OpenADMIXTURE.jl

This software package is an open-source Julia reimplementation of the ADMIXTURE package. With more efficient multi-threading scheme, it is 8 times faster than the original software. It also supports computation on an Nvidia CUDA GPU. By directly using the data format of the PLINK BED file, the memory usage is 16x-32x smaller than using Float32 or Float64 type.

It estimates ancestry with maximum-likelihood method for a large SNP genotype datasets, where individuals are assumed to be unrelated. The input is binary PLINK 1 BED-formatted file (.bed). Also, you will need an idea of $K$, the number of ancestral populations. If the number of SNPs is too large, you may choose to run on a subset of SNPs selected by their information content, using the sparse $K$-means via feature ranking (SKFR) method.

Installation

This package requires Julia v1.6 or later, which can be obtained from https://julialang.org/downloads/ or by building Julia from the sources in the https://github.com/JuliaLang/julia repository.

The package can be installed by running the following code:

using Pkg
pkg"add https://github.com/kose-y/SparseKmeansFeatureRanking.jl"
pkg"add https://github.com/OpenMendel/OpenADMIXTURE.jl"

For running the examples below, the following are also necessary.

pkg"add SnpArrays CSV DelimitedFiles"

For GPU support, an Nvidia GPU is required. Also, the following package has to be installed:

pkg"add CUDA"

Basic Usage

We first import necessary packages:

using LinearAlgebra, Random, SnpArrays
using OpenADMIXTURE
using CSV, DelimitedFiles

We will use the PLINK file included in the SnpArrays package, whose path is obtained by:

filename = SnpArrays.datadir("EUR_subset.bed");

This file contains information on 54051 single nucleotide polymorphisms (SNP)s of 379 samples. The main driver function for admixture proportion estimation is called run_admixture().

d, clusters, aims = OpenADMIXTURE.run_admixture(filename, 4; T=Float64, use_gpu=false, rng=MersenneTwister(7856))

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 55.143828 seconds (24.93 M allocations: 1.403 GiB, 1.45% gc time, 22.49% compilation time)





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SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[-0.00012052768567257065, 0.0005243291188868516, 0.0740234914604904, 1.0, 0.07759491792130875]], SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[114151.93577995931, 112764.8322387724, 112402.00967340921, 108102.02109867314, 0.0, 0.0]], SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[0.5522037149772232, 0.5265175267226798, 1.0, 0.00022851969219851807, -0.00868396722208467, -0.008645197003287726]], SubArray{Float64, 2, Array{Float64, 3}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[-0.00021765700313519876 0.00010560139303391282 … -0.1017151721365145 0.0; 0.00010560139303391282 -0.0003967945725390119 … 0.4424894271067903 0.0; … ; -0.1017151721365145 0.4424894271067903 … 843.9154171833779 65.48354752887124; 0.0 0.0 … 65.48354752887124 -0.0030486101809490407]], SubArray{Float64, 2, Array{Float64, 3}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[7029.161398740817 3759.8136305049893 … -489.62335872731694 -489.3949460151179; 3759.8136305049893 5717.770656784291 … -527.4797583425097 -527.2632190631304; … ; -489.62335872731694 -527.4797583425097 … 108102.02109867314 108102.00248300146; -489.3949460151179 -527.2632190631304 … 108102.00248300146 -0.01612153787936449]], SubArray{Bool, 1, Matrix{Bool}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[1, 1, 0, 0]], [4; 1; 2; 3;;], SubArray{Int64, 1, Matrix{Int64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[4, 1, 2, 3]], -1.5552194868097581e7, -1.5552193929721253e7), nothing, nothing)

The first argument is the path to the PLINK 1 .bed, and the second argument is the number of populations. The following keyword arguments are supported:

T: Precision of the estimation. Float64 or Float32. Default Float64.
use_gpu: Whether to use GPU for estimation. Default false.
rng: Random number generator. Default Random.GLOBAL_RNG.
prefix: Prefix of the PLINK file only with the SNPs selected using SKFR. The output file is named $(prefix)_$(K)_$(sparsity)aims.bed.
sparsity: Number of SNPs selected by SKFR. Default nothing and skip SKFR.
skfr_tries: Runs SKFR this many times and choose the best clustering. Default 1.
skfr_max_inner_iter: Runs each SKFR for up to this many iterations or until convergence. Default 50.
admix_n_iter: Maximum number of iterations for ADMIXTURE. Default 1000.
admix_rtol: Convergence criteria in terms of relative change in loglikelihood. Default 1e-7.
admix_n_em_iter: Number of EM iterations to get a good initial guess for estimation. Default 5.
Q: Number of steps to be used in quasi-Newton acceleration. Default 3.

The output are:

d: the strucutre to store Admixture data. In particular, d.p stores the allele frequencies and d.q stores the admixture proportions.
clusters: cluster labels of each samples, nothing if sparsity == nothing.
aims: The index of the selected SNPs in the decreasing order of importance, nothing if sparsity == nothing.

To see the allele frequencies of the first allele listed in the .bim file accompanying the .bed file:

d.p

4×54051 Matrix{Float64}:
 0.841704  0.971913  0.991518  0.546057  …  0.920156  0.99999   0.990385
 0.923591  0.992092  0.939205  0.471689     0.942705  0.993918  0.92073
 0.917793  0.982938  0.959373  0.565633     0.947937  0.981754  0.99999
 0.912906  0.999763  0.935531  0.456692     0.968599  0.969226  0.99999

To see the admixture proportion of each sample:

d.q

4×379 Matrix{Float64}:
 0.0709719  0.0344815  0.0801809  0.116321  …  0.098118   1.0e-5   1.0e-5
 0.417541   0.74624    0.714427   0.368537     0.0793005  1.0e-5   1.0e-5
 1.0e-5     0.219269   0.205382   1.0e-5       0.822571   1.0e-5   1.0e-5
 0.511478   1.0e-5     1.0e-5     0.515132     1.0e-5     0.99997  0.99997

The following shows the final loglikelihood of the parameters.

d.ll_new

-1.5552193929721253e7

The following is an example with sparsity defined.

d, clusters, aims = OpenADMIXTURE.run_admixture(filename, 4; T=Float64, use_gpu=false, rng=MersenneTwister(7856), sparsity=10000, admix_rtol=1e-7, prefix="./EUR_subset")

cnt of sparse1:6
./EUR_subset_4_10000aims
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  0.005338 seconds (8 allocations: 768 bytes)
-2.990061270031604e6
-2.98974042373545e6
-2.989726746092522e6
Iteration 10: ll = -2.989726746092522e6, reldiff = 0.00011187862350338979
  0.336451 seconds (8.49 k allocations: 1.975 MiB)


-2.989726746092522e6
  0.051309 seconds (4 allocations: 64 bytes)
  0.001235 seconds (2.66 k allocations: 125.109 KiB)
  0.068019 seconds (4 allocations: 64 bytes)
  0.005074 seconds (8 allocations: 768 bytes)
-2.989726746092522e6
  0.051070 seconds (4 allocations: 64 bytes)
  0.001263 seconds (2.66 k allocations: 125.109 KiB)
  0.067901 seconds (4 allocations: 64 bytes)
  0.005053 seconds (8 allocations: 768 bytes)
-2.989726746092522e6
-2.989633149826683e6
-2.989850885712909e6
Iteration 11: ll = -2.989633149826683e6, reldiff = 3.1305959971517296e-5
  0.326089 seconds (8.49 k allocations: 1.975 MiB)


-2.989633149826683e6
  0.051355 seconds (4 allocations: 64 bytes)
  0.001224 seconds (2.66 k allocations: 125.109 KiB)
  0.069572 seconds (4 allocations: 64 bytes)
  0.005054 seconds (8 allocations: 768 bytes)
-2.989633149826683e6
  0.051855 seconds (4 allocations: 64 bytes)
  0.001561 seconds (2.66 k allocations: 125.109 KiB)
  0.068535 seconds (4 allocations: 64 bytes)
  0.005109 seconds (8 allocations: 768 bytes)
-2.989633149826683e6
-2.9895800598967243e6
-2.9910787931252318e6
Iteration 12: ll = -2.9895800598967243e6, reldiff = 1.7758008189694848e-5
  0.329700 seconds (8.49 k allocations: 1.975 MiB)


-2.9895800598967243e6
  0.053446 seconds (4 allocations: 64 bytes)
  0.001343 seconds (2.66 k allocations: 125.109 KiB)
  0.068643 seconds (4 allocations: 64 bytes)
  0.005082 seconds (8 allocations: 768 bytes)
-2.9895800598967243e6
  0.051077 seconds (4 allocations: 64 bytes)
  0.001326 seconds (2.66 k allocations: 125.109 KiB)
  0.068270 seconds (4 allocations: 64 bytes)
  0.005109 seconds (8 allocations: 768 bytes)
-2.9895800598967243e6
-2.9895361151002464e6
-3.0470678619324937e6
Iteration 13: ll = -2.9895361151002464e6, reldiff = 1.4699320840207977e-5
  0.330408 seconds (8.49 k allocations: 1.975 MiB)


-2.9895361151002464e6
  0.051299 seconds (4 allocations: 64 bytes)
  0.001231 seconds (2.66 k allocations: 125.109 KiB)
  0.068383 seconds (4 allocations: 64 bytes)
  0.005068 seconds (8 allocations: 768 bytes)
-2.9895361151002464e6
  0.051155 seconds (4 allocations: 64 bytes)
  0.001107 seconds (2.66 k allocations: 125.109 KiB)
  0.068226 seconds (4 allocations: 64 bytes)
  0.005089 seconds (8 allocations: 768 bytes)
-2.9895361151002464e6
-2.989495350413259e6
-4.870537010936856e6
Iteration 14: ll = -2.989495350413259e6, reldiff = 1.363579010849405e-5
  0.326845 seconds (8.49 k allocations: 1.975 MiB)


-2.989495350413259e6
  0.051376 seconds (4 allocations: 64 bytes)
  0.001114 seconds (2.66 k allocations: 125.109 KiB)
  0.068882 seconds (4 allocations: 64 bytes)
  0.005072 seconds (8 allocations: 768 bytes)
-2.989495350413259e6
  0.051083 seconds (4 allocations: 64 bytes)
  0.001111 seconds (2.66 k allocations: 125.109 KiB)
  0.068961 seconds (4 allocations: 64 bytes)
  0.005080 seconds (8 allocations: 768 bytes)
-2.989495350413259e6
-2.989455754492594e6
-3.204234679307862e6
Iteration 15: ll = -2.989455754492594e6, reldiff = 1.3245018313781956e-5
  0.328163 seconds (8.49 k allocations: 1.975 MiB)


-2.989455754492594e6
  0.051956 seconds (4 allocations: 64 bytes)
  0.001235 seconds (2.66 k allocations: 125.109 KiB)
  0.068537 seconds (4 allocations: 64 bytes)
  0.005054 seconds (8 allocations: 768 bytes)
-2.989455754492594e6
  0.051440 seconds (4 allocations: 64 bytes)
  0.001220 seconds (2.66 k allocations: 125.109 KiB)
  0.068383 seconds (4 allocations: 64 bytes)
  0.005095 seconds (8 allocations: 768 bytes)
-2.989455754492594e6
-2.9894188142380556e6
-3.005116706744177e6
Iteration 16: ll = -2.9894188142380556e6, reldiff = 1.2356849397354584e-5
  0.329269 seconds (8.60 k allocations: 2.031 MiB)


-2.9894188142380556e6
  0.060329 seconds (4 allocations: 64 bytes)
  0.001310 seconds (2.66 k allocations: 125.109 KiB)
  0.070944 seconds (4 allocations: 64 bytes)
  0.005112 seconds (8 allocations: 768 bytes)
-2.9894188142380556e6
  0.051192 seconds (4 allocations: 64 bytes)
  0.001234 seconds (2.66 k allocations: 125.109 KiB)
  0.069936 seconds (4 allocations: 64 bytes)
  0.005086 seconds (8 allocations: 768 bytes)
-2.9894188142380556e6
-2.9893843473597807e6
-3.0024701291123424e6
Iteration 17: ll = -2.9893843473597807e6, reldiff = 1.152962512671757e-5
  0.341146 seconds (8.49 k allocations: 1.976 MiB)


-2.9893843473597807e6
  0.051523 seconds (4 allocations: 64 bytes)
  0.001348 seconds (2.66 k allocations: 125.109 KiB)
  0.068716 seconds (4 allocations: 64 bytes)
  0.005079 seconds (8 allocations: 768 bytes)
-2.9893843473597807e6
  0.051583 seconds (4 allocations: 64 bytes)
  0.001335 seconds (2.66 k allocations: 125.109 KiB)
  0.067773 seconds (4 allocations: 64 bytes)
  0.005060 seconds (8 allocations: 768 bytes)
-2.9893843473597807e6
-2.9893519062841535e6
-3.2076681927966746e6
Iteration 18: ll = -2.9893519062841535e6, reldiff = 1.0852092557411792e-5
  0.327834 seconds (8.49 k allocations: 1.977 MiB)


-2.9893519062841535e6
  0.051513 seconds (4 allocations: 64 bytes)
  0.001347 seconds (2.66 k allocations: 125.109 KiB)
  0.068581 seconds (4 allocations: 64 bytes)
  0.005065 seconds (8 allocations: 768 bytes)
-2.9893519062841535e6
  0.051358 seconds (4 allocations: 64 bytes)
  0.001324 seconds (2.66 k allocations: 125.109 KiB)
  0.067730 seconds (4 allocations: 64 bytes)
  0.005019 seconds (8 allocations: 768 bytes)
-2.9893519062841535e6
-2.989320160419182e6
-4.216603856297227e6
Iteration 19: ll = -2.989320160419182e6, reldiff = 1.0619647992866069e-5
  0.327422 seconds (8.49 k allocations: 1.979 MiB)


-2.989320160419182e6
  0.053565 seconds (4 allocations: 64 bytes)
  0.001343 seconds (2.66 k allocations: 125.109 KiB)
  0.068597 seconds (4 allocations: 64 bytes)
  0.005200 seconds (8 allocations: 768 bytes)
-2.989320160419182e6
  0.051766 seconds (4 allocations: 64 bytes)
  0.001229 seconds (2.66 k allocations: 125.109 KiB)
  0.068190 seconds (4 allocations: 64 bytes)
  0.005048 seconds (8 allocations: 768 bytes)
-2.989320160419182e6
-2.9892881573209567e6
-3.0190224119707076e6
Iteration 20: ll = -2.9892881573209567e6, reldiff = 1.0705811524963374e-5
  0.330434 seconds (8.49 k allocations: 1.975 MiB)


-2.9892881573209567e6
  0.051287 seconds (4 allocations: 64 bytes)
  0.001235 seconds (2.66 k allocations: 125.109 KiB)
  0.068540 seconds (4 allocations: 64 bytes)
  0.005040 seconds (8 allocations: 768 bytes)
-2.9892881573209567e6
  0.051115 seconds (4 allocations: 64 bytes)
  0.001226 seconds (2.66 k allocations: 125.109 KiB)
  0.068497 seconds (4 allocations: 64 bytes)
  0.005067 seconds (8 allocations: 768 bytes)
-2.9892881573209567e6
-2.989255848399305e6
-3.070369539860443e6
Iteration 21: ll = -2.989255848399305e6, reldiff = 1.0808232579648808e-5
  0.327615 seconds (8.49 k allocations: 1.975 MiB)


-2.989255848399305e6
  0.055029 seconds (4 allocations: 64 bytes)
  0.001283 seconds (2.66 k allocations: 125.109 KiB)
  0.068664 seconds (4 allocations: 64 bytes)
  0.005064 seconds (8 allocations: 768 bytes)
-2.989255848399305e6
  0.051607 seconds (4 allocations: 64 bytes)
  0.001233 seconds (2.66 k allocations: 125.109 KiB)
  0.068599 seconds (4 allocations: 64 bytes)
  0.005057 seconds (8 allocations: 768 bytes)
-2.989255848399305e6
-2.989223200480792e6
-2.721573989958778e7
Iteration 22: ll = -2.989223200480792e6, reldiff = 1.0921754499555953e-5
  0.332062 seconds (8.49 k allocations: 1.975 MiB)


-2.989223200480792e6
  0.051913 seconds (4 allocations: 64 bytes)
  0.001239 seconds (2.66 k allocations: 125.109 KiB)
  0.068575 seconds (4 allocations: 64 bytes)
  0.005057 seconds (8 allocations: 768 bytes)
-2.989223200480792e6
  0.051357 seconds (4 allocations: 64 bytes)
  0.001113 seconds (2.66 k allocations: 125.109 KiB)
  0.067779 seconds (4 allocations: 64 bytes)
  0.004986 seconds (8 allocations: 768 bytes)
-2.989223200480792e6
-2.98918862571243e6
-3.0027735217421465e6
Iteration 23: ll = -2.98918862571243e6, reldiff = 1.1566472639627613e-5
  0.327517 seconds (8.49 k allocations: 1.983 MiB)


-2.98918862571243e6
  0.051341 seconds (4 allocations: 64 bytes)
  0.001012 seconds (2.66 k allocations: 125.109 KiB)
  0.068575 seconds (4 allocations: 64 bytes)
  0.005209 seconds (8 allocations: 768 bytes)
-2.98918862571243e6
  0.051170 seconds (4 allocations: 64 bytes)
  0.001009 seconds (2.66 k allocations: 125.109 KiB)
  0.067795 seconds (4 allocations: 64 bytes)
  0.005078 seconds (8 allocations: 768 bytes)
-2.98918862571243e6
-2.9891504427890005e6
-3.055894439483546e6
Iteration 24: ll = -2.9891504427890005e6, reldiff = 1.2773674802989472e-5
  0.326734 seconds (8.49 k allocations: 1.975 MiB)


-2.9891504427890005e6
  0.052237 seconds (4 allocations: 64 bytes)
  0.001021 seconds (2.66 k allocations: 125.109 KiB)
  0.068584 seconds (4 allocations: 64 bytes)
  0.005008 seconds (8 allocations: 768 bytes)
-2.9891504427890005e6
  0.051356 seconds (4 allocations: 64 bytes)
  0.001006 seconds (2.66 k allocations: 125.109 KiB)
  0.067855 seconds (4 allocations: 64 bytes)
  0.005038 seconds (8 allocations: 768 bytes)
-2.9891504427890005e6
-2.9891102235109448e6
-2.9937728315902813e6
Iteration 25: ll = -2.9891102235109448e6, reldiff = 1.3455086595836446e-5
  0.327716 seconds (8.49 k allocations: 1.975 MiB)


-2.9891102235109448e6
  0.051503 seconds (4 allocations: 64 bytes)
  0.000797 seconds (2.66 k allocations: 125.109 KiB)
  0.072497 seconds (4 allocations: 64 bytes)
  0.005026 seconds (8 allocations: 768 bytes)
-2.9891102235109448e6
  0.051099 seconds (4 allocations: 64 bytes)
  0.000790 seconds (2.66 k allocations: 125.109 KiB)
  0.067850 seconds (4 allocations: 64 bytes)
  0.005050 seconds (8 allocations: 768 bytes)
-2.9891102235109448e6
-2.989069852298082e6
-2.993139156894906e6
Iteration 26: ll = -2.989069852298082e6, reldiff = 1.3506097080447741e-5
  0.330044 seconds (8.49 k allocations: 1.975 MiB)


-2.989069852298082e6
  0.051596 seconds (4 allocations: 64 bytes)
  0.000912 seconds (2.66 k allocations: 125.109 KiB)
  0.068444 seconds (4 allocations: 64 bytes)
  0.005081 seconds (8 allocations: 768 bytes)
-2.989069852298082e6
  0.051489 seconds (4 allocations: 64 bytes)
  0.000898 seconds (2.66 k allocations: 125.109 KiB)
  0.068667 seconds (4 allocations: 64 bytes)
  0.005089 seconds (8 allocations: 768 bytes)
-2.989069852298082e6
-2.9890318651039726e6
-2.991710920354535e6
Iteration 27: ll = -2.9890318651039726e6, reldiff = 1.2708700694979335e-5
  0.327652 seconds (8.49 k allocations: 1.975 MiB)


-2.9890318651039726e6
  0.051948 seconds (4 allocations: 64 bytes)
  0.000903 seconds (2.66 k allocations: 125.109 KiB)
  0.068620 seconds (4 allocations: 64 bytes)
  0.005098 seconds (8 allocations: 768 bytes)
-2.9890318651039726e6
  0.051546 seconds (4 allocations: 64 bytes)
  0.000907 seconds (2.66 k allocations: 125.109 KiB)
  0.068082 seconds (4 allocations: 64 bytes)
  0.005061 seconds (8 allocations: 768 bytes)
-2.9890318651039726e6
-2.9889978041921854e6
-2.9892098593712384e6
Iteration 28: ll = -2.9889978041921854e6, reldiff = 1.1395298987895992e-5
  0.327987 seconds (8.49 k allocations: 1.975 MiB)


-2.9889978041921854e6
  0.051315 seconds (4 allocations: 64 bytes)
  0.001014 seconds (2.66 k allocations: 125.109 KiB)
  0.068676 seconds (4 allocations: 64 bytes)
  0.005056 seconds (8 allocations: 768 bytes)
-2.9889978041921854e6
  0.051113 seconds (4 allocations: 64 bytes)
  0.000999 seconds (2.66 k allocations: 125.109 KiB)
  0.068374 seconds (4 allocations: 64 bytes)
  0.005035 seconds (8 allocations: 768 bytes)
-2.9889978041921854e6
-2.9889710379184415e6
-2.9892181158235935e6
Iteration 29: ll = -2.9889710379184415e6, reldiff = 8.954932555118614e-6
  0.327091 seconds (8.49 k allocations: 1.975 MiB)


-2.9889710379184415e6
  0.051287 seconds (4 allocations: 64 bytes)
  0.001010 seconds (2.66 k allocations: 125.109 KiB)
  0.067741 seconds (4 allocations: 64 bytes)
  0.005077 seconds (8 allocations: 768 bytes)
-2.9889710379184415e6
  0.051320 seconds (4 allocations: 64 bytes)
  0.001005 seconds (2.66 k allocations: 125.109 KiB)
  0.068327 seconds (4 allocations: 64 bytes)
  0.005077 seconds (8 allocations: 768 bytes)
-2.9889710379184415e6
-2.9889486095322985e6
-2.9900355066040237e6
Iteration 30: ll = -2.9889486095322985e6, reldiff = 7.503714776226964e-6
  0.326470 seconds (8.49 k allocations: 1.975 MiB)


-2.9889486095322985e6
  0.051307 seconds (4 allocations: 64 bytes)
  0.001011 seconds (2.66 k allocations: 125.109 KiB)
  0.068545 seconds (4 allocations: 64 bytes)
  0.005031 seconds (8 allocations: 768 bytes)
-2.9889486095322985e6
  0.051066 seconds (4 allocations: 64 bytes)
  0.000996 seconds (2.66 k allocations: 125.109 KiB)
  0.068230 seconds (4 allocations: 64 bytes)
  0.005030 seconds (8 allocations: 768 bytes)
-2.9889486095322985e6
-2.988929193837599e6
-2.9900550381234307e6
Iteration 31: ll = -2.988929193837599e6, reldiff = 6.495827542066974e-6
  0.329288 seconds (8.49 k allocations: 1.975 MiB)


-2.988929193837599e6
  0.051494 seconds (4 allocations: 64 bytes)
  0.001013 seconds (2.66 k allocations: 125.109 KiB)
  0.068373 seconds (4 allocations: 64 bytes)
  0.005045 seconds (8 allocations: 768 bytes)
-2.988929193837599e6
  0.051083 seconds (4 allocations: 64 bytes)
  0.001001 seconds (2.66 k allocations: 125.109 KiB)
  0.067739 seconds (4 allocations: 64 bytes)
  0.005013 seconds (8 allocations: 768 bytes)
-2.988929193837599e6
-2.988913407219005e6
-2.9889200662938342e6
Iteration 32: ll = -2.9889200662938342e6, reldiff = 3.053783871318594e-6
  0.326375 seconds (8.49 k allocations: 1.975 MiB)


-2.9889200662938342e6
  0.051381 seconds (4 allocations: 64 bytes)
  0.000797 seconds (2.66 k allocations: 125.109 KiB)
  0.070106 seconds (4 allocations: 64 bytes)
  0.005042 seconds (8 allocations: 768 bytes)
-2.9889200662938342e6
  0.051473 seconds (4 allocations: 64 bytes)
  0.001423 seconds (2.66 k allocations: 125.109 KiB)
  0.069658 seconds (4 allocations: 64 bytes)
  0.005092 seconds (8 allocations: 768 bytes)
-2.9889200662938342e6
-2.9888740258513074e6
-2.9888789198555816e6
Iteration 33: ll = -2.9888789198555816e6, reldiff = 1.3766322731964776e-5
  0.332496 seconds (8.60 k allocations: 2.032 MiB)


-2.9888789198555816e6
  0.051510 seconds (4 allocations: 64 bytes)
  0.000801 seconds (2.66 k allocations: 125.109 KiB)
  0.068655 seconds (4 allocations: 64 bytes)
  0.005081 seconds (8 allocations: 768 bytes)
-2.9888789198555816e6
  0.051496 seconds (4 allocations: 64 bytes)
  0.000782 seconds (2.66 k allocations: 125.109 KiB)
  0.068511 seconds (4 allocations: 64 bytes)
  0.005005 seconds (8 allocations: 768 bytes)
-2.9888789198555816e6
-2.9888553511574874e6
-2.988873849177302e6
Iteration 34: ll = -2.988873849177302e6, reldiff = 1.696515120117397e-6
  0.327016 seconds (8.49 k allocations: 1.976 MiB)


-2.988873849177302e6
  0.051493 seconds (4 allocations: 64 bytes)
  0.000796 seconds (2.66 k allocations: 125.109 KiB)
  0.068231 seconds (4 allocations: 64 bytes)
  0.005037 seconds (8 allocations: 768 bytes)
-2.988873849177302e6
  0.051156 seconds (4 allocations: 64 bytes)
  0.000784 seconds (2.66 k allocations: 125.109 KiB)
  0.068227 seconds (4 allocations: 64 bytes)
  0.004956 seconds (8 allocations: 768 bytes)
-2.988873849177302e6
-2.9888501509662215e6
-2.9888497143354164e6
Iteration 35: ll = -2.9888497143354164e6, reldiff = 8.074894794258681e-6
  0.326043 seconds (8.49 k allocations: 1.977 MiB)


-2.9888497143354164e6
  0.051530 seconds (4 allocations: 64 bytes)
  0.000795 seconds (2.66 k allocations: 125.109 KiB)
  0.068550 seconds (4 allocations: 64 bytes)
  0.005018 seconds (8 allocations: 768 bytes)
-2.9888497143354164e6
  0.051266 seconds (4 allocations: 64 bytes)
  0.000788 seconds (2.66 k allocations: 125.109 KiB)
  0.068305 seconds (4 allocations: 64 bytes)
  0.005013 seconds (8 allocations: 768 bytes)
-2.9888497143354164e6
-2.98884770192568e6
-2.98884653275144e6
Iteration 36: ll = -2.98884653275144e6, reldiff = 1.0644844272742283e-6
  0.328312 seconds (8.49 k allocations: 1.975 MiB)


-2.98884653275144e6
  0.051698 seconds (4 allocations: 64 bytes)
  0.000808 seconds (2.66 k allocations: 125.109 KiB)
  0.068499 seconds (4 allocations: 64 bytes)
  0.005027 seconds (8 allocations: 768 bytes)
-2.98884653275144e6
  0.051365 seconds (4 allocations: 64 bytes)
  0.000783 seconds (2.66 k allocations: 125.109 KiB)
  0.068251 seconds (4 allocations: 64 bytes)
  0.005036 seconds (8 allocations: 768 bytes)
-2.98884653275144e6
-2.9888461026714854e6
-2.9888459670782355e6
Iteration 37: ll = -2.9888459670782355e6, reldiff = 1.8926137505086115e-7
  0.326842 seconds (8.49 k allocations: 1.979 MiB)


-2.9888459670782355e6
  0.051509 seconds (4 allocations: 64 bytes)
  0.000800 seconds (2.66 k allocations: 125.109 KiB)
  0.068580 seconds (4 allocations: 64 bytes)
  0.005017 seconds (8 allocations: 768 bytes)
-2.9888459670782355e6
  0.051076 seconds (4 allocations: 64 bytes)
  0.000784 seconds (2.66 k allocations: 125.109 KiB)
  0.068157 seconds (4 allocations: 64 bytes)
  0.005003 seconds (8 allocations: 768 bytes)
-2.9888459670782355e6
-2.9888457179705338e6
-2.9888456882726927e6
Iteration 38: ll = -2.9888456882726927e6, reldiff = 9.328200442854993e-8
 12.511960 seconds (325.18 k allocations: 74.353 MiB)





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[0.16076233081185012; 0.046115945456698504; … ; -0.17815723178570345; -0.017383501184341836;;], [685.7862289240434 0.4600047136279448 … -110.60949016702281 76.78131250930491; 0.4600047136279447 -0.0005853034954839992 … 0.44816500634423034 -0.0; … ; -110.60949016702281 0.44816500634423034 … 543.1400346027904 257.21271509888857; 76.78131250930491 -0.0 … 257.21271509888857 -0.006306245873800798;;;], [2163.1821361956468 144.60904435156553 … -2001.9795123398549 161.09418147682655; 144.60904435156553 755.2723625330268 … -275.52072997020105 -130.90032710809507; … ; -2001.9795123398549 -275.52072997020105 … 21840.790994511528 19838.90594006875; 161.09418147682655 -130.90032710809507 … 19838.90594006875 -0.0138550945177498;;;], Bool[0; 1; 0; 0;;], SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[0.0, 0.0, 0.0, 0.0]], SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[1047.3154837338877, 1708.5153389919187, 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257.21271509888857 -0.006306245873800798]], SubArray{Float64, 2, Array{Float64, 3}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[2163.1821361956468 144.60904435156553 … -2001.9795123398549 161.09418147682655; 144.60904435156553 755.2723625330268 … -275.52072997020105 -130.90032710809507; … ; -2001.9795123398549 -275.52072997020105 … 21840.790994511528 19838.90594006875; 161.09418147682655 -130.90032710809507 … 19838.90594006875 -0.0138550945177498]], SubArray{Bool, 1, Matrix{Bool}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[0, 1, 0, 0]], [1; 2; 3; 4;;], SubArray{Int64, 1, Matrix{Int64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[1, 2, 3, 4]], -2.9888459670782355e6, -2.9888456882726927e6), [1, 2, 2, 2, 2, 2, 2, 2, 2, 2  …  1, 4, 2, 1, 2, 2, 2, 2, 1, 1], [5800, 5691, 5677, 5688, 5775, 5769, 5668, 5673, 5674, 5675  …  29537, 14293, 30551, 23892, 35746, 35747, 3783, 40709, 50996, 4707])

The following shows the clustering result of the samples:

clusters

379-element Vector{Int64}:
 1
 2
 2
 2
 2
 2
 2
 2
 2
 2
 1
 2
 2
 ⋮
 2
 2
 1
 4
 2
 1
 2
 2
 2
 2
 1
 1

And the following shows the SNPs selected.

aims

10000-element Vector{Int64}:
  5800
  5691
  5677
  5688
  5775
  5769
  5668
  5673
  5674
  5675
  5676
  5679
  5683
     ⋮
 12387
 21962
 29537
 14293
 30551
 23892
 35746
 35747
  3783
 40709
 50996
  4707

The allele frequencies can be shown as in:

d.p

4×10000 Matrix{Float64}:
 0.794601  0.869963  0.973735  0.989637  …  0.832251  0.932757  0.99999
 0.629542  0.988284  0.99999   0.99999      0.639828  0.859647  0.887711
 0.795333  0.900406  0.85795   0.916634     0.978529  0.959927  0.99999
 0.731412  0.891075  0.984187  0.997961     0.76765   0.810749  0.99999

!!! The order of alleles is in the order of index (as in sort(aim)). This can be verified by checking the .bim file generated along with the newly filtered .bed file.

The admixture proportions can be viewed by:

d.q

4×379 Matrix{Float64}:
 0.582215   1.0e-5    1.0e-5    0.447532   …  1.0e-5     0.99997  0.99997
 0.140929   0.412588  0.506956  0.0280593     0.0519387  1.0e-5   1.0e-5
 0.0540219  0.133946  0.103898  0.0626305     0.233832   1.0e-5   1.0e-5
 0.222834   0.453456  0.389137  0.461778      0.71422    1.0e-5   1.0e-5

d.ll_new

-2.9888456882726927e6

Multi-threading

Multi-threading is supported by default if the julia session is launched with multiple threads. For example, one may launch Julia with 8 thread using the following command:

julia -t 8

GPU support

GPU is enabled by setting the keyword argument use_gpu to true. The parts computing gradients and Hessians of the loglikelihood is moved to GPU.