DoingMathWithRuby

Ruby で数値計算をするのは環境構築がしんどそう． numo/narrayがいい感じになっているので，linalgを入れようとしたんですが．．． ううん，エラーが再現できない．学生さんに試してもらおう．問題なく動いたらしい．

blas, lapackのinstall

> brew install lapack
==> Downloading https://homebrew.bintray.com/bottles/lapack-3.8.0_1.high_sierra.bottle.tar.gz
######################################################################## 100.0%
==> Pouring lapack-3.8.0_1.high_sierra.bottle.tar.gz
==> Caveats

... 中略

==> Summary
🍺  /usr/local/Cellar/lapack/3.8.0_1: 28 files, 10MB


> brew install openblas
Updating Homebrew...
==> Auto-updated Homebrew!

... 中略

==> Summary
🍺  /usr/local/Cellar/openblas/0.3.4: 21 files, 117.8MB

pathのsetを薦められるが，numo-linalgには効かないみたい．

numo-linalgのinstall

gem installするときにpathを指定する必要がある．

> gem uninstall numo-linalg
> gem install numo-linalg -- --with-openblas-dir=/usr/local/opt/openblas

https://gist.github.com/sonots/6fadc6cbbb170b9c4a0c9396c91a88e1

ruby sample

最初の一歩．順番が大事みたい．

require 'numo/narray'
require "numo/linalg/use/openblas"
require 'numo/linalg'

p Numo::Linalg::Loader.libs

m = 10
a = Numo::SFloat.new(m).rand
b = Numo::SFloat.new(m).rand
p a*b


p ma = Numo::NArray[[1, 2, 3 ], [3, 4, 5], [6,7,8]]
p Numo::Linalg.eig(ma)

["/usr/local/opt/openblas/lib/libopenblas.dylib"]
Numo::SFloat#shape=[10]
[0.0552492, 0.0212455, 0.241172, 0.201437, 0.401844, 0.586427, 0.344554, ...]
Numo::Int32#shape=[3,3]
[[1, 2, 3], 
 [3, 4, 5], 
 [6, 7, 8]]
[Numo::DComplex#shape=[3]
[14.0664+0i, -1.06637+0i, 3.43928e-17+0i], nil, Numo::DComplex#shape=[3,3]
[[0.265648+0i, 0.744429+0i, 0.408248+0i], 
 [0.491207+0i, 0.190701+0i, -0.816497+0i], 
 [0.829546+0i, -0.63989+0i, 0.408248+0i]]]

narray 配列操作

flatten([dim0,dim1,...])
transpose([dim0,dim1,...])
expand_dims(dim)
diagonal(offset, [ax1,ax2])
reshape

narray 配列演算

NArray には以下の演算メソッドがある． '+,-,*,/,%,divmod,**,-@,abs'

narray 統計メソッド

次の統計メソッドが定義されている． sum, prod, mean, stddev, var, rms, min, min_index, max, max_index, minmax, cumsum, cumprod, sort, sort_index, median

linalgの関数

Matrix and vector products

dot, matmul

Decomposition

lu, lu_fact, lu_inv, lu_solve, ldl, cholesky, cho_fact, cho_inv, cho_solve, qr, svd, svdvals, orth, null_space

Matrix eigenvalues

eig, eigh, eigvals, eigvalsh

Norms and other numbers

norm, cond, det, slogdet, matrix_rank, matrix_power

Solving equations and inverting matrices

solve, lstsq, inv, pinv

ruby sample II

下の例はnumo/linalgを使って，データフィッティングして numo/gnuplotでグラフを書かせた例．

require 'numo/gnuplot'
require 'numo/narray'

pairs = []
File.readlines("data.txt").each do |line|
  vol, _d, _d, _d, _d, ene = line.split(/\s+/)
  pairs << [vol, ene]
end
pairs.sort!{|a,b| a[0].to_f <=> b[0].to_f }
p pairs

x,y=[],[]
pairs.each do |pair|
  x << pair[0].to_f
  y << pair[1].to_f
end

require "numo/narray"

def ff(x,i)
  x**i
end

m = 5
n = 3
av = Numo::DFloat.zeros(m, n)
yy = Numo::DFloat.zeros(m)
n.times do |i|
  m.times do |j|
    av[j,i]=ff(x[j],i)
    yy[j] = y[j]
  end
end

require 'numo/linalg'
p ai = Numo::Linalg.inv(Numo::Linalg.dot(av.transpose,av))
p b = Numo::Linalg.dot(av.transpose,yy)
p vars = Numo::Linalg.dot(ai,b)

eq = ''
vars.each_with_index do |var, i|
  eq << " + " + sprintf("%+6.2f",var) + "*x** #{i} "
end
#p eq = "#{vars[0]} + #{vars[1]}*x + #{vars[2]}*x**2"

Numo.gnuplot do
  set output: 'e_v.gif'
  set term: 'gif'
  set xlabel: 'Volume [%]'
  set ylabel: 'Energy [eV]'
  plot [x, y, w: :lp, pt: 6],
  [eq, w:"lines"]
end

system 'open ./e_v.gif'

[["-2.00", "-561.7895200000"], ["-1.00", "-564.1426100000"], ["+0.00", "-565.4727300000"], ["+1.00", "-565.8513000000"], ["+2.00", "-565.3645700000"]]
Numo::DFloat#shape=[3,3]
[[0.485714, -0, -0.142857], 
 [0, 0.1, 0], 
 [-0.142857, 0, 0.0714286]]
Numo::DFloat#shape=[3]
[-2822.62, -8.85879, -5638.61]
Numo::DFloat#shape=[3]
[-565.471, -0.885879, 0.473656]