#!/usr/bin/bash

# 2022-07-29
#
# read n^th line from BH-NN-qq.txt and check the defect of corresponding Butson
#
# usage:
# $ ./check_defect.sh BH-NN-qq.txt q line_number defect_BH_14_4.txt # where q = BUTSON parameter



M_FILE=TBH.m # <--- temporary file with BH

N=$(echo $1 | awk -F[--] '{print $2}') # get dimension from file name (always between "-"; eg. -12-
dots=$(for i in $(eval echo "{1..$N}"); do echo -n "."; done)
nth_line=$3

sed "${nth_line}q;d" $4 # defect_BH_14_4.txt ### we are going to compare this value with...

echo 'function TBH' > $M_FILE
##echo "warning('off', 'all');" >> $M_FILE
echo 'B=exp(2j*pi*[' >> $M_FILE


# for fucks sake... semicolon is temporarily replaced with #, which is replaced back to semicolon at the end, because semicolon is used to encode 11 (eleven)
sed "${nth_line}q;d" $1 | cut -c 7- | sed 's/\('$dots'\)/\1#\n/g' | sed 's/\(.\)/\1 /g' | sed 's/:/10/g' | sed 's/;/11/g' | sed 's/</12/g' | sed 's/=/13/g' | sed 's/>/14/g' | sed 's/?/15/g' | sed 's/@/16/g' | sed 's/#/;/g' >> $M_FILE
#sed "${nth_line}q;d" $1 | cut -c 7- | sed 's/\('$dots'\)/\1;\n/g' | sed 's/\(.\)/\1 /g' >> $M_FILE


echo "]/$2)/sqrt($N);" >> $M_FILE # all Butsons are normalized to UNITARY!
echo 'disp(sprintf("%g\t%g\t%g", ud(B,"S",1e-8), ud(B,"T"), ud(B,"R")))' >> $M_FILE
echo 'end' >> $M_FILE
octave TBH.m                                 ### ...the TRIPLE output from the CLI
                                             ### all FOUR values should match!