412 lines
12 KiB
Julia
412 lines
12 KiB
Julia
# This file is a part of Julia. License is MIT: https://julialang.org/license
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using Base.Test
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# middle
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@test middle(3) === 3.0
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@test middle(2, 3) === 2.5
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let x = ((realmax(1.0)/4)*3)
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@test middle(x, x) === x
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end
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@test middle(1:8) === 4.5
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@test middle([1:8;]) === 4.5
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# ensure type-correctness
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for T in [Bool,Int8,Int16,Int32,Int64,Int128,UInt8,UInt16,UInt32,UInt64,UInt128,Float16,Float32,Float64]
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@test middle(one(T)) === middle(one(T), one(T))
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end
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# median
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@test median([1.]) === 1.
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@test median([1.,3]) === 2.
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@test median([1.,3,2]) === 2.
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@test median([1,3,2]) === 2.0
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@test median([1,3,2,4]) === 2.5
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@test median([0.0,Inf]) == Inf
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@test median([0.0,-Inf]) == -Inf
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@test median([0.,Inf,-Inf]) == 0.0
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@test median([1.,-1.,Inf,-Inf]) == 0.0
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@test isnan(median([-Inf,Inf]))
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X = [2 3 1 -1; 7 4 5 -4]
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@test all(median(X, 2) .== [1.5, 4.5])
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@test all(median(X, 1) .== [4.5 3.5 3.0 -2.5])
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@test X == [2 3 1 -1; 7 4 5 -4] # issue #17153
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@test_throws ArgumentError median([])
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@test isnan(median([NaN]))
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@test isnan(median([0.0,NaN]))
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@test isnan(median([NaN,0.0]))
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@test isequal(median([NaN 0.0; 1.2 4.5], 2), reshape([NaN; 2.85], 2, 1))
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@test median!([1 2 3 4]) == 2.5
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@test median!([1 2; 3 4]) == 2.5
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@test invoke(median, Tuple{AbstractVector}, 1:10) == median(1:10) == 5.5
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# mean
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@test_throws ArgumentError mean(())
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@test mean((1,2,3)) === 2.
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@test mean([0]) === 0.
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@test mean([1.]) === 1.
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@test mean([1.,3]) == 2.
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@test mean([1,2,3]) == 2.
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@test mean([0 1 2; 4 5 6], 1) == [2. 3. 4.]
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@test mean([1 2 3; 4 5 6], 1) == [2.5 3.5 4.5]
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@test mean(i->i+1, 0:2) === 2.
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@test mean(isodd, [3]) === 1.
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@test mean(x->3x, (1,1)) === 3.
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@test isnan(mean([NaN]))
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@test isnan(mean([0.0,NaN]))
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@test isnan(mean([NaN,0.0]))
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@test isnan(mean([0.,Inf,-Inf]))
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@test isnan(mean([1.,-1.,Inf,-Inf]))
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@test isnan(mean([-Inf,Inf]))
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@test isequal(mean([NaN 0.0; 1.2 4.5], 2), reshape([NaN; 2.85], 2, 1))
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# test var & std
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# edge case: empty vector
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# iterable; this has to throw for type stability
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@test_throws ArgumentError var(())
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@test_throws ArgumentError var((); corrected=false)
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@test_throws ArgumentError var((); mean=2)
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@test_throws ArgumentError var((); mean=2, corrected=false)
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# reduction
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@test isnan(var(Int[]))
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@test isnan(var(Int[]; corrected=false))
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@test isnan(var(Int[]; mean=2))
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@test isnan(var(Int[]; mean=2, corrected=false))
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# reduction across dimensions
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@test isequal(var(Int[], 1), [NaN])
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@test isequal(var(Int[], 1; corrected=false), [NaN])
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@test isequal(var(Int[], 1; mean=[2]), [NaN])
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@test isequal(var(Int[], 1; mean=[2], corrected=false), [NaN])
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# edge case: one-element vector
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# iterable
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@test isnan(@inferred(var((1,))))
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@test var((1,); corrected=false) === 0.0
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@test var((1,); mean=2) === Inf
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@test var((1,); mean=2, corrected=false) === 1.0
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# reduction
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@test isnan(@inferred(var([1])))
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@test var([1]; corrected=false) === 0.0
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@test var([1]; mean=2) === Inf
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@test var([1]; mean=2, corrected=false) === 1.0
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# reduction across dimensions
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@test isequal(@inferred(var([1], 1)), [NaN])
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@test var([1], 1; corrected=false) ≈ [0.0]
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@test var([1], 1; mean=[2]) ≈ [Inf]
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@test var([1], 1; mean=[2], corrected=false) ≈ [1.0]
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@test var(1:8) == 6.
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@test varm(1:8,1) == varm(collect(1:8),1)
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@test isnan(varm(1:1,1))
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@test isnan(var(1:1))
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@test isnan(var(1:-1))
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@test @inferred(var(1.0:8.0)) == 6.
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@test varm(1.0:8.0,1.0) == varm(collect(1.0:8.0),1)
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@test isnan(varm(1.0:1.0,1.0))
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@test isnan(var(1.0:1.0))
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@test isnan(var(1.0:-1.0))
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@test @inferred(var(1.0f0:8.0f0)) === 6.f0
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@test varm(1.0f0:8.0f0,1.0f0) == varm(collect(1.0f0:8.0f0),1)
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@test isnan(varm(1.0f0:1.0f0,1.0f0))
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@test isnan(var(1.0f0:1.0f0))
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@test isnan(var(1.0f0:-1.0f0))
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@test varm([1,2,3], 2) ≈ 1.
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@test var([1,2,3]) ≈ 1.
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@test var([1,2,3]; corrected=false) ≈ 2.0/3
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@test var([1,2,3]; mean=0) ≈ 7.
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@test var([1,2,3]; mean=0, corrected=false) ≈ 14.0/3
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@test varm((1,2,3), 2) ≈ 1.
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@test var((1,2,3)) ≈ 1.
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@test var((1,2,3); corrected=false) ≈ 2.0/3
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@test var((1,2,3); mean=0) ≈ 7.
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@test var((1,2,3); mean=0, corrected=false) ≈ 14.0/3
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@test_throws ArgumentError var((1,2,3); mean=())
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@test var([1 2 3 4 5; 6 7 8 9 10], 2) ≈ [2.5 2.5]'
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@test var([1 2 3 4 5; 6 7 8 9 10], 2; corrected=false) ≈ [2.0 2.0]'
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@test stdm([1,2,3], 2) ≈ 1.
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@test std([1,2,3]) ≈ 1.
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@test std([1,2,3]; corrected=false) ≈ sqrt(2.0/3)
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@test std([1,2,3]; mean=0) ≈ sqrt(7.0)
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@test std([1,2,3]; mean=0, corrected=false) ≈ sqrt(14.0/3)
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@test stdm((1,2,3), 2) ≈ 1.
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@test std((1,2,3)) ≈ 1.
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@test std((1,2,3); corrected=false) ≈ sqrt(2.0/3)
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@test std((1,2,3); mean=0) ≈ sqrt(7.0)
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@test std((1,2,3); mean=0, corrected=false) ≈ sqrt(14.0/3)
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@test std([1 2 3 4 5; 6 7 8 9 10], 2) ≈ sqrt.([2.5 2.5]')
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@test std([1 2 3 4 5; 6 7 8 9 10], 2; corrected=false) ≈ sqrt.([2.0 2.0]')
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A = Complex128[exp(i*im) for i in 1:10^4]
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@test varm(A,0.) ≈ sum(map(abs2,A))/(length(A)-1)
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@test varm(A,mean(A)) ≈ var(A)
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# test covariance
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function safe_cov(x, y, zm::Bool, cr::Bool)
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n = length(x)
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if !zm
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x = x .- mean(x)
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y = y .- mean(y)
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end
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dot(vec(x), vec(y)) / (n - Int(cr))
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end
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X = [1. 2. 3. 4. 5.; 5. 4. 6. 2. 1.]'
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Y = [6. 1. 5. 3. 2.; 2. 7. 8. 4. 3.]'
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for vd in [1, 2], zm in [true, false], cr in [true, false]
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# println("vd = $vd: zm = $zm, cr = $cr")
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if vd == 1
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k = size(X, 2)
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Cxx = zeros(k, k)
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Cxy = zeros(k, k)
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for i = 1:k, j = 1:k
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Cxx[i,j] = safe_cov(X[:,i], X[:,j], zm, cr)
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Cxy[i,j] = safe_cov(X[:,i], Y[:,j], zm, cr)
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end
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x1 = vec(X[:,1])
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y1 = vec(Y[:,1])
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else
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k = size(X, 1)
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Cxx = zeros(k, k)
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Cxy = zeros(k, k)
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for i = 1:k, j = 1:k
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Cxx[i,j] = safe_cov(X[i,:], X[j,:], zm, cr)
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Cxy[i,j] = safe_cov(X[i,:], Y[j,:], zm, cr)
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end
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x1 = vec(X[1,:])
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y1 = vec(Y[1,:])
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end
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c = zm ? Base.covm(x1, 0, cr) :
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cov(x1, cr)
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@test isa(c, Float64)
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@test c ≈ Cxx[1,1]
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@inferred cov(x1, cr)
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@test cov(X) == Base.covm(X, mean(X, 1))
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C = zm ? Base.covm(X, 0, vd, cr) :
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cov(X, vd, cr)
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@test size(C) == (k, k)
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@test C ≈ Cxx
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@inferred cov(X, vd, cr)
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@test cov(x1, y1) == Base.covm(x1, mean(x1), y1, mean(y1))
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c = zm ? Base.covm(x1, 0, y1, 0, cr) :
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cov(x1, y1, cr)
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@test isa(c, Float64)
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@test c ≈ Cxy[1,1]
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@inferred cov(x1, y1, cr)
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if vd == 1
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@test cov(x1, Y) == Base.covm(x1, mean(x1), Y, mean(Y, 1))
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end
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C = zm ? Base.covm(x1, 0, Y, 0, vd, cr) :
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cov(x1, Y, vd, cr)
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@test size(C) == (1, k)
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@test vec(C) ≈ Cxy[1,:]
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@inferred cov(x1, Y, vd, cr)
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if vd == 1
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@test cov(X, y1) == Base.covm(X, mean(X, 1), y1, mean(y1))
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end
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C = zm ? Base.covm(X, 0, y1, 0, vd, cr) :
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cov(X, y1, vd, cr)
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@test size(C) == (k, 1)
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@test vec(C) ≈ Cxy[:,1]
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@inferred cov(X, y1, vd, cr)
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@test cov(X, Y) == Base.covm(X, mean(X, 1), Y, mean(Y, 1))
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C = zm ? Base.covm(X, 0, Y, 0, vd, cr) :
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cov(X, Y, vd, cr)
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@test size(C) == (k, k)
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@test C ≈ Cxy
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@inferred cov(X, Y, vd, cr)
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end
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# test correlation
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function safe_cor(x, y, zm::Bool)
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if !zm
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x = x .- mean(x)
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y = y .- mean(y)
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end
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x = vec(x)
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y = vec(y)
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dot(x, y) / (sqrt(dot(x, x)) * sqrt(dot(y, y)))
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end
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for vd in [1, 2], zm in [true, false]
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# println("vd = $vd: zm = $zm")
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if vd == 1
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k = size(X, 2)
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Cxx = zeros(k, k)
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Cxy = zeros(k, k)
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for i = 1:k, j = 1:k
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Cxx[i,j] = safe_cor(X[:,i], X[:,j], zm)
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Cxy[i,j] = safe_cor(X[:,i], Y[:,j], zm)
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end
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x1 = vec(X[:,1])
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y1 = vec(Y[:,1])
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else
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k = size(X, 1)
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Cxx = zeros(k, k)
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Cxy = zeros(k, k)
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for i = 1:k, j = 1:k
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Cxx[i,j] = safe_cor(X[i,:], X[j,:], zm)
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Cxy[i,j] = safe_cor(X[i,:], Y[j,:], zm)
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end
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x1 = vec(X[1,:])
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y1 = vec(Y[1,:])
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end
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c = zm ? Base.corm(x1, 0) : cor(x1)
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@test isa(c, Float64)
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@test c ≈ Cxx[1,1]
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@inferred cor(x1)
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@test cor(X) == Base.corm(X, mean(X, 1))
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C = zm ? Base.corm(X, 0, vd) : cor(X, vd)
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@test size(C) == (k, k)
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@test C ≈ Cxx
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@inferred cor(X, vd)
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@test cor(x1, y1) == Base.corm(x1, mean(x1), y1, mean(y1))
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c = zm ? Base.corm(x1, 0, y1, 0) : cor(x1, y1)
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@test isa(c, Float64)
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@test c ≈ Cxy[1,1]
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@inferred cor(x1, y1)
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if vd == 1
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@test cor(x1, Y) == Base.corm(x1, mean(x1), Y, mean(Y, 1))
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end
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C = zm ? Base.corm(x1, 0, Y, 0, vd) : cor(x1, Y, vd)
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@test size(C) == (1, k)
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@test vec(C) ≈ Cxy[1,:]
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@inferred cor(x1, Y, vd)
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if vd == 1
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@test cor(X, y1) == Base.corm(X, mean(X, 1), y1, mean(y1))
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end
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C = zm ? Base.corm(X, 0, y1, 0, vd) : cor(X, y1, vd)
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@test size(C) == (k, 1)
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@test vec(C) ≈ Cxy[:,1]
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@inferred cor(X, y1, vd)
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@test cor(X, Y) == Base.corm(X, mean(X, 1), Y, mean(Y, 1))
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C = zm ? Base.corm(X, 0, Y, 0, vd) : cor(X, Y, vd)
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@test size(C) == (k, k)
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@test C ≈ Cxy
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@inferred cor(X, Y, vd)
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end
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@test cor(repmat(1:17, 1, 17))[2] <= 1.0
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@test cor(1:17, 1:17) <= 1.0
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@test cor(1:17, 18:34) <= 1.0
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let tmp = linspace(1, 85, 100)
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tmp2 = collect(tmp)
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@test cor(tmp, tmp) <= 1.0
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@test cor(tmp, tmp2) <= 1.0
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end
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@test quantile([1,2,3,4],0.5) == 2.5
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@test quantile([1,2,3,4],[0.5]) == [2.5]
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@test quantile([1., 3],[.25,.5,.75])[2] == median([1., 3])
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@test quantile(100.0:-1.0:0.0, 0.0:0.1:1.0) == collect(0.0:10.0:100.0)
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@test quantile(0.0:100.0, 0.0:0.1:1.0, sorted=true) == collect(0.0:10.0:100.0)
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@test quantile(100f0:-1f0:0.0, 0.0:0.1:1.0) == collect(0f0:10f0:100f0)
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@test quantile([Inf,Inf],0.5) == Inf
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@test quantile([-Inf,1],0.5) == -Inf
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@test quantile([0,1],1e-18) == 1e-18
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# StatsBase issue 164
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y = [0.40003674665581906,0.4085630862624367,0.41662034698690303,0.41662034698690303,0.42189053966652057,0.42189053966652057,0.42553514344518345,0.43985732442991354]
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@test issorted(quantile(y, linspace(0.01, 0.99, 17)))
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# variance of complex arrays (#13309)
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let z = rand(Complex128, 10)
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@test var(z) ≈ invoke(var, Tuple{Any}, z) ≈ cov(z) ≈ var(z,1)[1] ≈ sum(abs2, z - mean(z))/9
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@test isa(var(z), Float64)
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@test isa(invoke(var, Tuple{Any}, z), Float64)
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@test isa(cov(z), Float64)
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@test isa(var(z,1), Vector{Float64})
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@test varm(z, 0.0) ≈ invoke(varm, Tuple{Any,Float64}, z, 0.0) ≈ sum(abs2, z)/9
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@test isa(varm(z, 0.0), Float64)
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@test isa(invoke(varm, Tuple{Any,Float64}, z, 0.0), Float64)
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@test cor(z) === 1.0
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end
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let v = varm([1.0+2.0im], 0; corrected = false)
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@test v ≈ 5
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@test isa(v, Float64)
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end
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# cov and cor of complex arrays (issue #21093)
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x = [2.7 - 3.3im, 0.9 + 5.4im, 0.1 + 0.2im, -1.7 - 5.8im, 1.1 + 1.9im]
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y = [-1.7 - 1.6im, -0.2 + 6.5im, 0.8 - 10.0im, 9.1 - 3.4im, 2.7 - 5.5im]
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@test cov(x, y) ≈ 4.8365 - 12.119im
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@test cov(y, x) ≈ 4.8365 + 12.119im
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@test cov(x, reshape(y, :, 1)) ≈ reshape([4.8365 - 12.119im], 1, 1)
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@test cov(reshape(x, :, 1), y) ≈ reshape([4.8365 - 12.119im], 1, 1)
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@test cov(reshape(x, :, 1), reshape(y, :, 1)) ≈ reshape([4.8365 - 12.119im], 1, 1)
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@test cov([x y]) ≈ [21.779 4.8365-12.119im;
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4.8365+12.119im 54.548]
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@test cor(x, y) ≈ 0.14032104449218274 - 0.35160772008699703im
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@test cor(y, x) ≈ 0.14032104449218274 + 0.35160772008699703im
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@test cor(x, reshape(y, :, 1)) ≈ reshape([0.14032104449218274 - 0.35160772008699703im], 1, 1)
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@test cor(reshape(x, :, 1), y) ≈ reshape([0.14032104449218274 - 0.35160772008699703im], 1, 1)
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@test cor(reshape(x, :, 1), reshape(y, :, 1)) ≈ reshape([0.14032104449218274 - 0.35160772008699703im], 1, 1)
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@test cor([x y]) ≈ [1.0 0.14032104449218274-0.35160772008699703im
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0.14032104449218274+0.35160772008699703im 1.0]
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# Issue #17153 and PR #17154
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let a = rand(10,10)
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b = deepcopy(a)
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x = median(a, 1)
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@test b == a
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x = median(a, 2)
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@test b == a
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x = mean(a, 1)
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@test b == a
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x = mean(a, 2)
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@test b == a
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x = var(a, 1)
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@test b == a
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x = var(a, 2)
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@test b == a
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x = std(a, 1)
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@test b == a
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x = std(a, 2)
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@test b == a
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end
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# dimensional correctness
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isdefined(Main, :TestHelpers) || @eval Main include("TestHelpers.jl")
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using TestHelpers.Furlong
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let r = Furlong(1):Furlong(1):Furlong(2), a = collect(r)
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@test sum(r) == sum(a) == Furlong(3)
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@test cumsum(r) == Furlong.([1,3])
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@test mean(r) == mean(a) == median(a) == median(r) == Furlong(1.5)
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@test var(r) == var(a) == Furlong{2}(0.5)
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@test std(r) == std(a) == Furlong{1}(sqrt(0.5))
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end
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