅². I will keep the 3D version since this should be fairly quick. I will have to have a think about how to do this generally.

This might do the trick:

@generated function double_contraction(a::SymFourthOrderTensorValue{D}, b::SymFourthOrderTensorValue{D}) where D str = "" for j in 1:D for i in j:D for m in 1:D for p in m:D s = "" for k in 1:D for l in 1:D s *= " a[$i,$j,$k,$l]*b[$k,$l,$p,$m] +" end end str *= s[1:(end-1)]*", " end end end end Meta.parse("SymFourthOrderTensorValue{D}($str)") end

Need to test.

Yes, keep ⋅² so we use the same notation for all >1 contractions.

- Added generalised contraction. - Removed ⊡.

fverdugo · 2020-10-14T13:49:01Z

@Omega-xyZac

can you include some comment on the new functionality in the https://github.com/gridap/Gridap.jl/blob/master/NEWS.md file ?

Please add the comments in a new section called [Unreleased], i.e.:

## [Unreleased]

## Added
- Your commend there...

Thanks!

3-tensor contractions with 2-tensor and 1-tensor

739df9c

Added functionality to compute ``` a_ij = b_kij*c_k a_i = b_ijk*c_jk ```

zjwegert mentioned this pull request Oct 7, 2020

3-tensor contractions with 2-tensor and 1-tensor #414

Closed

fverdugo requested changes Oct 8, 2020

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src/TensorValues/Operations.jl Outdated Show resolved Hide resolved

Fixed 3-tensor single contraction & Added testing

093e637

Omega-xyZac added 2 commits October 9, 2020 09:12

bug fix

3785310

Forgot to switch inner and outer for loop

Added double contractions w/ products

0499f67

- This new functionality calculates `a_ijpm = b_ijkl*c_jkpm` and also provides testing. - I have re-enabled use of `:` operator since this is the most suitable.

Omega-xyZac added 2 commits October 9, 2020 21:18

Changed : to ⊡

36ae454

- Also changed comment to correctly reflect computation

bug fix

4136684

santiagobadia requested changes Oct 10, 2020

View reviewed changes

Omega-xyZac added 3 commits October 10, 2020 16:07

Added further contractions & changed notation

3791058

Added ``` # a_ilm = b_ijk*c_jklm # a_ilm = b_ij*c_jlm # a_il = b_ijk*c_jkl # a_il = b_ij*c_jl ``` Implemented notation per S. Badia: ``` ⋅¹,⋅²,⋅³,⋅⁴,... # n-contractions ⋅¹ == ⋅ ⋅² == ⊡ ```

Bug fix

0ea786a

Remove ⊡ from op

Update Operations.jl

f704056

Omega-xyZac and others added 4 commits October 10, 2020 16:38

bug fix

01a4519

Removed `⋅¹` from line 598. Changed `\odot` to `\cdot\^2` in testing for double contraction (L487).

Update Operations.jl

0d5e64c

Update Operations.jl

6facb47

Removed duplicate

355179d

santiagobadia approved these changes Oct 10, 2020

View reviewed changes

santiagobadia requested changes Oct 10, 2020

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src/TensorValues/Operations.jl Outdated Show resolved Hide resolved

Removed duplicate

7a09a51

santiagobadia approved these changes Oct 10, 2020

View reviewed changes

Added zero method

83ca4e4

zjwegert changed the title ~~3-tensor contractions with 2-tensor and 1-tensor~~ 3-tensor contractions with 2-tensor and 1-tensor & 3-tensor zero method Oct 12, 2020

zero method testing

f1c1d3a

zjwegert changed the title ~~3-tensor contractions with 2-tensor and 1-tensor & 3-tensor zero method~~ 3-Tensor Operations and Constructors Oct 12, 2020

fverdugo requested changes Oct 13, 2020

View reviewed changes

Generalised double contraction

45ab2b3

- Added generalised contraction. - Removed ⊡.

fverdugo approved these changes Oct 14, 2020

View reviewed changes

fverdugo merged commit 9a09687 into gridap:master Oct 14, 2020

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3-Tensor Operations and Constructors #415

3-Tensor Operations and Constructors #415

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3-Tensor Operations and Constructors #415

3-Tensor Operations and Constructors #415

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