############################
# 正準相関分析
# coded by Y.Suganuma
############################
############################################
# 線形連立方程式を解く（逆行列を求める）
# w : 方程式の左辺及び右辺
# n : 方程式の数
# m : 方程式の右辺の列の数
# eps : 逆行列の存在を判定する規準
# return : =0 : 正常
# =1 : 逆行列が存在しない
# coded by Y.Suganuma
############################################
def gauss(w, n, m, eps)
nm = n + m;
ind = 0
for i1 in 0 ... n
y1 = 0.0
m1 = i1 + 1
m2 = 0
# ピボット要素の選択
for i2 in i1 ... n
y2 = w[i2][i1].abs()
if y1 < y2
y1 = y2
m2 = i2
end
end
# 逆行列が存在しない
if y1 < eps
ind = 1
break
# 逆行列が存在する
else # 行の入れ替え
for i2 in i1 ... nm
y1 = w[i1][i2]
w[i1][i2] = w[m2][i2]
w[m2][i2] = y1
end
# 掃き出し操作
y1 = 1.0 / w[i1][i1]
for i2 in m1 ... nm
w[i1][i2] *= y1
end
for i2 in 0 ... n
if i2 != i1
for i3 in m1 ... nm
w[i2][i3] -= (w[i2][i1] * w[i1][i3])
end
end
end
end
end
return ind
end
#***************************************/
# 最大固有値と固有ベクトル（べき乗法） */
# i : 何番目の固有値かを示す */
# n : 次数 */
# m : 丸め誤差の修正回数 */
# ct : 最大繰り返し回数 */
# eps : 収束判定条件 */
# a : 対象とする行列 */
# b : nxnの行列，最初は，単位行列 */
# c : 作業域，nxnの行列 */
# r : 固有値 */
# v : 各行が固有ベクトル（nxn） */
# v0 : 固有ベクトルの初期値 */
# v1,v2 : 作業域（n次元ベクトル） */
# return : 求まった固有値の数 */
# coded by Y.Suganuma */
#***************************************/
def power(i, n, m, ct, eps, a, b, c, r, v, v0, v1, v2)
# 初期設定
ind = i
k = 0
l1 = 0.0
for i1 in 0 ... n
l1 += v0[i1] * v0[i1]
v1[i1] = v0[i1]
end
l1 = Math.sqrt(l1)
# 繰り返し計算
while k < ct
# 丸め誤差の修正
if k%m == 0
l2 = 0.0
for i1 in 0 ... n
v2[i1] = 0.0
for i2 in 0 ... n
v2[i1] += b[i1][i2] * v1[i2]
end
l2 += v2[i1] * v2[i1]
end
l2 = Math.sqrt(l2)
for i1 in 0 ... n
v1[i1] = v2[i1] / l2
end
end
# 次の近似
l2 = 0.0
for i1 in 0 ... n
v2[i1] = 0.0
for i2 in 0 ... n
v2[i1] += a[i1][i2] * v1[i2]
end
l2 += v2[i1] * v2[i1]
end
l2 = Math.sqrt(l2)
for i1 in 0 ... n
v2[i1] /= l2
end
# 収束判定
# 収束した場合
if ((l2-l1)/l1).abs() < eps
k1 = -1
for i1 in 0 ... n
if v2[i1].abs() > 0.001
k1 = i1
if v2[k1]*v1[k1] < 0.0
l2 = -l2
end
end
if k1 >= 0
break
end
end
k = ct
r[i] = l2
for i1 in 0 ... n
v[i][i1] = v2[i1]
end
if i == n-1
ind = i + 1
else
for i1 in 0 ... n
for i2 in 0 ... n
c[i1][i2] = 0.0
for i3 in 0 ... n
x = (i1 == i3) ? a[i1][i3] - l2 : a[i1][i3]
c[i1][i2] += x * b[i3][i2]
end
end
end
for i1 in 0 ... n
for i2 in 0 ... n
b[i1][i2] = c[i1][i2]
end
end
for i1 in 0 ... n
v1[i1] = 0.0
for i2 in 0 ... n
v1[i1] += b[i1][i2] * v0[i2]
end
end
for i1 in 0 ... n
v0[i1] = v1[i1]
end
ind = power(i+1, n, m, ct, eps, a, b, c, r, v, v0, v1, v2)
end
# 収束しない場合
else
for i1 in 0 ... n
v1[i1] = v2[i1]
end
l1 = l2
k += 1
end
end
return ind
end
###################################
# 正準相関分析
# r,s : 各組における変数の数
# n : データの数
# x : データ
# ryz : 相関係数
# ab : 各組の係数（a,bの順）
# eps : 正則性を判定する規準
# v0 : 固有ベクトルの初期値
# m : 丸め誤差の修正回数
# ct : 最大繰り返し回数
# return : >0 : 相関係数の数
# =0 : エラー
# coded by Y.Suganuma
###################################
def canonical(r, s, n, x, ryz, ab, eps, v0, m, ct)
sw = 0
# 領域の確保
q = r + s
mean = Array.new(q)
w1 = Array.new(s)
v1 = Array.new(r)
v2 = Array.new(r)
a = Array.new(s)
b = Array.new(r)
c = Array.new(q)
c11 = Array.new(r)
c11i = Array.new(r)
c12 = Array.new(r)
c21 = Array.new(s)
c22 = Array.new(s)
c22i = Array.new(s)
w = Array.new(s)
for i1 in 0 ... q
c[i1] = Array.new(q)
end
for i1 in 0 ... s
a[i1] = Array.new(s)
c21[i1] = Array.new(r)
c22[i1] = Array.new(s)
c22i[i1] = Array.new(s)
w[i1] = Array.new(2*s)
end
for i1 in 0 ... r
b[i1] = Array.new(r)
c11[i1] = Array.new(r)
c11i[i1] = Array.new(r)
c12[i1] = Array.new(s)
end
# 平均値の計算
for i1 in 0 ... q
mean[i1] = 0.0
for i2 in 0 ... n
mean[i1] += x[i1][i2]
end
mean[i1] /= n
end
# 分散強分散行列の計算
for i1 in 0 ... q
for i2 in i1 ... q
vv = 0.0
for i3 in 0 ... n
vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2])
end
vv /= (n - 1)
c[i1][i2] = vv
if i1 != i2
c[i2][i1] = vv
end
end
end
# c11, c12, c21, c22 の設定
# c12
for i1 in 0 ... r
for i2 in 0 ... s
c12[i1][i2] = c[i1][i2+r]
end
end
# c21
for i1 in 0 ... s
for i2 in 0 ... r
c21[i1][i2] = c[i1+r][i2]
end
end
# c11とその逆行列
for i1 in 0 ... r
for i2 in 0 ... r
w[i1][i2] = c[i1][i2]
c11[i1][i2] = c[i1][i2]
end
for i2 in r ... 2*r
w[i1][i2] = 0.0
end
w[i1][i1+r] = 1.0
end
sw1 = gauss(w, r, r, 1.0e-10)
if sw1 == 0
for i1 in 0 ... r
for i2 in 0 ... r
c11i[i1][i2] = w[i1][i2+r]
end
end
else
sw = 1
end
# c22とその逆行列
for i1 in 0 ... s
for i2 in 0 ... s
w[i1][i2] = c[i1+r][i2+r]
c22[i1][i2] = c[i1+r][i2+r]
end
for i2 in s ... 2*s
w[i1][i2] = 0.0
end
w[i1][i1+s] = 1.0
end
sw1 = gauss(w, s, s, eps)
if sw1 == 0
for i1 in 0 ... s
for i2 in 0 ... s
c22i[i1][i2] = w[i1][i2+s]
end
end
else
sw = 1
end
# 固有値λ及び固有ベクトルaの計算
if sw == 0
# 行列の計算
for i1 in 0 ... s
for i2 in 0 ... r
a[i1][i2] = 0.0
for i3 in 0 ... s
a[i1][i2] += c22i[i1][i3] * c21[i3][i2]
end
end
end
for i1 in 0 ... r
for i2 in 0 ... s
w[i1][i2] = 0.0
for i3 in 0 ... s
w[i1][i2] += c12[i1][i3] * a[i3][i2]
end
end
end
for i1 in 0 ... r
for i2 in 0 ... r
a[i1][i2] = 0.0
for i3 in 0 ... r
a[i1][i2] += c11i[i1][i3] * w[i3][i2]
end
end
end
# 固有値と固有ベクトル（べき乗法）
for i1 in 0 ... r
for i2 in 0 ... r
b[i1][i2] = 0.0
end
b[i1][i1] = 1.0
end
sw = power(0, r, m, ct, eps, a, b, c, ryz, ab, v0, v1, v2)
if sw > 0
for i1 in 0 ... r
# 相関係数
ryz[i1] = Math.sqrt(ryz[i1])
# 大きさの調整(a)
for i2 in 0 ... r
w1[i2] = 0.0
for i3 in 0 ... r
w1[i2] += c11[i2][i3] * ab[i1][i3]
end
end
len = 0.0
for i2 in 0 ... r
len += ab[i1][i2] * w1[i2]
end
len = Math.sqrt(len)
for i2 in 0 ... r
ab[i1][i2] /= len
end
# bの計算
for i2 in 0 ... s
w1[i2] = 0.0
for i3 in 0 ... r
w1[i2] += c21[i2][i3] * ab[i1][i3]
end
end
for i2 in 0 ... s
ab[i1][i2+r] = 0.0
for i3 in 0 ... s
ab[i1][i2+r] += c22i[i2][i3] * w1[i3]
end
end
for i2 in 0 ... s
ab[i1][i2+r] /= ryz[i1]
end
# 大きさの調整(b)
for i2 in 0 ... s
w1[i2] = 0.0
for i3 in 0 ... s
w1[i2] += c22[i2][i3] * ab[i1][i3+r]
end
end
len = 0.0
for i2 in 0 ... s
len += ab[i1][i2+r] * w1[i2]
end
len = Math.sqrt(len)
for i2 in 0 ... s
ab[i1][i2+r] /= len
end
end
end
else
sw = 0
end
return sw
end
ss = gets().split(" ")
r = Integer(ss[0]) # 各組の変数
s = Integer(ss[1]) # 各組の変数
n = Integer(ss[2]) # データの数
q = r + s
ryz = Array.new(r)
v0 = Array.new(r)
for i1 in 0 ... r
v0[i1] = 1.0
end
x = Array.new(q)
for i1 in 0 ... q
x[i1] = Array.new(n)
end
ab = Array.new(r)
for i1 in 0 ... r
ab[i1] = Array.new(q)
end
for i1 in 0 ... n # データ
ss = gets().split()
for i2 in 0 ... q
x[i2][i1] = Float(ss[i2])
end
end
sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200)
if sw > 0
for i1 in 0 ... sw
print("相関係数 " + String(ryz[i1]) + "\n")
print(" a")
for i2 in 0 ... r
print(" " + String(ab[i1][i2]))
end
print("\n")
print(" b")
for i2 in 0 ... s
print(" " + String(ab[i1][r+i2]))
end
print("\n")
end
else
print("***error 解を求めることができませんでした\n")
end
=begin
---------データ例（コメント部分を除いて下さい）---------
2 2 100 # 各組の変数の数（r と s， r ≦ s）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