# -*- coding: UTF-8 -*-
from math import *
import numpy as np
############################################
# 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 range(0, n) :
for i2 in range(0, n) :
A1[i1][i2] = A[i1][i2]
X1[i1][i2] = 0.0
X1[i1][i1] = 1.0
# 計算
while ind > 0 and k < ct :
# 最大要素の探索
max = 0.0
for i1 in range(0, n) :
for i2 in range(0, n) :
if i2 != i1 :
if abs(A1[i1][i2]) > max :
max = fabs(A1[i1][i2])
p = i1
q = i2
# 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 = fabs(t) / sqrt(s * s + t * t)
sn = sqrt(0.5 * (1.0 - v))
if s*t < 0.0 :
sn = -sn
cs = sqrt(1.0 - sn * sn)
# Akの計算
for i1 in range(0, n) :
if i1 == p :
for i2 in range(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
elif i2 == q :
A2[p][q] = 0.0
else :
A2[p][i2] = A1[p][i2] * cs - A1[q][i2] * sn
elif i1 == q :
for i2 in range(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
elif i2 == p :
A2[q][p] = 0.0
else :
A2[q][i2] = A1[q][i2] * cs + A1[p][i2] * sn
else :
for i2 in range(0, n) :
if i2 == p :
A2[i1][p] = A1[i1][p] * cs - A1[i1][q] * sn
elif i2 == q :
A2[i1][q] = A1[i1][q] * cs + A1[i1][p] * sn
else :
A2[i1][i2] = A1[i1][i2]
# Xkの計算
for i1 in range(0, n) :
for i2 in range(0, n) :
if i2 == p :
X2[i1][p] = X1[i1][p] * cs - X1[i1][q] * sn
elif i2 == q :
X2[i1][q] = X1[i1][q] * cs + X1[i1][p] * sn
else :
X2[i1][i2] = X1[i1][i2]
# 次のステップへ
k += 1
for i1 in range(0, n) :
for i2 in range(0, n) :
A1[i1][i2] = A2[i1][i2]
X1[i1][i2] = X2[i1][i2]
return ind
###################################
# 因子分析 */
# p : 変数の数 */
# n : データの数 */
# m : 共通因子負荷量の数 */
# x : データ */
# iv : 固有値 */
# 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 factor(p, n, m, x, iv, a, eps, ct) :
sw = 1
count = 0
# 領域の確保
s = np.empty(p, np.int)
h1 = np.empty(p, np.float)
h2 = np.empty(p, np.float)
C = np.empty((p, p), np.float)
A1 = np.empty((p, p), np.float)
A2 = np.empty((p, p), np.float)
X1 = np.empty((p, p), np.float)
X2 = np.empty((p, p), np.float)
# データの基準化
for i1 in range(0, p) :
mean = 0.0
s2 = 0.0
for i2 in range(0, n) :
mean += x[i1][i2]
s2 += x[i1][i2] * x[i1][i2]
mean /= n
s2 /= n
s2 = n * (s2 - mean * mean) / (n - 1)
s2 = sqrt(s2)
for i2 in range(0, n) :
x[i1][i2] = (x[i1][i2] - mean) / s2
# 分散強分散行列の計算
for i1 in range(0, p) :
for i2 in range(0, p) :
s2 = 0.0
for i3 in range(0, n) :
s2 += x[i1][i3] * x[i2][i3]
s2 /= (n - 1)
C[i1][i2] = s2
if i1 != i2 :
C[i2][i1] = s2
# 共通性の初期値
for i1 in range(0, p) :
h1[i1] = 1.0
# 共通因子負荷量の計算
while count < ct and sw > 0 :
# 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 :
# 共通性及び共通因子負荷量の計算
for i1 in range(0, p) :
s[i1] = 0
for i1 in range(0, m) :
max_i = -1
max = 0.0
for i2 in range(0, p) :
if s[i2] == 0 and (max_i < 0 or A1[i2][i2] > max) :
max_i = i2
max = A1[i2][i2]
s[max_i] = 1
iv[i1] = A1[max_i][max_i]
s2 = sqrt(iv[i1])
for i2 in range(0, p) :
a[i1][i2] = s2 * X1[i2][max_i]
for i1 in range(0, p) :
h2[i1] = 0.0
for i2 in range(0, m) :
h2[i1] += a[i2][i1] * a[i2][i1]
for i1 in range(0, m) :
if abs(h2[i1]-h1[i1]) > eps :
sw = 1
break
# 収束しない場合
if sw > 0 :
count += 1
for i1 in range(0, p) :
h1[i1] = h2[i1]
C[i1][i1] = h1[i1]
return sw
----------------------------------
# -*- coding: UTF-8 -*-
import numpy as np
import sys
from math import *
from function import factor
############################
# 因子分析
# coded by Y.Suganuma
############################
line = sys.stdin.readline()
ss = line.split()
m = int(ss[0]) # 変数の数
p = int(ss[1]) # 変数の数
n = int(ss[2]) # データの数
iv = np.empty(p, np.float)
x = np.empty((p, n), np.float)
a = np.empty((p, p), np.float)
for i1 in range(0, n) : # データ
line = sys.stdin.readline()
ss = line.split()
for i2 in range(0, p) :
x[i2][i1] = float(ss[i2])
sw = factor(p, n, m, x, iv, a, 1.0e-10, 200)
if sw == 0 :
for i1 in range(0, m) :
print("固有値 " + str(iv[i1]), end="")
print(" 共通因子負荷量", end="")
for i2 in range(0, p) :
print(" " + str(a[i1][i2]), end="")
print()
else :
print("***error 解を求めることができませんでした")
---------データ例（コメント部分を除いて下さい）---------
2 4 100 // 共通因子負荷量の数（m），変数の数（p），及び，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