19cjl/figs/numerical.fig/simpleq/main.jl

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()