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Summation of LazyArrays #610

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zjwegert opened this issue Jun 3, 2021 · 6 comments
Closed

Summation of LazyArrays #610

zjwegert opened this issue Jun 3, 2021 · 6 comments

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@zjwegert
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zjwegert commented Jun 3, 2021

Suppose we are contracting, operating then integrating on tensors generated from an FE function. Then you can encounter very complex LazyArrays such as the example below. This is fine unless you want to sum up the array. Summing an array such as the one below can take almost 60 seconds - not a surprise given the typing.

Is there a faster way we could sum such an array? Maybe not given the nature of LazyArrays but I thought it worth the question.

27000-element LazyArray{FillArrays.Fill{IntegrationMap, 1, Tuple{Base.OneTo{Int64}}}, SymFourthOrderTensorValue{3, Float64, 36}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(-)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{var"#1545#tmp_operation#97"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{LazyArray{FillArrays.Fill{typeof(constant_field), 1, Tuple{Base.OneTo{Int64}}}, ConstantField{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{Vector{SymFourthOrderTensorValue{3, Float64, 36}}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(symmetric_part)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(symmetric_part)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(symmetric_part)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(symmetric_part)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(symmetric_part)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(symmetric_part)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{var"#1560#tmp_operation#98"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{SymFourthOrderTensorValue{3, Float64, 36}}, 1, Tuple{LazyArray{LazyArray{FillArrays.Fill{typeof(constant_field), 1, Tuple{Base.OneTo{Int64}}}, ConstantField{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(+)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(-)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(-)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(dot)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{FillArrays.Fill{Vector{TensorValue{3, 3, Float64, 9}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{Gridap.Fields.var"#k#58"}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{FillArrays.Fill{Vector{Float64}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, FillArrays.Fill{Vector{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}, LazyArray{FillArrays.Fill{Gridap.Fields.LinearCombinationMap{Colon}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, Tuple{LazyArray{FillArrays.Fill{Broadcasting{PosNegReindex{SubVector{Float64, Vector{Float64}}, Vector{Float64}}}, 1, Tuple{Base.OneTo{Int64}}}, Vector{Float64}, 1, Tuple{Table{Int32, Vector{Int32}, Vector{Int32}}}}, FillArrays.Fill{Matrix{VectorValue{3, Float64}}, 1, Tuple{Base.OneTo{Int64}}}}}}}}}}}, FillArrays.Fill{Vector{SymTensorValue{3, Float64, 6}}, 1, Tuple{Base.OneTo{Int64}}}}}}}, LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(outer)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{ThirdOrderTensorValue{3, 3, 3, Float64, 27}}, 1, Tuple{LazyArray{FillArrays.Fill{Gridap.Fields.BroadcastingFieldOpMap{typeof(-)}, 1, Tuple{Base.OneTo{Int64}}}, Vector{VectorValue{3, Float64}}, 1, 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         SymFourthOrderTensorValue{3, Float64, 36}(3.326384578763472e6, -4759.354498069034, -6167.650941781898, 1.6937766140657421e6, -1227.8772572185187, 1.531264691898474e6, -3779.8547294498626, 542253.4090725112, -530.4746890120374, -3190.4921063854044, -3250.2808523191684, -3737.005565550921, -5886.968030863616, -537.9081834620076, 483908.378000215, -6533.444834607184, -3059.146837490184, -4504.332859775186, 1.7018457652267967e6, -3008.2461183218784, -6846.25757196701, 3.0626411756796264e6, -1148.3079316655576, 1.420902913610159e6, -1213.2733723874962, -3546.198726956854, -3362.277943105761, -1258.8235599588681, 380384.082774545, -1054.9507892981542, 1.5302962101479059e6, -4172.723090937569, -4026.8574184926333, 1.4055213424563352e6, -1068.7681262730769, 2.6324979054000624e6)
        SymFourthOrderTensorValue{3, Float64, 36}(3.307927238171419e6, -4092.231533223082, -5272.029101372774, 1.6754747897149946e6, -1189.120346487391, 1.515764527304576e6, -3353.6934629426487, 529849.6001295896, -529.7138076818842, -2892.1243769929747, -2829.1068220335455, -3272.926076965264, -5175.948426844651, -535.7049725573326, 469971.66205195605, -5686.47210275731, -2665.800440308476, -3974.6060331268504, 1.685111924768359e6, -2835.9538131409245, -5920.47273166682, 3.1130605803294205e6, -1077.1266507319096, 1.4382344731069012e6, -1157.5337905319304, -3013.3675514548063, -2851.9045067277993, -1164.1867437995147, 398098.03864534333, -970.394148711003, 1.516239554926333e6, -3636.133424803255, -3681.7397034327887, 1.4244088933311244e6, -999.1298591053936, 2.6794580644026576e6)
   SymFourthOrderTensorValue{3, Float64, 36}(3.2922091288947263e6, -3204.7004245095964, -4102.670866486398, 1.6599193980600042e6, -1156.6727294613215, 1.502626115291784e6, -2718.523843240932, 519152.5122139548, -530.9921109742608, -2429.7922365201953, -2250.2574535742665, -2624.7479855545607, -4152.366973173972, -535.5516804995716, 458076.45227385336, -4523.833565511555, -2123.451725516238, -3229.909475487784, 1.6690527984245946e6, -2484.6252977178833, -4681.535912451936, 3.165626434817684e6, -1014.4425246331558, 1.4554389178806087e6, -1114.447732151855, -2337.8279680475634, -2208.6134172245834, -1085.3303851384785, 414983.61662915495, -900.3036274607767, 1.5017614507184234e6, -2905.5948194457355, -3114.3450592592208, 1.4424114741413693e6, -938.4420413472095, 2.727423659473587e6)
  SymFourthOrderTensorValue{3, Float64, 36}(3.2802920105320076e6, -2093.170536830325, -2662.1148696711707, 1.6481302881736977e6, -1133.0619208716075, 1.4926884954602055e6, -1845.0931118331237, 510873.57909317187, -534.4334076676331, -1749.288021378917, -1498.9703933388087, -1770.5469920090375, -2783.8506204957484, -537.7871205750372, 448991.8905147459, -3017.1956935756425, -1417.293027458986, -2228.984583969984, 1.6542200387956211e6, -1865.6090036613864, -3107.997915548268, 3.2194849492984475e6, -964.654176519693, 1.4719419952323171e6, -1088.810495365108, -1520.4257614861776, -1434.2558161547654, -1028.2129842448821, 430438.4457877767, -849.7599634649001, 1.4870772717951578e6, -1958.3385011818073, -2245.1298152817108, 1.4587775733867737e6, -890.6519445150162, 2.775443058998742e6)
      SymFourthOrderTensorValue{3, Float64, 36}(3.2733614795888294e6, -740.122829451769, -936.8797363137926, 1.6413684942583162e6, -1120.3984398478979, 1.4869663199683565e6, -672.4862375295417, 505998.78119303775, -538.7295718180377, -672.4862375325815, -538.7295718240928, -644.1564534998853, -1004.4821961458681, -541.3551224120052, 443729.52724463114, -1086.5002028736806, -510.2567610042307, -828.4757632571135, 1.6413684942583137e6, -740.1228294544629, -1120.3984398466541, 3.2733614795888215e6, -936.8797363170631, 1.4869663199683614e6, -1086.5002028743436, -541.3551224135616, -510.25676097809355, -1004.4821961514798, 443729.52724460047, -828.4757632536881, 1.4725385030013407e6, -715.0693925465622, -863.7419156470814, 1.4725385030013374e6, -863.7419156815893, 2.822217356479897e6)
@fverdugo
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fverdugo commented Jun 3, 2021

Hi @Omega-xyZac Can you share the code that generates this?

@fverdugo
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fverdugo commented Jun 3, 2021

It should be possible to have arbitrarily complex operations at gauss point level without blowing up the complexity of the type signature of the lazy array.

@zjwegert
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zjwegert commented Jun 3, 2021

Hi @fverdugo, thank you for the fast reply. I have a very large code base so sharing isn't really an option. However, that example is generated using the below:

    ....
    A = (ε((1/k_0)*data_1.uh) + δⁱʲ(1,1)) ⊗ δⁱʲ(1,1)+
          (ε((1/k_0)*data_2.uh) + δⁱʲ(2,2)) ⊗ δⁱʲ(2,2)+
          (ε((1/k_0)*data_3.uh) + δⁱʲ(3,3)) ⊗ δⁱʲ(3,3)+
          (ε((1/k_0)*data_4.uh) + 1/2*δⁱʲ(1,2)) ⊗ δⁱʲ(1,2)+
          (ε((1/k_0)*data_5.uh) + 1/2*δⁱʲ(1,3)) ⊗ δⁱʲ(1,3)+
          (ε((1/k_0)*data_6.uh) + 1/2*δⁱʲ(2,3)) ⊗ δⁱʲ(2,3)

    ℬ = ε((1/k_0)*data_7.uh) ⊗ eᵢ(1) +
          ε((1/k_0)*data_8.uh) ⊗ eᵢ(2) +
          ε((1/k_0)*data_9.uh) ⊗ eᵢ(3)

    𝒢 = (-∇((1/α_0)*data_1.ϕh)) ⊗ δⁱʲ(1,1)+
         (-∇((1/α_0)*data_2.ϕh)) ⊗ δⁱʲ(2,2)+
         (-∇((1/α_0)*data_3.ϕh)) ⊗ δⁱʲ(3,3)+
         (-∇((1/α_0)*data_4.ϕh)) ⊗ δⁱʲ(1,2)+
         (-∇((1/α_0)*data_5.ϕh)) ⊗ δⁱʲ(1,3)+
         (-∇((1/α_0)*data_6.ϕh)) ⊗ δⁱʲ(2,3)

    H = (-∇((1/α_0)*data_7.ϕh) + eᵢ(1)) ⊗ eᵢ(1) +
        (-∇((1/α_0)*data_8.ϕh) + eᵢ(2)) ⊗ eᵢ(2) +
        (-∇((1/α_0)*data_9.ϕh) + eᵢ(3)) ⊗ eᵢ(3)

    # Base Material
    C_b = material.C;  # (4-tensor)
    e_b = material.e;  # (3-tensor)
    Κ_b = material.Κ; # (2-tensor)
    nely,nelx,nelz = size(struc,1),size(struc,2),size(struc,3);
    density = data_1.density_vector
    Pᵤᵤ,Pᵤᵩ,Pᵩᵩ=penal; Pᵩᵤ = Pᵤᵩ;

    C = density.^Pᵤᵤ.*fill(C_b,nely*nelx*nelz)
    e = density.^Pᵤᵩ.*fill(e_b,nely*nelx*nelz)
    Κ = density.^Pᵩᵩ.*fill(Κ_b,nely*nelx*nelz)
    # Averaging
    dΩ = data_1.measure
    @GTensor CA[i,j,k,l] = C[i,j,m,p]*A[m,p,k,l]; @GTensor e𝒢[i,j,k,l] = e[m,i,j]*𝒢[m,k,l]
    Cᵉ = get_array(∫(CA - e𝒢)dΩ);
    ....

where data_1,data_2,... are of data type

struct SolverFEData
  loading::Int8
  vol::Float64
  uh::SingleFieldFEFunction
  ϕh::SingleFieldFEFunction
  X::Array
  Uϕ::FESpace
  trian::CartesianGrid
  measure::Measure
  density_vector::Any
  material_vals::Any
end

and the @gtensor macro is the script that I've mentioned in a previous issue for doing general contractions by leveraging the TensorOperations package. Though, these particular operations could be replaced by something like .⋅² and .⋅.

Hopefully that is decipherable..

@fverdugo
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fverdugo commented Jun 3, 2021

I cannot decipher the code, but it seems that you are implementing complex operations in a not so efficient way for the gridap backend.

You need to implement the complex operation in a function f that takes values at a generic integration point, and then use Operation(f)(...) or f\circ(....) just like in the linear elasticity or the hyperelasticity tutorial

@zjwegert
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zjwegert commented Jun 3, 2021

Thank you for the suggestion! I think I've found a faster way to do this by integrating the quantities A, ℬ, etc. prior to contractions. I will also try your suggestion. I'll close this issue for now :).

@zjwegert zjwegert closed this as completed Jun 3, 2021
@zjwegert
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zjwegert commented Jun 5, 2021

Hi again @fverdugo, I tried your suggestion and implemented some functions that take values at generic integration points:

Af(εuh...) = (((1/k_0)*εuh[1]) + δⁱʲ(1,1)) ⊗ δⁱʲ(1,1)+
            (((1/k_0)*εuh[2]) + δⁱʲ(2,2)) ⊗ δⁱʲ(2,2)+
            (((1/k_0)*εuh[3]) + δⁱʲ(3,3)) ⊗ δⁱʲ(3,3)+
            (((1/k_0)*εuh[4]) + 1/2*δⁱʲ(1,2)) ⊗ δⁱʲ(1,2)+
            (((1/k_0)*εuh[5]) + 1/2*δⁱʲ(1,3)) ⊗ δⁱʲ(1,3)+
            (((1/k_0)*εuh[6]) + 1/2*δⁱʲ(2,3)) ⊗ δⁱʲ(2,3);
    ℬf(εuh...) = ((1/k_0)*εuh[1]) ⊗ eᵢ(1) +
          ((1/k_0)*εuh[2]) ⊗ eᵢ(2) +
          ((1/k_0)*εuh[3]) ⊗ eᵢ(3)
    𝒢f(∇ϕh...) = (-((1/α_0)*∇ϕh[1])) ⊗ δⁱʲ(1,1)+
       (-((1/α_0)*∇ϕh[2])) ⊗ δⁱʲ(2,2)+
       (-((1/α_0)*∇ϕh[3])) ⊗ δⁱʲ(3,3)+
       (-((1/α_0)*∇ϕh[4])) ⊗ δⁱʲ(1,2)+
       (-((1/α_0)*∇ϕh[5])) ⊗ δⁱʲ(1,3)+
       (-((1/α_0)*∇ϕh[6])) ⊗ δⁱʲ(2,3)
    Hf(∇ϕh...) = (-((1/α_0)*∇ϕh[1]) + eᵢ(1)) ⊗ eᵢ(1) +
      (-((1/α_0)*∇ϕh[2]) + eᵢ(2)) ⊗ eᵢ(2) +
      (-((1/α_0)*∇ϕh[3]) + eᵢ(3)) ⊗ eᵢ(3)

    A = Af ∘ (ε(data_1.uh),ε(data_2.uh),ε(data_3.uh),ε(data_4.uh),ε(data_5.uh),ε(data_6.uh))
    ℬ = ℬf ∘ (ε(data_7.uh),ε(data_8.uh),ε(data_9.uh))
    𝒢 = 𝒢f ∘ (∇(data_1.ϕh),∇(data_2.ϕh),∇(data_3.ϕh),∇(data_4.ϕh),∇(data_5.ϕh),∇(data_6.ϕh))
    H = Hf ∘ (∇(data_7.ϕh),∇(data_8.ϕh),∇(data_9.ϕh))

    # Base Material
    C_b = material.C; e_b = material.e; Κ_b = material.Κ;
    nely,nelx,nelz = size(struc,1),size(struc,2),size(struc,3);
    density = data_1.density_vector
    Pᵤᵤ,Pᵤᵩ,Pᵩᵩ=penal; Pᵩᵤ = Pᵤᵩ;

    C = density.^Pᵤᵤ.*fill(C_b,nely*nelx*nelz)
    e = density.^Pᵤᵩ.*fill(e_b,nely*nelx*nelz)
    Κ = density.^Pᵩᵩ.*fill(Κ_b,nely*nelx*nelz)
    # Averaging
    dΩ = data_1.measure

    @GTensor CA[i,j,k,l] = C[i,j,m,p]*A[m,p,k,l]; @GTensor e𝒢[i,j,k,l] = e[m,i,j]*𝒢[m,k,l]
    Cᵉ = ∫(CA - e𝒢)dΩ; sum_C = sum(Cᵉ)
    @GTensor eA[i,j,k] = e[i,l,m]*A[l,m,j,k]; @GTensor Κ𝒢[i,j,k] = Κ[i,l]*𝒢[l,j,k]
    eᵉ = ∫(eA + Κ𝒢)dΩ; sum_e = sum(eᵉ)
    @GTensor eℬ[i,j] = e[i,l,m]*ℬ[l,m,j]; @GTensor ΚH[i,j] = Κ[i,l]*H[l,j]
    Κᵉ = ∫(eℬ + ΚH)dΩ; sum_Κ = sum(Κᵉ)

Is this along the lines of what you meant? Do you have any other ideas for how to speed this up? Appreciate any suggestions you might have.

@zjwegert zjwegert reopened this Jun 5, 2021
@zjwegert zjwegert reopened this Jul 15, 2021
amartinhuertas added a commit to gridapapps/GridapGeosciences.jl that referenced this issue Sep 2, 2021
@amartinhuertas
Trying to reduce JIT-compilation times using the advice in
ed2d47b 
gridap/Gridap.jl#610 (comment)
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