NgsAdmixv2

From software
Revision as of 09:50, 24 June 2019 by Sonia4 (talk | contribs) (→‎Bibtex)
Jump to navigation Jump to search

This page contains information about the program called NGSadmix, which is a very nice tool for estimating individual admixture proportions from NGS data. It is based on genotype likelihoods and works well for medium and low coverage NGS data. It is a fancy multithreaded c/c++ program which makes it useful for large datasets.

The great thing about NGSadmix is that it is a new method that takes the uncertainty introduced in NGS sequencing data into account when inferring an individual's ancestry by using genotype likelihoods that considers the uncertainty caused by unobserved genotypes.

The method was published in 2013 and can be found here: [1]

Citation

http://www.genetics.org/content/early/2013/09/03/genetics.113.154138.full.pdf

Skotte, L., Korneliussen, T. S., & Albrechtsen, A. (2013). Estimating individual admixture proportions from next generation sequencing data. Genetics, 195(3), 693–702. doi:10.1534/genetics.113.154138

==Bibtex==
% 24026093 
@Article{pmid24026093,
   Author="Skotte, L.  and Korneliussen, T. S.  and Albrechtsen, A. ",
   Title="{{E}stimating {I}ndividual {A}dmixture {P}roportions from {N}ext {G}eneration {S}equencing {D}ata}",
   Journal="Genetics",
   Year="2013",
   Pages=" ",
   Month="Sep"
}

Download

The latest version is 32 from June 25 2013 and can be downloaded here: [2].

Older Versions

Older versions can be found here: [3].

  • v32 june 25-2013; modified code such that it now compiles on OSX
  • v31 june 24-2013; First public version.

Installation


NGSadmix can be installed independently or as a part of ANGSD.

1) NGSadmix Independent Installation:


Login to your server using ssh on your terminal window.
Create the directory where you will install your software and enter it, such as 
mkdir ~/Software
cd ~/Software

Download the source code:
wget https://raw.githubusercontent.com/ANGSD/angsd/master/misc/ngsadmix32.cpp 

Configure, Compile and Install:
g++ ngsadmix32.cpp -O3 -lpthread -lz -o NGSadmix

Delete source code to save space:
rm ~/Software/ngsadmix32.cpp



Parameters

./NGSadmix


*** see doc for options/possible ranges/ and further explanation

Arguments:
	-likes .beagle format filename with genotype likelihoods
	-K Number of ancestral populations
Optional:
	-fname Ancestral population frequencies
	-qname Admixture proportions
	-outfiles Prefix for output files
	-printInfo print ID and mean maf for the SNPs that were analysed
Setup:
	-seed Seed for initial guess in EM
	-P Number of threads
	-method If 0 no acceleration of EM algorithm
	-misTol Tolerance for considering site as missing
Stop chriteria:
	-tolLike50 Loglikelihood difference in 50 iterations
	-tol Tolerance for convergence
	-dymBound Use dymamic boundaries (1: yes (default) 0: no)
	-maxiter Maximum number of EM iterations
Filtering
	-minMaf Minimum minor allele frequency
	-minLrt Minimum likelihood ratio value for maf>0
	-minInd Minumum number of informative individuals

NB All parameters are set using -par value. So to get additional information you would write -printInfo 1.

Input Files

Input files are contains genotype likelihoods in genotype likelihood beagle input file format [4]. We recommend ANGSD for easy transformation of Next-generation sequencing data to beagle format. See Creation of Beagle files with ANGSD

Example of a beagle genotype likelihood input file for 3 individuals.

marker       allele1  allele2   Ind0      Ind0    Ind0     Ind1     Ind1     Ind1     Ind2     Ind2     Ind2
1_14000023      1       0       0.941    0.058    0.000    0.799    0.199    0.001    0.666    0.333    0.001 
1_14000072      2       3       0.709    0.177    0.112    0.941    0.058    0.000    0.665    0.332    0.001
1_14000113      0       2       0.855    0.106    0.037    0.333    0.333    0.333    0.799    0.199    0.000 
1_14000202      2       0       0.835    0.104    0.060    0.799    0.199    0.000    0.333    0.333    0.333
...

Column 1:The marker name (the information is not atually used)

Column 2 and 3: the major and minor allele (these two columns are not used within the program and can contain whatever dummy value).

The rest of the colums are the genotypes likelihoods (not in log space). For each individual we have 3 columns. Note that the above values sum to one per sites for each individuals. This is just a normalization of the genotype likelihoods in order to avoid underflow problems in the beagle software it does not mean that they are genotype probabilities.

The input file is allowed to be compressed with gzip.


Output Files

Program outputs 3 files.

  1. PREFIX.log
  2. PREFIX.fopt.gz
  3. PREFIX.qopt
  • The .log file contains log information of the run. Commandline used for running the program, what the likelihood is every 50 iterations, and finally how long it took to do the run.
  • The .fopt.gz file is an compressed file, which contains an estimate of the frequency for each site for all populations.
  • The .qopt file contains the admixture proportions for all individuals.

Examples of the output files are found below.


Log file (.log)

Contents of the file log file

	-> Dumping file: tskSim/tsk6GL.beagle.s1.log
	-> Dumping file: tskSim/tsk6GL.beagle.s1.filter
Input: lname=tskSim/tsk6GL.beagle nPop=3, fname=(null) qname=(null) outfiles=tskSim/tsk6GL.beagle.s1
Setup: seed=1 nThreads=10 method=1
Convergence: maxIter=2000 tol=0.000000 tolLike50=0.010000 dymBound=0
Filters: misTol=0.050000 minMaf=0.000000 minLrt=0.000000 minInd=0
Input file has dim: nsites=100000 nind=75
Input file has dim (AFTER filtering): nsites=100000 nind=75
iter[start] like is=9299805.984931
iter[50] like is=-6531138.892608 thres=0.002800
iter[100] like is=-6528710.773349 thres=0.001289
iter[150] like is=-6528405.896951 thres=0.001211
iter[200] like is=-6528306.803820 thres=0.000420
iter[250] like is=-6528277.160993 thres=0.000546
iter[300] like is=-6528271.925055 thres=0.000033
iter[350] like is=-6528271.177692 thres=0.000008
iter[400] like is=-6528270.876315 thres=0.000005
iter[450] like is=-6528270.772894 thres=0.000140
iter[500] like is=-6528270.747721 thres=0.000002
iter[550] like is=-6528270.740654 thres=0.000002
Convergence achived because log likelihooditer difference for 50 iteraction is less than 0.010000
best like=-6528270.740654 after 550 iterations
	-> Dumping file: tskSim/tsk6GL.beagle.s1.qopt
	-> Dumping file: tskSim/tsk6GL.beagle.s1.fopt.gz
	[ALL done] cpu-time used =  671.82 sec
	[ALL done] walltime used =  114.00 sec

Allele frequency ouput (.fopt)

Each column correponds to the estimated allele frequencies for each population and each line is a SNP

Example of a .fopt file for -K 3

...
0.75331646167520038837 0.51190946588401886608 0.50134051056701267601 
0.99999999900000002828 0.80165850924934911603 0.97470665326916294813 
0.99999999900000002828 0.89560828888972687789 0.88062641752218895341 
0.99999999900000002828 0.99999999900000002828 0.86109994249930577048 
0.70560445653074521655 0.78994686954000448154 0.93076614062025020413 
0.99999999900000002828 0.88878537780630872955 0.92662857068149151463 
0.05322676762098016434 0.22871739860812340117 0.17394852600322696645 
0.00000000100000000000 0.27428885137150410545 0.19029599645013275944 
0.57086006389212373691 0.42232596591112880891 0.74080063581586474974 
0.77359733910003525281 0.47380864146016693494 0.72073560889718923939 
0.49946404159405927148 0.21684946347150244050 0.15201985942558055021 
0.41802171086717271331 0.55490556205954566504 0.85691127728452165524 
0.77095213528720529794 0.60074618451005279418 0.70219544996184157792 
0.26517850405564091787 0.48500265408436060710 0.85432254709914456914 
0.80055081986260245852 0.74423201242010783574 0.87110476762969968334 
0.30563054476851375663 0.05233529475348827620 0.25911912824038613179 
0.51084997710733415222 0.62263692178557350498 0.50738250264097506381 
0.64790272562679740442 0.91230541484222271720 0.73015721390331478347 
0.07124629651164265942 0.37896482494356753534 0.29218012479334326548 
0.00000000100000000000 0.26969100790961914038 0.28395781874856029781 
0.97074775756045073027 0.79093498372643300520 0.64006920058897498471 
0.64661948716978157048 0.84130009558421925409 0.76730057769159087933 
0.86990900887920663553 0.79410745692063922085 0.69416721874359499367 
0.34956069940263900797 0.27773038429396151860 0.25923476721423144298 
0.77739744690560164120 0.51272232330145017798 0.53888718200036844763 
0.35431569298041332150 0.20022780744715171219 0.43176580786072032980 
0.91858160919413811563 0.99999999900000002828 0.93584179237779097082 
0.90339823126358831384 0.94729687041528465308 0.84358671720630329371 
0.87068129661127857677 0.65267891763324525911 0.59315740612546075106 
0.24102496839012735319 0.42777100607917967201 0.39594098602469629533 
0.99999999900000002828 0.99999999900000002828 0.78549330115836857313 
0.15386277372522660922 0.18035502891341426146 0.26583557049163752950 
0.22456748943597096280 0.25110807159057474403 0.17244618960511531869 
0.74816053649164548922 0.54769319158907958656 0.44532166240679449398 
0.76350303696805599252 0.86547244122202959815 0.94111974586621383043 
0.40940400475566068872 0.67767095908245833513 0.40793761498610620064 
0.85389765162910868934 0.78901563183853873351 0.93614065916219291186 
0.54108661985898742763 0.61895909938546000983 0.88522763262549941654 
0.99051495581855464323 0.78855843624128341141 0.77646441702623147929 
0.51133721761171413434 0.74521610846562824637 0.32689774480116673416 
0.66618479413060949224 0.67891474309775079465 0.80762116232856140385 
0.81793598261160704865 0.77752326447671193943 0.95349025244041396565 
0.82120324647844433752 0.99999999900000002828 0.89800731971059466474 
...

Use the "-printInfo 1" option to get the position of the lines in the fopt file if some sites have been flltered from the analysis (-minMaf, minInd, minLRT etc)

Admixture proportion output file (.qopt)

Infered admixture proporsions. Each line is an individual and each column is a population.

Contents of the qopt file # cat tsk48GL.beagle.gz.s1.qopt

0.00254460532103031574 0.00108987228478324210 0.99636552239418640919 
0.00000015905647541105 0.00000000100000000000 0.99999983994352459327 
0.00034770382567266174 0.02639209238328452459 0.97326020379104283275 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00000467398081877176 0.00000000100000000000 0.99999532501918120264 
0.00000000907496942853 0.00585150933779484805 0.99414848158723567728 
0.00515826525767644137 0.01138897436535154552 0.98345276037697204607 
0.03914841746468285949 0.00000000100000000000 0.96085158153531713410 
0.00000000100000000000 0.00629199375758324100 0.99370800524241675866 
0.00771173022930659625 0.00000154720357311662 0.99228672256712036059 
0.00000000100000000000 0.00075135345721917719 0.99924864554278081119 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000005468413042120 0.00087279924180633879 0.99912714607406327705 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00712941313019542066 0.00118955677574110528 0.99168103009406338710 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00165385222968000606 0.99834614677032007535 
0.00000000100000000000 0.00006297763597355473 0.99993702136402651259 
0.00519087111391381209 0.00000000100000000000 0.99480912788608621966 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00202872783596746379 0.00000000100000000000 0.99797127116403261393 
0.00876424336999809782 0.00949457841911990376 0.98174117821088191516 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.01820430093358888640 0.00000694033297829119 0.98178875873343274261 
0.00351013812443964728 0.00000020340562512923 0.99648965846993520223 
0.00771897550085272680 0.00605259705033356268 0.98622842744881378252 
0.00600595292580561029 0.00000000100000000000 0.99399404607419439284 
0.01454910070242997067 0.00543457657939076105 0.98001632271817917808 
0.02567862615486414535 0.00160921436783232220 0.97271215947730349516 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00000000100000000000 0.00001041560507852223 0.99998958339492149960 
0.00000000100000000000 0.01383432553657116572 0.98616567346342876021 
0.00343840097404925389 0.00000000100000000000 0.99656159802595079000 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00051244065751142103 0.00404846039501185508 0.99543909894747661937 
0.02003953974792894652 0.00000004934009128878 0.97996041091197982897 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00000000100000000000 0.00000000100000000000 0.99999999799999994554 
0.02176809890633762956 0.00000000100000000000 0.97823190009366245423 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.01563096189267457192 0.00970868396771427770 0.97466035413961116252 
0.00000000100000000000 0.00000000100000000000 0.99999999800000005656 
0.00002540964943070735 0.00000000100000000000 0.99997458935056915408 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99501476026684787524 0.00000000100000000000 0.00498523873315206718 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99520671498720802983 0.00479241730266987201 0.00000086771012207898 
0.95884374919730619435 0.00000000100000000000 0.04115624980269377842 
0.99002104218586972628 0.00000000100000000000 0.00997895681413022567 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99999999770925251941 0.00000000129074746013 0.00000000100000000000 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.98980053177767901573 0.00000005577971952226 0.01019941244260143612 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99999785004878083416 0.00000000100000000000 0.00000214895121910354 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99220030909132039820 0.00000000100000000000 0.00779968990867968733 
0.99999996788621803301 0.00000000100000000000 0.00000003111378189772 
0.99736783433174225344 0.00255940950853666971 0.00007275615972113173 
0.99998096423035520708 0.00000000574461213317 0.00001903002503262207 
0.99711097909957713270 0.00288887008493822353 0.00000015081548462101 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99769262012085335734 0.00000000100000000000 0.00230737887914652393 
0.99999820787375570674 0.00000000433914936351 0.00000178778709493472 
0.98047422489554170166 0.00012980111977614777 0.01939597398468214523 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.98208006049140339488 0.00000000100000000000 0.01791993850859651197 
0.97530298545159921364 0.00000000100000000000 0.02469701354840085974 
0.99657542812406740840 0.00000000100000000000 0.00342457087593254226 
0.99954556420189066834 0.00045443479810919004 0.00000000100000000000 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99531584565237773976 0.00410740812985130408 0.00057674621777084644 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.99878572597704817770 0.00000000100000000000 0.00121427302295177490 
0.98571687209123504125 0.00400077401169816448 0.01028235389706666329 
0.99027397554762419674 0.00840892511494516215 0.00131709933743062008 
0.99999993504923445631 0.00000000100000000000 0.00000006395076564386 
0.95946639819101930957 0.00000000100000000000 0.04053360080898076034 
0.99999999800000005656 0.00000000100000000000 0.00000000100000000000 
0.98414939425022363029 0.01585059024074651421 0.00000001550902978739 
0.99999999622245250297 0.00000000277754757396 0.00000000100000000000 
0.99525652466242930938 0.00000001683386219288 0.00474345850370842034 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99999999799999994554 0.00000000100000000000 0.00000000100000000000 
0.99999965447943561792 0.00000000100000000000 0.00000034452056438734 
0.99864814059528783652 0.00135185840471215468 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000001076370464123 0.99999998823629543399 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000100000000000 0.99999999800000005656 0.00000000100000000000 
0.00000000100000000000 0.99999986659623718577 0.00000013240376283687 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000099999999999 0.99999999799999994554 0.00000000099999999999 
0.00000000100000000000 0.99632783404679736705 0.00367216495320256799 
0.00000000100000000000 0.99999999799999994554 0.00000000100000000000 
0.00000000099999999999 0.99999999800000005656 0.00000000099999999999 
0.35919621347731411909 0.32381633362411937904 0.31698745289856661289 
0.31048363757756514136 0.30902410742704566893 0.38049225499538924522 
0.36341140678787386964 0.33678307361394943520 0.29980551959817652863 
0.34550713774447228133 0.34037087985425079628 0.31412198240127681137 
0.34705579219215104692 0.35218792485566730033 0.30075628295218165276 
0.33646039412306782967 0.32632754139618752598 0.33721206448074481088 
0.31881401220765009930 0.34885621407165418040 0.33232977372069577582 
0.34999374672052624424 0.33030931848049555066 0.31969693479897826061 
0.33152251818028721786 0.32339147992992234304 0.34508600188979043910 
0.31959998197389311025 0.33152491237148390413 0.34887510565462298562 
0.34724548642936803322 0.31809475756470984020 0.33465975600592196004 
0.33378069767858009609 0.33223636639277298599 0.33398293592864686241 
0.32023090400419051971 0.33179989332826043125 0.34796920266754916007 
0.35205158009776410521 0.33547091017851976558 0.31247750972371612921 
0.34291063455495451873 0.31853488093100223999 0.33855448451404313026 
0.31929132670383747472 0.32755905579808902717 0.35314961749807355362 
0.34114474726121107873 0.34607065583774476725 0.31278459690104404300 
0.33725705347681012025 0.32910919226619778089 0.33363375425699209886 
0.33918213722968154622 0.32278745806952213737 0.33803040470079642743 
0.33788659799509024317 0.34692305448657090317 0.31519034751833896468 
0.35876135180876589370 0.33843260979944000955 0.30280603839179404124 
0.34721570614318736370 0.34395335873604998556 0.30883093512076259524 
0.34165097731337079612 0.32814110943000784903 0.33020791325662146587 
0.33922542743931027864 0.32639619830977489867 0.33437837425091476717 
0.34461619391735059947 0.33133174331942943924 0.32405206276321996128 
0.34277551565686120716 0.32746953398981676342 0.32975495035332202942 
0.33842982221926010133 0.31224638933762871584 0.34932378844311123833 
0.34443810815667752490 0.32640113997211872565 0.32916075187120380496 
0.31723258569943768581 0.34955203711397470068 0.33321537718658750249 
0.35394053250677920408 0.33291498389624818444 0.31314448359697255597 
0.33504517457864940733 0.34188143503173562543 0.32307339038961496724 
0.33240938202788244960 0.34671459781042585080 0.32087602016169164409 
0.31745792352948248860 0.33722730677636020280 0.34531476969415725309 
0.33098224522913716195 0.33312298285105168549 0.33589477191981131909 
0.34090909280056919117 0.32423671881295645925 0.33485418838647434958 
0.32985465610121944557 0.32124851771265583444 0.34889682618612483100 
0.33525528582568764335 0.31967441393853385234 0.34507030023577844879 
0.33823045943274382408 0.33932114218381809190 0.32244839838343819505 
0.34374166546335593875 0.33527470302709477812 0.32098363150954922762 
0.32177399566214615056 0.34277626859597382092 0.33544973574188002852 
0.34915111840878915173 0.33072079898488659921 0.32012808260632419355 
0.31132788816691708833 0.32844185942225745389 0.36023025241082540227 
0.33067206673512555826 0.34601992411426535368 0.32330800915060908807 
0.31337643746173032833 0.33835721859074846529 0.34826634394752131740 
0.32762993090356395953 0.34856645453438306337 0.32380361456205303261 
0.33558678075595765877 0.34449062515269568419 0.31992259409134682357 
0.33433652456352996873 0.32868556951924504661 0.33697790591722515119 
0.32115036446030281736 0.35050069566489522321 0.32834893987480190392 
0.32524569843140932468 0.33953480032298033464 0.33521950124561045170 
0.33520046917246110185 0.31124301814705779279 0.35355651268048110536 
0.51565151014669796670 0.00027180960956305278 0.48407668024373901039 
0.51978922685130035664 0.01333903580405943964 0.46687173734464021413 
0.48123878312258933088 0.00648941795451128591 0.51227179892289931296 
0.48941833241028537271 0.00512373007237581363 0.50545793751733880672 
0.48421136927686320162 0.00600153379448644612 0.50978709692865020742 
0.53246468447754891073 0.00000000100000000000 0.46753531452245111755 
0.50637710620505416159 0.01564455874020675985 0.47797833505473913407 
0.49416813414210103428 0.00000000100000000000 0.50583186485789899400 
0.51328206693115174808 0.00000000100000000000 0.48671793206884833571 
0.50420356848059588728 0.00779539942445491366 0.48800103209494921641 
0.51589943710654184716 0.00000000100000000000 0.48410056189345807010 
0.46643393286795947761 0.00024627960390510270 0.53331978752813535838 
0.50134326603627110686 0.00000000100000000000 0.49865673296372897694 
0.52516062216154979492 0.00887494007947397384 0.46596443775897622430 
0.50553300231497877437 0.00610541400596737328 0.48836158367905380118 
0.48505848053244243756 0.00412236953776635561 0.51081914992979127188 
0.50419106430093152404 0.00671707921410998055 0.48909185648495850929 
0.51266037905765671212 0.00565931340437971983 0.48168030753796364785 
0.50479638826213368841 0.00082364200405335279 0.49437996973381287402 
0.48963785250324892706 0.00000000100000000000 0.51036214649675115673 
0.49861342640726780129 0.00000000100000000000 0.50138657259273211597 
0.49321745088202589846 0.00000000100000000000 0.50678254811797418533 
0.52297921048641760056 0.00000000100000000000 0.47702078851358242773 
0.51351947193443381323 0.00000000100000000000 0.48648052706556610403 
0.49861600587139209839 0.01143470350387426789 0.48994929062473369097 
0.47497824395255133778 0.00413641430709298184 0.52088534174035572288 
0.50602874958787047444 0.00000013752429825494 0.49397111288783129845 
0.51347175918678078510 0.00477133273041653854 0.48175690808280269284 
0.50359809216181616875 0.00000002299679746021 0.49640188484138642044 
0.52201190781479689385 0.00000000100000000000 0.47798809118520296790 
0.52427554763933403859 0.01637369304678280152 0.45935075931388308357 
0.50464335890649447691 0.01062810063722730188 0.48472854045627822295 
0.48795095623978190780 0.00032508303858300066 0.51172396072163517378 
0.49273360783177866384 0.03185613233234574349 0.47541025983587564818 
0.49075081269029041664 0.00043182816413278401 0.50881735914557668643 
0.51236233643387329995 0.01050799870797843559 0.47712966485814828355 
0.51939186110717183720 0.00638063180499700081 0.47422750708783106832 
0.49685157861691658931 0.00000000100000000000 0.50314842038308338346 
0.50376251978896124939 0.00609062514993390959 0.49014685506110500235 
0.50469879197514677660 0.00000000100000000000 0.49530120702485330719 
0.48806858812981018803 0.00000000100000000000 0.51193141087018978475 
0.49345173654735252633 0.00767168036095551131 0.49887658309169191639 
0.51926063211476558568 0.00000000100000000000 0.48073936688523438709 
0.49182360714466144547 0.00000000100000000000 0.50817639185533869384 
0.50012065040991493525 0.00101172020552988784 0.49886762938455525562 
0.49490771372946151807 0.00000000100000000000 0.50509228527053839919 
0.50981594186492362741 0.01168450085559137597 0.47849955727948501050 
0.48459184220397827358 0.00000007440008454733 0.51540808339593724430 
0.51153925961371649045 0.00045999176804108893 0.48800074861824249695 
0.49380129779182529992 0.00214174101547949525 0.50405696119269527422 
0.10504303642339951619 0.45848347542219436423 0.43647348815440606407 
0.09383999674587484296 0.44580529318052469767 0.46035471007360045936 
0.11801124345951279071 0.44619343422410290279 0.43579532231638429263 
0.10150817897299509174 0.44474184109029252232 0.45374997993671234431 
0.14144944553914898244 0.47426718065022838156 0.38428337381062249722 
0.08656596263718574491 0.47201374694852676894 0.44142029041428754166 
0.10422682420288104099 0.45665008652196642513 0.43912308927515242285 
0.07422281507005458467 0.46668026430253822801 0.45909692062740725671 
0.11152984148911383733 0.44326164444242566187 0.44520851406846068121 
0.12101900721666984662 0.45534926548479054409 0.42363172729853953991 
0.19287147372937366030 0.40220634979635128126 0.40492217647427497518 
0.19868166550667537562 0.39952077624337684059 0.40179755824994778379 
0.20144056442189406386 0.40552701281654912613 0.39303242276155692103 
0.17400131741109717276 0.41572345587205422612 0.41027522671684846234 
0.19363830614785534912 0.39941552029693161430 0.40694617355521295332 
0.20932370419936904837 0.41063785306931777086 0.38003844273131326403 
0.21496306930156286463 0.41077627378883840858 0.37426065690959875454 
0.20887311245081657818 0.39219787302656328176 0.39892901452262014006 
0.18789467459437667052 0.42880445734573224836 0.38330086805989094234 
0.21467435158258502126 0.41396326091136687042 0.37136238750604805281 
0.30215275924600598634 0.35114326369103593395 0.34670397706295807971 
0.27985580964526363124 0.36766711333486662427 0.35247707701986974449 
0.29214764907998119758 0.34353124024041165052 0.36432111067960715189 
0.28098186396660507214 0.35436535705487937076 0.36465277897851555711 
0.29909659519210785028 0.34708664349540557792 0.35381676131248662731 
0.29960230758566036569 0.34764467237891033546 0.35275302003542929885 
0.28690707484319816212 0.36958476358894237768 0.34350816156785934918 
0.31218824558522878521 0.35988855578362860532 0.32792319863114272049 
0.29371283648699086921 0.34536893102077848017 0.36091823249223065062 
0.32028624797598659324 0.35059182523172049972 0.32912192679229296255 
0.39315538655109805166 0.30778919233772789044 0.29905542111117405790 
0.39625700997625840083 0.29350948690034872612 0.31023350312339292856 
0.40087160410050781678 0.31851581382017457589 0.28061258207931755182 
0.40117357253398744366 0.30569836130272198815 0.29312806616329067921 
0.40013703551439627759 0.28691859513594913933 0.31294436934965452757 
0.39131222513930874474 0.30759794867682349606 0.30108982618386764818 
0.40826221599444090238 0.30658973748486684219 0.28514804652069231095 
0.41420080477834714250 0.28227625784283560950 0.30352293737881719249 
0.39119930707342420728 0.32102763805993583812 0.28777305486664006562 
0.37635520411942069430 0.29805329179310008358 0.32559150408747933314 
0.51400585200303006150 0.26100245041580294458 0.22499169758116702167 
0.50336119658518030384 0.25110166586697690860 0.24553713754784287082 
0.47299237773462793344 0.26084178003823194070 0.26616584222714018138 
0.49359314224598493936 0.26013978211456978418 0.24626707563944530421 
0.52795469779405246324 0.26499345968140075591 0.20705184252454675309 
0.48219467330650939152 0.25987283477635270135 0.25793249191713785162 
0.47626160019217189667 0.25351817092177358903 0.27022022888605456981 
0.51617477226059282902 0.23162353057460718930 0.25220169716479995392 
0.49698887507445854705 0.24557159475841641716 0.25743953016712495252 
0.52733914260860248469 0.25309832534801629533 0.21956253204338116447 
0.56749881833694781896 0.19172441472755546998 0.24077676693549673881 
0.59339160859286765870 0.19241414198845174788 0.21419424941868048240 
0.62308540846251914136 0.18054125203843729430 0.19637333949904353658 
0.59485531592769125275 0.20909554531024135415 0.19604913876206744860 
0.61310545246842529377 0.20645329445333451823 0.18044125307824007698 
0.60102956519838679483 0.21237444166376903687 0.18659599313784405727 
0.59278179178128642679 0.20826418834431797977 0.19895401987439562119 
0.60456224253100432353 0.20686687908046738626 0.18857087838852840123 
0.59417710257213784963 0.21264514488765640099 0.19317775254020574938 
0.59059286756608764257 0.21451811369415349495 0.19488901873975889023 
0.69484036887292865980 0.14634823390637874407 0.15881139722069256837 
0.69945423984127830241 0.16333221995631252987 0.13721354020240922322 
0.69115689116107958956 0.14927316115273414621 0.15956994768618620872 
0.68851717088680941536 0.14201541767923545057 0.16946741143395496754 
0.69288781352263861812 0.14270021794166909412 0.16441196853569234326 
0.68819873910998985433 0.16242980538224471854 0.14937145550776548264 
0.68619763716276405141 0.14370194479775053042 0.17010041803948539041 
0.68596343194490616568 0.16051691534743553480 0.15351965270765843830 
0.70684340251150390433 0.16654037983665334610 0.12661621765184280508 
0.70657158115262697073 0.14984891346689468983 0.14357950538047842270 
0.79161214498168253062 0.10430887542937690438 0.10407897958894059276 
0.79477141808375573184 0.10274451187208989700 0.10248407004415439892 
0.80425538032447896342 0.10720945367236509038 0.08853516600315590457 
0.79445836435866723502 0.11481368508653701233 0.09072795055479568327 
0.80626524450581027459 0.08599284906042292675 0.10774190643376663212 
0.77991736902186048486 0.08777798585427237787 0.13230464512386716502 
0.77897241390666871474 0.11419808069913564563 0.10682950539419577840 
0.80225596727756287585 0.10739115862914316857 0.09035287409329402497 
0.81035643868218754093 0.11405964018980654928 0.07558392112800596530 
0.80474324803558927588 0.09992219310105134034 0.09533455886335934215 
0.89147290804053958002 0.05818869713285088757 0.05033839482660958098 
0.87135519951168793895 0.04885203404408157424 0.07979276644423052844 
0.90273220877706750187 0.05642671780738096193 0.04084107341555152232 
0.90299890240805003039 0.05982401615206547896 0.03717708143988454617 
0.88622329583732417646 0.03227381365259313073 0.08150289051008267893 
0.89149278212958615875 0.03556871666107842139 0.07293850120933542680 
0.90540444756330573650 0.06637446770308205735 0.02822108473361228942 
0.89581315874618450135 0.06675457610008654619 0.03743226515372900798 
0.86941364504212315101 0.03330392614486758773 0.09728242881300920575 
0.88098981477392690476 0.04673780362475228600 0.07227238160132080924 


Run example

Please refer to the tutorial [5]