https://github.com/javierbarbero/DataEnvelopmentAnalysis.jl
Tip revision: 5eb588ce29e6486e98174cbb0371d3bf4d95597c authored by Javier Barbero on 18 September 2021, 14:51:16 UTC
Fix issues in lambda matrix and model without slacks
Fix issues in lambda matrix and model without slacks
Tip revision: 5eb588c
dea.jl
# Tests for Radial DEA Models
@testset "RadialDEAModel" begin
## Test Radial DEA Models with FLS Book data
# Test against results in R
X = [5 13; 16 12; 16 26; 17 15; 18 14; 23 6; 25 10; 27 22; 37 14; 42 25; 5 17]
Y = [12; 14; 25; 26; 8; 9; 27; 30; 31; 26; 12]
# Input oriented CRS
deaio = dea(X, Y, orient = :Input, rts = :CRS)
@test typeof(deaio) == RadialDEAModel
@test nobs(deaio) == 11
@test ninputs(deaio) == 2
@test noutputs(deaio) == 1
@test efficiency(deaio) ≈ [1.0000000000;
0.6222896791;
0.8198562444;
1.0000000000;
0.3103709311;
0.5555555556;
1.0000000000;
0.7576690896;
0.8201058201;
0.4905660377;
1.0000000000]
@test convert(Matrix, peers(deaio)) ≈
[1.000000000 0 0 0.0000000000 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 0.4249783174 0 0 0.10928013877 0 0 0 0;
1.134321653 0 0 0.4380053908 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 1.0000000000 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 0.2573807721 0 0 0.04844814534 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 0.33333333333 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 1.00000000000 0 0 0 0;
0.000000000 0 0 1.0348650979 0 0 0.11457435013 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 1.14814814815 0 0 0 0;
0.000000000 0 0 0.4905660377 0 0 0.49056603774 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 0.00000000000 0 0 0 1.000000000]
@test slacks(deaio, :X) ≈ [0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
4.444444444 0;
0.000000000 0;
0.000000000 0;
1.640211640 0;
0.000000000 0;
0.000000000 4]
@test slacks(deaio, :Y) ≈ zeros(11)
@test efficiency(dea(targets(deaio, :X), targets(deaio, :Y), orient = :Input, rts = :CRS, slack = false)) ≈ ones(11)
@test efficiency(deaadd(targets(deaio, :X), targets(deaio, :Y))) ≈ zeros(11) atol=1e-14
@test peersmatrix(deaio) == deaio.lambda
# Otuput oriented CRS
deaoo = dea(X, Y, orient = :Output, rts = :CRS)
@test nobs(deaoo) == 11
@test ninputs(deaoo) == 2
@test noutputs(deaoo) == 1
@test efficiency(deaoo) ≈ [1.0000000000;
1.606968641;
1.219726027;
1.0000000000;
3.221951220;
1.800000000;
1.0000000000;
1.319837398;
1.219354839;
2.038461538;
1.0000000000]
@test convert(Matrix, peers(deaoo)) ≈
[1.000000000 0 0 0.0000000000 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 0.6829268293 0 0 0.1756097561 0 0 0 0;
1.383561644 0 0 0.5342465753 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 1.0000000000 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 0.8292682927 0 0 0.1560975610 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 0.6000000000 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 1.00000000000 0 0 0 0;
0.000000000 0 0 1.3658536585 0 0 0.1512195122 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 1.4000000000 0 0 0 0;
0.000000000 0 0 1.0000000000 0 0 1.0000000000 0 0 0 0;
1.000000000 0 0 0.0000000000 0 0 0.00000000000 0 0 0 0]
@test slacks(deaoo, :X) ≈ [0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
8 0;
0.000000000 0;
0.000000000 0;
2 0;
0.000000000 0;
0.000000000 4]
@test slacks(deaoo, :Y) ≈ zeros(11)
@test efficiency(dea(targets(deaoo, :X), targets(deaoo, :Y), orient = :Output, rts = :CRS, slack = false)) ≈ ones(11)
@test efficiency(deaadd(targets(deaoo, :X), targets(deaoo, :Y))) ≈ zeros(11) atol=1e-10
# Input oriented VRS
deaiovrs = dea(X, Y, orient = :Input, rts = :VRS)
@test nobs(deaiovrs) == 11
@test ninputs(deaiovrs) == 2
@test noutputs(deaiovrs) == 1
@test efficiency(deaiovrs) ≈ [1.0000000000;
0.8699861687;
1.0000000000;
1.0000000000;
0.7116402116;
1.0000000000;
1.0000000000;
1.0000000000;
1.0000000000;
0.4931209269;
1.0000000000]
@test convert(Matrix, peers(deaiovrs)) ≈
[1.000000000 0 0 0.0000000000 0 0.00000000000 0.00000000000 0 0 0 0;
0.52558782849 0 0 0.0000000000 0 0.2842323651 0.1901798064 0 0 0 0;
0.000000000 0 1 0.0000000000 0 0.00000000000 0.00000000000 0 0 0 0;
0.000000000 0 0 1.0000000000 0 0.00000000000 0.00000000000 0 0 0 0;
0.56613756614 0 0 0.0000000000 0 0.4338624339 0.00000000000 0 0 0 0;
0.000000000 0 0 0.0000000000 0 1.00000000000 0.00000000000 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0.00000000000 1.00000000000 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0.00000000000 0.00000000000 1 0 0 0;
0.000000000 0 0 0.0000000000 0 0.00000000000 0.00000000000 0 1 0 0;
0.03711078928 0 0 0.4433381608 0 0.00000000000 0.5195510500 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0.00000000000 0.00000000000 0 0 0 1.000000000]
@test slacks(deaiovrs, :X) ≈ [0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0 0;
0.000000000 0;
0.000000000 0;
0 0;
0.000000000 0;
0.000000000 4]
@test slacks(deaiovrs, :Y) ≈ [0.000000000;
0.000000000;
0.000000000;
0.000000000;
2.698412698;
0.000000000;
0.000000000;
0.000000000;
0.000000000;
0.000000000;
0.000000000]
@test efficiency(dea(targets(deaiovrs, :X), targets(deaiovrs, :Y), orient = :Input, rts = :VRS, slack = false)) ≈ ones(11)
@test efficiency(deaadd(targets(deaiovrs, :X), targets(deaiovrs, :Y))) ≈ zeros(11) atol=1e-12
# Output oriented VRS
deaoovrs = dea(X, Y, orient = :Output, rts = :VRS)
@test nobs(deaoovrs) == 11
@test ninputs(deaoovrs) == 2
@test noutputs(deaoovrs) == 1
@test efficiency(deaoovrs) ≈ [1.0000000000;
1.507518797;
1.0000000000;
1.0000000000;
3.203947368;
1.000000000;
1.0000000000;
1.000000000;
1.000000000;
1.192307692;
1.0000000000]
@test convert(Matrix, peers(deaoovrs)) ≈
[1.000000000 0 0 0.0000000000 0 0 0.00000000000 0 0 0 0;
0.38157894737 0 0 0.1710526316 0 0 0.4473684211 0 0 0 0;
0.000000000 0 1 0.0000000000 0 0 0.00000000000 0 0 0 0;
0.000000000 0 0 1.0000000000 0 0 0.00000000000 0 0 0 0;
0.03947368421 0 0 0.7763157895 0 0 0.1842105263 0 0 0 0;
0.000000000 0 0 0.0000000000 0 1 0.00000000000 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 1.00000000000 0 0 0 0;
0.000000000 0 0 0.0000000000 0 0 0.00000000000 1 0 0 0;
0.000000000 0 0 0.0000000000 0 0 0.00000000000 0 1 0 0;
0.000000000 0 0 0.0000000000 0 0 0.00000000000 0 1 0 0;
1.000000000 0 0 0.0000000000 0 0 0.00000000000 0 0 0 0]
@test slacks(deaoovrs, :X) ≈ [0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
0.000000000 0;
5 11;
0.000000000 4]
@test slacks(deaoovrs, :Y) ≈ zeros(11) atol=1e-10
@test efficiency(dea(targets(deaoovrs, :X), targets(deaoovrs, :Y), orient = :Output, rts = :VRS, slack = false)) ≈ ones(11)
@test efficiency(deaadd(targets(deaoovrs, :X), targets(deaoovrs, :Y))) ≈ zeros(11) atol=1e-12
# Test no slacks
deaionoslack = dea(X, Y, slack = false)
@test efficiency(deaionoslack) == efficiency(deaio)
@test isempty(slacks(deaionoslack, :X)) == 1
@test isempty(slacks(deaionoslack, :Y)) == 1
@test efficiency(dea(targets(deaionoslack, :X), targets(deaionoslack, :Y), slack = false)) ≈ ones(11)
@test efficiency(deaadd(targets(deaionoslack, :X), targets(deaionoslack, :Y))) != zeros(11) # Different as there is no slacks in first model
## Test if one-by-one DEA using evaluation and reference sets match initial results
deaio_ref_eff = zeros(size(X, 1))
deaoo_ref_eff = zeros(size(X, 1))
deaiovrs_ref_eff = zeros(size(X, 1))
deaoovrs_ref_eff = zeros(size(X, 1))
deaiovrs_ref_slackX = zeros(size(X))
deaiovrs_ref_slackY = zeros(size(Y))
Xref = X[:,:]
Yref = Y[:,:]
for i = 1:size(X, 1)
Xeval = X[i:i,:]
Xeval = Xeval[:,:]
Yeval = Y[i:i,:]
Yeval = Yeval[:,:]
deaio_ref_eff[i] = efficiency(dea(Xeval, Yeval, orient = :Input, rts = :CRS, Xref = Xref, Yref = Yref))[1]
deaoo_ref_eff[i] = efficiency(dea(Xeval, Yeval, orient = :Output, rts = :CRS, Xref = Xref, Yref = Yref))[1]
deaiovrs_ref_eff[i] = efficiency(dea(Xeval, Yeval, orient = :Input, rts = :VRS, Xref = Xref, Yref = Yref))[1]
deaoovrs_ref_eff[i] = efficiency(dea(Xeval, Yeval, orient = :Output, rts = :VRS, Xref = Xref, Yref = Yref))[1]
deaiovrs_ref_slackX[i,:] = slacks(dea(Xeval, Yeval, orient = :Input, rts = :VRS, Xref = Xref, Yref = Yref), :X)
deaiovrs_ref_slackY[i,:] = slacks(dea(Xeval, Yeval, orient = :Input, rts = :VRS, Xref = Xref, Yref = Yref), :Y)
end
@test deaio_ref_eff ≈ efficiency(deaio)
@test deaoo_ref_eff ≈ efficiency(deaoo)
@test deaiovrs_ref_eff ≈ efficiency(deaiovrs)
@test deaoovrs_ref_eff ≈ efficiency(deaoovrs)
@test deaiovrs_ref_slackX ≈ slacks(deaiovrs, :X) atol=1e-14
@test deaiovrs_ref_slackY ≈ slacks(deaiovrs, :Y) atol=1e-15
# Print
show(IOBuffer(), deaio)
show(IOBuffer(), deaionoslack)
# Test errors
@test_throws DimensionMismatch dea([1; 2 ; 3], [4 ; 5]) # Different number of observations
@test_throws DimensionMismatch dea([1; 2], [4 ; 5], Xref = [1; 2; 3; 4]) # Different number of observations in reference sets
@test_throws DimensionMismatch dea([1 1; 2 2], [4 4; 5 5], Xref = [1 1 1; 2 2 2]) # Different number of inputs
@test_throws DimensionMismatch dea([1 1; 2 2], [4 4; 5 5], Yref = [4 4 4; 5 5 5]) # Different number of inputs
@test_throws ArgumentError dea([1; 2; 3], [4; 5; 6], orient = :Error) # Invalid orientation
@test_throws ArgumentError dea([1; 2; 3], [4; 5; 6], rts = :Error) # Invalid returns to scale
@test_throws ArgumentError dea([1; 2 ; 3], [4 ; 5; 6], disposX = :Error) # Invalid inputs disposability
@test_throws ArgumentError dea([1; 2 ; 3], [4 ; 5; 6], disposY = :Error) # Invalid outputs disposability
@test_throws ArgumentError targets(deaio, :Error) # Invalid target
@test_throws ArgumentError slacks(deaio, :Error) # Invalid slacks
# ------------------
# Weak Disposability Tests
# ------------------
X = [1; 2; 3; 2; 4]
Y = [2; 3; 4; 1; 3]
deaioStrong = dea(X, Y, orient = :Input, rts = :VRS)
@test efficiency(deaioStrong ) ≈ [1.0; 1.0; 1.0; 0.5; 0.5]
@test slacks(deaioStrong, :X) ≈ [0; 0; 0; 0; 0] atol=1e-15
@test slacks(deaioStrong, :Y) ≈ [0; 0; 0; 1; 0] atol=1e-15
deaioWeak = dea(X, Y, orient = :Input, rts = :VRS, disposY = :Weak)
@test efficiency(deaioWeak ) ≈ [1.0; 1.0; 1.0; 1.0; 0.5]
@test slacks(deaioWeak, :X) ≈ [0; 0; 0; 0; 0] atol=1e-15
@test slacks(deaioWeak, :Y) ≈ [0; 0; 0; 0; 0] atol=1e-15
deaooStrong = dea(X, Y, orient = :Output, rts = :VRS)
@test efficiency(deaooStrong ) ≈ [1.0; 1.0; 1.0; 3.0; 1.3333333333333333]
@test slacks(deaooStrong, :X) ≈ [0; 0; 0; 0; 1] atol=1e-15
@test slacks(deaooStrong, :Y) ≈ [0; 0; 0; 0; 0] atol=1e-15
deaooWeak = dea(X, Y, orient = :Output, rts = :VRS, disposX = :Weak)
@test efficiency(deaooWeak ) ≈ [1.0; 1.0; 1.0; 3.0; 1.0]
@test slacks(deaooWeak, :X) ≈ [0; 0; 0; 0; 0] atol=1e-14
@test slacks(deaooWeak, :Y) ≈ [0; 0; 0; 0; 0] atol=1e-14
# Test if weak disposability in inputs in the Input oriented model works
# In this example, same result as stron disposability
@test efficiency(dea(X, Y, orient = :Input, disposX = :Strong)) ==
efficiency(dea(X, Y, orient = :Input, disposX = :Weak))
# Test if weak disposability in outputs in the Output oriented model works
# In this example, same result as strong disposability
@test efficiency(dea(X, Y, orient = :Output, disposY = :Strong)) ==
efficiency(dea(X, Y, orient = :Output, disposY = :Weak))
# ------------------
# DMU names
# ------------------
X = [1; 2; 3; 2; 4]
Y = [2; 3; 4; 1; 3]
@test names(dea(X, Y)) == ["1"; "2"; "3"; "4"; "5"]
@test names(dea(X, Y, names = ["A", "B", "C", "D", "E"])) == ["A", "B", "C", "D", "E"]
logs, value = Test.collect_test_logs() do
names(dea(X, Y, names = ["A", "B", "C", "D"]))
end
@test occursin("Length of names lower than number of observations", string(logs))
@test value == ["A", "B", "C", "D", "5"]
logs, value = Test.collect_test_logs() do
names(dea(X, Y, names = ["A", "B", "C", "D", "E", "F"]))
end
@test occursin("Length of names greater than number of observations", string(logs))
@test value == ["A", "B", "C", "D", "E"]
# ------------------
# Test Vector and Matrix inputs and outputs
# ------------------
# Tests against results in R
# Inputs is Matrix, Outputs is Vector
X = [2 2; 1 4; 4 1; 4 3; 5 5; 6 1; 2 5; 1.6 8]
Y = [1; 1; 1; 1; 1; 1; 1; 1]
@test efficiency(dea(X, Y, orient = :Input)) ≈ [1; 1; 1; 0.6; 0.4; 1; 0.6666666667; 0.625]
# Inputs is Vector, Output is Matrix
X = [1; 1; 1; 1; 1; 1; 1; 1]
Y = [7 7; 4 8; 8 4; 3 5; 3 3; 8 2; 6 4; 1.5 5]
@test efficiency(dea(X, Y, orient = :Output)) ≈ [1; 1; 1; 1.555555556; 2.333333333; 1; 1.272727273; 1.6]
# Inputs is Vector, Output is Vector
X = [2; 4; 8; 12; 6; 14; 14; 9.412]
Y = [1; 5; 8; 9; 3; 7; 9; 2.353]
@test efficiency(dea(X, Y, orient = :Input)) ≈ [0.4; 1; 0.8; 0.6; 0.4; 0.4; 0.5142857143; 0.2]
# ------------------
# Run with different progress meter options
# ------------------
# Just run the code for code coverage as the progress meter does not affect the result
X = [5 13; 16 12; 16 26; 17 15; 18 14; 23 6; 25 10; 27 22; 37 14; 42 25; 5 17]
Y = [12; 14; 25; 26; 8; 9; 27; 30; 31; 26; 12]
dea(X, Y, progress = true)
dea(X, Y, progress = false)
end
