# 8.3.jl
# 2020-11-01, 2020-11-03
# $Id: 8.3.jl 1.1 2020/11/03 00:00:00 s Exp $

using LinearAlgebra: eigen
using Printf
using Statistics: cov, mean, normalize, var

# input
s1 = [11.91, 18.37,  3.64, 24.37, 30.42,
      -1.45, 20.11,  9.28, 17.63, 15.71]
s2 = [29.59, 15.25,  3.53, 17.67, 12.74,
      -2.56, 25.46,  6.92,  9.73, 25.09]
s3 = [23.27, 19.47, -6.58, 15.08, 16.24,
     -15.05, 17.80, 18.82,  3.05, 16.94]
s4 = [27.24, 17.05, 10.20, 20.26, 19.84,
       1.51, 12.24, 16.12, 22.93,  3.49]
s = hcat(s1, s2, s3, s4)

average  = Array{Float64}(undef, 4)
variance = Array{Float64}(undef, 4)

# calculate
for j = 1:4
  average[j] = mean(s[:, j])
end

for j = 1:4
  variance[j] = var(s[:, j])
end

covariance = cov(s)
eigenvalue, eigenvector = eigen(covariance)
eigenvector0 = normalize(eigenvector[:, 4], 1)

# output
println("8.3.jl")
println("s1 ", s1)
println("s2 ", s2)
println("s3 ", s3)
println("s4 ", s4)
println("s")
for i = 1:10
  (map(x -> @printf("%6.2f ", round(x; digits = 2)), s[i,:]))
  println()
end

println("mean\n", map(x -> round(x; digits = 1), average))
println("variance\n", map(x -> round(x; digits = 2), variance))
println("covariance matrix")
for i=1:4
  (map(x -> @printf("%6.2f ",round(x; digits = 2)), covariance[i, :]))
  println()
end

println("eigenvalue\n", map(x -> round(x; digits = 1), eigenvalue))
println("eigenvector")
for i = 1:4
  (map(x -> @printf("%6.3f ", round(x; digits = 3)), eigenvector[i, :]))
  println()
end
println()
println("eigen value\n", round(eigenvalue[4]; digits=2))
println("normalized eigenvector\n", map(x->round(x; digits = 3), eigenvector0))
# eof