quick filter in awk

 make a list of animals in col2 of 1st file, then print 2nd file if animals ar NOT in the list

awk 'FNR==NR{inn[$2]; next}  !($2 in inn)' test5 relGenApprox

python like awk

 so I want to put Python in a pipe where it reads from std in , does something, writes to std out:

$ cat test.py

#!/usr/bin/env python3

import sys

# https://stackoverflow.com/questions/1450393/how-do-i-read-from-stdin

for n,line in enumerate(sys.stdin):

    a=line.split()

    if n%5==0:

        sys.stdout.write(line)

extract UPG allocation from renumf90 log

 so you want to know from the output of renumf90 (say ren.log) how many animals were allocated to each UPG?

The output looks like this:

 Unknown parent group allocation

 Equation   Group       #Animals

 59815785       1   21349

...

 Max group = 424; Max UPG ID = 59816208

...

Use this in the command line:

$ sed -n '/allocation/,/Max\ group/p' ren.log | awk '$1 ~ /^[0-9]+$/' 

e.g.

 59815785       1   21349

 59815786       2    4615

explanations:

find between two patterns:

https://askubuntu.com/a/849016

check if the 1st column is a (positive) integer: 

https://stackoverflow.com/questions/28878995/check-if-a-field-is-an-integer-in-awk

Dictionary of arrays in Julia and breed fractions

 So in Julia I want to create a dictionary (hash table or associative array) of arrays to store breed composition in dairy cattle. It took me a while but I found out how to declare it:

julia> a=Dict{String,Array{Float64,1}}()

Imagine the following pedigree

A 0 0 Holstein
B 0 0 Jersey
C A B
D A C

then this Julia script computes breed fractions

#=

A 0 0 Holstein

B 0 0 Jersey

C A B

D A C

=#

breedcomp=Dict{String,Array{Float64,1}}()

#purebred founders

breedcomp["A"]=[1.0,0.0]

breedcomp["B"]=[0.0,1.0]

#rest of pedigree

breedcomp["C"]=0.5*(breedcomp["A"]+breedcomp["B"])

breedcomp["D"]=0.5*(breedcomp["A"]+breedcomp["C"])

display(breedcomp)

Dict{String, Vector{Float64}} with 4 entries:

  "B" => [0.0, 1.0]

  "A" => [1.0, 0.0]

  "C" => [0.5, 0.5]

  "D" => [0.75, 0.25]

SNP effects from Single Step GBLUP with APY

 APY is a technique that allows representing the inverse of a genomic relationship matrix in a sparse format by choosing a "core" of animals (here and here). The authoritative guide to APY is Bermann et al. 2022: this paper . 

One of the key aspects of genomic models is the ability of estimating SNP effects and then apply them to newly genotyped animals, what is know as Indirect Predictions. Matias and I found out that it's easier than we thought as shown here.

Among many other things Bermann et al. show that one can write indirect predictions of "non-core" animals as (I use the original equation numbering)

eq. (10) : $latex \mathbf{{u}_n}= \mathbf{Z}_n \mathbf{Z}'_c (\mathbf{Z}_c \mathbf{Z}'_c)^{-1} \mathbf{Z}_c  \mathbf{{a}} + \boldsymbol{\xi} $latex

where $latex \mathbf{{a}} $latex are SNP effects and $latex \boldsymbol{\xi} $latex is an error term that does not depend on $latex \mathbf{{u}_c} $latex. 

we obtain SNP effects from eq. 21 in Bermann et al:

$latex \mathbf{\hat{a}}=k \mathbf{Z}'_c \mathbf{G}_{cc}^{-1} \mathbf{\hat{u}}_{c}  $latex

we plug that into (10) and expand:

$latex \mathbf{\hat{u}_n}= \mathbf{Z}_n \mathbf{Z}'_c (\mathbf{Z}_c \mathbf{Z}'_c)^{-1} \mathbf{Z}_c \mathbf{\hat{a}} =k \mathbf{Z}_n \mathbf{Z}'_c (k \mathbf{Z}_c \mathbf{Z}'_c)^{-1} \mathbf{Z}_c \mathbf{\hat{a}} $latex

we substitute for $latex \mathbf{\hat{a}} $latex:

$latex \mathbf{\hat{u}_n} =k \mathbf{Z}_n \mathbf{Z}'_c (k \mathbf{Z}_c \mathbf{Z}'_c)^{-1} \mathbf{Z}_c k \mathbf{Z}'_c \mathbf{G}_{cc}^{-1} \mathbf{\hat{u}}_{c}=k \mathbf{Z}_n \mathbf{Z}'_c \mathbf{G}_{cc}^{-1} \mathbf{\hat{u}}_{c} =  \mathbf{Z}_n \mathbf{\hat{a}} $latex

which is the original eq. 21. This is because $latex \hat{a} $latex  is part of the  column space of  $latex \mathbf{Z}'_c $latex, then $latex \mathcal{P}\mathbf{\hat{a}} = \mathbf{\hat{a}} $latex.

Finally, obtaining Indirect Predictions from APY is deadly simple and intuitive:

• $latex \mathbf{\hat{a}}=k \mathbf{Z}'_c \mathbf{G}_{cc}^{-1} \mathbf{\hat{u}}_{c}  $latex
• $latex \mathbf{\hat{u}_n} =  \mathbf{Z}_n \mathbf{\hat{a}} $latex

compiling macs in MacBook with Ventura

 I wanted to compile the coalescent simulator macs in the Mac running Ventura with M2 chips. This was of course the beginning of a great adventure. I end up doing the following:

- install library boost using homebrew

- dig out the path for the boost library e.g. as here, which turned out to be /opt/homebrew/Cellar/boost/1.81.0_1/include

- finally, modify the makefile as follows

# compile options

CFLAGS = -Wall -g

#CFLAGS = -Wall -O3

# Add location of any library locations below with -L

LINKFLAGS =

#LINKFLAGS = -static

# compiler

CC = g++

# libraries. For a local Boost installation

# Example:

#LIB = -I /Users/garychen/software/boost_1_36_0

# Default:

#LIB = -I .

LIB = -I /opt/homebrew/Cellar/boost/1.81.0_1/include

# simulator name

SIM=macs

OBJS = simulator.o algorithm.o datastructures.o

$(SIM) : $(OBJS)

$(CC) -o $(SIM) $(OBJS) $(LINKFLAGS)

simulator.o: simulator.cpp simulator.h

$(CC) $(CFLAGS) $(LIB) -c $<

algorithm.o: algorithm.cpp simulator.h

$(CC) $(CFLAGS) $(LIB) -c $<

datastructures.o: datastructures.cpp simulator.h

$(CC) $(CFLAGS) $(LIB) -c $<

draw many elements julia

 # a vector of frequencies

p=rand(Beta(2,2),10)

# a vector of "distributions"

a=Binomial.(2,p)

# a vector of vectors

 b=rand.(a,1)

# collapsed (row vector)

reduce(hcat,b)

# draw 5 animals at once

b=rand.(a,5)

# collapse

bb=reduce(hcat,b)

#compute frequencies

pest = mean(bb,dims=1)/2