pkofod

# This code is a Julia translation of the C code from Openlibm (http://www.openlibm.org/)
# with the following license:

# Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
# 1. Redistributions of source code must retain the above copyright

pkofod

julia> @profile res = optimize(fung, x0, LBFGS(), Optim.Options(show_trace=false,iterations=100_000,g_tol=1e-6,f_tol=1e-20))
Profile.print()Results of Optimization Algorithm
 * Algorithm: L-BFGS
 * Starting Point: [0.5611813319535237,0.3528280830687891, ...]
 * Minimizer: [0.063775434544103,0.49327292600719447, ...]
 * Minimum: 3.682547e+03
 * Iterations: 11
 * Convergence: true
   * |x - x'| ≤ 0.0e+00: false
     |x - x'| = 1.18e-09

pkofod

β = 0.9995
Wₕ = 100
W̄ₕ = Wₕ/(1-β)
Wₗ = 50
W̄ₗ = Wₗ/(1-β)
pₕ = 0.35
pₗ = 0.65
Bₖ = 0.6*Wₗ
U(x) = sqrt(x)
Uₕ  = U(Bₖ-1)

pkofod

"""
    frexp_exp(x)

Compute ``exp(x)``, scaled to avoid spurious overflow.  An exponent is
returned separately in ``expt``.

# Examples
```jldoctest
julia> frexp_exp(1354.9)

pkofod

 --- Benchmarking 0.0
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     3.977 ns (0.00% GC)
  median time:      4.582 ns (0.00% GC)
  mean time:        4.687 ns (0.00% GC)
  maximum time:     19.703 ns (0.00% GC)
  --------------

pkofod

Benchmarking 0.0
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     3.992 ns (0.00% GC)
  median time:      4.586 ns (0.00% GC)
  mean time:        4.647 ns (0.00% GC)
  maximum time:     18.766 ns (0.00% GC)
  --------------

pkofod

# Adapted from https://tpapp.github.io/post/log1p/
# consistent random numbers
T = Float32
srand(UInt32[0xfd909253, 0x7859c364, 0x7cd42419, 0x4c06a3b6])

"""
    err(x, [prec])

Return two values, which are the log2 relative errors for calculating
`log(x)`, using `Base.log` and `Base.Math.JuliaLibm.log`.

pkofod

pkm@pkm:~/.julia$ mkdir fakepkg
pkm@pkm:~/.julia$ julia
               _
   _       _ _(_)_     |  A fresh approach to technical computing
  (_)     | (_) (_)    |  Documentation: https://docs.julialang.org
   _ _   _| |_  __ _   |  Type "?help" for help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 0.6.0 (2017-06-19 13:05 UTC)
 _/ |\__'_|_|_|\__'_|  |  Official http://julialang.org/ release
|__/                   |  x86_64-pc-linux-gnu

pkofod

function tauchen(ρ, σₛ, m, N)
    const Φ = normcdf # CDF of standard normal
    s̃₁, s̃ₙ = -m*σₛ, m*σₛ # end points
    s̃ = linspace(s̃₁, s̃ₙ, N) # grid
    w = (s̃[2]-s̃[1])/2 # half distance between grid points
    F = zeros(N, N) # empty transition matrix
    F[:, 1] = Φ.((s̃[1]-ρ.*s̃+w)/sqrt(σₛ))
    F[:, N] = 1-Φ.((s̃[end]-ρ.*s̃-w)/sqrt(σₛ))
    for j = 2:N-1
        for i = 1:N

pkofod

Pkg.add("BenchmarkTools")
using BenchmarkTools
function inplace_sq_mat(m::Array{Float64, 2}, n::Array{Float64, 2})
    s = size(m, 1)
    t = s+1
    v = zeros(t)

    @inbounds for i=1:s
        for j=1:s
            v[j] = m[j, i]