From eb0ca632d7bef13f86a196b093a6d17c059e6cb0 Mon Sep 17 00:00:00 2001 From: Fredrik Ekre Date: Wed, 27 Jun 2018 11:02:14 +0200 Subject: [PATCH] Revert "move cor, cov, std, stdm, var, varm and linreg to StatsBase (#27152)" This reverts commit 746d08fdfe65888ca8a30e8cfa3ef2b439251d22. --- base/deprecated.jl | 22 +- base/exports.jl | 6 + base/statistics.jl | 481 ++++++++++++++++++++++ base/sysimg.jl | 1 + doc/src/base/math.md | 6 + doc/src/manual/interfaces.md | 10 +- stdlib/LinearAlgebra/docs/src/index.md | 1 + stdlib/LinearAlgebra/src/LinearAlgebra.jl | 1 + stdlib/LinearAlgebra/src/generic.jl | 40 ++ stdlib/LinearAlgebra/test/generic.jl | 47 +++ stdlib/SparseArrays/src/sparsematrix.jl | 61 +++ stdlib/SparseArrays/test/sparse.jl | 62 ++- test/docs.jl | 1 + test/offsetarray.jl | 3 + test/reducedim.jl | 6 + test/statistics.jl | 348 +++++++++++++++- 16 files changed, 1079 insertions(+), 17 deletions(-) diff --git a/base/deprecated.jl b/base/deprecated.jl index fb4192098323a..22608b826528a 100644 --- a/base/deprecated.jl +++ b/base/deprecated.jl @@ -293,6 +293,12 @@ deprecate(Base, :DSP, 2) using .DSP export conv, conv2, deconv, filt, filt!, xcorr +# PR #21709 +@deprecate cov(x::AbstractVector, corrected::Bool) cov(x, corrected=corrected) +@deprecate cov(x::AbstractMatrix, vardim::Int, corrected::Bool) cov(x, dims=vardim, corrected=corrected) +@deprecate cov(X::AbstractVector, Y::AbstractVector, corrected::Bool) cov(X, Y, corrected=corrected) +@deprecate cov(X::AbstractVecOrMat, Y::AbstractVecOrMat, vardim::Int, corrected::Bool) cov(X, Y, dims=vardim, corrected=corrected) + # PR #22325 # TODO: when this replace is removed from deprecated.jl: # 1) rename the function replace_new from strings/util.jl to replace @@ -1367,6 +1373,13 @@ export readandwrite @deprecate findmin(A::AbstractArray, dims) findmin(A, dims=dims) @deprecate mean(A::AbstractArray, dims) mean(A, dims=dims) +@deprecate varm(A::AbstractArray, m::AbstractArray, dims; kwargs...) varm(A, m; kwargs..., dims=dims) +@deprecate var(A::AbstractArray, dims; kwargs...) var(A; kwargs..., dims=dims) +@deprecate std(A::AbstractArray, dims; kwargs...) std(A; kwargs..., dims=dims) +@deprecate cov(X::AbstractMatrix, dim::Int; kwargs...) cov(X; kwargs..., dims=dim) +@deprecate cov(x::AbstractVecOrMat, y::AbstractVecOrMat, dim::Int; kwargs...) cov(x, y; kwargs..., dims=dim) +@deprecate cor(X::AbstractMatrix, dim::Int) cor(X, dims=dim) +@deprecate cor(x::AbstractVecOrMat, y::AbstractVecOrMat, dim::Int) cor(x, y, dims=dim) @deprecate median(A::AbstractArray, dims; kwargs...) median(A; kwargs..., dims=dims) @deprecate mapreducedim(f, op, A::AbstractArray, dims) mapreduce(f, op, A, dims=dims) @@ -1691,15 +1704,6 @@ end # PR #25168 @deprecate ipermute!(a, p::AbstractVector) invpermute!(a, p) -# #27140, #27152 -@deprecate_moved cor "StatsBase" -@deprecate_moved cov "StatsBase" -@deprecate_moved std "StatsBase" -@deprecate_moved stdm "StatsBase" -@deprecate_moved var "StatsBase" -@deprecate_moved varm "StatsBase" -@deprecate_moved linreg "StatsBase" - # ?? more special functions to SpecialFunctions.jl @deprecate_moved gamma "SpecialFunctions" @deprecate_moved lgamma "SpecialFunctions" diff --git a/base/exports.jl b/base/exports.jl index 37da399892e43..cdbca8df0f6f5 100644 --- a/base/exports.jl +++ b/base/exports.jl @@ -627,6 +627,8 @@ export set_zero_subnormals, # statistics + cor, + cov, mean!, mean, median!, @@ -634,6 +636,10 @@ export middle, quantile!, quantile, + std, + stdm, + var, + varm, # iteration done, diff --git a/base/statistics.jl b/base/statistics.jl index 31f5630635b76..36698dd26ff50 100644 --- a/base/statistics.jl +++ b/base/statistics.jl @@ -79,6 +79,487 @@ mean(A::AbstractArray; dims=:) = _mean(A, dims) _mean(A::AbstractArray{T}, region) where {T} = mean!(reducedim_init(t -> t/2, +, A, region), A) _mean(A::AbstractArray, ::Colon) = sum(A) / _length(A) +##### variances ##### + +# faster computation of real(conj(x)*y) +realXcY(x::Real, y::Real) = x*y +realXcY(x::Complex, y::Complex) = real(x)*real(y) + imag(x)*imag(y) + +var(iterable; corrected::Bool=true, mean=nothing) = _var(iterable, corrected, mean) + +function _var(iterable, corrected::Bool, mean) + y = iterate(iterable) + if y === nothing + throw(ArgumentError("variance of empty collection undefined: $(repr(iterable))")) + end + count = 1 + value, state = y + y = iterate(iterable, state) + if mean === nothing + # Use Welford algorithm as seen in (among other places) + # Knuth's TAOCP, Vol 2, page 232, 3rd edition. + M = value / 1 + S = real(zero(M)) + while y !== nothing + value, state = y + y = iterate(iterable, state) + count += 1 + new_M = M + (value - M) / count + S = S + realXcY(value - M, value - new_M) + M = new_M + end + return S / (count - Int(corrected)) + elseif isa(mean, Number) # mean provided + # Cannot use a compensated version, e.g. the one from + # "Updating Formulae and a Pairwise Algorithm for Computing Sample Variances." + # by Chan, Golub, and LeVeque, Technical Report STAN-CS-79-773, + # Department of Computer Science, Stanford University, + # because user can provide mean value that is different to mean(iterable) + sum2 = abs2(value - mean::Number) + while y !== nothing + value, state = y + y = iterate(iterable, state) + count += 1 + sum2 += abs2(value - mean) + end + return sum2 / (count - Int(corrected)) + else + throw(ArgumentError("invalid value of mean, $(mean)::$(typeof(mean))")) + end +end + +centralizedabs2fun(m) = x -> abs2.(x - m) +centralize_sumabs2(A::AbstractArray, m) = + mapreduce(centralizedabs2fun(m), +, A) +centralize_sumabs2(A::AbstractArray, m, ifirst::Int, ilast::Int) = + mapreduce_impl(centralizedabs2fun(m), +, A, ifirst, ilast) + +function centralize_sumabs2!(R::AbstractArray{S}, A::AbstractArray, means::AbstractArray) where S + # following the implementation of _mapreducedim! at base/reducedim.jl + lsiz = check_reducedims(R,A) + isempty(R) || fill!(R, zero(S)) + isempty(A) && return R + + if has_fast_linear_indexing(A) && lsiz > 16 + nslices = div(_length(A), lsiz) + ibase = first(LinearIndices(A))-1 + for i = 1:nslices + @inbounds R[i] = centralize_sumabs2(A, means[i], ibase+1, ibase+lsiz) + ibase += lsiz + end + return R + end + indsAt, indsRt = safe_tail(axes(A)), safe_tail(axes(R)) # handle d=1 manually + keep, Idefault = Broadcast.shapeindexer(indsRt) + if reducedim1(R, A) + i1 = first(indices1(R)) + @inbounds for IA in CartesianIndices(indsAt) + IR = Broadcast.newindex(IA, keep, Idefault) + r = R[i1,IR] + m = means[i1,IR] + @simd for i in axes(A, 1) + r += abs2(A[i,IA] - m) + end + R[i1,IR] = r + end + else + @inbounds for IA in CartesianIndices(indsAt) + IR = Broadcast.newindex(IA, keep, Idefault) + @simd for i in axes(A, 1) + R[i,IR] += abs2(A[i,IA] - means[i,IR]) + end + end + end + return R +end + +function varm!(R::AbstractArray{S}, A::AbstractArray, m::AbstractArray; corrected::Bool=true) where S + if isempty(A) + fill!(R, convert(S, NaN)) + else + rn = div(_length(A), _length(R)) - Int(corrected) + centralize_sumabs2!(R, A, m) + R .= R .* (1 // rn) + end + return R +end + +""" + varm(v, m; dims, corrected::Bool=true) + +Compute the sample variance of a collection `v` with known mean(s) `m`, +optionally over the given dimensions. `m` may contain means for each dimension of +`v`. If `corrected` is `true`, then the sum is scaled with `n-1`, +whereas the sum is scaled with `n` if `corrected` is `false` where `n = length(x)`. + +!!! note + Julia does not ignore `NaN` values in the computation. Use the [`missing`](@ref) type + to represent missing values, and the [`skipmissing`](@ref) function to omit them. +""" +varm(A::AbstractArray, m::AbstractArray; corrected::Bool=true, dims=:) = _varm(A, m, corrected, dims) + +_varm(A::AbstractArray{T}, m, corrected::Bool, region) where {T} = + varm!(reducedim_init(t -> abs2(t)/2, +, A, region), A, m; corrected=corrected) + +varm(A::AbstractArray, m; corrected::Bool=true) = _varm(A, m, corrected, :) + +function _varm(A::AbstractArray{T}, m, corrected::Bool, ::Colon) where T + n = _length(A) + n == 0 && return typeof((abs2(zero(T)) + abs2(zero(T)))/2)(NaN) + return centralize_sumabs2(A, m) / (n - Int(corrected)) +end + + +""" + var(v; dims, corrected::Bool=true, mean=nothing) + +Compute the sample variance of a vector or array `v`, optionally along the given dimensions. +The algorithm will return an estimator of the generative distribution's variance +under the assumption that each entry of `v` is an IID drawn from that generative +distribution. This computation is equivalent to calculating `sum(abs2, v - mean(v)) / +(length(v) - 1)`. If `corrected` is `true`, then the sum is scaled with `n-1`, +whereas the sum is scaled with `n` if `corrected` is `false` where `n = length(x)`. +The mean `mean` over the region may be provided. + +!!! note + Julia does not ignore `NaN` values in the computation. Use the [`missing`](@ref) type + to represent missing values, and the [`skipmissing`](@ref) function to omit them. +""" +var(A::AbstractArray; corrected::Bool=true, mean=nothing, dims=:) = _var(A, corrected, mean, dims) + +_var(A::AbstractArray, corrected::Bool, mean, dims) = + varm(A, coalesce(mean, Base.mean(A, dims=dims)); corrected=corrected, dims=dims) + +_var(A::AbstractArray, corrected::Bool, mean, ::Colon) = + real(varm(A, coalesce(mean, Base.mean(A)); corrected=corrected)) + +varm(iterable, m; corrected::Bool=true) = _var(iterable, corrected, m) + +## variances over ranges + +varm(v::AbstractRange, m::AbstractArray) = range_varm(v, m) +varm(v::AbstractRange, m) = range_varm(v, m) + +function range_varm(v::AbstractRange, m) + f = first(v) - m + s = step(v) + l = length(v) + vv = f^2 * l / (l - 1) + f * s * l + s^2 * l * (2 * l - 1) / 6 + if l == 0 || l == 1 + return typeof(vv)(NaN) + end + return vv +end + +function var(v::AbstractRange) + s = step(v) + l = length(v) + vv = abs2(s) * (l + 1) * l / 12 + if l == 0 || l == 1 + return typeof(vv)(NaN) + end + return vv +end + + +##### standard deviation ##### + +function sqrt!(A::AbstractArray) + for i in eachindex(A) + @inbounds A[i] = sqrt(A[i]) + end + A +end + +stdm(A::AbstractArray, m; corrected::Bool=true) = + sqrt.(varm(A, m; corrected=corrected)) + +""" + std(v; corrected::Bool=true, mean=nothing, dims) + +Compute the sample standard deviation of a vector or array `v`, optionally along the given +dimensions. The algorithm returns an estimator of the generative distribution's standard +deviation under the assumption that each entry of `v` is an IID drawn from that generative +distribution. This computation is equivalent to calculating `sqrt(sum((v - mean(v)).^2) / +(length(v) - 1))`. A pre-computed `mean` may be provided. If `corrected` is `true`, +then the sum is scaled with `n-1`, whereas the sum is scaled with `n` if `corrected` is +`false` where `n = length(x)`. + +!!! note + Julia does not ignore `NaN` values in the computation. Use the [`missing`](@ref) type + to represent missing values, and the [`skipmissing`](@ref) function to omit them. +""" +std(A::AbstractArray; corrected::Bool=true, mean=nothing, dims=:) = _std(A, corrected, mean, dims) + +_std(A::AbstractArray, corrected::Bool, mean, dims) = + sqrt.(var(A; corrected=corrected, mean=mean, dims=dims)) + +_std(A::AbstractArray, corrected::Bool, mean, ::Colon) = + sqrt.(var(A; corrected=corrected, mean=mean)) + +_std(A::AbstractArray{<:AbstractFloat}, corrected::Bool, mean, dims) = + sqrt!(var(A; corrected=corrected, mean=mean, dims=dims)) + +_std(A::AbstractArray{<:AbstractFloat}, corrected::Bool, mean, ::Colon) = + sqrt.(var(A; corrected=corrected, mean=mean)) + +std(iterable; corrected::Bool=true, mean=nothing) = + sqrt(var(iterable, corrected=corrected, mean=mean)) + +""" + stdm(v, m; corrected::Bool=true) + +Compute the sample standard deviation of a vector `v` +with known mean `m`. If `corrected` is `true`, +then the sum is scaled with `n-1`, whereas the sum is +scaled with `n` if `corrected` is `false` where `n = length(x)`. + +!!! note + Julia does not ignore `NaN` values in the computation. Use the [`missing`](@ref) type + to represent missing values, and the [`skipmissing`](@ref) function to omit them. +""" +stdm(iterable, m; corrected::Bool=true) = + std(iterable, corrected=corrected, mean=m) + + +###### covariance ###### + +# auxiliary functions + +_conj(x::AbstractArray{<:Real}) = x +_conj(x::AbstractArray) = conj(x) + +_getnobs(x::AbstractVector, vardim::Int) = _length(x) +_getnobs(x::AbstractMatrix, vardim::Int) = size(x, vardim) + +function _getnobs(x::AbstractVecOrMat, y::AbstractVecOrMat, vardim::Int) + n = _getnobs(x, vardim) + _getnobs(y, vardim) == n || throw(DimensionMismatch("dimensions of x and y mismatch")) + return n +end + +_vmean(x::AbstractVector, vardim::Int) = mean(x) +_vmean(x::AbstractMatrix, vardim::Int) = mean(x, dims=vardim) + +# core functions + +unscaled_covzm(x::AbstractVector{<:Number}) = sum(abs2, x) +unscaled_covzm(x::AbstractVector) = sum(t -> t*t', x) +unscaled_covzm(x::AbstractMatrix, vardim::Int) = (vardim == 1 ? _conj(x'x) : x * x') + +unscaled_covzm(x::AbstractVector, y::AbstractVector) = sum(conj(y[i])*x[i] for i in eachindex(y, x)) +unscaled_covzm(x::AbstractVector, y::AbstractMatrix, vardim::Int) = + (vardim == 1 ? *(transpose(x), _conj(y)) : *(transpose(x), transpose(_conj(y)))) +unscaled_covzm(x::AbstractMatrix, y::AbstractVector, vardim::Int) = + (c = vardim == 1 ? *(transpose(x), _conj(y)) : x * _conj(y); reshape(c, length(c), 1)) +unscaled_covzm(x::AbstractMatrix, y::AbstractMatrix, vardim::Int) = + (vardim == 1 ? *(transpose(x), _conj(y)) : *(x, adjoint(y))) + +# covzm (with centered data) + +covzm(x::AbstractVector; corrected::Bool=true) = unscaled_covzm(x) / (_length(x) - Int(corrected)) +function covzm(x::AbstractMatrix, vardim::Int=1; corrected::Bool=true) + C = unscaled_covzm(x, vardim) + T = promote_type(typeof(first(C) / 1), eltype(C)) + A = convert(AbstractMatrix{T}, C) + b = 1//(size(x, vardim) - corrected) + A .= A .* b + return A +end +covzm(x::AbstractVector, y::AbstractVector; corrected::Bool=true) = + unscaled_covzm(x, y) / (_length(x) - Int(corrected)) +function covzm(x::AbstractVecOrMat, y::AbstractVecOrMat, vardim::Int=1; corrected::Bool=true) + C = unscaled_covzm(x, y, vardim) + T = promote_type(typeof(first(C) / 1), eltype(C)) + A = convert(AbstractArray{T}, C) + b = 1//(_getnobs(x, y, vardim) - corrected) + A .= A .* b + return A +end + +# covm (with provided mean) +## Use map(t -> t - xmean, x) instead of x .- xmean to allow for Vector{Vector} +## which can't be handled by broadcast +covm(x::AbstractVector, xmean; corrected::Bool=true) = + covzm(map(t -> t - xmean, x); corrected=corrected) +covm(x::AbstractMatrix, xmean, vardim::Int=1; corrected::Bool=true) = + covzm(x .- xmean, vardim; corrected=corrected) +covm(x::AbstractVector, xmean, y::AbstractVector, ymean; corrected::Bool=true) = + covzm(map(t -> t - xmean, x), map(t -> t - ymean, y); corrected=corrected) +covm(x::AbstractVecOrMat, xmean, y::AbstractVecOrMat, ymean, vardim::Int=1; corrected::Bool=true) = + covzm(x .- xmean, y .- ymean, vardim; corrected=corrected) + +# cov (API) +""" + cov(x::AbstractVector; corrected::Bool=true) + +Compute the variance of the vector `x`. If `corrected` is `true` (the default) then the sum +is scaled with `n-1`, whereas the sum is scaled with `n` if `corrected` is `false` where `n = length(x)`. +""" +cov(x::AbstractVector; corrected::Bool=true) = covm(x, Base.mean(x); corrected=corrected) + +""" + cov(X::AbstractMatrix; dims::Int=1, corrected::Bool=true) + +Compute the covariance matrix of the matrix `X` along the dimension `dims`. If `corrected` +is `true` (the default) then the sum is scaled with `n-1`, whereas the sum is scaled with `n` +if `corrected` is `false` where `n = size(X, dims)`. +""" +cov(X::AbstractMatrix; dims::Int=1, corrected::Bool=true) = + covm(X, _vmean(X, dims), dims; corrected=corrected) + +""" + cov(x::AbstractVector, y::AbstractVector; corrected::Bool=true) + +Compute the covariance between the vectors `x` and `y`. If `corrected` is `true` (the +default), computes ``\\frac{1}{n-1}\\sum_{i=1}^n (x_i-\\bar x) (y_i-\\bar y)^*`` where +``*`` denotes the complex conjugate and `n = length(x) = length(y)`. If `corrected` is +`false`, computes ``\\frac{1}{n}\\sum_{i=1}^n (x_i-\\bar x) (y_i-\\bar y)^*``. +""" +cov(x::AbstractVector, y::AbstractVector; corrected::Bool=true) = + covm(x, Base.mean(x), y, Base.mean(y); corrected=corrected) + +""" + cov(X::AbstractVecOrMat, Y::AbstractVecOrMat; dims::Int=1, corrected::Bool=true) + +Compute the covariance between the vectors or matrices `X` and `Y` along the dimension +`dims`. If `corrected` is `true` (the default) then the sum is scaled with `n-1`, whereas +the sum is scaled with `n` if `corrected` is `false` where `n = size(X, dims) = size(Y, dims)`. +""" +cov(X::AbstractVecOrMat, Y::AbstractVecOrMat; dims::Int=1, corrected::Bool=true) = + covm(X, _vmean(X, dims), Y, _vmean(Y, dims), dims; corrected=corrected) + +##### correlation ##### + +""" + clampcor(x) + +Clamp a real correlation to between -1 and 1, leaving complex correlations unchanged +""" +clampcor(x::Real) = clamp(x, -1, 1) +clampcor(x) = x + +# cov2cor! + +function cov2cor!(C::AbstractMatrix{T}, xsd::AbstractArray) where T + nx = length(xsd) + size(C) == (nx, nx) || throw(DimensionMismatch("inconsistent dimensions")) + for j = 1:nx + for i = 1:j-1 + C[i,j] = adjoint(C[j,i]) + end + C[j,j] = oneunit(T) + for i = j+1:nx + C[i,j] = clampcor(C[i,j] / (xsd[i] * xsd[j])) + end + end + return C +end +function cov2cor!(C::AbstractMatrix, xsd, ysd::AbstractArray) + nx, ny = size(C) + length(ysd) == ny || throw(DimensionMismatch("inconsistent dimensions")) + for (j, y) in enumerate(ysd) # fixme (iter): here and in all `cov2cor!` we assume that `C` is efficiently indexed by integers + for i in 1:nx + C[i,j] = clampcor(C[i, j] / (xsd * y)) + end + end + return C +end +function cov2cor!(C::AbstractMatrix, xsd::AbstractArray, ysd) + nx, ny = size(C) + length(xsd) == nx || throw(DimensionMismatch("inconsistent dimensions")) + for j in 1:ny + for (i, x) in enumerate(xsd) + C[i,j] = clampcor(C[i,j] / (x * ysd)) + end + end + return C +end +function cov2cor!(C::AbstractMatrix, xsd::AbstractArray, ysd::AbstractArray) + nx, ny = size(C) + (length(xsd) == nx && length(ysd) == ny) || + throw(DimensionMismatch("inconsistent dimensions")) + for (i, x) in enumerate(xsd) + for (j, y) in enumerate(ysd) + C[i,j] = clampcor(C[i,j] / (x * y)) + end + end + return C +end + +# corzm (non-exported, with centered data) + +corzm(x::AbstractVector{T}) where {T} = one(real(T)) +function corzm(x::AbstractMatrix, vardim::Int=1) + c = unscaled_covzm(x, vardim) + return cov2cor!(c, collect(sqrt(c[i,i]) for i in 1:min(size(c)...))) +end +corzm(x::AbstractVector, y::AbstractMatrix, vardim::Int=1) = + cov2cor!(unscaled_covzm(x, y, vardim), sqrt(sum(abs2, x)), sqrt!(sum(abs2, y, dims=vardim))) +corzm(x::AbstractMatrix, y::AbstractVector, vardim::Int=1) = + cov2cor!(unscaled_covzm(x, y, vardim), sqrt!(sum(abs2, x, dims=vardim)), sqrt(sum(abs2, y))) +corzm(x::AbstractMatrix, y::AbstractMatrix, vardim::Int=1) = + cov2cor!(unscaled_covzm(x, y, vardim), sqrt!(sum(abs2, x, dims=vardim)), sqrt!(sum(abs2, y, dims=vardim))) + +# corm + +corm(x::AbstractVector{T}, xmean) where {T} = one(real(T)) +corm(x::AbstractMatrix, xmean, vardim::Int=1) = corzm(x .- xmean, vardim) +function corm(x::AbstractVector, mx, y::AbstractVector, my) + n = length(x) + length(y) == n || throw(DimensionMismatch("inconsistent lengths")) + n > 0 || throw(ArgumentError("correlation only defined for non-empty vectors")) + + @inbounds begin + # Initialize the accumulators + xx = zero(sqrt(abs2(x[1]))) + yy = zero(sqrt(abs2(y[1]))) + xy = zero(x[1] * y[1]') + + @simd for i in eachindex(x, y) + xi = x[i] - mx + yi = y[i] - my + xx += abs2(xi) + yy += abs2(yi) + xy += xi * yi' + end + end + return clampcor(xy / max(xx, yy) / sqrt(min(xx, yy) / max(xx, yy))) +end + +corm(x::AbstractVecOrMat, xmean, y::AbstractVecOrMat, ymean, vardim::Int=1) = + corzm(x .- xmean, y .- ymean, vardim) + +# cor +""" + cor(x::AbstractVector) + +Return the number one. +""" +cor(x::AbstractVector) = one(real(eltype(x))) + +""" + cor(X::AbstractMatrix; dims::Int=1) + +Compute the Pearson correlation matrix of the matrix `X` along the dimension `dims`. +""" +cor(X::AbstractMatrix; dims::Int=1) = corm(X, _vmean(X, dims), dims) + +""" + cor(x::AbstractVector, y::AbstractVector) + +Compute the Pearson correlation between the vectors `x` and `y`. +""" +cor(x::AbstractVector, y::AbstractVector) = corm(x, Base.mean(x), y, Base.mean(y)) + +""" + cor(X::AbstractVecOrMat, Y::AbstractVecOrMat; dims=1) + +Compute the Pearson correlation between the vectors or matrices `X` and `Y` along the dimension `dims`. +""" +cor(x::AbstractVecOrMat, y::AbstractVecOrMat; dims::Int=1) = + corm(x, _vmean(x, dims), y, _vmean(y, dims), dims) + ##### median & quantiles ##### """ diff --git a/base/sysimg.jl b/base/sysimg.jl index cb82306742dc7..65056a7108f2d 100644 --- a/base/sysimg.jl +++ b/base/sysimg.jl @@ -746,6 +746,7 @@ end # @deprecate_stdlib kron LinearAlgebra true @deprecate_stdlib ldltfact LinearAlgebra true @deprecate_stdlib ldltfact! LinearAlgebra true + @deprecate_stdlib linreg LinearAlgebra true @deprecate_stdlib logabsdet LinearAlgebra true @deprecate_stdlib logdet LinearAlgebra true @deprecate_stdlib lu LinearAlgebra true diff --git a/doc/src/base/math.md b/doc/src/base/math.md index 91e8d07fa6501..eecbdb808c980 100644 --- a/doc/src/base/math.md +++ b/doc/src/base/math.md @@ -183,9 +183,15 @@ Base.FastMath.@fastmath ```@docs Base.mean Base.mean! +Base.std +Base.stdm +Base.var +Base.varm Base.middle Base.median Base.median! Base.quantile Base.quantile! +Base.cov +Base.cor ``` diff --git a/doc/src/manual/interfaces.md b/doc/src/manual/interfaces.md index abdf61186cf3a..176b45a0bb5b6 100644 --- a/doc/src/manual/interfaces.md +++ b/doc/src/manual/interfaces.md @@ -65,6 +65,7 @@ julia> struct Squares end julia> Base.iterate(S::Squares, state=1) = state > S.count ? nothing : (state*state, state+1) + ``` With only [`iterate`](@ref) definition, the `Squares` type is already pretty powerful. @@ -83,18 +84,17 @@ julia> for i in Squares(7) 49 ``` -We can use many of the builtin methods that work with iterables, like [`in`](@ref), -[`sum`](@ref) and [`mean`](@ref): +We can use many of the builtin methods that work with iterables, like [`in`](@ref), [`mean`](@ref) and [`std`](@ref): ```jldoctest squaretype julia> 25 in Squares(10) true -julia> sum(Squares(100)) -338350 - julia> mean(Squares(100)) 3383.5 + +julia> std(Squares(100)) +3024.355854282583 ``` There are a few more methods we can extend to give Julia more information about this iterable diff --git a/stdlib/LinearAlgebra/docs/src/index.md b/stdlib/LinearAlgebra/docs/src/index.md index 6e7d122da83cc..415d3d60cd1d7 100644 --- a/stdlib/LinearAlgebra/docs/src/index.md +++ b/stdlib/LinearAlgebra/docs/src/index.md @@ -370,6 +370,7 @@ Base.inv(::AbstractMatrix) LinearAlgebra.pinv LinearAlgebra.nullspace Base.kron +LinearAlgebra.linreg LinearAlgebra.exp(::StridedMatrix{<:LinearAlgebra.BlasFloat}) LinearAlgebra.log(::StridedMatrix) LinearAlgebra.sqrt(::StridedMatrix{<:Real}) diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl index d841f2fc8f2e5..c0af08ebd9816 100644 --- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl +++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl @@ -103,6 +103,7 @@ export ldiv!, ldlt!, ldlt, + linreg, logabsdet, logdet, lowrankdowndate, diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl index d0dc58607597a..cd2c92a22a549 100644 --- a/stdlib/LinearAlgebra/src/generic.jl +++ b/stdlib/LinearAlgebra/src/generic.jl @@ -1143,6 +1143,46 @@ isdiag(A::AbstractMatrix) = isbanded(A, 0, 0) isdiag(x::Number) = true +""" + linreg(x, y) + +Perform simple linear regression using Ordinary Least Squares. Returns `a` and `b` such +that `a + b*x` is the closest straight line to the given points `(x, y)`, i.e., such that +the squared error between `y` and `a + b*x` is minimized. + +# Examples +```julia +using PyPlot +x = 1.0:12.0 +y = [5.5, 6.3, 7.6, 8.8, 10.9, 11.79, 13.48, 15.02, 17.77, 20.81, 22.0, 22.99] +a, b = linreg(x, y) # Linear regression +plot(x, y, "o") # Plot (x, y) points +plot(x, a + b*x) # Plot line determined by linear regression +``` + +See also: + +`\\`, [`cov`](@ref), [`std`](@ref), [`mean`](@ref). + +""" +function linreg(x::AbstractVector, y::AbstractVector) + # Least squares given + # Y = a + b*X + # where + # b = cov(X, Y)/var(X) + # a = mean(Y) - b*mean(X) + if size(x) != size(y) + throw(DimensionMismatch("x has size $(size(x)) and y has size $(size(y)), " * + "but these must be the same size")) + end + mx = mean(x) + my = mean(y) + # don't need to worry about the scaling (n vs n - 1) since they cancel in the ratio + b = Base.covm(x, mx, y, my)/Base.varm(x, mx) + a = my - b*mx + return (a, b) +end + # BLAS-like in-place y = x*α+y function (see also the version in blas.jl # for BlasFloat Arrays) function axpy!(α, x::AbstractArray, y::AbstractArray) diff --git a/stdlib/LinearAlgebra/test/generic.jl b/stdlib/LinearAlgebra/test/generic.jl index 6675e025a7912..3009d4ce8ab4b 100644 --- a/stdlib/LinearAlgebra/test/generic.jl +++ b/stdlib/LinearAlgebra/test/generic.jl @@ -89,6 +89,53 @@ n = 5 # should be odd end end +@testset "linrange" begin + # make sure unequal input arrays throw an error + x = [2; 5; 6] + y = [3; 7; 10; 10] + @test_throws DimensionMismatch linreg(x, y) + x = [2 5 6] + y = [3; 7; 10] + @test_throws MethodError linreg(x, y) + + # check (UnitRange, Array) + x = 1:12 + y = [5.5; 6.3; 7.6; 8.8; 10.9; 11.79; 13.48; 15.02; 17.77; 20.81; 22.0; 22.99] + @test [linreg(x,y)...] ≈ [2.5559090909090867, 1.6960139860139862] + @test [linreg(view(x,1:6),view(y,1:6))...] ≈ [3.8366666666666642,1.3271428571428574] + + # check (LinRange, UnitRange) + x = range(1.0, stop=12.0, length=100) + y = -100:-1 + @test [linreg(x, y)...] ≈ [-109.0, 9.0] + + # check (UnitRange, UnitRange) + x = 1:12 + y = 12:-1:1 + @test [linreg(x, y)...] ≈ [13.0, -1.0] + + # check (LinRange, LinRange) + x = range(-5, stop=10, length=100) + y = range(50, stop=200, length=100) + @test [linreg(x, y)...] ≈ [100.0, 10.0] + + # check (Array, Array) + # Anscombe's quartet (https://en.wikipedia.org/wiki/Anscombe%27s_quartet) + x123 = [10.0; 8.0; 13.0; 9.0; 11.0; 14.0; 6.0; 4.0; 12.0; 7.0; 5.0] + y1 = [8.04; 6.95; 7.58; 8.81; 8.33; 9.96; 7.24; 4.26; 10.84; 4.82; 5.68] + @test [linreg(x123,y1)...] ≈ [3.0,0.5] atol=15e-5 + + y2 = [9.14; 8.14; 8.74; 8.77; 9.26; 8.10; 6.12; 3.10; 9.13; 7.26; 4.74] + @test [linreg(x123,y2)...] ≈ [3.0,0.5] atol=10e-3 + + y3 = [7.46; 6.77; 12.74; 7.11; 7.81; 8.84; 6.08; 5.39; 8.15; 6.42; 5.73] + @test [linreg(x123,y3)...] ≈ [3.0,0.5] atol=10e-3 + + x4 = [8.0; 8.0; 8.0; 8.0; 8.0; 8.0; 8.0; 19.0; 8.0; 8.0; 8.0] + y4 = [6.58; 5.76; 7.71; 8.84; 8.47; 7.04; 5.25; 12.50; 5.56; 7.91; 6.89] + @test [linreg(x4,y4)...] ≈ [3.0,0.5] atol=10e-3 +end + @testset "diag" begin A = Matrix(1.0I, 4, 4) @test diag(A) == fill(1, 4) diff --git a/stdlib/SparseArrays/src/sparsematrix.jl b/stdlib/SparseArrays/src/sparsematrix.jl index 47fe84a7cd194..6986b12cd2cf5 100644 --- a/stdlib/SparseArrays/src/sparsematrix.jl +++ b/stdlib/SparseArrays/src/sparsematrix.jl @@ -3489,6 +3489,67 @@ function hash(A::SparseMatrixCSC{T}, h::UInt) where T hashrun(0, length(A)-lastidx, h) # Hash zeros at end end +## Statistics + +# This is the function that does the reduction underlying var/std +function Base.centralize_sumabs2!(R::AbstractArray{S}, A::SparseMatrixCSC{Tv,Ti}, means::AbstractArray) where {S,Tv,Ti} + lsiz = Base.check_reducedims(R,A) + size(means) == size(R) || error("size of means must match size of R") + isempty(R) || fill!(R, zero(S)) + isempty(A) && return R + + colptr = A.colptr + rowval = A.rowval + nzval = A.nzval + m = size(A, 1) + n = size(A, 2) + + if size(R, 1) == size(R, 2) == 1 + # Reduction along both columns and rows + R[1, 1] = Base.centralize_sumabs2(A, means[1]) + elseif size(R, 1) == 1 + # Reduction along rows + @inbounds for col = 1:n + mu = means[col] + r = convert(S, (m-colptr[col+1]+colptr[col])*abs2(mu)) + @simd for j = colptr[col]:colptr[col+1]-1 + r += abs2(nzval[j] - mu) + end + R[1, col] = r + end + elseif size(R, 2) == 1 + # Reduction along columns + rownz = fill(convert(Ti, n), m) + @inbounds for col = 1:n + @simd for j = colptr[col]:colptr[col+1]-1 + row = rowval[j] + R[row, 1] += abs2(nzval[j] - means[row]) + rownz[row] -= 1 + end + end + for i = 1:m + R[i, 1] += rownz[i]*abs2(means[i]) + end + else + # Reduction along a dimension > 2 + @inbounds for col = 1:n + lastrow = 0 + @simd for j = colptr[col]:colptr[col+1]-1 + row = rowval[j] + for i = lastrow+1:row-1 + R[i, col] = abs2(means[i, col]) + end + R[row, col] = abs2(nzval[j] - means[row, col]) + lastrow = row + end + for i = lastrow+1:m + R[i, col] = abs2(means[i, col]) + end + end + end + return R +end + ## Uniform matrix arithmetic (+)(A::SparseMatrixCSC, J::UniformScaling) = A + sparse(J, size(A)...) diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl index 6309efc11b8a0..46651803cc215 100644 --- a/stdlib/SparseArrays/test/sparse.jl +++ b/stdlib/SparseArrays/test/sparse.jl @@ -522,7 +522,7 @@ end pA = sparse(rand(3, 7)) for arr in (se33, sA, pA) - for f in (sum, prod, minimum, maximum) + for f in (sum, prod, minimum, maximum, var) farr = Array(arr) @test f(arr) ≈ f(farr) @test f(arr, dims=1) ≈ f(farr, dims=1) @@ -551,8 +551,9 @@ end @test prod(sparse(Int[])) === 1 @test_throws ArgumentError minimum(sparse(Int[])) @test_throws ArgumentError maximum(sparse(Int[])) + @test var(sparse(Int[])) === NaN - for f in (sum, prod) + for f in (sum, prod, var) @test isequal(f(spzeros(0, 1), dims=1), f(Matrix{Int}(I, 0, 1), dims=1)) @test isequal(f(spzeros(0, 1), dims=2), f(Matrix{Int}(I, 0, 1), dims=2)) @test isequal(f(spzeros(0, 1), dims=(1, 2)), f(Matrix{Int}(I, 0, 1), dims=(1, 2))) @@ -2064,6 +2065,63 @@ end @test issymmetric(B) end +# Faster covariance function for sparse matrices +# Prevents densifying the input matrix when subtracting the mean +# Test against dense implementation +# PR https://github.com/JuliaLang/julia/pull/22735 +# Part of this test needed to be hacked due to the treatment +# of Inf in sparse matrix algebra +# https://github.com/JuliaLang/julia/issues/22921 +# The issue will be resolved in +# https://github.com/JuliaLang/julia/issues/22733 +@testset "optimizing sparse $elty covariance" for elty in (Float64, Complex{Float64}) + n = 10 + p = 5 + np2 = div(n*p, 2) + nzvals, x_sparse = guardsrand(1) do + if elty <: Real + nzvals = randn(np2) + else + nzvals = complex.(randn(np2), randn(np2)) + end + nzvals, sparse(rand(1:n, np2), rand(1:p, np2), nzvals, n, p) + end + x_dense = convert(Matrix{elty}, x_sparse) + @testset "Test with no Infs and NaNs, vardim=$vardim, corrected=$corrected" for vardim in (1, 2), + corrected in (true, false) + @test cov(x_sparse, dims=vardim, corrected=corrected) ≈ + cov(x_dense , dims=vardim, corrected=corrected) + end + + @testset "Test with $x11, vardim=$vardim, corrected=$corrected" for x11 in (NaN, Inf), + vardim in (1, 2), + corrected in (true, false) + x_sparse[1,1] = x11 + x_dense[1 ,1] = x11 + + cov_sparse = cov(x_sparse, dims=vardim, corrected=corrected) + cov_dense = cov(x_dense , dims=vardim, corrected=corrected) + @test cov_sparse[2:end, 2:end] ≈ cov_dense[2:end, 2:end] + @test isfinite.(cov_sparse) == isfinite.(cov_dense) + @test isfinite.(cov_sparse) == isfinite.(cov_dense) + end + + @testset "Test with NaN and Inf, vardim=$vardim, corrected=$corrected" for vardim in (1, 2), + corrected in (true, false) + x_sparse[1,1] = Inf + x_dense[1 ,1] = Inf + x_sparse[2,1] = NaN + x_dense[2 ,1] = NaN + + cov_sparse = cov(x_sparse, dims=vardim, corrected=corrected) + cov_dense = cov(x_dense , dims=vardim, corrected=corrected) + @test cov_sparse[(1 + vardim):end, (1 + vardim):end] ≈ + cov_dense[ (1 + vardim):end, (1 + vardim):end] + @test isfinite.(cov_sparse) == isfinite.(cov_dense) + @test isfinite.(cov_sparse) == isfinite.(cov_dense) + end +end + @testset "similar should not alias the input sparse array" begin a = sparse(rand(3,3) .+ 0.1) b = similar(a, Float32, Int32) diff --git a/test/docs.jl b/test/docs.jl index 3a925d65a4334..cf20dbd1d5495 100644 --- a/test/docs.jl +++ b/test/docs.jl @@ -669,6 +669,7 @@ end @test (@repl :@r_str) !== nothing # Simple tests for apropos: +@test occursin("cor", sprint(apropos, "pearson")) @test occursin("eachindex", sprint(apropos, r"ind(exes|ices)")) using Profile @test occursin("Profile.print", sprint(apropos, "print")) diff --git a/test/offsetarray.jl b/test/offsetarray.jl index 5d73d4be8a4dc..0aa4248198788 100644 --- a/test/offsetarray.jl +++ b/test/offsetarray.jl @@ -374,6 +374,9 @@ I = findall(!iszero, z) @test mean(x->2x, A_3_3) == 10 @test mean(A_3_3, dims=1) == median(A_3_3, dims=1) == OffsetArray([2 5 8], (0,A_3_3.offsets[2])) @test mean(A_3_3, dims=2) == median(A_3_3, dims=2) == OffsetArray(reshape([4,5,6],(3,1)), (A_3_3.offsets[1],0)) +@test var(A_3_3) == 7.5 +@test std(A_3_3, dims=1) == OffsetArray([1 1 1], (0,A_3_3.offsets[2])) +@test std(A_3_3, dims=2) == OffsetArray(reshape([3,3,3], (3,1)), (A_3_3.offsets[1],0)) @test sum(OffsetArray(fill(1,3000), -1000)) == 3000 @test norm(v) ≈ norm(parent(v)) diff --git a/test/reducedim.jl b/test/reducedim.jl index fcc7df1bf98d7..8e80dc750a3e6 100644 --- a/test/reducedim.jl +++ b/test/reducedim.jl @@ -127,6 +127,7 @@ end @test prod(A) === 1 @test_throws ArgumentError minimum(A) @test_throws ArgumentError maximum(A) + @test var(A) === NaN @test isequal(sum(A, dims=1), zeros(Int, 1, 1)) @test isequal(sum(A, dims=2), zeros(Int, 0, 1)) @@ -136,6 +137,10 @@ end @test isequal(prod(A, dims=2), fill(1, 0, 1)) @test isequal(prod(A, dims=(1, 2)), fill(1, 1, 1)) @test isequal(prod(A, dims=3), fill(1, 0, 1)) + @test isequal(var(A, dims=1), fill(NaN, 1, 1)) + @test isequal(var(A, dims=2), fill(NaN, 0, 1)) + @test isequal(var(A, dims=(1, 2)), fill(NaN, 1, 1)) + @test isequal(var(A, dims=3), fill(NaN, 0, 1)) for f in (minimum, maximum) @test_throws ArgumentError f(A, dims=1) @@ -315,6 +320,7 @@ end # issue #6672 @test sum(Real[1 2 3; 4 5.3 7.1], dims=2) == reshape([6, 16.4], 2, 1) +@test std(AbstractFloat[1,2,3], dims=1) == [1.0] @test sum(Any[1 2;3 4], dims=1) == [4 6] @test sum(Vector{Int}[[1,2],[4,3]], dims=1)[1] == [5,5] diff --git a/test/statistics.jl b/test/statistics.jl index edc401c4c937d..3d7f2c846c8f5 100644 --- a/test/statistics.jl +++ b/test/statistics.jl @@ -80,6 +80,288 @@ end end end +@testset "var & std" begin + # edge case: empty vector + # iterable; this has to throw for type stability + @test_throws ArgumentError var(()) + @test_throws ArgumentError var((); corrected=false) + @test_throws ArgumentError var((); mean=2) + @test_throws ArgumentError var((); mean=2, corrected=false) + # reduction + @test isnan(var(Int[])) + @test isnan(var(Int[]; corrected=false)) + @test isnan(var(Int[]; mean=2)) + @test isnan(var(Int[]; mean=2, corrected=false)) + # reduction across dimensions + @test isequal(var(Int[], dims=1), [NaN]) + @test isequal(var(Int[], dims=1; corrected=false), [NaN]) + @test isequal(var(Int[], dims=1; mean=[2]), [NaN]) + @test isequal(var(Int[], dims=1; mean=[2], corrected=false), [NaN]) + + # edge case: one-element vector + # iterable + @test isnan(@inferred(var((1,)))) + @test var((1,); corrected=false) === 0.0 + @test var((1,); mean=2) === Inf + @test var((1,); mean=2, corrected=false) === 1.0 + # reduction + @test isnan(@inferred(var([1]))) + @test var([1]; corrected=false) === 0.0 + @test var([1]; mean=2) === Inf + @test var([1]; mean=2, corrected=false) === 1.0 + # reduction across dimensions + @test isequal(@inferred(var([1], dims=1)), [NaN]) + @test var([1], dims=1; corrected=false) ≈ [0.0] + @test var([1], dims=1; mean=[2]) ≈ [Inf] + @test var([1], dims=1; mean=[2], corrected=false) ≈ [1.0] + + @test var(1:8) == 6. + @test varm(1:8,1) == varm(Vector(1:8),1) + @test isnan(varm(1:1,1)) + @test isnan(var(1:1)) + @test isnan(var(1:-1)) + + @test @inferred(var(1.0:8.0)) == 6. + @test varm(1.0:8.0,1.0) == varm(Vector(1.0:8.0),1) + @test isnan(varm(1.0:1.0,1.0)) + @test isnan(var(1.0:1.0)) + @test isnan(var(1.0:-1.0)) + + @test @inferred(var(1.0f0:8.0f0)) === 6.f0 + @test varm(1.0f0:8.0f0,1.0f0) == varm(Vector(1.0f0:8.0f0),1) + @test isnan(varm(1.0f0:1.0f0,1.0f0)) + @test isnan(var(1.0f0:1.0f0)) + @test isnan(var(1.0f0:-1.0f0)) + + @test varm([1,2,3], 2) ≈ 1. + @test var([1,2,3]) ≈ 1. + @test var([1,2,3]; corrected=false) ≈ 2.0/3 + @test var([1,2,3]; mean=0) ≈ 7. + @test var([1,2,3]; mean=0, corrected=false) ≈ 14.0/3 + + @test varm((1,2,3), 2) ≈ 1. + @test var((1,2,3)) ≈ 1. + @test var((1,2,3); corrected=false) ≈ 2.0/3 + @test var((1,2,3); mean=0) ≈ 7. + @test var((1,2,3); mean=0, corrected=false) ≈ 14.0/3 + @test_throws ArgumentError var((1,2,3); mean=()) + + @test var([1 2 3 4 5; 6 7 8 9 10], dims=2) ≈ [2.5 2.5]' + @test var([1 2 3 4 5; 6 7 8 9 10], dims=2; corrected=false) ≈ [2.0 2.0]' + + @test stdm([1,2,3], 2) ≈ 1. + @test std([1,2,3]) ≈ 1. + @test std([1,2,3]; corrected=false) ≈ sqrt(2.0/3) + @test std([1,2,3]; mean=0) ≈ sqrt(7.0) + @test std([1,2,3]; mean=0, corrected=false) ≈ sqrt(14.0/3) + + @test stdm([1.0,2,3], 2) ≈ 1. + @test std([1.0,2,3]) ≈ 1. + @test std([1.0,2,3]; corrected=false) ≈ sqrt(2.0/3) + @test std([1.0,2,3]; mean=0) ≈ sqrt(7.0) + @test std([1.0,2,3]; mean=0, corrected=false) ≈ sqrt(14.0/3) + + @test std([1.0,2,3]; dims=1)[] ≈ 1. + @test std([1.0,2,3]; dims=1, corrected=false)[] ≈ sqrt(2.0/3) + @test std([1.0,2,3]; dims=1, mean=[0])[] ≈ sqrt(7.0) + @test std([1.0,2,3]; dims=1, mean=[0], corrected=false)[] ≈ sqrt(14.0/3) + + @test stdm((1,2,3), 2) ≈ 1. + @test std((1,2,3)) ≈ 1. + @test std((1,2,3); corrected=false) ≈ sqrt(2.0/3) + @test std((1,2,3); mean=0) ≈ sqrt(7.0) + @test std((1,2,3); mean=0, corrected=false) ≈ sqrt(14.0/3) + + @test std([1 2 3 4 5; 6 7 8 9 10], dims=2) ≈ sqrt.([2.5 2.5]') + @test std([1 2 3 4 5; 6 7 8 9 10], dims=2; corrected=false) ≈ sqrt.([2.0 2.0]') + + let A = ComplexF64[exp(i*im) for i in 1:10^4] + @test varm(A, 0.) ≈ sum(map(abs2, A)) / (length(A) - 1) + @test varm(A, mean(A)) ≈ var(A) + end + + @test var([1//1, 2//1]) isa Rational{Int} + @test var([1//1, 2//1], dims=1) isa Vector{Rational{Int}} + + @test std([1//1, 2//1]) isa Float64 + @test std([1//1, 2//1], dims=1) isa Vector{Float64} +end + +function safe_cov(x, y, zm::Bool, cr::Bool) + n = length(x) + if !zm + x = x .- mean(x) + y = y .- mean(y) + end + dot(vec(x), vec(y)) / (n - Int(cr)) +end +X = [1.0 5.0; + 2.0 4.0; + 3.0 6.0; + 4.0 2.0; + 5.0 1.0] +Y = [6.0 2.0; + 1.0 7.0; + 5.0 8.0; + 3.0 4.0; + 2.0 3.0] + +@testset "covariance" begin + for vd in [1, 2], zm in [true, false], cr in [true, false] + # println("vd = $vd: zm = $zm, cr = $cr") + if vd == 1 + k = size(X, 2) + Cxx = zeros(k, k) + Cxy = zeros(k, k) + for i = 1:k, j = 1:k + Cxx[i,j] = safe_cov(X[:,i], X[:,j], zm, cr) + Cxy[i,j] = safe_cov(X[:,i], Y[:,j], zm, cr) + end + x1 = vec(X[:,1]) + y1 = vec(Y[:,1]) + else + k = size(X, 1) + Cxx = zeros(k, k) + Cxy = zeros(k, k) + for i = 1:k, j = 1:k + Cxx[i,j] = safe_cov(X[i,:], X[j,:], zm, cr) + Cxy[i,j] = safe_cov(X[i,:], Y[j,:], zm, cr) + end + x1 = vec(X[1,:]) + y1 = vec(Y[1,:]) + end + + c = zm ? Base.covm(x1, 0, corrected=cr) : + cov(x1, corrected=cr) + @test isa(c, Float64) + @test c ≈ Cxx[1,1] + @inferred cov(x1, corrected=cr) + + @test cov(X) == Base.covm(X, mean(X, dims=1)) + C = zm ? Base.covm(X, 0, vd, corrected=cr) : + cov(X, dims=vd, corrected=cr) + @test size(C) == (k, k) + @test C ≈ Cxx + @inferred cov(X, dims=vd, corrected=cr) + + @test cov(x1, y1) == Base.covm(x1, mean(x1), y1, mean(y1)) + c = zm ? Base.covm(x1, 0, y1, 0, corrected=cr) : + cov(x1, y1, corrected=cr) + @test isa(c, Float64) + @test c ≈ Cxy[1,1] + @inferred cov(x1, y1, corrected=cr) + + if vd == 1 + @test cov(x1, Y) == Base.covm(x1, mean(x1), Y, mean(Y, dims=1)) + end + C = zm ? Base.covm(x1, 0, Y, 0, vd, corrected=cr) : + cov(x1, Y, dims=vd, corrected=cr) + @test size(C) == (1, k) + @test vec(C) ≈ Cxy[1,:] + @inferred cov(x1, Y, dims=vd, corrected=cr) + + if vd == 1 + @test cov(X, y1) == Base.covm(X, mean(X, dims=1), y1, mean(y1)) + end + C = zm ? Base.covm(X, 0, y1, 0, vd, corrected=cr) : + cov(X, y1, dims=vd, corrected=cr) + @test size(C) == (k, 1) + @test vec(C) ≈ Cxy[:,1] + @inferred cov(X, y1, dims=vd, corrected=cr) + + @test cov(X, Y) == Base.covm(X, mean(X, dims=1), Y, mean(Y, dims=1)) + C = zm ? Base.covm(X, 0, Y, 0, vd, corrected=cr) : + cov(X, Y, dims=vd, corrected=cr) + @test size(C) == (k, k) + @test C ≈ Cxy + @inferred cov(X, Y, dims=vd, corrected=cr) + end +end + +function safe_cor(x, y, zm::Bool) + if !zm + x = x .- mean(x) + y = y .- mean(y) + end + x = vec(x) + y = vec(y) + dot(x, y) / (sqrt(dot(x, x)) * sqrt(dot(y, y))) +end +@testset "correlation" begin + for vd in [1, 2], zm in [true, false] + # println("vd = $vd: zm = $zm") + if vd == 1 + k = size(X, 2) + Cxx = zeros(k, k) + Cxy = zeros(k, k) + for i = 1:k, j = 1:k + Cxx[i,j] = safe_cor(X[:,i], X[:,j], zm) + Cxy[i,j] = safe_cor(X[:,i], Y[:,j], zm) + end + x1 = vec(X[:,1]) + y1 = vec(Y[:,1]) + else + k = size(X, 1) + Cxx = zeros(k, k) + Cxy = zeros(k, k) + for i = 1:k, j = 1:k + Cxx[i,j] = safe_cor(X[i,:], X[j,:], zm) + Cxy[i,j] = safe_cor(X[i,:], Y[j,:], zm) + end + x1 = vec(X[1,:]) + y1 = vec(Y[1,:]) + end + + c = zm ? Base.corm(x1, 0) : cor(x1) + @test isa(c, Float64) + @test c ≈ Cxx[1,1] + @inferred cor(x1) + + @test cor(X) == Base.corm(X, mean(X, dims=1)) + C = zm ? Base.corm(X, 0, vd) : cor(X, dims=vd) + @test size(C) == (k, k) + @test C ≈ Cxx + @inferred cor(X, dims=vd) + + @test cor(x1, y1) == Base.corm(x1, mean(x1), y1, mean(y1)) + c = zm ? Base.corm(x1, 0, y1, 0) : cor(x1, y1) + @test isa(c, Float64) + @test c ≈ Cxy[1,1] + @inferred cor(x1, y1) + + if vd == 1 + @test cor(x1, Y) == Base.corm(x1, mean(x1), Y, mean(Y, dims=1)) + end + C = zm ? Base.corm(x1, 0, Y, 0, vd) : cor(x1, Y, dims=vd) + @test size(C) == (1, k) + @test vec(C) ≈ Cxy[1,:] + @inferred cor(x1, Y, dims=vd) + + if vd == 1 + @test cor(X, y1) == Base.corm(X, mean(X, dims=1), y1, mean(y1)) + end + C = zm ? Base.corm(X, 0, y1, 0, vd) : cor(X, y1, dims=vd) + @test size(C) == (k, 1) + @test vec(C) ≈ Cxy[:,1] + @inferred cor(X, y1, dims=vd) + + @test cor(X, Y) == Base.corm(X, mean(X, dims=1), Y, mean(Y, dims=1)) + C = zm ? Base.corm(X, 0, Y, 0, vd) : cor(X, Y, dims=vd) + @test size(C) == (k, k) + @test C ≈ Cxy + @inferred cor(X, Y, dims=vd) + end + + @test cor(repeat(1:17, 1, 17))[2] <= 1.0 + @test cor(1:17, 1:17) <= 1.0 + @test cor(1:17, 18:34) <= 1.0 + let tmp = range(1, stop=85, length=100) + tmp2 = Vector(tmp) + @test cor(tmp, tmp) <= 1.0 + @test cor(tmp, tmp2) <= 1.0 + end +end + @testset "quantile" begin @test quantile([1,2,3,4],0.5) == 2.5 @test quantile([1,2,3,4],[0.5]) == [2.5] @@ -101,6 +383,41 @@ let y = [0.40003674665581906, 0.4085630862624367, 0.41662034698690303, 0.4166203 @test issorted(quantile(y, range(0.01, stop=0.99, length=17))) end +@testset "variance of complex arrays (#13309)" begin + z = rand(ComplexF64, 10) + @test var(z) ≈ invoke(var, Tuple{Any}, z) ≈ cov(z) ≈ var(z,dims=1)[1] ≈ sum(abs2, z .- mean(z))/9 + @test isa(var(z), Float64) + @test isa(invoke(var, Tuple{Any}, z), Float64) + @test isa(cov(z), Float64) + @test isa(var(z,dims=1), Vector{Float64}) + @test varm(z, 0.0) ≈ invoke(varm, Tuple{Any,Float64}, z, 0.0) ≈ sum(abs2, z)/9 + @test isa(varm(z, 0.0), Float64) + @test isa(invoke(varm, Tuple{Any,Float64}, z, 0.0), Float64) + @test cor(z) === 1.0 + v = varm([1.0+2.0im], 0; corrected = false) + @test v ≈ 5 + @test isa(v, Float64) +end + +@testset "cov and cor of complex arrays (issue #21093)" begin + x = [2.7 - 3.3im, 0.9 + 5.4im, 0.1 + 0.2im, -1.7 - 5.8im, 1.1 + 1.9im] + y = [-1.7 - 1.6im, -0.2 + 6.5im, 0.8 - 10.0im, 9.1 - 3.4im, 2.7 - 5.5im] + @test cov(x, y) ≈ 4.8365 - 12.119im + @test cov(y, x) ≈ 4.8365 + 12.119im + @test cov(x, reshape(y, :, 1)) ≈ reshape([4.8365 - 12.119im], 1, 1) + @test cov(reshape(x, :, 1), y) ≈ reshape([4.8365 - 12.119im], 1, 1) + @test cov(reshape(x, :, 1), reshape(y, :, 1)) ≈ reshape([4.8365 - 12.119im], 1, 1) + @test cov([x y]) ≈ [21.779 4.8365-12.119im; + 4.8365+12.119im 54.548] + @test cor(x, y) ≈ 0.14032104449218274 - 0.35160772008699703im + @test cor(y, x) ≈ 0.14032104449218274 + 0.35160772008699703im + @test cor(x, reshape(y, :, 1)) ≈ reshape([0.14032104449218274 - 0.35160772008699703im], 1, 1) + @test cor(reshape(x, :, 1), y) ≈ reshape([0.14032104449218274 - 0.35160772008699703im], 1, 1) + @test cor(reshape(x, :, 1), reshape(y, :, 1)) ≈ reshape([0.14032104449218274 - 0.35160772008699703im], 1, 1) + @test cor([x y]) ≈ [1.0 0.14032104449218274-0.35160772008699703im + 0.14032104449218274+0.35160772008699703im 1.0] +end + @testset "Issue #17153 and PR #17154" begin a = rand(10,10) b = copy(a) @@ -112,6 +429,14 @@ end @test b == a x = mean(a, dims=2) @test b == a + x = var(a, dims=1) + @test b == a + x = var(a, dims=2) + @test b == a + x = std(a, dims=1) + @test b == a + x = std(a, dims=2) + @test b == a end # dimensional correctness @@ -123,20 +448,34 @@ using .Main.TestHelpers: Furlong @test sum(r) == sum(a) == Furlong(3) @test cumsum(r) == Furlong.([1,3]) @test mean(r) == mean(a) == median(a) == median(r) == Furlong(1.5) + @test var(r) == var(a) == Furlong{2}(0.5) + @test std(r) == std(a) == Furlong{1}(sqrt(0.5)) # Issue #21786 A = [Furlong{1}(rand(-5:5)) for i in 1:2, j in 1:2] @test mean(mean(A, dims=1), dims=2)[1] === mean(A) + @test var(A, dims=1)[1] === var(A[:, 1]) + @test std(A, dims=1)[1] === std(A[:, 1]) end # Issue #22901 -@testset "quantile of Any arrays" begin +@testset "var and quantile of Any arrays" begin x = Any[1, 2, 4, 10] y = Any[1, 2, 4, 10//1] + @test var(x) === 16.25 + @test var(y) === 65//4 + @test std(x) === sqrt(16.25) @test quantile(x, 0.5) === 3.0 @test quantile(x, 1//2) === 3//1 end +@testset "Promotion in covzm. Issue #8080" begin + A = [1 -1 -1; -1 1 1; -1 1 -1; 1 -1 -1; 1 -1 1] + @test Base.covzm(A) - mean(A, dims=1)'*mean(A, dims=1)*size(A, 1)/(size(A, 1) - 1) ≈ cov(A) + A = [1//1 -1 -1; -1 1 1; -1 1 -1; 1 -1 -1; 1 -1 1] + @test (A'A - size(A, 1)*Base.mean(A, dims=1)'*Base.mean(A, dims=1))/4 == cov(A) +end + @testset "Mean along dimension of empty array" begin a0 = zeros(0) a00 = zeros(0, 0) @@ -147,3 +486,10 @@ end @test isequal(mean(a01, dims=1) , fill(NaN, 1, 1)) @test isequal(mean(a10, dims=2) , fill(NaN, 1, 1)) end + +@testset "cov/var/std of Vector{Vector}" begin + x = [[2,4,6],[4,6,8]] + @test var(x) ≈ vec(var([x[1] x[2]], dims=2)) + @test std(x) ≈ vec(std([x[1] x[2]], dims=2)) + @test cov(x) ≈ cov([x[1] x[2]], dims=2) +end