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spell check of docs
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As of 01/01/2017 [kdomino](https://github.com/kdomino) is the lead maintainer of this package.

## Instalation
## Installation

Within Julia, run

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julia> @everywhere using Cumulants
```

Naive algorithms of moment and cumulant tesors calculations are also available.
Naive algorithms of moment and cumulant tensors calculations are also available.

```julia
julia> {T <: AbstractFloat}naivemoment(data::Matrix{T}, m::Int = 4)
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# Performance analysis

To analyse the computional time of cumulants vs naivecumulants and moment vs naivemoment, we supply the executable script `comptimes.jl`.
This script returns to a .jld file computional times, given folowing parameters:
To analyse the computational time of cumulants vs naivecumulants and moment vs naivemoment, we supply the executable script `comptimes.jl`.
This script returns to a .jld file computational times, given following parameters:
* `-m (Int)`: cumulant's order, by default `m = 4`,
* `-n (vararg Int)`: numbers of marginal variables, by default `m = 20 24 28`,
* `-t (vararg Int)`: number of realistations of random variable, by defalut `t = 10000`.
Be carefull while using `n`>`4` and large `m`, where naive algorithms might need a large computional time and memory usage. Naive algorithms does not use the block structures, hence they computes and stores a whole cumulant tensor regardless its symmetry. All comparisons performed by this script use one core.
* `-t (vararg Int)`: number of realisations of random variable, by defalut `t = 10000`.
Be careful while using `n`>`4` and large `m`, where naive algorithms might need a large computational time and memory usage. Naive algorithms does not use the block structures, hence they computes and stores a whole cumulant tensor regardless its symmetry. All comparisons performed by this script use one core.

To analyse the computional time of cumulants for diferent block sizes `1 < b =< Int(sqrt(n))`, we supply the executable script `comptimes.jl`.
This script returns to a .jld file computional times, given folowing parameters:
To analyse the computational time of cumulants for different block sizes `1 < b =< Int(sqrt(n))`, we supply the executable script `comptimeblocks.jl`.
This script returns to a .jld file computational times, given following parameters:
* `-m (Int)`: cumulant's order, by default `m = 4`,
* `-n (Int)`: numbers of marginal variables, by default `m = 48`,
* `-t (vararg Int)`: number of realistations of random variable, by defalut `t = 10000 20000`.
Computional times and parameters are saved in the .jld file in /res directory. All comparisons performed by this script use one core.
* `-t (vararg Int)`: number of realisations of random variable, by default `t = 10000 20000`.
Computational times and parameters are saved in the .jld file in /res directory. All comparisons performed by this script use one core.

To analyse the computional time of moment on different numbers of proseses, we supply the executable script `comptimeprocs.jl`.
This script returns to a .jld file computional times, given folowing parameters:
To analyse the computational time of moment on different numbers of processes, we supply the executable script `comptimeprocs.jl`.
This script returns to a .jld file computational times, given following parameters:
* `-m (Int)`: moment's order, by default `m = 4`,
* `-n (Int)`: numbers of marginal variables, by default `m = 50`,
* `-t (Int)`: number of realistations of random variable, by defalut `t = 100000`,
* `-p (Int)`: maximal number of proceses, by default `p = 4`,
* `-t (Int)`: number of realisations of random variable, by default `t = 100000`,
* `-p (Int)`: maximal number of processes, by default `p = 4`,
* `-b (Int)`: blocks size, by default `b = 2`.

All result files are saved in /res directory. To plot a graph run /res/plotcomptimes.jl followed by a `*.jld` file name

For the computional example on data use the following.
For the computational example on data use the following.

The script `gandata.jl` generates `t = 150000000` realisations of `n = 4` dimensional data form the `t`-multivariate distribution with `\nu = 14` degrees of freedom, and theoretical
super-diagonal elements of those cumulants. Rasults are saved in `data/datafortests.jld`
super-diagonal elements of those cumulants. Results are saved in `data/datafortests.jld`

The script `testondata.jl` computes cumulant tensors of order `m = 1 - 6` for `data/datafortests.jld`, results are saved in `data/cumulants.jld`.

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```

To plot super-diagonal elements of those cumulants and their theoretical values from t-student dostrobution pleas run `plotsuperdiag.jl`
To plot super-diagonal elements of those cumulants and their theoretical values from t-student distribution pleas run `plotsuperdiag.jl`


# Citing this work
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