# Wrong cov2cor()?

**URL:** <https://discourse.julialang.org/t/wrong-cov2cor/19423>\
**Category:** New to Julia\
**Created:** [January 9, 2019, 12:20pm UTC](https://discourse.julialang.org/t/wrong-cov2cor/19423 "2019-01-09T12:20:25Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![tomtom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomtom/32/5106_2.png) [@tomtom](https://discourse.julialang.org/u/tomtom)\
**Post date:** [January 9, 2019, 12:20pm UTC](https://discourse.julialang.org/t/wrong-cov2cor/19423/1 "2019-01-09T12:20:25Z")

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seems like `StatsBase.cov2cor()` is not doing correctly. First, it takes **_2_** arguments: the covariance matrix and a “a vector of standard deviations”, which should **_NOT_** be required. (noted that in `cor2cov()` we do need both of these two arguments).

now, doing some experiments, seems like `cov2cor()` could **_NOT_** recover the correlation matrix:

```julia
using StatsBase
s = [2.0, 3.0]
corr = [1.0 0.2; -0.5 1.0]
covv = transpose(s .* transpose(corr) ) .* s

julia> covv
2×2 Array{Float64,2}:
  4.0 1.2
 -3.0 9.0

julia> corr
2×2 Array{Float64,2}:
  1.0 0.2
 -0.5 1.0

julia> StatsBase.cov2cor(corr, s)
2×2 Array{Float64,2}:
  1.0 -0.0833333
 -0.0833333 1.0

julia> StatsBase.cov2cor(corr, s * 0.5)
2×2 Array{Float64,2}:
  1.0 -0.333333
 -0.333333 1.0

julia> StatsBase.cov2cor(corr, [1.0, 1.0])
2×2 Array{Float64,2}:
  1.0 -0.5
 -0.5 1.0

```

^^^ all correlation matrices obtained by `StatsBase.cov2cor()` are **incorrect**. Noted that the results are always symmetric: which is wrong.

`R` does give the correct correlation matrix. It takes **_one_** argument only:

```julia
> cov2cor(matrix(c(4, -3, 1.2, 9), nr = 2))
     [,1] [,2]
[1,] 1.0 0.2
[2,] -0.5 1.0

```

Moreover, going into the source code, while `covcor()` is implemented inside `cov.jl` under `StatsBase`, it actually calls `covcor!()` that is implemented inside `Statistics.jl` under `Statistics`. It’s kind of **strange** , isn’t it?

Finally, I don’t see the implementation of `covcor!()` is correct …

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<div class="post-metadata">

**Author:** ![tomtom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomtom/32/5106_2.png) [@tomtom](https://discourse.julialang.org/u/tomtom)\
**Post date:** [January 9, 2019, 1:44pm UTC](https://discourse.julialang.org/t/wrong-cov2cor/19423/2 "2019-01-09T13:44:23Z")

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I would like to propose the following based on `R`’s implementation:

```julia
function cov2cor_proposing(C::AbstractMatrix)
    (nr, nc) = size(C)
    @assert nr == nc

    s = sqrt.(1.0 ./ LinearAlgebra.diag(C) )
    corr = transpose(s .* transpose(C) ) .* s
    corr[LinearAlgebra.diagind(corr)] .= 1.0

    return corr
end

julia> cov2cor_proposing(covv)
2×2 Array{Float64,2}:
  1.0 0.2
 -0.5 1.0

```

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**Author:** ![scheidan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/scheidan/32/9889_2.png) [@scheidan](https://discourse.julialang.org/u/scheidan)\
**Post date:** [January 9, 2019, 1:52pm UTC](https://discourse.julialang.org/t/wrong-cov2cor/19423/3 "2019-01-09T13:52:59Z")

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I agree that it should not be necessary to provide the standard deviations to ‘cov2cor’.

However, the current implementation does provide the correct result .This works fine:

```nohighlight
import StatsBase

s = [2.0, 3.0]
corr = [1.0 -0.5; -0.5 1.0]
covv = (s * s') .* corr

StatsBase.cov2cor(covv, s)

```

The problem in your example is that you used a ill-defined, unsymmetric covariance matrix (which should be positive semidefinite, check with ‘LinearAlgebra.isposdef’)

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<div class="post-metadata">

**Author:** ![tomtom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomtom/32/5106_2.png) [@tomtom](https://discourse.julialang.org/u/tomtom)\
**Post date:** [January 9, 2019, 2:07pm UTC](https://discourse.julialang.org/t/wrong-cov2cor/19423/4 "2019-01-09T14:07:52Z")

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why don’t we use a simpler implementation that works in all cases?

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<div class="post-metadata">

**Author:** ![scheidan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/scheidan/32/9889_2.png) [@scheidan](https://discourse.julialang.org/u/scheidan)\
**Post date:** [January 9, 2019, 4:23pm UTC](https://discourse.julialang.org/t/wrong-cov2cor/19423/5 "2019-01-09T16:23:51Z")

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I’ve opened an issue in StatsBase: [`cov2cor` why must the standard deviations be given as argument? · Issue #444 · JuliaStats/StatsBase.jl · GitHub](https://github.com/JuliaStats/StatsBase.jl/issues/444)