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824831d
add exercise05 with julia without for/if
Shunsuke-Hori Feb 25, 2018
487917b
Exercise 05 adding loop and format
vikjam Mar 2, 2018
ffe973e
fix my previous code, simplify and extend functions
Shunsuke-Hori Mar 2, 2018
98fef6e
Added a bit more documentation
vikjam Mar 4, 2018
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercise 5\n",
"- Required packages:\n",
" - `Plots.jl` (for plotting)\n",
" - `ExcelReaders.jl` (to read excel file)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using Plots\n",
"pyplot()\n",
"using ExcelReaders"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Functions for Hodrick-Prescott (HP) filter\n",
"This exercise allows us to showcase how different methods of computing the HP filter affects runtime and memory use.\n",
"\n",
"- First, we'll use the loop method with a dense matrix to create matrix $H$.\n",
"- Second, we'll do a loop again, but with a sparse matrix.\n",
"- Third, we'll vectorize the calculation with a dense matrix and via the function `spdiagm` to create matrix $H$.\n",
"- Finally, we'll vectorize the calculation with a sparse matrix and via the function `spdiagm` to create matrix $H$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Declare the matrices"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"abstract type MatrixType end\n",
"struct Dense <: MatrixType end\n",
"struct Sparse <: MatrixType end\n",
"abstract type AssignMethod end\n",
"struct Loop <: AssignMethod end\n",
"struct Vectorized <: AssignMethod end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Loop version"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"function create_matrix(λ, N::Integer, ::Dense, ::Loop)\n",
" H = zeros(N, N)\n",
" assign!(H, λ, N)\n",
" return H\n",
"end;\n",
"\n",
"function create_matrix(λ, N::Integer, ::Sparse, ::Loop)\n",
" H = spzeros(N, N)\n",
" assign!(H, λ, N)\n",
" return H\n",
"end;\n",
"\n",
"function assign!(H::AbstractMatrix, λ, N) \n",
" for j = 1:N\n",
" for i = 1:N\n",
" if j == 1\n",
" H[1, 1] = 1+λ;\n",
" H[2, 1] = -2λ;\n",
" H[3, 1] = λ;\n",
" elseif j == 2\n",
" H[1, 2] = -2λ;\n",
" H[2, 2] = 1 + 5λ;\n",
" H[3, 2] = -4λ;\n",
" H[4, 2] = λ;\n",
" elseif j == N - 1\n",
" H[N - 3, N - 1] = λ;\n",
" H[N - 2, N - 1] = -4λ;\n",
" H[N - 1, N - 1] = 1 + 5λ;\n",
" H[N, N - 1] = -2λ;\n",
" elseif j == N\n",
" H[N - 2, N] = λ;\n",
" H[N - 1, N] = -2λ;\n",
" H[N, N] = 1+λ;\n",
" else\n",
" H[j - 2, j] = λ;\n",
" H[j - 1, j] = -4λ;\n",
" H[j, j] = 1 + 6λ;\n",
" H[j + 1, j] = -4λ;\n",
" H[j + 2, j] = λ;\n",
" end\n",
" end\n",
" end\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Vectorized version"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"function create_matrix(λ::Real, N::Integer, ::Sparse, ::Vectorized) \n",
" return spdiagm(-2 => fill(λ, N-2),\n",
" -1 => vcat(-2λ, fill(-4λ, N - 3), -2λ),\n",
" 0 => vcat(1 + λ, 1 + 5λ, fill(1 + 6λ, N-4),\n",
" 1 + 5λ, 1 + λ),\n",
" 1 => vcat(-2λ, fill(-4λ, N - 3), -2λ),\n",
" 2 => fill(λ, N-2))\n",
"end;\n",
"\n",
"function create_matrix(λ::Real, N::Integer, ::Dense, ::Vectorized)\n",
" H = zeros(N, N)\n",
" H += diagm(fill(λ, N-2), -2)\n",
" H += diagm(vcat(-2λ, fill(-4λ, N - 3), -2λ), -1)\n",
" H += diagm(vcat(1 + λ, 1 + 5λ, fill(1 + 6λ, N-4),\n",
" 1 + 5λ, 1 + λ), 0)\n",
" H += diagm(vcat(-2λ, fill(-4λ, N - 3), -2λ), 1)\n",
" H += diagm(fill(λ, N-2), 2)\n",
" return H\n",
"end;"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"function hp_filter(y::AbstractVector{T}, λ::Real, mt::MatrixType, am::AssignMethod) where T <: Real\n",
" N = length(y)\n",
" H = create_matrix(T(λ), N, mt, am)\n",
" y_trend = H \\ y\n",
" y_cyclical = y - y_trend\n",
" return y_trend, y_cyclical\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Apply HP filter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Note*: First run for each include compilation time, so don't take it seriously. Run a second time to get a better sense of the differences."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Looped dense\n",
" 5.267661 seconds (1.31 M allocations: 69.188 MiB, 6.57% gc time)\n",
" 0.048105 seconds (998 allocations: 954.137 KiB)\n",
"Looped sparse\n",
" 1.623298 seconds (250.93 k allocations: 13.624 MiB, 2.09% gc time)\n",
" 0.025615 seconds (1.21 k allocations: 255.492 KiB)\n",
"Vectorized dense\n",
" 1.128149 seconds (288.31 k allocations: 20.795 MiB, 3.79% gc time)\n",
" 0.024424 seconds (1.24 k allocations: 5.349 MiB)\n",
"Vectorized sparse\n",
" 3.065138 seconds (1.49 M allocations: 81.303 MiB, 3.46% gc time)\n",
" 0.014130 seconds (1.39 k allocations: 284.764 KiB)\n"
]
}
],
"source": [
"data = readxlsheet(\"data/US_Data.xlsx\", \"Data\");\n",
"y = collect(data[4:end, 2]); # removing header\n",
"T = length(y);\n",
"\n",
"# Looped dense version\n",
"println(\"Looped dense\")\n",
"@time (ytr1600, yc1600) = hp_filter(Float64.(y), 1600, Dense(), Loop());\n",
"@time (ytr1e5, yc1e5) = hp_filter(Float64.(y), 1e5, Dense(), Loop());\n",
"\n",
"# Looped sparse version\n",
"println(\"Looped sparse\")\n",
"@time (ytr1600, yc1600) = hp_filter(Float64.(y), 1600, Sparse(), Loop());\n",
"@time (ytr1e5, yc1e5) = hp_filter(Float64.(y), 1e5, Sparse(), Loop());\n",
"\n",
"# Dense matrix version\n",
"println(\"Vectorized dense\")\n",
"@time (ytr1600, yc1600) = hp_filter(Float64.(y), 1600, Dense(), Vectorized());\n",
"@time (ytr1e5, yc1e5) = hp_filter(Float64.(y), 1e5, Dense(), Vectorized());\n",
"\n",
"# Sparse matrix version\n",
"println(\"Vectorized sparse\")\n",
"@time (ytr1600, yc1600) = hp_filter(Float64.(y), 1600, Sparse(), Vectorized());\n",
"@time (ytr1e5, yc1e5) = hp_filter(Float64.(y), 1e5, Sparse(), Vectorized());"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## With large data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Looped dense\n",
" 8.708596 seconds (27 allocations: 381.585 MiB, 5.26% gc time)\n",
"Looped sparse\n",
" "
]
}
],
"source": [
"N_test = 5_000\n",
"y_test = randn(N_test)\n",
"\n",
"# Looped dense version\n",
"println(\"Looped dense\")\n",
"@time (ytrtest_del, yctest_del) = hp_filter(y_test, 1600, Dense(), Loop());\n",
"\n",
"# Looped sparse version\n",
"println(\"Looped sparse\")\n",
"@time (ytrtest_spl, yctest_spl) = hp_filter(y_test, 1600, Sparse(), Loop());\n",
"\n",
"# Dense matrix version\n",
"println(\"Vectorized dense\")\n",
"@time (ytrtest_dev, yctest_dev) = hp_filter(y_test, 1600, Dense(), Vectorized());\n",
"\n",
"# # Sparse matrix version\n",
"println(\"Vectorized sparse\")\n",
"@time (ytrtest_spv, yctest_spv) = hp_filter(y_test, 1600, Sparse(), Vectorized());"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot trend component\n",
"Now back to the actual assignment."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plot([log.(ytr1600), log.(ytr1e5), log.(y)], lw = 2,\n",
" lab = [\"λ = 1600\" \"λ = 10⁵\" \"Raw Data\"],\n",
" title = \"log of real GDP\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot cyclical component"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"p = plot([yc1600, yc1e5], lw = 2,\n",
" lab = [\"λ = 1600\" \"λ = 10⁵\" \"Raw Data\"],\n",
" title = \"log of real GDP\")"
]
}
],
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"hide_input": false,
"kernelspec": {
"display_name": "Julia 0.6.0",
"language": "julia",
"name": "julia-0.6"
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"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
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"toc": {
"colors": {
"hover_highlight": "#DAA520",
"running_highlight": "#FF0000",
"selected_highlight": "#FFD700"
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"moveMenuLeft": true,
"nav_menu": {
"height": "161px",
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"nbformat_minor": 2
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