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Aravind Sankaran
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Added gls algorithms from linnea
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‎examples/data/gls_algorithms_julia/README.md‎

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## Installation of Linnea
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```
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git clone https://github.com/HPAC/linnea.git
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cd linnea/
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git checkout traces
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pip install .
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```
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## Algorithm Generation
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```
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python gls.py
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```
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## Running the experiments
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```
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cd experiments
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./run.sh
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```

‎examples/data/gls_algorithms_julia/algorithms/Julia/generated/algorithm0.jl‎

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using LinearAlgebra.BLAS
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using LinearAlgebra
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"""
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algorithm0(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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Compute
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b = ((X^T M^-1 X)^-1 X^T M^-1 y).
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Requires at least Julia v1.0.
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# Arguments
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- `ml0::Array{Float64,2}`: Matrix X of size 1000 x 100 with property FullRank.
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- `ml1::Array{Float64,2}`: Matrix M of size 1000 x 1000 with property SPD.
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- `ml2::Array{Float64,1}`: Vector y of size 1000.
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"""
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function algorithm0(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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# cost: 4.45e+08 FLOPs
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run_id = get(ENV, "LINNEA_RUN_ID", -1)
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t_start = time_ns()
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# X: ml0, full, M: ml1, full, y: ml2, full
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# (L2 L2^T) = M
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t1 = time_ns()
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LAPACK.potrf!('L', ml1)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333333.3333333 $(t2-t1)")
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# X: ml0, full, y: ml2, full, L2: ml1, lower_triangular
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# tmp12 = (L2^-1 X)
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t1 = time_ns()
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trsm!('L', 'L', 'N', 'N', 1.0, ml1, ml0)
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t2 = time_ns()
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println("$(run_id) $(t1) trsm 100000000 $(t2-t1)")
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# y: ml2, full, L2: ml1, lower_triangular, tmp12: ml0, full
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# tmp38 = (L2^-1 y)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml1, ml2)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 1000000 $(t2-t1)")
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# tmp12: ml0, full, tmp38: ml2, full
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ml3 = Array{Float64}(undef, 100, 100)
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# tmp14 = (tmp12^T tmp12)
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t1 = time_ns()
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syrk!('L', 'T', 1.0, ml0, 0.0, ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) syrk 10000000 $(t2-t1)")
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# tmp12: ml0, full, tmp38: ml2, full, tmp14: ml3, symmetric_lower_triangular
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ml4 = Array{Float64}(undef, 100)
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# tmp21 = (tmp12^T tmp38)
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t1 = time_ns()
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gemv!('T', 1.0, ml0, ml2, 0.0, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) gemv 200000 $(t2-t1)")
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# tmp14: ml3, symmetric_lower_triangular, tmp21: ml4, full
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# (L15 L15^T) = tmp14
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t1 = time_ns()
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LAPACK.potrf!('L', ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333.3333333333 $(t2-t1)")
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# tmp21: ml4, full, L15: ml3, lower_triangular
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# tmp23 = (L15^-1 tmp21)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml3, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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# L15: ml3, lower_triangular, tmp23: ml4, full
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# tmp24 = (L15^-T tmp23)
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t1 = time_ns()
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trsv!('L', 'T', 'N', ml3, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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t_end = time_ns()
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println("$(run_id) $(t_end) algorithm0 444886666.6666666 $(t_end-t_start)")
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# tmp24: ml4, full
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# b = tmp24
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return (ml4)
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end

‎examples/data/gls_algorithms_julia/algorithms/Julia/generated/algorithm1.jl‎

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using LinearAlgebra.BLAS
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using LinearAlgebra
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"""
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algorithm1(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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Compute
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b = ((X^T M^-1 X)^-1 X^T M^-1 y).
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Requires at least Julia v1.0.
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# Arguments
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- `ml0::Array{Float64,2}`: Matrix X of size 1000 x 100 with property FullRank.
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- `ml1::Array{Float64,2}`: Matrix M of size 1000 x 1000 with property SPD.
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- `ml2::Array{Float64,1}`: Vector y of size 1000.
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"""
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function algorithm1(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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# cost: 4.45e+08 FLOPs
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run_id = get(ENV, "LINNEA_RUN_ID", -1)
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t_start = time_ns()
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# X: ml0, full, M: ml1, full, y: ml2, full
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# (L2 L2^T) = M
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t1 = time_ns()
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LAPACK.potrf!('L', ml1)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333333.3333333 $(t2-t1)")
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# X: ml0, full, y: ml2, full, L2: ml1, lower_triangular
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# tmp38 = (L2^-1 y)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml1, ml2)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 1000000 $(t2-t1)")
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# X: ml0, full, L2: ml1, lower_triangular, tmp38: ml2, full
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# tmp12 = (L2^-1 X)
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t1 = time_ns()
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trsm!('L', 'L', 'N', 'N', 1.0, ml1, ml0)
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t2 = time_ns()
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println("$(run_id) $(t1) trsm 100000000 $(t2-t1)")
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# tmp38: ml2, full, tmp12: ml0, full
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ml3 = Array{Float64}(undef, 100, 100)
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# tmp14 = (tmp12^T tmp12)
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t1 = time_ns()
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syrk!('L', 'T', 1.0, ml0, 0.0, ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) syrk 10000000 $(t2-t1)")
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# tmp38: ml2, full, tmp12: ml0, full, tmp14: ml3, symmetric_lower_triangular
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# (L15 L15^T) = tmp14
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t1 = time_ns()
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LAPACK.potrf!('L', ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333.3333333333 $(t2-t1)")
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# tmp38: ml2, full, tmp12: ml0, full, L15: ml3, lower_triangular
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ml4 = Array{Float64}(undef, 100)
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# tmp21 = (tmp12^T tmp38)
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t1 = time_ns()
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gemv!('T', 1.0, ml0, ml2, 0.0, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) gemv 200000 $(t2-t1)")
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# L15: ml3, lower_triangular, tmp21: ml4, full
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# tmp23 = (L15^-1 tmp21)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml3, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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# L15: ml3, lower_triangular, tmp23: ml4, full
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# tmp24 = (L15^-T tmp23)
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t1 = time_ns()
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trsv!('L', 'T', 'N', ml3, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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t_end = time_ns()
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println("$(run_id) $(t_end) algorithm1 444886666.6666666 $(t_end-t_start)")
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# tmp24: ml4, full
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# b = tmp24
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return (ml4)
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end

‎examples/data/gls_algorithms_julia/algorithms/Julia/generated/algorithm2.jl‎

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using LinearAlgebra.BLAS
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using LinearAlgebra
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"""
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algorithm2(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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Compute
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b = ((X^T M^-1 X)^-1 X^T M^-1 y).
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Requires at least Julia v1.0.
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# Arguments
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- `ml0::Array{Float64,2}`: Matrix X of size 1000 x 100 with property FullRank.
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- `ml1::Array{Float64,2}`: Matrix M of size 1000 x 1000 with property SPD.
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- `ml2::Array{Float64,1}`: Vector y of size 1000.
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"""
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function algorithm2(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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# cost: 4.47e+08 FLOPs
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run_id = get(ENV, "LINNEA_RUN_ID", -1)
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t_start = time_ns()
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# X: ml0, full, M: ml1, full, y: ml2, full
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# (L2 L2^T) = M
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t1 = time_ns()
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LAPACK.potrf!('L', ml1)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333333.3333333 $(t2-t1)")
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# X: ml0, full, y: ml2, full, L2: ml1, lower_triangular
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# tmp12 = (L2^-1 X)
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t1 = time_ns()
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trsm!('L', 'L', 'N', 'N', 1.0, ml1, ml0)
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t2 = time_ns()
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println("$(run_id) $(t1) trsm 100000000 $(t2-t1)")
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# y: ml2, full, L2: ml1, lower_triangular, tmp12: ml0, full
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# tmp67 = (L2^-1 y)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml1, ml2)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 1000000 $(t2-t1)")
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# tmp12: ml0, full, tmp67: ml2, full
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ml3 = Array{Float64}(undef, 100, 100)
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# tmp14 = (tmp12^T tmp12)
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t1 = time_ns()
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syrk!('L', 'T', 1.0, ml0, 0.0, ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) syrk 10000000 $(t2-t1)")
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# tmp12: ml0, full, tmp67: ml2, full, tmp14: ml3, symmetric_lower_triangular
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ml4 = Array{Float64}(undef, 100)
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# tmp21 = (tmp12^T tmp67)
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t1 = time_ns()
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gemv!('T', 1.0, ml0, ml2, 0.0, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) gemv 200000 $(t2-t1)")
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# tmp14: ml3, symmetric_lower_triangular, tmp21: ml4, full
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t1 = time_ns()
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for i = 1:100-1;
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view(ml3, i, i+1:100)[:] = view(ml3, i+1:100, i);
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end;
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t2 = time_ns()
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println("$(run_id) $(t1) view 1000000 $(t2-t1)")
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# (Q16 R17) = tmp14
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t1 = time_ns()
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ml3 = qr!(ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) qr 2666666.6666666665 $(t2-t1)")
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# tmp21: ml4, full, Q16: ml3, QRfact_Q, R17: ml3, QRfact_R
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ml5 = Array(ml3.Q)
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ml6 = Array{Float64}(undef, 100)
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# tmp25 = (Q16^T tmp21)
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t1 = time_ns()
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gemv!('T', 1.0, ml5, ml4, 0.0, ml6)
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t2 = time_ns()
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println("$(run_id) $(t1) gemv 20000 $(t2-t1)")
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# R17: ml3, QRfact_R, tmp25: ml6, full
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ml7 = ml3.R
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# tmp24 = (R17^-1 tmp25)
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t1 = time_ns()
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trsv!('U', 'N', 'N', ml7, ml6)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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t_end = time_ns()
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println("$(run_id) $(t_end) algorithm2 447230000.0 $(t_end-t_start)")
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# tmp24: ml6, full
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# b = tmp24
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return (ml6)
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end

‎examples/data/gls_algorithms_julia/algorithms/Julia/generated/algorithm3.jl‎

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using LinearAlgebra.BLAS
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using LinearAlgebra
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"""
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algorithm3(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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Compute
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b = ((X^T M^-1 X)^-1 X^T M^-1 y).
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Requires at least Julia v1.0.
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# Arguments
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- `ml0::Array{Float64,2}`: Matrix X of size 1000 x 100 with property FullRank.
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- `ml1::Array{Float64,2}`: Matrix M of size 1000 x 1000 with property SPD.
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- `ml2::Array{Float64,1}`: Vector y of size 1000.
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"""
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function algorithm3(ml0::Array{Float64,2}, ml1::Array{Float64,2}, ml2::Array{Float64,1})
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# cost: 4.55e+08 FLOPs
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run_id = get(ENV, "LINNEA_RUN_ID", -1)
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t_start = time_ns()
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# X: ml0, full, M: ml1, full, y: ml2, full
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# (L2 L2^T) = M
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t1 = time_ns()
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LAPACK.potrf!('L', ml1)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333333.3333333 $(t2-t1)")
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# X: ml0, full, y: ml2, full, L2: ml1, lower_triangular
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# tmp67 = (L2^-1 y)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml1, ml2)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 1000000 $(t2-t1)")
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# X: ml0, full, L2: ml1, lower_triangular, tmp67: ml2, full
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# tmp12 = (L2^-1 X)
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t1 = time_ns()
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trsm!('L', 'L', 'N', 'N', 1.0, ml1, ml0)
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t2 = time_ns()
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println("$(run_id) $(t1) trsm 100000000 $(t2-t1)")
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# tmp67: ml2, full, tmp12: ml0, full
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ml3 = Array{Float64}(undef, 100, 100)
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# tmp14 = (tmp12^T tmp12)
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t1 = time_ns()
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gemm!('T', 'N', 1.0, ml0, ml0, 0.0, ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) gemm 20000000 $(t2-t1)")
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# tmp67: ml2, full, tmp12: ml0, full, tmp14: ml3, full
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# (L15 L15^T) = tmp14
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t1 = time_ns()
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LAPACK.potrf!('L', ml3)
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t2 = time_ns()
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println("$(run_id) $(t1) LAPACK.potrf 333333.3333333333 $(t2-t1)")
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# tmp67: ml2, full, tmp12: ml0, full, L15: ml3, lower_triangular
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ml4 = Array{Float64}(undef, 100)
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# tmp21 = (tmp12^T tmp67)
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t1 = time_ns()
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gemv!('T', 1.0, ml0, ml2, 0.0, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) gemv 200000 $(t2-t1)")
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# L15: ml3, lower_triangular, tmp21: ml4, full
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# tmp23 = (L15^-1 tmp21)
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t1 = time_ns()
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trsv!('L', 'N', 'N', ml3, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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# L15: ml3, lower_triangular, tmp23: ml4, full
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# tmp24 = (L15^-T tmp23)
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t1 = time_ns()
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trsv!('L', 'T', 'N', ml3, ml4)
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t2 = time_ns()
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println("$(run_id) $(t1) trsv 10000 $(t2-t1)")
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t_end = time_ns()
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println("$(run_id) $(t_end) algorithm3 454886666.6666666 $(t_end-t_start)")
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# tmp24: ml4, full
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# b = tmp24
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return (ml4)
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end

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