``````# Tests for Radial Multiplier DEA Models

## Test Radial Multiplier DEA Models with FLS Book data
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
deamio = deam(X, Y, orient = :Input, rts = :CRS)

@test nobs(deamio) == 11
@test ninputs(deamio) == 2
@test noutputs(deamio) == 1
@test efficiency(deamio) ≈ [
1.0000000000;
0.6222896791;
0.8198562444;
1.0000000000;
0.3103709311;
0.5555555556;
1.0000000000;
0.7576690896;
0.8201058201;
0.4905660377;
1.0000000000] atol = 1e-5

@test multipliers(deamio, :X) ≈ [
0.0901826  0.0422374
0.0314397  0.0414137
0.0354897  0.0166217
0.0416228  0.0194942
0.0274413  0.0361469
0.0        0.166667
0.0261969  0.0345077
0.0178637  0.0235309
0.0        0.0714286
0.0133456  0.0175794
0.2        2.61229e-17
] atol = 1e-5
@test multipliers(deamio, :Y) ≈ [
0.08333333333333336
0.04444926279271466
0.032794249775381853
0.038461538461538464
0.03879636638909917
0.06172839506172836
0.03703703703703704
0.02525563631883701
0.026455026455026464
0.018867924528301886
0.0833333333333333
] atol = 1e-5

@test efficiency(deam(targets(deamio, :X), targets(deamio, :Y), orient = :Input, rts = :CRS)) ≈ ones(11) atol = 1e-5
@test rts(deamio) ≈ zeros(11)

# Otuput oriented CRS
deamoo = deam(X, Y, orient = :Output, rts = :CRS)

@test nobs(deamoo) == 11
@test ninputs(deamoo) == 2
@test noutputs(deamoo) == 1
@test efficiency(deamoo) ≈ [
1.0000000000;
1.606968641;
1.219726027;
1.0000000000;
3.221951220;
1.800000000;
1.0000000000;
1.319837398;
1.219354839;
2.038461538;
1.0000000000] atol = 1e-5

@test multipliers(deamoo, :X) ≈ [
0.0901826  0.0422374
0.0505226  0.0665505
0.0432877  0.020274
0.0272045  0.0358349
0.0884146  0.116463
0.0        0.3
0.0261969  0.0345077
0.0235772  0.0310569
0.0        0.0870968
0.0272045  0.0358349
0.2        0.0
] atol = 1e-5
@test multipliers(deamoo, :Y) ≈ [
0.08333333333333329
0.07142857142857142
0.04000000000000001
0.03846153846153846
0.12499999999999999
0.11111111111111112
0.037037037037037035
0.03333333333333334
0.03225806451612903
0.03846153846153846
0.08333333333333318
] atol = 1e-5

@test efficiency(deam(targets(deamoo, :X), targets(deamoo, :Y), orient = :Output, rts = :CRS)) ≈ ones(11) atol = 1e-5
@test rts(deamoo) ≈ zeros(11)

# Input oriented VRS
deamiovrs = deam(X, Y, orient = :Input, rts = :VRS)

@test nobs(deamiovrs) == 11
@test ninputs(deamiovrs) == 2
@test noutputs(deamiovrs) == 1
@test efficiency(deamiovrs) ≈ [
1.0000000000;
0.8699861687;
1.0000000000;
1.0000000000;
0.7116402116;
1.0000000000;
1.0000000000;
1.0000000000;
1.0000000000;
0.4931209269;
1.0000000000]

@test multipliers(deamiovrs, :X) ≈ [
0.0901826  0.0422374
0.0197095  0.0570539
0.0612245  0.000784929
0.0416228  0.0194942
0.0185185  0.047619
0.0        0.166667
0.0261969  0.0345077
0.0227671  0.0175131
0.0        0.0714286
0.013034   0.0181028
0.2        2.61229e-17
] atol = 1e-5
@test multipliers(deamiovrs, :Y) ≈ [
0.08333333333333336
0.014868603042876911
0.05259026687598115
0.038461538461538464
0.0
0.03703703703703698
0.03703703703703704
0.08756567425569173
0.07142857142857138
0.013758146270818254
0.0833333333333333
] atol = 1e-5

@test efficiency(deam(targets(deamiovrs, :X), targets(deamiovrs, :Y), orient = :Input, rts = :VRS)) ≈ ones(11) atol = 1e-5
@test rts(deamiovrs) ≈ [0.0; -0.661826; 0.314757; 0.0; -0.711640; -0.666667; 0.0; 1.626970; 1.214286; -0.135409; 0.0] atol = 1e-5

# Output oriented VRS
deamoovrs = deam(X, Y, orient = :Output, rts = :VRS)

@test nobs(deamoovrs) == 11
@test ninputs(deamoovrs) == 2
@test noutputs(deamoovrs) == 1
@test efficiency(deamoovrs) ≈ [
1.0000000000;
1.507518797;
1.0000000000;
1.0000000000;
3.203947368;
1.000000000;
1.0000000000;
1.000000000;
1.000000000;
1.192307692;
1.0000000000]

@test multipliers(deamoovrs, :X) ≈ [
0.0901826   0.0422374
0.0676692   0.093985
0.0465672   0.000597015
0.0272045   0.0358349
0.118421    0.164474
0.0         0.5
0.0261969   0.0345077
0.00866667  0.00666667
0.0         0.0322581
0.0         0.0
0.2         0.0
] atol = 1e-5
@test multipliers(deamoovrs, :Y) ≈ [
0.08333333333333329
0.07142857142857144
0.040000000000000015
0.03846153846153846
0.125
0.11111111111111109
0.037037037037037035
0.03333333333333333
0.03225806451612903
0.038461538461538464
0.08333333333333318
] atol = 1e-5

@test efficiency(deam(targets(deamoovrs, :X), targets(deamoovrs, :Y), orient = :Output, rts = :VRS)) ≈ ones(11) atol = 1e-5
@test rts(deamoovrs) ≈ [0.0; -0.703008; 0.239403; 0.0; -1.230263; -2.0; 0.0; 0.619333; 0.548387; 1.192308; 0.0] atol = 1e-5

## Test if one-by-one DEA using evaluation and reference sets match initial results
deamio_ref_eff = zeros(size(X, 1))
deamoo_ref_eff = zeros(size(X, 1))

deamiovrs_ref_eff = zeros(size(X, 1))
deamoovrs_ref_eff = zeros(size(X, 1))

deamiovrs_ref_multX = zeros(size(X))
deamiovrs_ref_multY = 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[:,:]

deamio_ref_eff[i] = efficiency(deam(Xeval, Yeval, orient = :Input, rts = :CRS, Xref = Xref, Yref = Yref))[1]
deamoo_ref_eff[i] = efficiency(deam(Xeval, Yeval, orient = :Output, rts = :CRS, Xref = Xref, Yref = Yref))[1]

deamiovrs_ref_eff[i] = efficiency(deam(Xeval, Yeval, orient = :Input, rts = :VRS, Xref = Xref, Yref = Yref))[1]
deamoovrs_ref_eff[i] = efficiency(deam(Xeval, Yeval, orient = :Output, rts = :VRS, Xref = Xref, Yref = Yref))[1]

deamiovrs_ref_multX[i,:] = multipliers(deam(Xeval, Yeval, orient = :Input, rts = :VRS, Xref = Xref, Yref = Yref), :X)
deamiovrs_ref_multY[i,:] = multipliers(deam(Xeval, Yeval, orient = :Input, rts = :VRS, Xref = Xref, Yref = Yref), :Y)
end

@test deamio_ref_eff ≈ efficiency(deamio)
@test deamoo_ref_eff ≈ efficiency(deamoo)

@test deamiovrs_ref_eff ≈ efficiency(deamiovrs)
@test deamoovrs_ref_eff ≈ efficiency(deamoovrs)

@test deamiovrs_ref_multX ≈ multipliers(deamiovrs, :X)
@test deamiovrs_ref_multY ≈ multipliers(deamiovrs, :Y)

# Print
show(IOBuffer(), deamio)

# Test errors
@test_throws DimensionMismatch deam([1; 2 ; 3], [4 ; 5]) #  Different number of observations
@test_throws DimensionMismatch deam([1; 2], [4 ; 5], Xref = [1; 2; 3; 4]) # Different number of observations in reference sets
@test_throws DimensionMismatch deam([1 1; 2 2], [4 4; 5 5], Xref = [1 1 1; 2 2 2]) # Different number of inputs
@test_throws DimensionMismatch deam([1 1; 2 2], [4 4; 5 5], Yref = [4 4 4; 5 5 5]) # Different number of inputs
@test_throws ArgumentError deam([1; 2; 3], [4; 5; 6], orient = :Error) # Invalid orientation
@test_throws ArgumentError deam([1; 2; 3], [4; 5; 6], rts = :Error) # Invalid returns to scale

@test_throws ArgumentError targets(deamio, :Error)    # Invalid target
@test_throws ErrorException slacks(deamio, :X)        # No slacks in multiplier model
@test_throws ArgumentError multipliers(deamio, :Error) # Invalid slacks

# ------------------
# 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(deam(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(deam(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(deam(X, Y, orient = :Input)) ≈ [0.4; 1; 0.8; 0.6; 0.4; 0.4; 0.5142857143; 0.2]

end
``````