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using FastGaussQuadrature
using Printf
using LinearAlgebra
include("tools.jl")
include("integration.jl")
include("simpleq.jl")
include("simpleq-newton.jl")
include("iteration.jl")
function main()
## defaults
tolerance=1e-14
order=100
maxiter=21
rho=1e-6
e=1e-4
d=3
v=v_exp3d
a0=a0_exp3d
# plot range when plotting in x
xmin=0
xmax=100
nx=100
# read cli arguments
(params,command)=read_args(ARGS)
# read params
if params!=""
for param in split(params,";")
terms=split(param,"=")
if length(terms)!=2
print(stderr,"error: could not read parameter '",param,"'.\n")
exit(-1)
end
lhs=terms[1]
rhs=terms[2]
if lhs=="rho"
rho=parse(Float64,rhs)
elseif lhs=="e"
e=parse(Float64,rhs)
elseif lhs=="tolerance"
tolerance=parse(Float64,rhs)
elseif lhs=="order"
order=parse(Int64,rhs)
elseif lhs=="maxiter"
maxiter=parse(Int64,rhs)
elseif lhs=="xmin"
xmin=parse(Float64,rhs)
elseif lhs=="xmax"
xmax=parse(Float64,rhs)
elseif lhs=="nx"
nx=parse(Int64,rhs)
else
print(stderr,"unrecognized parameter '",lhs,"'.\n")
exit(-1)
end
end
end
## run command
# e(rho)
if command=="energy_rho"
energy_rho(order,a0,d,v,maxiter,tolerance)
# d^2(rho*e(rho))
elseif command=="convexity"
ddrhoe(order,a0,d,v,maxiter,tolerance)
# u_n(x)
elseif command=="iteration"
iteration_ux(order,e,a0,d,v,maxiter)
else
print(stderr,"unrecognized command '",command,"'.\n")
exit(-1)
end
end
# read cli arguments
function read_args(ARGS)
# flag
flag=""
# output strings
params=""
command=""
# loop over arguments
for arg in ARGS
# argument that starts with a dash
if arg[1]=='-'
# go through characters after dash
for char in arg[2:length(arg)]
# set params
if char=='p'
# raise flag
flag="params"
else
print_usage()
exit(-1)
end
end
# arguments that do not start with a dash
else
if flag=="params"
params=arg
else
command=arg
end
# reset flag
flag=""
end
end
if command==""
print_usage()
exit(-1)
end
return (params,command)
end
# usage
function print_usage()
print(stderr,"usage: simpleq [-p params] <command>\n")
end
# exponential potential in 3 dimensions
function v_exp3d(k)
return 8*pi/(1+k^2)^2
end
a0_exp3d=1.254356410591064819505409291110046864031181245635821944528
# compute energy as a function of rho
function energy_rho(order,a0,d,v,maxiter,tolerance)
minlrho=-6
maxlrho=2
nlrho=100
for j in 0:nlrho-1
rho=10^(minlrho+(maxlrho-minlrho)*j/nlrho)
# linear spacing
#rho=10.0^minlrho+(10.0^maxlrho-10.0^minlrho)*j/nlrho
(u,E)=hatu_newton(order,rho,a0,d,v,maxiter,tolerance)
@printf("% .8e % .8e\n",rho,real(E))
end
end
# compute \partial^2(e\rho) as a function of rho
function ddrhoe(order,a0,d,v,maxiter,tolerance)
minlrho=-6
maxlrho=2
nlrho=100
for j in 0:nlrho-1
rho=10^(minlrho+(maxlrho-minlrho)*j/nlrho)
# interval
drho=rho*1.01
(u,E)=hatu_newton(order,rho,a0,d,v,maxiter,tolerance)
(up,Ep)=hatu_newton(order,rho+drho,a0,d,v,maxiter,tolerance)
(um,Em)=hatu_newton(order,rho-drho,a0,d,v,maxiter,tolerance)
@printf("% .8e % .8e\n",rho,real((rho+drho)*Ep+(rho-drho)*Em-2*rho*E)/drho^2)
end
end
# compute \int u_n(x) at every step
function iteration_ux(order,e,a0,d,v,maxiter)
(u,rho)=hatun_iteration(e,order,d,v,maxiter)
weights=gausslegendre(order)
intun=0.
for n in 2:maxiter+1
# compute \hat u_n(0)=1/(2*rho_n)+rho_{n-1}/2*\hat u_{n-1}(0)^2
intun=real(1/(2*rho[n])+rho[n-1]/2*intun^2)
@printf("%2d % .15e\n",n-1,abs(intun-1/rho[maxiter+1]))
end
end
main()
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