############################
# 主成分分析
# coded by Y.Suganuma
############################
#************************************************************/
# 実対称行列の固有値・固有ベクトル（ヤコビ法） */
# n : 次数 */
# ct : 最大繰り返し回数 */
# eps : 収束判定条件 */
# a : 対象とする行列 */
# a1, a2 : 作業域（nxnの行列），a1の対角要素が固有値 */
# x1, x2 : 作業域（nxnの行列），x1の各列が固有ベクトル */
# return : =0 : 正常 */
# =1 : 収束せず */
# coded by Y.Suganuma */
#************************************************************/
def Jacobi(n, ct, eps, a, a1, a2, x1, x2)
# 初期設定
k = 0
ind = 1
p = 0
q = 0
for i1 in 0 ... n
for i2 in 0 ... n
a1[i1][i2] = a[i1][i2]
x1[i1][i2] = 0.0
end
x1[i1][i1] = 1.0
end
# 計算
while ind > 0 && k < ct
# 最大要素の探索
max = 0.0
for i1 in 0 ... n
for i2 in 0 ... n
if i2 != i1
if a1[i1][i2].abs() > max
max = a1[i1][i2].abs()
p = i1
q = i2
end
end
end
end
# 収束判定
# 収束した
if max < eps
ind = 0
# 収束しない
else
# 準備
s = -a1[p][q]
t = 0.5 * (a1[p][p] - a1[q][q])
v = t.abs() / Math.sqrt(s * s + t * t)
sn = Math.sqrt(0.5 * (1.0 - v))
if s*t < 0.0
sn = -sn
end
cs = Math.sqrt(1.0 - sn * sn)
# akの計算
for i1 in 0 ... n
if i1 == p
for i2 in 0 ... n
if i2 == p
a2[p][p] = a1[p][p] * cs * cs + a1[q][q] * sn * sn -
2.0 * a1[p][q] * sn * cs
elsif i2 == q
a2[p][q] = 0.0
else
a2[p][i2] = a1[p][i2] * cs - a1[q][i2] * sn
end
end
elsif i1 == q
for i2 in 0 ... n
if (i2 == q)
a2[q][q] = a1[p][p] * sn * sn + a1[q][q] * cs * cs +
2.0 * a1[p][q] * sn * cs
elsif i2 == p
a2[q][p] = 0.0
else
a2[q][i2] = a1[q][i2] * cs + a1[p][i2] * sn
end
end
else
for i2 in 0 ... n
if i2 == p
a2[i1][p] = a1[i1][p] * cs - a1[i1][q] * sn
elsif i2 == q
a2[i1][q] = a1[i1][q] * cs + a1[i1][p] * sn
else
a2[i1][i2] = a1[i1][i2]
end
end
end
end
# xkの計算
for i1 in 0 ... n
for i2 in 0 ... n
if i2 == p
x2[i1][p] = x1[i1][p] * cs - x1[i1][q] * sn
elsif i2 == q
x2[i1][q] = x1[i1][q] * cs + x1[i1][p] * sn
else
x2[i1][i2] = x1[i1][i2]
end
end
end
# 次のステップへ
k += 1
for i1 in 0 ... n
for i2 in 0 ... n
a1[i1][i2] = a2[i1][i2]
x1[i1][i2] = x2[i1][i2]
end
end
end
end
return ind
end
###################################
# 主成分分析
# p : 変数の数
# n : データの数
# x : データ
# r : 分散（主成分）
# a : 係数
# eps : 収束性を判定する規準
# ct : 最大繰り返し回数
# return : =0 : 正常
# =1 : エラー
# coded by Y.Suganuma
###################################
def principal(p, n, x, r, a, eps, ct)
sw = 0
# 領域の確保
c = Array.new(p)
a1 = Array.new(p)
a2 = Array.new(p)
x1 = Array.new(p)
x2 = Array.new(p)
for i1 in 0 ... p
c[i1] = Array.new(p)
a1[i1] = Array.new(p)
a2[i1] = Array.new(p)
x1[i1] = Array.new(p)
x2[i1] = Array.new(p)
end
# データの基準化
for i1 in 0 ... p
mean = 0.0
s2 = 0.0
for i2 in 0 ... n
mean += x[i1][i2]
s2 += x[i1][i2] * x[i1][i2]
end
mean /= n
s2 /= n
s2 = n * (s2 - mean * mean) / (n - 1)
s2 = Math.sqrt(s2)
for i2 in 0 ... n
x[i1][i2] = (x[i1][i2] - mean) / s2
end
end
# 分散強分散行列の計算
for i1 in 0 ... p
for i2 in 0 ... p
s2 = 0.0
for i3 in 0 ... n
s2 += x[i1][i3] * x[i2][i3]
end
s2 /= (n - 1)
c[i1][i2] = s2
if i1 != i2
c[i2][i1] = s2
end
end
end
# 固有値と固有ベクトルの計算（ヤコビ法）
sw = Jacobi(p, ct, eps, c, a1, a2, x1, x2)
if sw == 0
for i1 in 0 ... p
r[i1] = a1[i1][i1]
for i2 in 0 ... p
a[i1][i2] = x1[i2][i1]
end
end
end
return sw
end
ss = gets().split(" ")
p = Integer(ss[0]) # 変数の数
n = Integer(ss[1]) # データの数
r = Array.new(p)
x = Array.new(p)
a = Array.new(p)
for i1 in 0 ... p
x[i1] = Array.new(n)
a[i1] = Array.new(p)
end
for i1 in 0 ... n # データ
ss = gets().split(" ")
for i2 in 0 ... p
x[i2][i1] = Float(ss[i2])
end
end
sw = principal(p, n, x, r, a, 1.0e-10, 200)
if sw == 0
for i1 in 0 ... p
print("主成分 " + String(r[i1]))
print(" 係数")
for i2 in 0 ... p
print(" " + String(a[i1][i2]))
end
print("\n")
end
else
print("***error 解を求めることができませんでした")
end
=begin
---------データ例（コメント部分を除いて下さい）---------
4 100 # 変数の数（p）とデータの数（n）
66 22 44 31 # x1, x2, x3, x4
25 74 17 81
50 23 53 71
25 57 19 81
74 47 64 47
39 33 48 46
14 22 9 69
67 60 49 26
42 40 77 65
11 80 0 86
32 0 43 74
68 69 44 68
24 49 9 71
42 74 28 46
60 58 73 28
36 37 33 68
24 44 19 83
30 40 31 50
55 40 60 49
63 47 94 41
72 30 100 45
19 22 13 75
43 39 43 34
90 83 92 31
51 77 52 82
53 70 34 31
28 51 53 44
40 62 42 79
31 48 22 68
57 29 51 30
64 89 57 42
49 82 72 29
53 31 55 43
79 52 70 10
45 19 43 57
35 34 34 89
4 69 0 100
49 49 66 66
92 82 97 6
5 89 0 100
65 26 83 28
56 36 64 38
48 50 25 22
30 30 15 55
40 65 38 42
14 67 9 67
84 96 90 8
53 64 51 54
50 89 60 52
76 41 68 9
49 40 53 49
78 66 66 17
76 58 90 29
41 15 40 49
63 60 55 33
40 36 49 67
78 54 71 18
62 72 69 12
64 47 42 53
56 64 9 15
77 35 56 25
44 12 46 87
80 9 56 19
36 21 52 78
48 63 64 48
43 61 50 47
58 23 28 50
90 12 100 0
13 33 11 77
67 44 48 28
75 45 68 17
81 22 89 9
46 45 59 55
56 49 64 55
65 62 72 27
34 49 29 77
45 33 60 63
20 45 14 99
33 38 26 87
44 51 69 52
64 57 64 48
44 64 51 28
63 48 56 11
29 39 33 84
40 48 51 54
40 38 26 62
68 46 61 26
58 45 68 48
64 44 77 63
59 62 44 66
81 53 93 19
23 34 12 68
51 35 55 46
74 70 84 17
42 33 56 44
46 31 46 53
33 57 38 63
40 24 20 42
53 36 60 31
0 34 0 100
=end