#!/bin/sh  
# \
exec tclsh "$0" "$@"
if [catch {set device $env(SDDS_DEVICE)}] {
    set device motif
}

set interval 5e-2
puts stderr "**Zeroes of J0:"
puts stderr [exec sddssequence -define=z,type=double -sequence=begin=0,end=50,delta=$interval -pipe=out \
| sddsprocess -pipe -rpndef=defns.rpn \
    "-define=column,J0,z 0 Jn" "-define=column,J1,z 1 Jn" \
| sddszerofind -pipe -zero=J0 -column=z,J1 \
| sddsprocess -pipe -rpndef=defns.rpn \
    "-define=col,J0check,z 0 Jn" "-define=col,J1check,z 1 Jn" \
| sddsprintout -column=(z,J0,J0check,J1,J1check) -pipe=in -format=double=%16.9e]

puts stderr "**Iterative solution for better accuracy:"
set offset 1e-4
exec sddssequence -define=z,type=double -sequence=begin=0,end=50,number=5000 -pipe=out \
| sddsprocess -rpndef=defns.rpn -pipe "-define=column,J0,z 0 Jn" \
| sddszerofind -pipe=in -zero=J0 -column=z J0zeros.sdds
exec sddsprocess -rpndef=defns.rpn J0zeros.sdds J0zeros1.sdds "-redefine=column,z,z $offset -" "-redefine=col,J0,z 0 Jn"
exec sddsprocess -rpndef=defns.rpn J0zeros.sdds J0zeros2.sdds "-redefine=column,z,z $offset +" "-redefine=col,J0,z 0 Jn"
exec sddscombine J0zeros1.sdds J0zeros2.sdds -merge -pipe=out \
| sddssort -pipe -col=z \
| sddszerofind -pipe -zero=J0 -column=z \
| sddsprocess -rpndef=defns.rpn -pipe=in J0zeros.sdds "-define=col,J0check,z 0 Jn" "-defi=col,zOverPi,z pi /" 
puts stderr "first iteration done"

set offset 1e-6
exec sddsprocess -rpndef=defns.rpn J0zeros.sdds J0zeros1.sdds "-redefine=column,z,z $offset -" "-redefine=col,J0,z 0 Jn"
exec sddsprocess -rpndef=defns.rpn J0zeros.sdds J0zeros2.sdds "-redefine=column,z,z $offset +" \
    "-redefine=col,J0,z 0 Jn"
exec sddscombine J0zeros1.sdds J0zeros2.sdds -merge -pipe=out \
| sddssort -pipe -col=z \
| sddszerofind -pipe -zero=J0 -column=z \
| sddsprocess -rpndef=defns.rpn -pipe=in J0zeros.sdds "-define=col,J0check,z 0 Jn" "-defi=col,zOverPi,z pi /" 
puts stderr "second iteration done"

set offset 1e-8
exec sddsprocess -rpndef=defns.rpn J0zeros.sdds J0zeros1.sdds "-redefine=column,z,z $offset -" "-redefine=col,J0,z 0 Jn"
exec sddsprocess -rpndef=defns.rpn J0zeros.sdds J0zeros2.sdds "-redefine=column,z,z $offset +" "-redefine=col,J0,z 0 Jn"
puts stderr [exec sddscombine J0zeros1.sdds J0zeros2.sdds -merge -pipe=out \
| sddssort -pipe -col=z \
| sddszerofind -pipe -zero=J0 -column=z \
| sddsprocess -rpndef=defns.rpn -pipe "-define=col,J0check,z 0 Jn" "-defi=col,zOverPi,z pi /" \
| tee J0zeros.sdds \
| sddsprintout -column=(z,zOverPi),format=%16.12f -column=J0check -pipe=in -format=double=%16.9e]

file delete J0*