Calculating Ising Model with ArrayFire¶

MIT License
Copyright (C) 2018 Lirimy

In [1]:

using ArrayFire

ArrayFire v3.6.0 (CUDA, 64-bit Linux, build 2858662)
Platform: CUDA Toolkit 9.1, Driver: 396.26
[0] GeForce GTX 980, 4041 MB, CUDA Compute 5.2

In [2]:

import Colors: Gray
#import Images: display
import Plots: gif, mp4, frame

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include("SimpleAnimation.jl")
using SimpleAnimation
#using Plots

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const MB = UInt64(2^20);

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gpu32(a) = AFArray([Float32(a)])
rnd() = rand(AFArray{Float32}, m, n)
initS() = AFArray(Float32.(rand([1, -1], m, n)))

Out[5]:

initS (generic function with 1 method)

In [6]:

# generate padding matrix of circular edge
function genP(n)
    P = eye(AFArray{Float32}, n+2)
    P[1, 1] = P[end, end] = 0
    P[1, end-1] = P[end, 2] = 1
    return P
end

Out[6]:

genP (generic function with 1 method)

In [7]:

function pconv!(u, ret, K=kernel, Pl=Pl, Pr=Pr)
    conved = convolve2(u, K, AF_CONV_EXPAND, AF_CONV_SPATIAL)
    ret .= (Pl' * conved * Pr)[2:end-1, 2:end-1]
    nothing
end

"""Padding and Convolution
K: kernel
P: padding matrix
size(P) = size(u) + size(K) - 1

P example of free edge:

AFArray: 5×5 Array{Float32,2}:
 0.0  1.0  0.0  0.0  0.0
 0.0  1.0  0.0  0.0  0.0
 0.0  0.0  1.0  0.0  0.0
 0.0  0.0  0.0  1.0  0.0
 0.0  0.0  0.0  1.0  0.0
"""
function pconv(u, K=kernel, Pl=Pl, Pr=Pr)
    ret = similar(u)
    pconv!(u, ret, K, Pl, Pr)
    ret
end

Out[7]:

pconv

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b = gpu32(-log(1+sqrt(2))) # 2b
kernel = AFArray(Float32.([0 1 0; 1 0 1; 0 1 0]))

function prob(s::AFArray{Float32, 2})::AFArray{Float32, 2}
    exp(b .* s .* pconv(s))
end

Out[8]:

prob (generic function with 1 method)

In [9]:

function update!(s::AFArray{Float32, 2}, elim=1/10)
    s .*= 1 - 2 * signbit(rnd() - prob(s) .* signbit(rnd().-gpu32(elim)))
end

Out[9]:

update! (generic function with 2 methods)

In [10]:

#m, n = 1080, 1920
m, n = 360, 640

Pl, Pr = genP(m), genP(n)

s = initS();

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b = gpu32(-log(1+sqrt(2)))

afgc(1)
s = initS()
anim = SimpleAnim()

@time for count in 1:450
    for i in 1:10
        update!(s)
    end
    
    frame(anim, Gray.((Array(sync(s))+1)/2))
    
    # when benchmarking, uncomment these 2 lines and comment out frame
    #sync(s)
    #gc(false)
    
    afgc(3200MB)
end

@time gif(anim, "ising.gif")

  7.548005 seconds (573.27 k allocations: 1.753 GiB, 3.72% gc time)
  4.014858 seconds (971 allocations: 55.891 KiB)

Out[14]:

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@time mp4(anim, "ising.mp4")

  5.856016 seconds (940 allocations: 51.953 KiB)

Out[15]:

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Gray.((Array(sync(s))+1)/2)

Out[16]:

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