静岡理工科大学 菅沼ホーム 目次 索引

正準相関分析

    1. A. C++
    2. B. Java
    3. C. JavaScript
    4. D. PHP
    5. E. Ruby
    6. F. Python
    7. G. C#
    8. H. VB

  プログラムは,正準相関分析を行うためのものです.データの入力方法に関しては,プログラムの最後に提示してある入力例に対する説明を参考にして下さい.

  1. C++

    /****************************/
    /* 正準相関分析             */
    /*      coded by Y.Suganuma */
    /****************************/
    #include <stdio.h>
    #include <math.h>
    
    int gauss(double **, int, int, double);
    int canonical(int, int, int, double **, double *, double **, double, double *, int, int);
    int power(int, int, int, int, double, double **, double **,
              double **, double *, double **, double *, double *, double *);
    
    int main()
    {
    	double **x, *ryz, **ab, *v0;
    	int i1, i2, q, r, s, n, sw;
    
    	scanf("%d %d %d", &r, &s, &n);   // 各組の変数の数とデータの数
    	q = r + s;
    
    	ryz = new double [r];
    	v0  = new double [r];
    	x   = new double * [q];
    	ab  = new double * [r];
    	for (i1 = 0; i1 < q; i1++)
    		x[i1]  = new double [n];
    	for (i1 = 0; i1 < r; i1++) {
    		ab[i1] = new double [q];
    		v0[i1] = 1.0;
    	}
    
    	for (i1 = 0; i1 < n; i1++) {   // データ
    		for (i2 = 0; i2 < q; i2++)
    			scanf("%lf", &x[i2][i1]);
    	}
    
    	sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200);
    
    	if (sw > 0) {
    		for (i1 = 0; i1 < sw; i1++) {
    			printf("相関係数 %f\n", ryz[i1]);
    			printf("   a");
    			for (i2 = 0; i2 < r; i2++)
    				printf(" %f", ab[i1][i2]);
    			printf("\n");
    			printf("   b");
    			for (i2 = 0; i2 < s; i2++)
    				printf(" %f", ab[i1][r+i2]);
    			printf("\n");
    		}
    	}
    	else
    		printf("***error  解を求めることができませんでした\n");
    
    	for (i1 = 0; i1 < q; i1++)
    		delete [] x[i1];
    	for (i1 = 0; i1 < r; i1++)
    		delete [] ab[i1];
    	delete [] x;
    	delete [] ab;
    	delete [] ryz;
    	delete [] v0;
    
    	return 0;
    }
    
    /***********************************/
    /* 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       */
    /***********************************/
    int canonical(int r, int s, int n, double **x, double *ryz, double **ab, double eps,
                  double *v0, int m, int ct)
    {
    	double **A, **B, **C, **C11, **C11i, **C12, **C21, **C22, **C22i,
               *mean, vv, **w, *w1, len, *v1, *v2;
    	int i1, i2, i3, q, sw = 0, sw1;
    					// 領域の確保
    	q    = r + s;
    	mean = new double [q];
    	w1   = new double [s];
    	v1   = new double [r];
    	v2   = new double [r];
    	A    = new double * [s];
    	B    = new double * [r];
    	C    = new double * [q];
    	C11  = new double * [r];
    	C11i = new double * [r];
    	C12  = new double * [r];
    	C21  = new double * [s];
    	C22  = new double * [s];
    	C22i = new double * [s];
    	w    = new double * [s];
    	for (i1 = 0; i1 < q; i1++)
    		C[i1] = new double [q];
    	for (i1 = 0; i1 < r; i1++) {
    		B[i1]    = new double [r];
    		C11[i1]  = new double [r];
    		C11i[i1] = new double [r];
    		C12[i1]  = new double [s];
    	}
    	for (i1 = 0; i1 < s; i1++) {
    		A[i1]    = new double [s];
    		C21[i1]  = new double [r];
    		C22[i1]  = new double [s];
    		C22i[i1] = new double [s];
    		w[i1]    = new double [2*s];
    	}
    					// 平均値の計算
    	for (i1 = 0; i1 < q; i1++) {
    		mean[i1] = 0.0;
    		for (i2 = 0; i2 < n; i2++)
    			mean[i1] += x[i1][i2];
    		mean[i1] /= n;
    	}
    					// 分散強分散行列の計算
    	for (i1 = 0; i1 < q; i1++) {
    		for (i2 = i1; i2 < q; i2++) {
    			vv = 0.0;
    			for (i3 = 0; i3 < n; i3++)
    				vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2]);
    			vv        /= (n - 1);
    			C[i1][i2]  = vv;
    			if (i1 != i2)
    				C[i2][i1] = vv;
    		}
    	}
    					// C11, C12, C21, C22 の設定
    						// C12
    	for (i1 = 0; i1 < r; i1++) {
    		for (i2 = 0; i2 < s; i2++)
    			C12[i1][i2] = C[i1][i2+r];
    	}
    						// C21
    	for (i1 = 0; i1 < s; i1++) {
    		for (i2 = 0; i2 < r; i2++)
    			C21[i1][i2] = C[i1+r][i2];
    	}
    						// C11とその逆行列
    	for (i1 = 0; i1 < r; i1++) {
    		for (i2 = 0; i2 < r; i2++) {
    			w[i1][i2]   = C[i1][i2];
    			C11[i1][i2] = C[i1][i2];
    		}
    		for (i2 = r; i2 < 2*r; i2++)
    			w[i1][i2] = 0.0;
    		w[i1][i1+r] = 1.0;
    	}
    	sw1 = gauss(w, r, r, 1.0e-10);
    	if (sw1 == 0) {
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < r; i2++)
    				C11i[i1][i2] = w[i1][i2+r];
    		}
    	}
    	else
    		sw = 1;
    						// C22とその逆行列
    	for (i1 = 0; i1 < s; i1++) {
    		for (i2 = 0; i2 < s; i2++) {
    			w[i1][i2]   = C[i1+r][i2+r];
    			C22[i1][i2] = C[i1+r][i2+r];
    		}
    		for (i2 = s; i2 < 2*s; i2++)
    			w[i1][i2] = 0.0;
    		w[i1][i1+s] = 1.0;
    	}
    	sw1 = gauss(w, s, s, eps);
    	if (sw1 == 0) {
    		for (i1 = 0; i1 < s; i1++) {
    			for (i2 = 0; i2 < s; i2++)
    				C22i[i1][i2] = w[i1][i2+s];
    		}
    	}
    	else
    		sw = 1;
    					// 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 = 0; i1 < s; i1++) {
    			for (i2 = 0; i2 < r; i2++) {
    				A[i1][i2] = 0.0;
    				for (i3 = 0; i3 < s; i3++)
    					A[i1][i2] += C22i[i1][i3] * C21[i3][i2];
    			}
    		}
    
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < s; i2++) {
    				w[i1][i2] = 0.0;
    				for (i3 = 0; i3 < s; i3++)
    					w[i1][i2] += C12[i1][i3] * A[i3][i2];
    			}
    		}
    
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < r; i2++) {
    				A[i1][i2] = 0.0;
    				for (i3 = 0; i3 < r; i3++)
    					A[i1][i2] += C11i[i1][i3] * w[i3][i2];
    			}
    		}
    						// 固有値と固有ベクトル(べき乗法)
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < r; i2++)
    				B[i1][i2] = 0.0;
    			B[i1][i1] = 1.0;
    		}
    
    		sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2);
    
    		if (sw > 0) {
    
    			for (i1 = 0; i1 < r; i1++) {
    							// 相関係数
    				ryz[i1] = sqrt(ryz[i1]);
    							// 大きさの調整(a)
    				for (i2 = 0; i2 < r; i2++) {
    					w1[i2] = 0.0;
    					for (i3 = 0; i3 < r; i3++)
    						w1[i2] += C11[i2][i3] * ab[i1][i3];
    				}
    				len = 0.0;
    				for (i2 = 0; i2 < r; i2++)
    					len += ab[i1][i2] * w1[i2];
    				len = sqrt(len);
    				for (i2 = 0; i2 < r; i2++)
    					ab[i1][i2] /= len;
    							// bの計算
    				for (i2 = 0; i2 < s; i2++) {
    					w1[i2] = 0.0;
    					for (i3 = 0; i3 < r; i3++)
    						w1[i2] += C21[i2][i3] * ab[i1][i3];
    				}
    				for (i2 = 0; i2 < s; i2++) {
    					ab[i1][i2+r] = 0.0;
    					for (i3 = 0; i3 < s; i3++)
    						ab[i1][i2+r] += C22i[i2][i3] * w1[i3];
    				}
    				for (i2 = 0; i2 < s; i2++)
    					ab[i1][i2+r] /= ryz[i1];
    							// 大きさの調整(b)
    				for (i2 = 0; i2 < s; i2++) {
    					w1[i2] = 0.0;
    					for (i3 = 0; i3 < s; i3++)
    						w1[i2] += C22[i2][i3] * ab[i1][i3+r];
    				}
    				len = 0.0;
    				for (i2 = 0; i2 < s; i2++)
    					len += ab[i1][i2+r] * w1[i2];
    				len = sqrt(len);
    				for (i2 = 0; i2 < s; i2++)
    					ab[i1][i2+r] /= len;
    			}
    		}
    	}
    	else
    		sw = 0;
    					// 領域の解放
    	for (i1 = 0; i1 < q; i1++)
    		delete [] C[i1];
    	for (i1 = 0; i1 < r; i1++) {
    		delete [] B[i1];
    		delete [] C11[i1];
    		delete [] C11i[i1];
    		delete [] C12[i1];
    	}
    	for (i1 = 0; i1 < s; i1++) {
    		delete [] A[i1];
    		delete [] C21[i1];
    		delete [] C22[i1];
    		delete [] C22i[i1];
    		delete [] w[i1];
    	}
    	delete [] mean;
    	delete [] w1;
    	delete [] v1;
    	delete [] v2;
    	delete [] A;
    	delete [] B;
    	delete [] C;
    	delete [] C11;
    	delete [] C11i;
    	delete [] C12;
    	delete [] C21;
    	delete [] C22;
    	delete [] C22i;
    	delete [] w;
    
    	return sw;
    }
    
    /*******************************************************/
    /* 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 : 正則性を判定する規準                     */
    /*      return : =0 : 正常                             */
    /*               =1 : 逆行列が存在しない               */
    /*******************************************************/
    int gauss(double **w, int n, int m, double eps)
    {
    	double y1, y2;
    	int ind = 0, nm, m1, m2, i1, i2, i3;
    
    	nm = n + m;
    
    	for (i1 = 0; i1 < n && ind == 0; i1++) {
    
    		y1 = .0;
    		m1 = i1 + 1;
    		m2 = 0;
    
    		for (i2 = i1; i2 < n; i2++) {
    			y2 = fabs(w[i2][i1]);
    			if (y1 < y2) {
    				y1 = y2;
    				m2 = i2;
    			}
    		}
    
    		if (y1 < eps)
    			ind = 1;
    
    		else {
    
    			for (i2 = i1; i2 < nm; i2++) {
    				y1        = w[i1][i2];
    				w[i1][i2] = w[m2][i2];
    				w[m2][i2] = y1;
    			}
    
    			y1 = 1.0 / w[i1][i1];
    
    			for (i2 = m1; i2 < nm; i2++)
    				w[i1][i2] *= y1;
    
    			for (i2 = 0; i2 < n; i2++) {
    				if (i2 != i1) {
    					for (i3 = m1; i3 < nm; i3++)
    						w[i2][i3] -= w[i2][i1] * w[i1][i3];
    				}
    			}
    		}
    	}
    
    	return(ind);
    }
    
    /****************************************/
    /* 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             */
    /****************************************/
    #include <math.h>
    
    int power(int i, int n, int m, int ct, double eps, double **A, double **B,
              double **C, double *r, double **v, double *v0, double *v1, double *v2)
    {
    	double l1, l2, x;
    	int i1, i2, i3, ind, k, k1;
    					// 初期設定
    	ind = i;
    	k   = 0;
    	l1  = 0.0;
    	for (i1 = 0; i1 < n; i1++) {
    		l1     += v0[i1] * v0[i1];
    		v1[i1]  = v0[i1];
    	}
    	l1 = 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 = 0; i1 < n; i1++) {
    				v2[i1] = 0.0;
    				for (i2 = 0; i2 < n; i2++)
    					v2[i1] += B[i1][i2] * v1[i2];
    				l2 += v2[i1] * v2[i1];
    			}
    			l2 = sqrt(l2);
    			for (i1 = 0; i1 < n; i1++)
    				v1[i1] = v2[i1] / l2;
    		}
    						// 次の近似
    		l2 = 0.0;
    		for (i1 = 0; i1 < n; i1++) {
    			v2[i1] = 0.0;
    			for (i2 = 0; i2 < n; i2++)
    				v2[i1] += A[i1][i2] * v1[i2];
    			l2 += v2[i1] * v2[i1];
    		}
    		l2 = sqrt(l2);
    		for (i1 = 0; i1 < n; i1++)
    			v2[i1] /= l2;
    						// 収束判定
    							// 収束した場合
    		if (fabs((l2-l1)/l1) < eps) {
    			k1 = -1;
    			for (i1 = 0; i1 < n && k1 < 0; i1++) {
    				if (fabs(v2[i1]) > 0.001) {
    					k1 = i1;
    					if (v2[k1]*v1[k1] < 0.0)
    						l2 = -l2;
    				}
    			}
    			k    = ct;
    			r[i] = l2;
    			for (i1 = 0; i1 < n; i1++)
    				v[i][i1] = v2[i1];
    			if (i == n-1)
    				ind = i + 1;
    			else {
    				for (i1 = 0; i1 < n; i1++) {
    					for (i2 = 0; i2 < n; i2++) {
    						C[i1][i2] = 0.0;
    						for (i3 = 0; i3 < n; i3++) {
    							x          = (i1 == i3) ? A[i1][i3] - l2 : A[i1][i3];
    							C[i1][i2] += x * B[i3][i2];
    						}
    					}
    				}
    				for (i1 = 0; i1 < n; i1++) {
    					for (i2 = 0; i2 < n; i2++)
    						B[i1][i2] = C[i1][i2];
    				}
    				for (i1 = 0; i1 < n; i1++) {
    					v1[i1] = 0.0;
    					for (i2 = 0; i2 < n; i2++)
    						v1[i1] += B[i1][i2] * v0[i2];
    				}
    				for (i1 = 0; i1 < n; i1++)
    					v0[i1] = v1[i1];
    				ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2);
    			}
    		}
    							// 収束しない場合
    		else {
    			for (i1 = 0; i1 < n; i1++)
    				v1[i1] = v2[i1];
    			l1 = l2;
    			k++;
    		}
    	}
    
    	return ind;
    }
    
    /*
    ---------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
    */
    			

  2. Java

      アプレット版では,任意のデータに対して画面上で実行することができます.
    /****************************/
    /* 正準相関分析             */
    /*      coded by Y.Suganuma */
    /****************************/
    import java.io.*;
    import java.util.StringTokenizer;
    
    public class Test {
    	public static void main(String args[]) throws IOException
    	{
    		double x[][], ryz[], ab[][], v0[];
    		int i1, i2, q, r, s, n, sw;
    		StringTokenizer str;
    		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    					// 各組の変数の数とデータの数
    		str = new StringTokenizer(in.readLine(), " ");
    		r   = Integer.parseInt(str.nextToken());
    		s   = Integer.parseInt(str.nextToken());
    		n   = Integer.parseInt(str.nextToken());
    		q = r + s;
    
    		ryz = new double [r];
    		v0  = new double [r];
    		x   = new double [q][n];
    		ab  = new double [r][q];
    		for (i1 = 0; i1 < r; i1++)
    			v0[i1] = 1.0;
    					// データ
    		for (i1 = 0; i1 < n; i1++) {
    			str = new StringTokenizer(in.readLine(), " ");
    			for (i2 = 0; i2 < q; i2++)
    				x[i2][i1] = Double.parseDouble(str.nextToken());
    		}
    
    		sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200);
    
    		if (sw > 0) {
    			for (i1 = 0; i1 < sw; i1++) {
    				System.out.println("相関係数 " + ryz[i1]);
    				System.out.print("   a");
    				for (i2 = 0; i2 < r; i2++)
    					System.out.print(" " + ab[i1][i2]);
    				System.out.println();
    				System.out.print("   b");
    				for (i2 = 0; i2 < s; i2++)
    					System.out.print(" " + ab[i1][r+i2]);
    				System.out.println();
    			}
    		}
    		else
    			System.out.println("***error  解を求めることができませんでした");
    	}
    
    	/***********************************/
    	/* 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       */
    	/***********************************/
    	static int canonical(int r, int s, int n, double x[][], double ryz[],
                             double ab[][], double eps, double v0[], int m, int ct)
    	{
    		double A[][], B[][], C[][], C11[][], C11i[][], C12[][], C21[][], C22[][], C22i[][],
    	           mean[], vv, w[][], w1[], len, v1[], v2[];
    		int i1, i2, i3, q, sw = 0, sw1;
    					// 領域の確保
    		q    = r + s;
    		mean = new double [q];
    		w1   = new double [s];
    		v1   = new double [r];
    		v2   = new double [r];
    		A    = new double [s][s];
    		B    = new double [r][r];
    		C    = new double [q][q];
    		C11  = new double [r][r];
    		C11i = new double [r][r];
    		C12  = new double [r][s];
    		C21  = new double [s][r];
    		C22  = new double [s][s];
    		C22i = new double [s][s];
    		w    = new double [s][2*s];
    					// 平均値の計算
    		for (i1 = 0; i1 < q; i1++) {
    			mean[i1] = 0.0;
    			for (i2 = 0; i2 < n; i2++)
    				mean[i1] += x[i1][i2];
    			mean[i1] /= n;
    		}
    					// 分散強分散行列の計算
    		for (i1 = 0; i1 < q; i1++) {
    			for (i2 = i1; i2 < q; i2++) {
    				vv = 0.0;
    				for (i3 = 0; i3 < n; i3++)
    					vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2]);
    				vv        /= (n - 1);
    				C[i1][i2]  = vv;
    				if (i1 != i2)
    					C[i2][i1] = vv;
    			}
    		}
    					// C11, C12, C21, C22 の設定
    						// C12
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < s; i2++)
    				C12[i1][i2] = C[i1][i2+r];
    		}
    						// C21
    		for (i1 = 0; i1 < s; i1++) {
    			for (i2 = 0; i2 < r; i2++)
    				C21[i1][i2] = C[i1+r][i2];
    		}
    						// C11とその逆行列
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < r; i2++) {
    				w[i1][i2]   = C[i1][i2];
    				C11[i1][i2] = C[i1][i2];
    			}
    			for (i2 = r; i2 < 2*r; i2++)
    				w[i1][i2] = 0.0;
    			w[i1][i1+r] = 1.0;
    		}
    		sw1 = gauss(w, r, r, 1.0e-10);
    		if (sw1 == 0) {
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++)
    					C11i[i1][i2] = w[i1][i2+r];
    			}
    		}
    		else
    			sw = 1;
    						// C22とその逆行列
    		for (i1 = 0; i1 < s; i1++) {
    			for (i2 = 0; i2 < s; i2++) {
    				w[i1][i2]   = C[i1+r][i2+r];
    				C22[i1][i2] = C[i1+r][i2+r];
    			}
    			for (i2 = s; i2 < 2*s; i2++)
    				w[i1][i2] = 0.0;
    			w[i1][i1+s] = 1.0;
    		}
    		sw1 = gauss(w, s, s, eps);
    		if (sw1 == 0) {
    			for (i1 = 0; i1 < s; i1++) {
    				for (i2 = 0; i2 < s; i2++)
    					C22i[i1][i2] = w[i1][i2+s];
    			}
    		}
    		else
    			sw = 1;
    					// 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 = 0; i1 < s; i1++) {
    				for (i2 = 0; i2 < r; i2++) {
    					A[i1][i2] = 0.0;
    					for (i3 = 0; i3 < s; i3++)
    						A[i1][i2] += C22i[i1][i3] * C21[i3][i2];
    				}
    			}
    
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < s; i2++) {
    					w[i1][i2] = 0.0;
    					for (i3 = 0; i3 < s; i3++)
    						w[i1][i2] += C12[i1][i3] * A[i3][i2];
    				}
    			}
    
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++) {
    					A[i1][i2] = 0.0;
    					for (i3 = 0; i3 < r; i3++)
    						A[i1][i2] += C11i[i1][i3] * w[i3][i2];
    				}
    			}
    						// 固有値と固有ベクトル(べき乗法)
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++)
    					B[i1][i2] = 0.0;
    				B[i1][i1] = 1.0;
    			}
    
    			sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2);
    
    			if (sw > 0) {
    
    				for (i1 = 0; i1 < r; i1++) {
    							// 相関係数
    					ryz[i1] = Math.sqrt(ryz[i1]);
    							// 大きさの調整(a)
    					for (i2 = 0; i2 < r; i2++) {
    						w1[i2] = 0.0;
    						for (i3 = 0; i3 < r; i3++)
    							w1[i2] += C11[i2][i3] * ab[i1][i3];
    					}
    					len = 0.0;
    					for (i2 = 0; i2 < r; i2++)
    						len += ab[i1][i2] * w1[i2];
    					len = Math.sqrt(len);
    					for (i2 = 0; i2 < r; i2++)
    						ab[i1][i2] /= len;
    							// bの計算
    					for (i2 = 0; i2 < s; i2++) {
    						w1[i2] = 0.0;
    						for (i3 = 0; i3 < r; i3++)
    							w1[i2] += C21[i2][i3] * ab[i1][i3];
    					}
    					for (i2 = 0; i2 < s; i2++) {
    						ab[i1][i2+r] = 0.0;
    						for (i3 = 0; i3 < s; i3++)
    							ab[i1][i2+r] += C22i[i2][i3] * w1[i3];
    					}
    					for (i2 = 0; i2 < s; i2++)
    						ab[i1][i2+r] /= ryz[i1];
    							// 大きさの調整(b)
    					for (i2 = 0; i2 < s; i2++) {
    						w1[i2] = 0.0;
    						for (i3 = 0; i3 < s; i3++)
    							w1[i2] += C22[i2][i3] * ab[i1][i3+r];
    					}
    					len = 0.0;
    					for (i2 = 0; i2 < s; i2++)
    						len += ab[i1][i2+r] * w1[i2];
    					len = Math.sqrt(len);
    					for (i2 = 0; i2 < s; i2++)
    						ab[i1][i2+r] /= len;
    				}
    			}
    		}
    		else
    			sw = 0;
    
    		return sw;
    	}
    
    	/****************************************/
    	/* 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             */
    	/****************************************/
    	static int power(int i, int n, int m, int ct, double eps, double A[][], double B[][],
    	          double C[][], double r[], double v[][], double v0[], double v1[], double v2[])
    	{
    		double l1, l2, x;
    		int i1, i2, i3, ind, k, k1;
    					// 初期設定
    		ind = i;
    		k   = 0;
    		l1  = 0.0;
    		for (i1 = 0; i1 < n; i1++) {
    			l1     += v0[i1] * v0[i1];
    			v1[i1]  = v0[i1];
    		}
    		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 = 0; i1 < n; i1++) {
    					v2[i1] = 0.0;
    					for (i2 = 0; i2 < n; i2++)
    						v2[i1] += B[i1][i2] * v1[i2];
    					l2 += v2[i1] * v2[i1];
    				}
    				l2 = Math.sqrt(l2);
    				for (i1 = 0; i1 < n; i1++)
    					v1[i1] = v2[i1] / l2;
    			}
    						// 次の近似
    			l2 = 0.0;
    			for (i1 = 0; i1 < n; i1++) {
    				v2[i1] = 0.0;
    				for (i2 = 0; i2 < n; i2++)
    					v2[i1] += A[i1][i2] * v1[i2];
    				l2 += v2[i1] * v2[i1];
    			}
    			l2 = Math.sqrt(l2);
    			for (i1 = 0; i1 < n; i1++)
    				v2[i1] /= l2;
    						// 収束判定
    							// 収束した場合
    			if (Math.abs((l2-l1)/l1) < eps) {
    				k1 = -1;
    				for (i1 = 0; i1 < n && k1 < 0; i1++) {
    					if (Math.abs(v2[i1]) > 0.001) {
    						k1 = i1;
    						if (v2[k1]*v1[k1] < 0.0)
    							l2 = -l2;
    					}
    				}
    				k    = ct;
    				r[i] = l2;
    				for (i1 = 0; i1 < n; i1++)
    					v[i][i1] = v2[i1];
    				if (i == n-1)
    					ind = i + 1;
    				else {
    					for (i1 = 0; i1 < n; i1++) {
    						for (i2 = 0; i2 < n; i2++) {
    							C[i1][i2] = 0.0;
    							for (i3 = 0; i3 < n; i3++) {
    								x          = (i1 == i3) ? A[i1][i3] - l2 : A[i1][i3];
    								C[i1][i2] += x * B[i3][i2];
    							}
    						}
    					}
    					for (i1 = 0; i1 < n; i1++) {
    						for (i2 = 0; i2 < n; i2++)
    							B[i1][i2] = C[i1][i2];
    					}
    					for (i1 = 0; i1 < n; i1++) {
    						v1[i1] = 0.0;
    						for (i2 = 0; i2 < n; i2++)
    							v1[i1] += B[i1][i2] * v0[i2];
    					}
    					for (i1 = 0; i1 < n; i1++)
    						v0[i1] = v1[i1];
    					ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2);
    				}
    			}
    							// 収束しない場合
    			else {
    				for (i1 = 0; i1 < n; i1++)
    					v1[i1] = v2[i1];
    				l1 = l2;
    				k++;
    			}
    		}
    
    		return ind;
    	}
    
    	/*******************************************************/
    	/* 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               */
    	/*******************************************************/
    	static int gauss(double w[][], int n, int m, double eps)
    	{
    		double y1, y2;
    		int ind = 0, nm, m1, m2, i1, i2, i3;
    
    		nm = n + m;
    
    		for (i1 = 0; i1 < n && ind == 0; i1++) {
    
    			y1 = .0;
    			m1 = i1 + 1;
    			m2 = 0;
    						// ピボット要素の選択
    			for (i2 = i1; i2 < n; i2++) {
    				y2 = Math.abs(w[i2][i1]);
    				if (y1 < y2) {
    					y1 = y2;
    					m2 = i2;
    				}
    			}
    						// 逆行列が存在しない
    			if (y1 < eps)
    				ind = 1;
    						// 逆行列が存在する
    			else {
    							// 行の入れ替え
    				for (i2 = i1; i2 < nm; i2++) {
    					y1        = w[i1][i2];
    					w[i1][i2] = w[m2][i2];
    					w[m2][i2] = y1;
    				}
    							// 掃き出し操作
    				y1 = 1.0 / w[i1][i1];
    
    				for (i2 = m1; i2 < nm; i2++)
    					w[i1][i2] *= y1;
    
    				for (i2 = 0; i2 < n; i2++) {
    					if (i2 != i1) {
    						for (i3 = m1; i3 < nm; i3++)
    							w[i2][i3] -= w[i2][i1] * w[i1][i3];
    					}
    				}
    			}
    		}
    
    		return(ind);
    	}
    }
    
    /*
    ---------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
    */
    			
    アプレット版
    /****************************/
    /* 正準相関分析             */
    /*      coded by Y.Suganuma */
    /****************************/
    import java.awt.*;
    import java.awt.event.*;
    import java.applet.*;
    import java.util.StringTokenizer;
    
    public class Can extends Applet implements ActionListener {
    	TextField tx1, tx2, tx3;
    	TextArea ta1, ta2;
    	Button bt;
    	Font f = new Font("TimesRoman", Font.BOLD, 20);
    
    	/************/
    	/* 初期設定 */
    	/************/
    	public void init()
    	{
    					// レイアウト,背景色,フォント
    		setLayout(new BorderLayout(5, 5));
    		setBackground(new Color(225, 255, 225));
    		setFont(f);
    					// 上のパネル
    		Panel pn1 = new Panel();
    		add(pn1, BorderLayout.NORTH);
    
    		pn1.add(new Label("変数の数1:"));
    		tx1 = new TextField("2", 2);
    		pn1.add(tx1);
    
    		pn1.add(new Label("変数の数2:"));
    		tx2 = new TextField("2", 2);
    		pn1.add(tx2);
    
    		pn1.add(new Label("データの数:"));
    		tx3 = new TextField("100", 3);
    		pn1.add(tx3);
    					// 中央のパネル(データ)
    		Panel pn2 = new Panel();
    		add(pn2, BorderLayout.CENTER);
    
    		pn2.add(new Label("データ:"));
    		ta1 = new TextArea("66 22 44 31\n25 74 17 81\n50 23 53 71\n25 57 19 81\n74 47 64 47\n39 33 48 46\n14 22 9 69\n67 60 49 26\n42 40 77 65\n11 80 0 86\n32 0 43 74\n68 69 44 68\n24 49 9 71\n42 74 28 46\n60 58 73 28\n36 37 33 68\n24 44 19 83\n30 40 31 50\n55 40 60 49\n63 47 94 41\n72 30 100 45\n19 22 13 75\n43 39 43 34\n90 83 92 31\n51 77 52 82\n53 70 34 31\n28 51 53 44\n40 62 42 79\n31 48 22 68\n57 29 51 30\n64 89 57 42\n49 82 72 29\n53 31 55 43\n79 52 70 10\n45 19 43 57\n35 34 34 89\n4 69 0 100\n49 49 66 66\n92 82 97 6\n5 89 0 100\n65 26 83 28\n56 36 64 38\n48 50 25 22\n30 30 15 55\n40 65 38 42\n14 67 9 67\n84 96 90 8\n53 64 51 54\n50 89 60 52\n76 41 68 9\n49 40 53 49\n78 66 66 17\n76 58 90 29\n41 15 40 49\n63 60 55 33\n40 36 49 67\n78 54 71 18\n62 72 69 12\n64 47 42 53\n56 64 9 15\n77 35 56 25\n44 12 46 87\n80 9 56 19\n36 21 52 78\n48 63 64 48\n43 61 50 47\n58 23 28 50\n90 12 100 0\n13 33 11 77\n67 44 48 28\n75 45 68 17\n81 22 89 9\n46 45 59 55\n56 49 64 55\n65 62 72 27\n34 49 29 77\n45 33 60 63\n20 45 14 99\n33 38 26 87\n44 51 69 52\n64 57 64 48\n44 64 51 28\n63 48 56 11\n29 39 33 84\n40 48 51 54\n40 38 26 62\n68 46 61 26\n58 45 68 48\n64 44 77 63\n59 62 44 66\n81 53 93 19\n23 34 12 68\n51 35 55 46\n74 70 84 17\n42 33 56 44\n46 31 46 53\n33 57 38 63\n40 24 20 42\n53 36 60 31\n0 34 0 100\n", 15, 15);
    		pn2.add(ta1);
    
    		pn2.add(new Label(" "));
    		bt = new Button("OK");
    		bt.setBackground(Color.pink);
    		bt.addActionListener(this);
    		pn2.add(bt);
    					// 下のパネル(結果)
    		Panel pn3 = new Panel();
    		add(pn3, BorderLayout.SOUTH);
    
    		pn3.add(new Label("結果:"));
    		ta2 = new TextArea(7, 25);
    		pn3.add(ta2);
    	}
    
    	/******************************/
    	/* ボタンが押されたときの処理 */
    	/******************************/
    	public void actionPerformed(ActionEvent e)
    	{
    		if (e.getSource() == bt) {
    					// データ
    			int r = Integer.parseInt(tx1.getText());
    			int s = Integer.parseInt(tx2.getText());
    			int n = Integer.parseInt(tx3.getText());
    			int q = r + s;
    
    			double ryz[] = new double [r];
    			double v0[] = new double [r];
    			double x[][] = new double [q][n];
    			double ab[][] = new double [r][q];
    			for (int i1 = 0; i1 < r; i1++)
    				v0[i1] = 1.0;
    
    			String ss = ta1.getText();
    			StringTokenizer str = new StringTokenizer(ss, " \n");
    			for (int i1 = 0; str.hasMoreTokens() && i1 < n; i1++) {
    				for (int i2 = 0; i2 < q; i2++)
    					x[i2][i1] = Double.parseDouble(str.nextToken());
    			}
    					// 計算
    			int sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200);
    
    			if (sw == 0)
    				ta2.setText("逆行列が存在しない");
    			else {
    				ta2.setText("");
    				for (int i1 = 0; i1 < sw; i1++) {
    					ta2.append("相関係数 " + String.format("%.5f",ryz[i1]) + "\n");
    					ta2.append("   a");
    					for (int i2 = 0; i2 < r; i2++)
    						ta2.append(" " + String.format("%.5f",ab[i1][i2]));
    					ta2.append("\n");
    					ta2.append("   b");
    					for (int i2 = 0; i2 < s; i2++)
    						ta2.append(" " + String.format("%.5f",ab[i1][r+i2]));
    					ta2.append("\n");
    				}
    			}
    		}
    	}
    
    	/***********************************/
    	/* 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       */
    	/***********************************/
    	int canonical(int r, int s, int n, double x[][], double ryz[],
                             double ab[][], double eps, double v0[], int m, int ct)
    	{
    		double A[][], B[][], C[][], C11[][], C11i[][], C12[][], C21[][], C22[][], C22i[][],
    	           mean[], vv, w[][], w1[], len, v1[], v2[];
    		int i1, i2, i3, q, sw = 0, sw1;
    					// 領域の確保
    		q    = r + s;
    		mean = new double [q];
    		w1   = new double [s];
    		v1   = new double [r];
    		v2   = new double [r];
    		A    = new double [s][s];
    		B    = new double [r][r];
    		C    = new double [q][q];
    		C11  = new double [r][r];
    		C11i = new double [r][r];
    		C12  = new double [r][s];
    		C21  = new double [s][r];
    		C22  = new double [s][s];
    		C22i = new double [s][s];
    		w    = new double [s][2*s];
    					// 平均値の計算
    		for (i1 = 0; i1 < q; i1++) {
    			mean[i1] = 0.0;
    			for (i2 = 0; i2 < n; i2++)
    				mean[i1] += x[i1][i2];
    			mean[i1] /= n;
    		}
    					// 分散強分散行列の計算
    		for (i1 = 0; i1 < q; i1++) {
    			for (i2 = i1; i2 < q; i2++) {
    				vv = 0.0;
    				for (i3 = 0; i3 < n; i3++)
    					vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2]);
    				vv        /= (n - 1);
    				C[i1][i2]  = vv;
    				if (i1 != i2)
    					C[i2][i1] = vv;
    			}
    		}
    					// C11, C12, C21, C22 の設定
    						// C12
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < s; i2++)
    				C12[i1][i2] = C[i1][i2+r];
    		}
    						// C21
    		for (i1 = 0; i1 < s; i1++) {
    			for (i2 = 0; i2 < r; i2++)
    				C21[i1][i2] = C[i1+r][i2];
    		}
    						// C11とその逆行列
    		for (i1 = 0; i1 < r; i1++) {
    			for (i2 = 0; i2 < r; i2++) {
    				w[i1][i2]   = C[i1][i2];
    				C11[i1][i2] = C[i1][i2];
    			}
    			for (i2 = r; i2 < 2*r; i2++)
    				w[i1][i2] = 0.0;
    			w[i1][i1+r] = 1.0;
    		}
    		sw1 = gauss(w, r, r, 1.0e-10);
    		if (sw1 == 0) {
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++)
    					C11i[i1][i2] = w[i1][i2+r];
    			}
    		}
    		else
    			sw = 1;
    						// C22とその逆行列
    		for (i1 = 0; i1 < s; i1++) {
    			for (i2 = 0; i2 < s; i2++) {
    				w[i1][i2]   = C[i1+r][i2+r];
    				C22[i1][i2] = C[i1+r][i2+r];
    			}
    			for (i2 = s; i2 < 2*s; i2++)
    				w[i1][i2] = 0.0;
    			w[i1][i1+s] = 1.0;
    		}
    		sw1 = gauss(w, s, s, eps);
    		if (sw1 == 0) {
    			for (i1 = 0; i1 < s; i1++) {
    				for (i2 = 0; i2 < s; i2++)
    					C22i[i1][i2] = w[i1][i2+s];
    			}
    		}
    		else
    			sw = 1;
    					// 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 = 0; i1 < s; i1++) {
    				for (i2 = 0; i2 < r; i2++) {
    					A[i1][i2] = 0.0;
    					for (i3 = 0; i3 < s; i3++)
    						A[i1][i2] += C22i[i1][i3] * C21[i3][i2];
    				}
    			}
    
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < s; i2++) {
    					w[i1][i2] = 0.0;
    					for (i3 = 0; i3 < s; i3++)
    						w[i1][i2] += C12[i1][i3] * A[i3][i2];
    				}
    			}
    
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++) {
    					A[i1][i2] = 0.0;
    					for (i3 = 0; i3 < r; i3++)
    						A[i1][i2] += C11i[i1][i3] * w[i3][i2];
    				}
    			}
    						// 固有値と固有ベクトル(べき乗法)
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++)
    					B[i1][i2] = 0.0;
    				B[i1][i1] = 1.0;
    			}
    
    			sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2);
    
    			if (sw > 0) {
    
    				for (i1 = 0; i1 < r; i1++) {
    							// 相関係数
    					ryz[i1] = Math.sqrt(ryz[i1]);
    							// 大きさの調整(a)
    					for (i2 = 0; i2 < r; i2++) {
    						w1[i2] = 0.0;
    						for (i3 = 0; i3 < r; i3++)
    							w1[i2] += C11[i2][i3] * ab[i1][i3];
    					}
    					len = 0.0;
    					for (i2 = 0; i2 < r; i2++)
    						len += ab[i1][i2] * w1[i2];
    					len = Math.sqrt(len);
    					for (i2 = 0; i2 < r; i2++)
    						ab[i1][i2] /= len;
    							// bの計算
    					for (i2 = 0; i2 < s; i2++) {
    						w1[i2] = 0.0;
    						for (i3 = 0; i3 < r; i3++)
    							w1[i2] += C21[i2][i3] * ab[i1][i3];
    					}
    					for (i2 = 0; i2 < s; i2++) {
    						ab[i1][i2+r] = 0.0;
    						for (i3 = 0; i3 < s; i3++)
    							ab[i1][i2+r] += C22i[i2][i3] * w1[i3];
    					}
    					for (i2 = 0; i2 < s; i2++)
    						ab[i1][i2+r] /= ryz[i1];
    							// 大きさの調整(b)
    					for (i2 = 0; i2 < s; i2++) {
    						w1[i2] = 0.0;
    						for (i3 = 0; i3 < s; i3++)
    							w1[i2] += C22[i2][i3] * ab[i1][i3+r];
    					}
    					len = 0.0;
    					for (i2 = 0; i2 < s; i2++)
    						len += ab[i1][i2+r] * w1[i2];
    					len = Math.sqrt(len);
    					for (i2 = 0; i2 < s; i2++)
    						ab[i1][i2+r] /= len;
    				}
    			}
    		}
    		else
    			sw = 0;
    
    		return sw;
    	}
    
    	/****************************************/
    	/* 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             */
    	/****************************************/
    	int power(int i, int n, int m, int ct, double eps, double A[][], double B[][],
    	          double C[][], double r[], double v[][], double v0[], double v1[], double v2[])
    	{
    		double l1, l2, x;
    		int i1, i2, i3, ind, k, k1;
    					// 初期設定
    		ind = i;
    		k   = 0;
    		l1  = 0.0;
    		for (i1 = 0; i1 < n; i1++) {
    			l1     += v0[i1] * v0[i1];
    			v1[i1]  = v0[i1];
    		}
    		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 = 0; i1 < n; i1++) {
    					v2[i1] = 0.0;
    					for (i2 = 0; i2 < n; i2++)
    						v2[i1] += B[i1][i2] * v1[i2];
    					l2 += v2[i1] * v2[i1];
    				}
    				l2 = Math.sqrt(l2);
    				for (i1 = 0; i1 < n; i1++)
    					v1[i1] = v2[i1] / l2;
    			}
    						// 次の近似
    			l2 = 0.0;
    			for (i1 = 0; i1 < n; i1++) {
    				v2[i1] = 0.0;
    				for (i2 = 0; i2 < n; i2++)
    					v2[i1] += A[i1][i2] * v1[i2];
    				l2 += v2[i1] * v2[i1];
    			}
    			l2 = Math.sqrt(l2);
    			for (i1 = 0; i1 < n; i1++)
    				v2[i1] /= l2;
    						// 収束判定
    							// 収束した場合
    			if (Math.abs((l2-l1)/l1) < eps) {
    				k1 = -1;
    				for (i1 = 0; i1 < n && k1 < 0; i1++) {
    					if (Math.abs(v2[i1]) > 0.001) {
    						k1 = i1;
    						if (v2[k1]*v1[k1] < 0.0)
    							l2 = -l2;
    					}
    				}
    				k    = ct;
    				r[i] = l2;
    				for (i1 = 0; i1 < n; i1++)
    					v[i][i1] = v2[i1];
    				if (i == n-1)
    					ind = i + 1;
    				else {
    					for (i1 = 0; i1 < n; i1++) {
    						for (i2 = 0; i2 < n; i2++) {
    							C[i1][i2] = 0.0;
    							for (i3 = 0; i3 < n; i3++) {
    								x          = (i1 == i3) ? A[i1][i3] - l2 : A[i1][i3];
    								C[i1][i2] += x * B[i3][i2];
    							}
    						}
    					}
    					for (i1 = 0; i1 < n; i1++) {
    						for (i2 = 0; i2 < n; i2++)
    							B[i1][i2] = C[i1][i2];
    					}
    					for (i1 = 0; i1 < n; i1++) {
    						v1[i1] = 0.0;
    						for (i2 = 0; i2 < n; i2++)
    							v1[i1] += B[i1][i2] * v0[i2];
    					}
    					for (i1 = 0; i1 < n; i1++)
    						v0[i1] = v1[i1];
    					ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2);
    				}
    			}
    							// 収束しない場合
    			else {
    				for (i1 = 0; i1 < n; i1++)
    					v1[i1] = v2[i1];
    				l1 = l2;
    				k++;
    			}
    		}
    
    		return ind;
    	}
    
    	/******************************************/
    	/* 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  */
    	/******************************************/
    	int gauss(double w[][], int n, int m, double eps)
    	{
    		double y1, y2;
    		int ind = 0, nm, m1, m2, i1, i2, i3;
    
    		nm = n + m;
    
    		for (i1 = 0; i1 < n && ind == 0; i1++) {
    
    			y1 = .0;
    			m1 = i1 + 1;
    			m2 = 0;
    						// ピボット要素の選択
    			for (i2 = i1; i2 < n; i2++) {
    				y2 = Math.abs(w[i2][i1]);
    				if (y1 < y2) {
    					y1 = y2;
    					m2 = i2;
    				}
    			}
    						// 逆行列が存在しない
    			if (y1 < eps)
    				ind = 1;
    						// 逆行列が存在する
    			else {
    							// 行の入れ替え
    				for (i2 = i1; i2 < nm; i2++) {
    					y1        = w[i1][i2];
    					w[i1][i2] = w[m2][i2];
    					w[m2][i2] = y1;
    				}
    							// 掃き出し操作
    				y1 = 1.0 / w[i1][i1];
    
    				for (i2 = m1; i2 < nm; i2++)
    					w[i1][i2] *= y1;
    
    				for (i2 = 0; i2 < n; i2++) {
    					if (i2 != i1) {
    						for (i3 = m1; i3 < nm; i3++)
    							w[i2][i3] -= w[i2][i1] * w[i1][i3];
    					}
    				}
    			}
    		}
    
    		return(ind);
    	}
    }
    			

  3. JavaScript

      ここをクリックすると,任意のデータに対して画面上で実行することができます.
    <!DOCTYPE HTML>
    
    <HTML>
    
    <HEAD>
    
    	<TITLE>正準相関分析</TITLE>
    	<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=utf-8">
    	<SCRIPT TYPE="text/javascript">
    		function main()
    		{
    					// データ
    			let r = parseInt(document.getElementById("r").value);
    			let s = parseInt(document.getElementById("s").value);
    			let n = parseInt(document.getElementById("n").value);
    			let q = r + s;
    			let ryz = new Array();
    			let v0 = new Array();
    			let ab = new Array();
    			for (let i1 = 0; i1 < r; i1++) {
    				v0[i1] = 1.0;
    				ab[i1] = new Array();
    			}
    			let x = new Array();
    			for (let i1 = 0; i1 < q; i1++)
    				x[i1] = new Array();
    			let ss = (document.getElementById("data").value).split(/ {1,}|\n{1,}/);
    			let k = 0;
    			for (let i1 = 0; i1 < n; i1++) {
    				for (let i2 = 0; i2 < q; i2++) {
    					x[i2][i1] = parseFloat(ss[k]);
    					k++;
    				}
    			}
    					// 計算
    			let sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200);
    
    			if (sw == 0)
    				document.getElementById("ans").value = "逆行列が存在しない";
    			else {
    				let str = "";
    				for (let i1 = 0; i1 < sw; i1++) {
    					str = str + "相関係数 " + ryz[i1] + "\n";
    					str = str + "   a";
    					for (let i2 = 0; i2 < r; i2++)
    						str = str + " " + ab[i1][i2];
    					str = str + "\n   b";
    					for (let i2 = 0; i2 < s; i2++)
    						str = str + " " + ab[i1][r+i2];
    					str = str + "\n";
    				}
    				document.getElementById("ans").value = str;
    			}
    		}
    
    		/***********************************/
    		/* 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       */
    		/***********************************/
    		function canonical(r, s, n, x, ryz, ab, eps, v0, m, ct)
    		{
    			let vv;
    			let len;
    			let i1;
    			let i2;
    			let i3;
    			let q = r + s;
    			let sw = 0;
    			let sw1;
    						// 領域の確保
    			let mean = new Array();
    			let w1   = new Array();
    			let v1   = new Array();
    			let v2   = new Array();
    			let C    = new Array();
    			for (i1 = 0; i1 < q; i1++)
    				C[i1] = new Array();
    			let B    = new Array();
    			let C11  = new Array();
    			let C11i = new Array();
    			let C12  = new Array();
    			for (i1 = 0; i1 < r; i1++) {
    				B[i1]    = new Array();
    				C11[i1]  = new Array();
    				C11i[i1] = new Array();
    				C12[i1]  = new Array();
    			}
    			let A    = new Array();
    			let C21  = new Array();
    			let C22  = new Array();
    			let C22i = new Array();
    			let w    = new Array();
    			for (i1 = 0; i1 < s; i1++) {
    				A[i1]    = new Array();
    				C21[i1]  = new Array();
    				C22[i1]  = new Array();
    				C22i[i1] = new Array();
    				w[i1]    = new Array();
    			}
    						// 平均値の計算
    			for (i1 = 0; i1 < q; i1++) {
    				mean[i1] = 0.0;
    				for (i2 = 0; i2 < n; i2++)
    					mean[i1] += x[i1][i2];
    				mean[i1] /= n;
    			}
    						// 分散強分散行列の計算
    			for (i1 = 0; i1 < q; i1++) {
    				for (i2 = i1; i2 < q; i2++) {
    					vv = 0.0;
    					for (i3 = 0; i3 < n; i3++)
    						vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2]);
    					vv        /= (n - 1);
    					C[i1][i2]  = vv;
    					if (i1 != i2)
    						C[i2][i1] = vv;
    				}
    			}
    						// C11, C12, C21, C22 の設定
    							// C12
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < s; i2++)
    					C12[i1][i2] = C[i1][i2+r];
    			}
    							// C21
    			for (i1 = 0; i1 < s; i1++) {
    				for (i2 = 0; i2 < r; i2++)
    					C21[i1][i2] = C[i1+r][i2];
    			}
    							// C11とその逆行列
    			for (i1 = 0; i1 < r; i1++) {
    				for (i2 = 0; i2 < r; i2++) {
    					w[i1][i2]   = C[i1][i2];
    					C11[i1][i2] = C[i1][i2];
    				}
    				for (i2 = r; i2 < 2*r; i2++)
    					w[i1][i2] = 0.0;
    				w[i1][i1+r] = 1.0;
    			}
    
    			sw1 = gauss(w, r, r, 1.0e-10);
    
    			if (sw1 == 0) {
    				for (i1 = 0; i1 < r; i1++) {
    					for (i2 = 0; i2 < r; i2++)
    						C11i[i1][i2] = w[i1][i2+r];
    				}
    			}
    			else
    				sw = 1;
    							// C22とその逆行列
    			for (i1 = 0; i1 < s; i1++) {
    				for (i2 = 0; i2 < s; i2++) {
    					w[i1][i2]   = C[i1+r][i2+r];
    					C22[i1][i2] = C[i1+r][i2+r];
    				}
    				for (i2 = s; i2 < 2*s; i2++)
    					w[i1][i2] = 0.0;
    				w[i1][i1+s] = 1.0;
    			}
    
    			sw1 = gauss(w, s, s, eps);
    
    			if (sw1 == 0) {
    				for (i1 = 0; i1 < s; i1++) {
    					for (i2 = 0; i2 < s; i2++)
    						C22i[i1][i2] = w[i1][i2+s];
    				}
    			}
    			else
    				sw = 1;
    						// 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 = 0; i1 < s; i1++) {
    					for (i2 = 0; i2 < r; i2++) {
    						A[i1][i2] = 0.0;
    						for (i3 = 0; i3 < s; i3++)
    							A[i1][i2] += C22i[i1][i3] * C21[i3][i2];
    					}
    				}
    
    				for (i1 = 0; i1 < r; i1++) {
    					for (i2 = 0; i2 < s; i2++) {
    						w[i1][i2] = 0.0;
    						for (i3 = 0; i3 < s; i3++)
    							w[i1][i2] += C12[i1][i3] * A[i3][i2];
    					}
    				}
    
    				for (i1 = 0; i1 < r; i1++) {
    					for (i2 = 0; i2 < r; i2++) {
    						A[i1][i2] = 0.0;
    						for (i3 = 0; i3 < r; i3++)
    							A[i1][i2] += C11i[i1][i3] * w[i3][i2];
    					}
    				}
    							// 固有値と固有ベクトル(べき乗法)
    				for (i1 = 0; i1 < r; i1++) {
    					for (i2 = 0; i2 < r; i2++)
    						B[i1][i2] = 0.0;
    					B[i1][i1] = 1.0;
    				}
    
    				sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2);
    
    				if (sw > 0) {
    
    					for (i1 = 0; i1 < r; i1++) {
    								// 相関係数
    						ryz[i1] = Math.sqrt(ryz[i1]);
    								// 大きさの調整(a)
    						for (i2 = 0; i2 < r; i2++) {
    							w1[i2] = 0.0;
    							for (i3 = 0; i3 < r; i3++)
    								w1[i2] += C11[i2][i3] * ab[i1][i3];
    						}
    						len = 0.0;
    						for (i2 = 0; i2 < r; i2++)
    							len += ab[i1][i2] * w1[i2];
    						len = Math.sqrt(len);
    						for (i2 = 0; i2 < r; i2++)
    							ab[i1][i2] /= len;
    								// bの計算
    						for (i2 = 0; i2 < s; i2++) {
    							w1[i2] = 0.0;
    							for (i3 = 0; i3 < r; i3++)
    								w1[i2] += C21[i2][i3] * ab[i1][i3];
    						}
    						for (i2 = 0; i2 < s; i2++) {
    							ab[i1][i2+r] = 0.0;
    							for (i3 = 0; i3 < s; i3++)
    								ab[i1][i2+r] += C22i[i2][i3] * w1[i3];
    						}
    						for (i2 = 0; i2 < s; i2++)
    							ab[i1][i2+r] /= ryz[i1];
    								// 大きさの調整(b)
    						for (i2 = 0; i2 < s; i2++) {
    							w1[i2] = 0.0;
    							for (i3 = 0; i3 < s; i3++)
    								w1[i2] += C22[i2][i3] * ab[i1][i3+r];
    						}
    						len = 0.0;
    						for (i2 = 0; i2 < s; i2++)
    							len += ab[i1][i2+r] * w1[i2];
    						len = Math.sqrt(len);
    						for (i2 = 0; i2 < s; i2++)
    							ab[i1][i2+r] /= len;
    					}
    				}
    			}
    			else
    				sw = 0;
    
    			return sw;
    		}
    
    		/****************************************/
    		/* 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             */
    		/****************************************/
    		function power(i, n, m, ct, eps, A, B, C, r, v, v0, v1, v2)
    		{
    			let l1;
    			let l2;
    			let x;
    			let i1;
    			let i2;
    			let i3;
    			let ind;
    			let k;
    			let k1;
    						// 初期設定
    			ind = i;
    			k   = 0;
    			l1  = 0.0;
    			for (i1 = 0; i1 < n; i1++) {
    				l1     += v0[i1] * v0[i1];
    				v1[i1]  = v0[i1];
    			}
    			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 = 0; i1 < n; i1++) {
    						v2[i1] = 0.0;
    						for (i2 = 0; i2 < n; i2++)
    							v2[i1] += B[i1][i2] * v1[i2];
    						l2 += v2[i1] * v2[i1];
    					}
    					l2 = Math.sqrt(l2);
    					for (i1 = 0; i1 < n; i1++)
    						v1[i1] = v2[i1] / l2;
    				}
    							// 次の近似
    				l2 = 0.0;
    				for (i1 = 0; i1 < n; i1++) {
    					v2[i1] = 0.0;
    					for (i2 = 0; i2 < n; i2++)
    						v2[i1] += A[i1][i2] * v1[i2];
    					l2 += v2[i1] * v2[i1];
    				}
    				l2 = Math.sqrt(l2);
    				for (i1 = 0; i1 < n; i1++)
    					v2[i1] /= l2;
    							// 収束判定
    								// 収束した場合
    				if (Math.abs((l2-l1)/l1) < eps) {
    					k1 = -1;
    					for (i1 = 0; i1 < n && k1 < 0; i1++) {
    						if (Math.abs(v2[i1]) > 0.001) {
    							k1 = i1;
    							if (v2[k1]*v1[k1] < 0.0)
    								l2 = -l2;
    						}
    					}
    					k    = ct;
    					r[i] = l2;
    					for (i1 = 0; i1 < n; i1++)
    						v[i][i1] = v2[i1];
    					if (i == n-1)
    						ind = i + 1;
    					else {
    						for (i1 = 0; i1 < n; i1++) {
    							for (i2 = 0; i2 < n; i2++) {
    								C[i1][i2] = 0.0;
    								for (i3 = 0; i3 < n; i3++) {
    									x          = (i1 == i3) ? A[i1][i3] - l2 : A[i1][i3];
    									C[i1][i2] += x * B[i3][i2];
    								}
    							}
    						}
    						for (i1 = 0; i1 < n; i1++) {
    							for (i2 = 0; i2 < n; i2++)
    								B[i1][i2] = C[i1][i2];
    						}
    						for (i1 = 0; i1 < n; i1++) {
    							v1[i1] = 0.0;
    							for (i2 = 0; i2 < n; i2++)
    								v1[i1] += B[i1][i2] * v0[i2];
    						}
    						for (i1 = 0; i1 < n; i1++)
    							v0[i1] = v1[i1];
    						ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2);
    					}
    				}
    								// 収束しない場合
    				else {
    					for (i1 = 0; i1 < n; i1++)
    						v1[i1] = v2[i1];
    					l1 = l2;
    					k++;
    				}
    			}
    
    			return ind;
    		}
    
    		/******************************************/
    		/* 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  */
    		/******************************************/
    		function gauss(w, n, m, eps)
    		{
    			let y1, y2;
    			let ind = 0;
    			let nm;
    			let m1;
    			let m2;
    			let i1;
    			let i2;
    			let i3;
    
    			nm = n + m;
    
    			for (i1 = 0; i1 < n && ind == 0; i1++) {
    
    				y1 = .0;
    				m1 = i1 + 1;
    				m2 = 0;
    						// ピボット要素の選択
    				for (i2 = i1; i2 < n; i2++) {
    					y2 = Math.abs(w[i2][i1]);
    					if (y1 < y2) {
    						y1 = y2;
    						m2 = i2;
    					}
    				}
    						// 逆行列が存在しない
    				if (y1 < eps)
    					ind = 1;
    						// 逆行列が存在する
    				else {
    							// 行の入れ替え
    					for (i2 = i1; i2 < nm; i2++) {
    						y1        = w[i1][i2];
    						w[i1][i2] = w[m2][i2];
    						w[m2][i2] = y1;
    					}
    							// 掃き出し操作
    					y1 = 1.0 / w[i1][i1];
    
    					for (i2 = m1; i2 < nm; i2++)
    						w[i1][i2] *= y1;
    
    					for (i2 = 0; i2 < n; i2++) {
    						if (i2 != i1) {
    							for (i3 = m1; i3 < nm; i3++)
    								w[i2][i3] -= w[i2][i1] * w[i1][i3];
    						}
    					}
    				}
    			}
    
    			return(ind);
    		}
    	</SCRIPT>
    
    </HEAD>
    
    <BODY STYLE="font-size: 130%; background-color: #eeffee;">
    
    	<H2 STYLE="text-align:center"><B>正準相関分析</B></H2>
    
    	<DL>
    		<DT>  テキストフィールドおよびテキストエリアには,例として,テキストエリアに与えられた 100 個のデータに対して正準相関分析を行う場合に対する値が設定されています.他の問題を実行する場合は,それらを適切に修正してください.
    	</DL>
    
    	<DIV STYLE="text-align:center">
    		変数の数(r):<INPUT ID="r" STYLE="font-size: 100%" TYPE="text" SIZE="2" VALUE="2"> 
    		変数の数(s):<INPUT ID="s" STYLE="font-size: 100%" TYPE="text" SIZE="2" VALUE="2"> 
    		データの数:<INPUT ID="n" STYLE="font-size: 100%" TYPE="text" SIZE="2" VALUE="100"><BR><BR>
    		データ:<TEXTAREA ID="data" COLS="30" ROWS="15" STYLE="font-size: 100%">
    66 22 44 31
    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
    		</TEXTAREA> 
    		<BUTTON STYLE="font-size: 100%; background-color: pink" onClick="main()">OK</BUTTON><BR><BR>
    		<TEXTAREA ID="ans" COLS="50" ROWS="5" STYLE="font-size: 100%;"></TEXTAREA>
    	</DIV>
    
    </BODY>
    
    </HTML>
    			

  4. PHP

    <?php
    /****************************/
    /* 正準相関分析             */
    /*      coded by Y.Suganuma */
    /****************************/
    
    	fscanf(STDIN, "%d %d %d", $r, $s, $n);   // 各組の変数の数とデータの数
    	$q   = $r + $s;
    
    	$ryz = array($r);
    	$v0  = array($r);
    	$x   = array($q);
    	$ab  = array($r);
    	for ($i1 = 0; $i1 < $q; $i1++)
    		$x[$i1]  = array($n);
    	for ($i1 = 0; $i1 < $r; $i1++) {
    		$ab[$i1] = array($q);
    		$v0[$i1] = 1.0;
    	}
    
    	for ($i1 = 0; $i1 < $n; $i1++) {   // データ
    		$str       = trim(fgets(STDIN));
    		$x[0][$i1] = floatval(strtok($str, " "));
    		for ($i2 = 1; $i2 < $q; $i2++)
    			$x[$i2][$i1] = floatval(strtok(" "));
    	}
    
    	$sw = canonical($r, $s, $n, $x, $ryz, $ab, 1.0e-10, $v0, 15, 200);
    
    	if ($sw > 0) {
    		for ($i1 = 0; $i1 < $sw; $i1++) {
    			printf("相関係数 %f\n", $ryz[$i1]);
    			printf("   a");
    			for ($i2 = 0; $i2 < $r; $i2++)
    				printf(" %f", $ab[$i1][$i2]);
    			printf("\n");
    			printf("   b");
    			for ($i2 = 0; $i2 < $s; $i2++)
    				printf(" %f", $ab[$i1][$r+$i2]);
    			printf("\n");
    		}
    	}
    	else
    		printf("***error  解を求めることができませんでした\n");
    
    /***********************************/
    /* 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       */
    /***********************************/
    function canonical($r, $s, $n, $x, &$ryz, &$ab, $eps, $v0, $m, $ct)
    {
    	$sw = 0;
    					// 領域の確保
    	$q    = $r + $s;
    	$mean = array($q);
    	$w1   = array($s);
    	$v1   = array($r);
    	$v2   = array($r);
    	$A    = array($s);
    	$B    = array($r);
    	$C    = array($q);
    	$C11  = array($r);
    	$C11i = array($r);
    	$C12  = array($r);
    	$C21  = array($s);
    	$C22  = array($s);
    	$C22i = array($s);
    	$w    = array($s);
    	for ($i1 = 0; $i1 < $q; $i1++)
    		$C[$i1] = array($q);
    	for ($i1 = 0; $i1 < $r; $i1++) {
    		$B[$i1]    = array($r);
    		$C11[$i1]  = array($r);
    		$C11i[$i1] = array($r);
    		$C12[$i1]  = array($s);
    	}
    	for ($i1 = 0; $i1 < $s; $i1++) {
    		$A[$i1]    = array($s);
    		$C21[$i1]  = array($r);
    		$C22[$i1]  = array($s);
    		$C22i[$i1] = array($s);
    		$w[$i1]    = array(2*$s);
    	}
    					// 平均値の計算
    	for ($i1 = 0; $i1 < $q; $i1++) {
    		$mean[$i1] = 0.0;
    		for ($i2 = 0; $i2 < $n; $i2++)
    			$mean[$i1] += $x[$i1][$i2];
    		$mean[$i1] /= $n;
    	}
    					// 分散強分散行列の計算
    	for ($i1 = 0; $i1 < $q; $i1++) {
    		for ($i2 = $i1; $i2 < $q; $i2++) {
    			$vv = 0.0;
    			for ($i3 = 0; $i3 < $n; $i3++)
    				$vv += ($x[$i1][$i3] - $mean[$i1]) * ($x[$i2][$i3] - $mean[$i2]);
    			$vv        /= ($n - 1);
    			$C[$i1][$i2]  = $vv;
    			if ($i1 != $i2)
    				$C[$i2][$i1] = $vv;
    		}
    	}
    					// C11, C12, C21, C22 の設定
    						// C12
    	for ($i1 = 0; $i1 < $r; $i1++) {
    		for ($i2 = 0; $i2 < $s; $i2++)
    			$C12[$i1][$i2] = $C[$i1][$i2+$r];
    	}
    						// C21
    	for ($i1 = 0; $i1 < $s; $i1++) {
    		for ($i2 = 0; $i2 < $r; $i2++)
    			$C21[$i1][$i2] = $C[$i1+$r][$i2];
    	}
    						// C11とその逆行列
    	for ($i1 = 0; $i1 < $r; $i1++) {
    		for ($i2 = 0; $i2 < $r; $i2++) {
    			$w[$i1][$i2]   = $C[$i1][$i2];
    			$C11[$i1][$i2] = $C[$i1][$i2];
    		}
    		for ($i2 = $r; $i2 < 2*$r; $i2++)
    			$w[$i1][$i2] = 0.0;
    		$w[$i1][$i1+$r] = 1.0;
    	}
    	$sw1 = gauss($w, $r, $r, 1.0e-10);
    	if ($sw1 == 0) {
    		for ($i1 = 0; $i1 < $r; $i1++) {
    			for ($i2 = 0; $i2 < $r; $i2++)
    				$C11i[$i1][$i2] = $w[$i1][$i2+$r];
    		}
    	}
    	else
    		$sw = 1;
    						// C22とその逆行列
    	for ($i1 = 0; $i1 < $s; $i1++) {
    		for ($i2 = 0; $i2 < $s; $i2++) {
    			$w[$i1][$i2]   = $C[$i1+$r][$i2+$r];
    			$C22[$i1][$i2] = $C[$i1+$r][$i2+$r];
    		}
    		for ($i2 = $s; $i2 < 2*$s; $i2++)
    			$w[$i1][$i2] = 0.0;
    		$w[$i1][$i1+$s] = 1.0;
    	}
    	$sw1 = gauss($w, $s, $s, $eps);
    	if ($sw1 == 0) {
    		for ($i1 = 0; $i1 < $s; $i1++) {
    			for ($i2 = 0; $i2 < $s; $i2++)
    				$C22i[$i1][$i2] = $w[$i1][$i2+$s];
    		}
    	}
    	else
    		$sw = 1;
    					// 固有値λ及び固有ベクトルaの計算
    	if ($sw == 0) {
    						// 行列の計算
    		for ($i1 = 0; $i1 < $s; $i1++) {
    			for ($i2 = 0; $i2 < $r; $i2++) {
    				$A[$i1][$i2] = 0.0;
    				for ($i3 = 0; $i3 < $s; $i3++)
    					$A[$i1][$i2] += $C22i[$i1][$i3] * $C21[$i3][$i2];
    			}
    		}
    
    		for ($i1 = 0; $i1 < $r; $i1++) {
    			for ($i2 = 0; $i2 < $s; $i2++) {
    				$w[$i1][$i2] = 0.0;
    				for ($i3 = 0; $i3 < $s; $i3++)
    					$w[$i1][$i2] += $C12[$i1][$i3] * $A[$i3][$i2];
    			}
    		}
    
    		for ($i1 = 0; $i1 < $r; $i1++) {
    			for ($i2 = 0; $i2 < $r; $i2++) {
    				$A[$i1][$i2] = 0.0;
    				for ($i3 = 0; $i3 < $r; $i3++)
    					$A[$i1][$i2] += $C11i[$i1][$i3] * $w[$i3][$i2];
    			}
    		}
    						// 固有値と固有ベクトル(べき乗法)
    		for ($i1 = 0; $i1 < $r; $i1++) {
    			for ($i2 = 0; $i2 < $r; $i2++)
    				$B[$i1][$i2] = 0.0;
    			$B[$i1][$i1] = 1.0;
    		}
    
    		$sw = power(0, $r, $m, $ct, $eps, $A, $B, $C, $ryz, $ab, $v0, $v1, $v2);
    
    		if ($sw > 0) {
    
    			for ($i1 = 0; $i1 < $r; $i1++) {
    							// 相関係数
    				$ryz[$i1] = sqrt($ryz[$i1]);
    							// 大きさの調整(a)
    				for ($i2 = 0; $i2 < $r; $i2++) {
    					$w1[$i2] = 0.0;
    					for ($i3 = 0; $i3 < $r; $i3++)
    						$w1[$i2] += $C11[$i2][$i3] * $ab[$i1][$i3];
    				}
    				$len = 0.0;
    				for ($i2 = 0; $i2 < $r; $i2++)
    					$len += $ab[$i1][$i2] * $w1[$i2];
    				$len = sqrt($len);
    				for ($i2 = 0; $i2 < $r; $i2++)
    					$ab[$i1][$i2] /= $len;
    							// bの計算
    				for ($i2 = 0; $i2 < $s; $i2++) {
    					$w1[$i2] = 0.0;
    					for ($i3 = 0; $i3 < $r; $i3++)
    						$w1[$i2] += $C21[$i2][$i3] * $ab[$i1][$i3];
    				}
    				for ($i2 = 0; $i2 < $s; $i2++) {
    					$ab[$i1][$i2+$r] = 0.0;
    					for ($i3 = 0; $i3 < $s; $i3++)
    						$ab[$i1][$i2+$r] += $C22i[$i2][$i3] * $w1[$i3];
    				}
    				for ($i2 = 0; $i2 < $s; $i2++)
    					$ab[$i1][$i2+$r] /= $ryz[$i1];
    							// 大きさの調整(b)
    				for ($i2 = 0; $i2 < $s; $i2++) {
    					$w1[$i2] = 0.0;
    					for ($i3 = 0; $i3 < $s; $i3++)
    						$w1[$i2] += $C22[$i2][$i3] * $ab[$i1][$i3+$r];
    				}
    				$len = 0.0;
    				for ($i2 = 0; $i2 < $s; $i2++)
    					$len += $ab[$i1][$i2+$r] * $w1[$i2];
    				$len = sqrt($len);
    				for ($i2 = 0; $i2 < $s; $i2++)
    					$ab[$i1][$i2+$r] /= $len;
    			}
    		}
    	}
    	else
    		$sw = 0;
    
    	return $sw;
    }
    
    /*******************************************************/
    /* 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 : 正則性を判定する規準                     */
    /*      return : =0 : 正常                             */
    /*               =1 : 逆行列が存在しない               */
    /*******************************************************/
    function gauss(&$w, $n, $m, $eps)
    {
    	$ind = 0;
    	$nm  = $n + $m;
    
    	for ($i1 = 0; $i1 < $n && $ind == 0; $i1++) {
    
    		$y1 = .0;
    		$m1 = $i1 + 1;
    		$m2 = 0;
    
    		for ($i2 = $i1; $i2 < $n; $i2++) {
    			$y2 = abs($w[$i2][$i1]);
    			if ($y1 < $y2) {
    				$y1 = $y2;
    				$m2 = $i2;
    			}
    		}
    
    		if ($y1 < $eps)
    			$ind = 1;
    
    		else {
    
    			for ($i2 = $i1; $i2 < $nm; $i2++) {
    				$y1          = $w[$i1][$i2];
    				$w[$i1][$i2] = $w[$m2][$i2];
    				$w[$m2][$i2] = $y1;
    			}
    
    			$y1 = 1.0 / $w[$i1][$i1];
    
    			for ($i2 = $m1; $i2 < $nm; $i2++)
    				$w[$i1][$i2] *= $y1;
    
    			for ($i2 = 0; $i2 < $n; $i2++) {
    				if ($i2 != $i1) {
    					for ($i3 = $m1; $i3 < $nm; $i3++)
    						$w[$i2][$i3] -= $w[$i2][$i1] * $w[$i1][$i3];
    				}
    			}
    		}
    	}
    
    	return($ind);
    }
    
    /****************************************/
    /* 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             */
    /****************************************/
    function 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 = 0; $i1 < $n; $i1++) {
    		$l1      += $v0[$i1] * $v0[$i1];
    		$v1[$i1]  = $v0[$i1];
    	}
    	$l1 = sqrt($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 = 0; $i1 < $n; $i1++) {
    				$v2[$i1] = 0.0;
    				for ($i2 = 0; $i2 < $n; $i2++)
    					$v2[$i1] += $B[$i1][$i2] * $v1[$i2];
    				$l2 += $v2[$i1] * $v2[$i1];
    			}
    			$l2 = sqrt($l2);
    			for ($i1 = 0; $i1 < $n; $i1++)
    				$v1[$i1] = $v2[$i1] / $l2;
    		}
    						// 次の近似
    		$l2 = 0.0;
    		for ($i1 = 0; $i1 < $n; $i1++) {
    			$v2[$i1] = 0.0;
    			for ($i2 = 0; $i2 < $n; $i2++)
    				$v2[$i1] += $A[$i1][$i2] * $v1[$i2];
    			$l2 += $v2[$i1] * $v2[$i1];
    		}
    		$l2 = sqrt($l2);
    		for ($i1 = 0; $i1 < $n; $i1++)
    			$v2[$i1] /= $l2;
    						// 収束判定
    							// 収束した場合
    		if (abs(($l2-$l1)/$l1) < $eps) {
    			$k1 = -1;
    			for ($i1 = 0; $i1 < $n && $k1 < 0; $i1++) {
    				if (abs($v2[$i1]) > 0.001) {
    					$k1 = $i1;
    					if ($v2[$k1]*$v1[$k1] < 0.0)
    						$l2 = -$l2;
    				}
    			}
    			$k     = $ct;
    			$r[$i] = $l2;
    			for ($i1 = 0; $i1 < $n; $i1++)
    				$v[$i][$i1] = $v2[$i1];
    			if ($i == $n-1)
    				$ind = $i + 1;
    			else {
    				for ($i1 = 0; $i1 < $n; $i1++) {
    					for ($i2 = 0; $i2 < $n; $i2++) {
    						$C[$i1][$i2] = 0.0;
    						for ($i3 = 0; $i3 < $n; $i3++) {
    							$x            = ($i1 == $i3) ? $A[$i1][$i3] - $l2 : $A[$i1][$i3];
    							$C[$i1][$i2] += $x * $B[$i3][$i2];
    						}
    					}
    				}
    				for ($i1 = 0; $i1 < $n; $i1++) {
    					for ($i2 = 0; $i2 < $n; $i2++)
    						$B[$i1][$i2] = $C[$i1][$i2];
    				}
    				for ($i1 = 0; $i1 < $n; $i1++) {
    					$v1[$i1] = 0.0;
    					for ($i2 = 0; $i2 < $n; $i2++)
    						$v1[$i1] += $B[$i1][$i2] * $v0[$i2];
    				}
    				for ($i1 = 0; $i1 < $n; $i1++)
    					$v0[$i1] = $v1[$i1];
    				$ind = power($i+1, $n, $m, $ct, $eps, $A, $B, $C, $r, $v, $v0, $v1, $v2);
    			}
    		}
    							// 収束しない場合
    		else {
    			for ($i1 = 0; $i1 < $n; $i1++)
    				$v1[$i1] = $v2[$i1];
    			$l1 = $l2;
    			$k++;
    		}
    	}
    
    	return $ind;
    }
    
    /*
    ---------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
    */
    
    ?>
    			

  5. Ruby

    ############################
    # 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
    			

  6. Python

    # -*- coding: UTF-8 -*-
    import numpy as np
    import sys
    from math import *
    
    ############################################
    # 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 range(0, n) :
    
    		y1 = 0.0
    		m1 = i1 + 1
    		m2 = 0
    					# ピボット要素の選択
    		for i2 in range(i1, n) :
    			y2 = abs(w[i2][i1])
    			if y1 < y2 :
    				y1 = y2
    				m2 = i2
    					# 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 range(i1, nm) :
    				y1        = w[i1][i2]
    				w[i1][i2] = w[m2][i2]
    				w[m2][i2] = y1
    						# 掃き出し操作
    			y1 = 1.0 / w[i1][i1]
    
    			for i2 in range(m1, nm) :
    				w[i1][i2] *= y1
    
    			for i2 in range(0, n) :
    				if i2 != i1 :
    					for i3 in range(m1, nm) :
    						w[i2][i3] -= (w[i2][i1] * w[i1][i3])
    
    	return ind
    
    ############################################
    # 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 range(0, n) :
    		l1     += v0[i1] * v0[i1]
    		v1[i1]  = v0[i1]
    	l1 = 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 range(0, n) :
    				v2[i1] = 0.0
    				for i2 in range(0, n) :
    					v2[i1] += B[i1][i2] * v1[i2]
    				l2 += v2[i1] * v2[i1]
    			l2 = sqrt(l2)
    			for i1 in range(0, n) :
    				v1[i1] = v2[i1] / l2
    				# 次の近似
    		l2 = 0.0
    		for i1 in range(0, n) :
    			v2[i1] = 0.0
    			for i2 in range(0, n) :
    				v2[i1] += A[i1][i2] * v1[i2]
    			l2 += v2[i1] * v2[i1]
    		l2 = sqrt(l2)
    		for i1 in range(0, n) :
    			v2[i1] /= l2
    				# 収束判定
    					# 収束した場合
    		if abs((l2-l1)/l1) < eps :
    			k1 = -1
    			for i1 in range(0, n) :
    				if abs(v2[i1]) > 0.001 :
    					k1 = i1
    					if v2[k1]*v1[k1] < 0.0 :
    						l2 = -l2
    					break
    			k    = ct
    			r[i] = l2
    			for i1 in range(0, n) :
    				v[i][i1] = v2[i1]
    			if i == n-1 :
    				ind = i + 1
    			else :
    				for i1 in range(0, n) :
    					for i2 in range(0, n) :
    						C[i1][i2] = 0.0
    						for i3 in range(0, n) :
    							if i1 == i3 :
    								x = A[i1][i3] - l2
    							else :
    								x = A[i1][i3]
    							C[i1][i2] += x * B[i3][i2]
    				for i1 in range(0, n) :
    					for i2 in range(0, n) :
    						B[i1][i2] = C[i1][i2]
    				for i1 in range(0, n) :
    					v1[i1] = 0.0
    					for i2 in range(0, n) :
    						v1[i1] += B[i1][i2] * v0[i2]
    				for i1 in range(0, n) :
    					v0[i1] = v1[i1]
    				ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2)
    					# 収束しない場合
    		else :
    			for i1 in range(0, n) :
    				v1[i1] = v2[i1]
    			l1 = l2
    			k += 1
    
    	return ind
    
    ###################################
    # 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 = np.empty(q, np.float)
    	w1   = np.empty(s, np.float)
    	v1   = np.empty(r, np.float)
    	v2   = np.empty(r, np.float)
    	A    = np.empty((s, s), np.float)
    	B    = np.empty((r, r), np.float)
    	C    = np.empty((q, q), np.float)
    	C11  = np.empty((r, r), np.float)
    	C11i = np.empty((r, r), np.float)
    	C12  = np.empty((r, s), np.float)
    	C21  = np.empty((s, r), np.float)
    	C22  = np.empty((s, s), np.float)
    	C22i = np.empty((s, s), np.float)
    	w    = np.empty((s, 2*s), np.float)
    			# 平均値の計算
    	for i1 in range(0, q) :
    		mean[i1] = 0.0
    		for i2 in range(0, n) :
    			mean[i1] += x[i1][i2]
    		mean[i1] /= n
    			# 分散強分散行列の計算
    	for i1 in range(0, q) :
    		for i2 in range(i1, q) :
    			vv = 0.0
    			for i3 in range(0, n) :
    				vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2])
    			vv        /= (n - 1)
    			C[i1][i2]  = vv
    			if i1 != i2 :
    				C[i2][i1] = vv
    			# C11, C12, C21, C22 の設定
    				# C12
    	for i1 in range(0, r) :
    		for i2 in range(0, s) :
    			C12[i1][i2] = C[i1][i2+r]
    				# C21
    	for i1 in range(0, s) :
    		for i2 in range(0, r) :
    			C21[i1][i2] = C[i1+r][i2]
    				# C11とその逆行列
    	for i1 in range(0, r) :
    		for i2 in range(0, r) :
    			w[i1][i2]   = C[i1][i2]
    			C11[i1][i2] = C[i1][i2]
    		for i2 in range(r, 2*r) :
    			w[i1][i2] = 0.0
    		w[i1][i1+r] = 1.0
    	sw1 = gauss(w, r, r, 1.0e-10)
    	if sw1 == 0 :
    		for i1 in range(0, r) :
    			for i2 in range(0, r) :
    				C11i[i1][i2] = w[i1][i2+r]
    	else :
    		sw = 1
    				# C22とその逆行列
    	for i1 in range(0, s) :
    		for i2 in range(0, s) :
    			w[i1][i2]   = C[i1+r][i2+r]
    			C22[i1][i2] = C[i1+r][i2+r]
    		for i2 in range(s, 2*s) :
    			w[i1][i2] = 0.0
    		w[i1][i1+s] = 1.0
    	sw1 = gauss(w, s, s, eps)
    	if sw1 == 0 :
    		for i1 in range(0, s) :
    			for i2 in range(0, s) :
    				C22i[i1][i2] = w[i1][i2+s]
    	else :
    		sw = 1
    			# 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 range(0, s) :
    			for i2 in range(0, r) :
    				A[i1][i2] = 0.0
    				for i3 in range(0, s) :
    					A[i1][i2] += C22i[i1][i3] * C21[i3][i2]
    
    		for i1 in range(0, r) :
    			for i2 in range(0, s) :
    				w[i1][i2] = 0.0
    				for i3 in range(0, s) :
    					w[i1][i2] += C12[i1][i3] * A[i3][i2]
    
    		for i1 in range(0, r) :
    			for i2 in range(0, r) :
    				A[i1][i2] = 0.0
    				for i3 in range(0, r) :
    					A[i1][i2] += C11i[i1][i3] * w[i3][i2]
    				# 固有値と固有ベクトル(べき乗法)
    		for i1 in range(0, r) :
    			for i2 in range(0, r) :
    				B[i1][i2] = 0.0
    			B[i1][i1] = 1.0
    
    		sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2)
    
    		if sw > 0 :
    
    			for i1 in range(0, r) :
    					# 相関係数
    				ryz[i1] = sqrt(ryz[i1])
    					# 大きさの調整(a)
    				for i2 in range(0, r) :
    					w1[i2] = 0.0
    					for i3 in range(0, r) :
    						w1[i2] += C11[i2][i3] * ab[i1][i3]
    				len = 0.0
    				for i2 in range(0, r) :
    					len += ab[i1][i2] * w1[i2]
    				len = sqrt(len)
    				for i2 in range(0, r) :
    					ab[i1][i2] /= len
    					# bの計算
    				for i2 in range(0, s) :
    					w1[i2] = 0.0
    					for i3 in range(0, r) :
    						w1[i2] += C21[i2][i3] * ab[i1][i3]
    				for i2 in range(0, s) :
    					ab[i1][i2+r] = 0.0
    					for i3 in range(0, s) :
    						ab[i1][i2+r] += C22i[i2][i3] * w1[i3]
    				for i2 in range(0, s) :
    					ab[i1][i2+r] /= ryz[i1]
    					# 大きさの調整(b)
    				for i2 in range(0, s) :
    					w1[i2] = 0.0
    					for i3 in range(0, s) :
    						w1[i2] += C22[i2][i3] * ab[i1][i3+r]
    				len = 0.0
    				for i2 in range(0, s) :
    					len += ab[i1][i2+r] * w1[i2]
    				len = sqrt(len)
    				for i2 in range(0, s) :
    					ab[i1][i2+r] /= len
    	else :
    		sw = 0
    
    	return sw
    
    ############################
    # 正準相関分析
    #      coded by Y.Suganuma
    ############################
    
    line = sys.stdin.readline()
    ss   = line.split()
    r    = int(ss[0])   # 各組の変数
    s    = int(ss[1])   # 各組の変数
    n    = int(ss[2])   # データの数
    q    = r + s
    
    ryz  = np.empty(r, np.float)
    v0   = np.ones(r, np.float)
    x    = np.empty((q, n), np.float)
    ab   = np.empty((r, q), np.float)
    
    for i1 in range(0, n) :   # データ
    	line = sys.stdin.readline()
    	ss   = line.split()
    	for i2 in range(0, q) :
    		x[i2][i1] = float(ss[i2])
    
    sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200)
    
    if sw > 0 :
    	for i1 in range(0, sw) :
    		print("相関係数 " + str(ryz[i1]))
    		print("   a", end="")
    		for i2 in range(0, r) :
    			print(" " + str(ab[i1][i2]), end="")
    		print()
    		print("   b", end="")
    		for i2 in range(0, s) :
    			print(" " + str(ab[i1][r+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 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
    """
    			

  7. C#

    /****************************/
    /* 正準相関分析             */
    /*      coded by Y.Suganuma */
    /****************************/
    using System;
    
    class Program
    {
    	static void Main()
    	{
    		Test1 ts = new Test1();
    	}
    }
    
    class Test1
    {
    	public Test1()
    	{
    		char[] charSep = new char[] {' '};
    					// 各組の変数の数とデータの数
    		String[] str = Console.ReadLine().Split(charSep, StringSplitOptions.RemoveEmptyEntries);
    		int r        = int.Parse(str[0]);
    		int s        = int.Parse(str[1]);
    		int n        = int.Parse(str[2]);
    		int q        = r + s;
    
    		double[] ryz = new double [r];
    		double[] v0  = new double [r];
    		for (int i1 = 0; i1 < r; i1++)
    			v0[i1] = 1.0;
    		double[][] x = new double [q][];
    		for (int i1 = 0; i1 < q; i1++)
    			x[i1] = new double [n];
    		double[][] ab = new double [r][];
    		for (int i1 = 0; i1 < r; i1++)
    			ab[i1] = new double [q];
    					// データ
    		for (int i1 = 0; i1 < n; i1++) {
    			str = Console.ReadLine().Split(charSep, StringSplitOptions.RemoveEmptyEntries);
    			for (int i2 = 0; i2 < q; i2++)
    				x[i2][i1] = int.Parse(str[i2]);
    		}
    
    		int sw = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200);
    
    		if (sw > 0) {
    			for (int i1 = 0; i1 < sw; i1++) {
    				Console.WriteLine("相関係数 " + ryz[i1]);
    				Console.Write("   a");
    				for (int i2 = 0; i2 < r; i2++)
    					Console.Write(" " + ab[i1][i2]);
    				Console.WriteLine();
    				Console.Write("   b");
    				for (int i2 = 0; i2 < s; i2++)
    					Console.Write(" " + ab[i1][r+i2]);
    				Console.WriteLine();
    			}
    		}
    		else
    			Console.WriteLine("***error  解を求めることができませんでした");
    	}
    
    	/***********************************/
    	/* 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       */
    	/***********************************/
    	int canonical(int r, int s, int n, double[][] x, double[] ryz,
                      double[][] ab, double eps, double[] v0, int m, int ct)
    	{
    		int sw = 0;
    					// 領域の確保
    		int q           = r + s;
    		double[] mean   = new double [q];
    		double[] w1     = new double [s];
    		double[] v1     = new double [r];
    		double[] v2     = new double [r];
    		double[][] A    = new double [s][];
    		double[][] B    = new double [r][];
    		double[][] C    = new double [q][];
    		double[][] C11  = new double [r][];
    		double[][] C11i = new double [r][];
    		double[][] C12  = new double [r][];
    		double[][] C21  = new double [s][];
    		double[][] C22  = new double [s][];
    		double[][] C22i = new double [s][];
    		double[][] w    = new double [s][];
    		for (int i1 = 0; i1 < q; i1++)
    			C[i1] = new double [q];
    		for (int i1 = 0; i1 < s; i1++) {
    			A[i1]    = new double [s];
    			C21[i1]  = new double [r];
    			C22[i1]  = new double [s];
    			C22i[i1] = new double [s];
    			w[i1]    = new double [2*s];
    		}
    		for (int i1 = 0; i1 < r; i1++) {
    			B[i1]    = new double [r];
    			C11[i1]  = new double [r];
    			C11i[i1] = new double [r];
    			C12[i1]  = new double [s];
    		}
    					// 平均値の計算
    		for (int i1 = 0; i1 < q; i1++) {
    			mean[i1] = 0.0;
    			for (int i2 = 0; i2 < n; i2++)
    				mean[i1] += x[i1][i2];
    			mean[i1] /= n;
    		}
    					// 分散強分散行列の計算
    		for (int i1 = 0; i1 < q; i1++) {
    			for (int i2 = i1; i2 < q; i2++) {
    				double vv = 0.0;
    				for (int i3 = 0; i3 < n; i3++)
    					vv += (x[i1][i3] - mean[i1]) * (x[i2][i3] - mean[i2]);
    				vv        /= (n - 1);
    				C[i1][i2]  = vv;
    				if (i1 != i2)
    					C[i2][i1] = vv;
    			}
    		}
    					// C11, C12, C21, C22 の設定
    						// C12
    		for (int i1 = 0; i1 < r; i1++) {
    			for (int i2 = 0; i2 < s; i2++)
    				C12[i1][i2] = C[i1][i2+r];
    		}
    						// C21
    		for (int i1 = 0; i1 < s; i1++) {
    			for (int i2 = 0; i2 < r; i2++)
    				C21[i1][i2] = C[i1+r][i2];
    		}
    						// C11とその逆行列
    		for (int i1 = 0; i1 < r; i1++) {
    			for (int i2 = 0; i2 < r; i2++) {
    				w[i1][i2]   = C[i1][i2];
    				C11[i1][i2] = C[i1][i2];
    			}
    			for (int i2 = r; i2 < 2*r; i2++)
    				w[i1][i2] = 0.0;
    			w[i1][i1+r] = 1.0;
    		}
    
    		int sw1 = gauss(w, r, r, 1.0e-10);
    
    		if (sw1 == 0) {
    			for (int i1 = 0; i1 < r; i1++) {
    				for (int i2 = 0; i2 < r; i2++)
    					C11i[i1][i2] = w[i1][i2+r];
    			}
    		}
    		else
    			sw = 1;
    						// C22とその逆行列
    		for (int i1 = 0; i1 < s; i1++) {
    			for (int i2 = 0; i2 < s; i2++) {
    				w[i1][i2]   = C[i1+r][i2+r];
    				C22[i1][i2] = C[i1+r][i2+r];
    			}
    			for (int i2 = s; i2 < 2*s; i2++)
    				w[i1][i2] = 0.0;
    			w[i1][i1+s] = 1.0;
    		}
    
    		sw1 = gauss(w, s, s, eps);
    
    		if (sw1 == 0) {
    			for (int i1 = 0; i1 < s; i1++) {
    				for (int i2 = 0; i2 < s; i2++)
    					C22i[i1][i2] = w[i1][i2+s];
    			}
    		}
    		else
    			sw = 1;
    					// 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 (int i1 = 0; i1 < s; i1++) {
    				for (int i2 = 0; i2 < r; i2++) {
    					A[i1][i2] = 0.0;
    					for (int i3 = 0; i3 < s; i3++)
    						A[i1][i2] += C22i[i1][i3] * C21[i3][i2];
    				}
    			}
    
    			for (int i1 = 0; i1 < r; i1++) {
    				for (int i2 = 0; i2 < s; i2++) {
    					w[i1][i2] = 0.0;
    					for (int i3 = 0; i3 < s; i3++)
    						w[i1][i2] += C12[i1][i3] * A[i3][i2];
    				}
    			}
    
    			for (int i1 = 0; i1 < r; i1++) {
    				for (int i2 = 0; i2 < r; i2++) {
    					A[i1][i2] = 0.0;
    					for (int i3 = 0; i3 < r; i3++)
    						A[i1][i2] += C11i[i1][i3] * w[i3][i2];
    				}
    			}
    						// 固有値と固有ベクトル(べき乗法)
    			for (int i1 = 0; i1 < r; i1++) {
    				for (int i2 = 0; i2 < r; i2++)
    					B[i1][i2] = 0.0;
    				B[i1][i1] = 1.0;
    			}
    
    			sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2);
    
    			if (sw > 0) {
    
    				for (int i1 = 0; i1 < r; i1++) {
    							// 相関係数
    					ryz[i1] = Math.Sqrt(ryz[i1]);
    							// 大きさの調整(a)
    					for (int i2 = 0; i2 < r; i2++) {
    						w1[i2] = 0.0;
    						for (int i3 = 0; i3 < r; i3++)
    							w1[i2] += C11[i2][i3] * ab[i1][i3];
    					}
    					double len = 0.0;
    					for (int i2 = 0; i2 < r; i2++)
    						len += ab[i1][i2] * w1[i2];
    					len = Math.Sqrt(len);
    					for (int i2 = 0; i2 < r; i2++)
    						ab[i1][i2] /= len;
    							// bの計算
    					for (int i2 = 0; i2 < s; i2++) {
    						w1[i2] = 0.0;
    						for (int i3 = 0; i3 < r; i3++)
    							w1[i2] += C21[i2][i3] * ab[i1][i3];
    					}
    					for (int i2 = 0; i2 < s; i2++) {
    						ab[i1][i2+r] = 0.0;
    						for (int i3 = 0; i3 < s; i3++)
    							ab[i1][i2+r] += C22i[i2][i3] * w1[i3];
    					}
    					for (int i2 = 0; i2 < s; i2++)
    						ab[i1][i2+r] /= ryz[i1];
    							// 大きさの調整(b)
    					for (int i2 = 0; i2 < s; i2++) {
    						w1[i2] = 0.0;
    						for (int i3 = 0; i3 < s; i3++)
    							w1[i2] += C22[i2][i3] * ab[i1][i3+r];
    					}
    					len = 0.0;
    					for (int i2 = 0; i2 < s; i2++)
    						len += ab[i1][i2+r] * w1[i2];
    					len = Math.Sqrt(len);
    					for (int i2 = 0; i2 < s; i2++)
    						ab[i1][i2+r] /= len;
    				}
    			}
    		}
    		else
    			sw = 0;
    
    		return sw;
    	}
    
    	/****************************************/
    	/* 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             */
    	/****************************************/
    	int power(int i, int n, int m, int ct, double eps, double[][] A,
    	                 double[][] B, double[][] C, double[] r, double[][] v,
    	                 double[] v0, double[] v1, double[] v2)
    	{
    					// 初期設定
    		int ind   = i;
    		int k     = 0;
    		double l1 = 0.0;
    		for (int i1 = 0; i1 < n; i1++) {
    			l1     += v0[i1] * v0[i1];
    			v1[i1]  = v0[i1];
    		}
    		l1 = Math.Sqrt(l1);
    					// 繰り返し計算
    		while (k < ct) {
    						// 丸め誤差の修正
    			double l2;
    			if (k%m == 0) {
    				l2 = 0.0;
    				for (int i1 = 0; i1 < n; i1++) {
    					v2[i1] = 0.0;
    					for (int i2 = 0; i2 < n; i2++)
    						v2[i1] += B[i1][i2] * v1[i2];
    					l2 += v2[i1] * v2[i1];
    				}
    				l2 = Math.Sqrt(l2);
    				for (int i1 = 0; i1 < n; i1++)
    					v1[i1] = v2[i1] / l2;
    			}
    						// 次の近似
    			l2 = 0.0;
    			for (int i1 = 0; i1 < n; i1++) {
    				v2[i1] = 0.0;
    				for (int i2 = 0; i2 < n; i2++)
    					v2[i1] += A[i1][i2] * v1[i2];
    				l2 += v2[i1] * v2[i1];
    			}
    			l2 = Math.Sqrt(l2);
    			for (int i1 = 0; i1 < n; i1++)
    				v2[i1] /= l2;
    						// 収束判定
    							// 収束した場合
    			if (Math.Abs((l2-l1)/l1) < eps) {
    				int k1 = -1;
    				for (int i1 = 0; i1 < n && k1 < 0; i1++) {
    					if (Math.Abs(v2[i1]) > 0.001) {
    						k1 = i1;
    						if (v2[k1]*v1[k1] < 0.0)
    							l2 = -l2;
    					}
    				}
    				k    = ct;
    				r[i] = l2;
    				for (int i1 = 0; i1 < n; i1++)
    					v[i][i1] = v2[i1];
    				if (i == n-1)
    					ind = i + 1;
    				else {
    					for (int i1 = 0; i1 < n; i1++) {
    						for (int i2 = 0; i2 < n; i2++) {
    							C[i1][i2] = 0.0;
    							for (int i3 = 0; i3 < n; i3++) {
    								double x   = (i1 == i3) ? A[i1][i3] - l2 : A[i1][i3];
    								C[i1][i2] += x * B[i3][i2];
    							}
    						}
    					}
    					for (int i1 = 0; i1 < n; i1++) {
    						for (int i2 = 0; i2 < n; i2++)
    							B[i1][i2] = C[i1][i2];
    					}
    					for (int i1 = 0; i1 < n; i1++) {
    						v1[i1] = 0.0;
    						for (int i2 = 0; i2 < n; i2++)
    							v1[i1] += B[i1][i2] * v0[i2];
    					}
    					for (int i1 = 0; i1 < n; i1++)
    						v0[i1] = v1[i1];
    					ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2);
    				}
    			}
    							// 収束しない場合
    			else {
    				for (int i1 = 0; i1 < n; i1++)
    					v1[i1] = v2[i1];
    				l1 = l2;
    				k++;
    			}
    		}
    
    		return ind;
    	}
    
    	/*******************************************************/
    	/* 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               */
    	/*******************************************************/
    	int gauss(double[][] w, int n, int m, double eps)
    	{
    		int ind = 0;
    		int nm  = n + m;
    
    		for (int i1 = 0; i1 < n && ind == 0; i1++) {
    
    			double y1 = .0;
    			int m1    = i1 + 1;
    			int m2    = 0;
    						// ピボット要素の選択
    			for (int i2 = i1; i2 < n; i2++) {
    				double y2 = Math.Abs(w[i2][i1]);
    				if (y1 < y2) {
    					y1 = y2;
    					m2 = i2;
    				}
    			}
    						// 逆行列が存在しない
    			if (y1 < eps)
    				ind = 1;
    						// 逆行列が存在する
    			else {
    							// 行の入れ替え
    				for (int i2 = i1; i2 < nm; i2++) {
    					y1        = w[i1][i2];
    					w[i1][i2] = w[m2][i2];
    					w[m2][i2] = y1;
    				}
    							// 掃き出し操作
    				y1 = 1.0 / w[i1][i1];
    
    				for (int i2 = m1; i2 < nm; i2++)
    					w[i1][i2] *= y1;
    
    				for (int i2 = 0; i2 < n; i2++) {
    					if (i2 != i1) {
    						for (int i3 = m1; i3 < nm; i3++)
    							w[i2][i3] -= w[i2][i1] * w[i1][i3];
    					}
    				}
    			}
    		}
    
    		return ind;
    	}
    }
    
    /*
    ---------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
    */
    			

  8. VB

    '**************************'
    ' 正準相関分析             '
    '      coded by Y.Suganuma '
    '**************************'
    Imports System.Text.RegularExpressions
    
    Module Test
    
    	Sub Main()
    
    		Dim MS As Regex = New Regex("\s+") 
    					' 各組の変数の数とデータの数
    		Dim str() As String = MS.Split(Console.ReadLine().Trim())
    		Dim r As Integer    = Integer.Parse(str(0))
    		Dim s As Integer    = Integer.Parse(str(1))
    		Dim n As Integer    = Integer.Parse(str(2))
    		Dim q As Integer    = r + s
    
    		Dim ryz(r) As Double
    		Dim v0(r) As Double
    		For i1 As Integer = 0 To r-1
    			v0(i1) = 1.0
    		Next
    		Dim x(q,n) As Double
    		Dim ab(r,q) As Double
    					' データ
    		For i1 As Integer = 0 To n-1
    			str = MS.Split(Console.ReadLine().Trim())
    			For i2 As Integer = 0 To q-1
    				x(i2,i1) = Integer.Parse(str(i2))
    			Next
    		Next
    
    		Dim sw As Integer = canonical(r, s, n, x, ryz, ab, 1.0e-10, v0, 15, 200)
    
    		If sw > 0
    			For i1 As Integer = 0 To sw-1
    				Console.WriteLine("相関係数 " & ryz(i1))
    				Console.Write("   a")
    				For i2 As Integer = 0 To r-1
    					Console.Write(" " & ab(i1,i2))
    				Next
    				Console.WriteLine()
    				Console.Write("   b")
    				For i2 As Integer = 0 To s-1
    					Console.Write(" " & ab(i1,r+i2))
    				Next
    				Console.WriteLine()
    			Next
    		Else
    			Console.WriteLine("***error  解を求めることができませんでした")
    		End If
    
    	End Sub
    
    	'*********************************'
    	' 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       '
    	'*********************************'
    	Function canonical(r As Integer, s As Integer, n As Integer, x(,) As Double,
    	                   ryz() As Double, ab(,) As Double, eps As Double, v0() As Double,
    	                   m As Integer, ct As Integer)
    
    		Dim sw As Integer = 0
    		Dim q As Integer  = r + s
    					' 領域の確保
    		Dim mean(q) As Double
    		Dim w1(s) As Double
    		Dim v1(r) As Double
    		Dim v2(r) As Double
    		Dim A(s,s) As Double
    		Dim B(r,r) As Double
    		Dim C(q,q) As Double
    		Dim C11(r,r) As Double
    		Dim C11i(r,r) As Double
    		Dim C12(r,s) As Double
    		Dim C21(s,r) As Double
    		Dim C22(s,s) As Double
    		Dim C22i(s,s) As Double
    		Dim w(s,2*s) As Double
    					' 平均値の計算
    		For i1 As Integer = 0 To q-1
    			mean(i1) = 0.0
    			For i2 As Integer = 0 To n-1
    				mean(i1) += x(i1,i2)
    			Next
    			mean(i1) /= n
    		Next
    					' 分散強分散行列の計算
    		For i1 As Integer = 0 To q-1
    			For i2 As Integer = i1 To q-1
    				Dim vv As Double = 0.0
    				For i3 As Integer = 0 To n-1
    					vv += (x(i1,i3) - mean(i1)) * (x(i2,i3) - mean(i2))
    				Next
    				vv       /= (n - 1)
    				C(i1,i2)  = vv
    				If i1 <> i2
    					C(i2,i1) = vv
    				End If
    			Next
    		Next
    					' C11, C12, C21, C22 の設定
    						' C12
    		For i1 As Integer = 0 To r-1
    			For i2 As Integer = 0 To s-1
    				C12(i1,i2) = C(i1,i2+r)
    			Next
    		Next
    						' C21
    		For i1 As Integer = 0 To s-1
    			For i2 As Integer = 0 To r-1
    				C21(i1,i2) = C(i1+r,i2)
    			Next
    		Next
    						' C11とその逆行列
    		For i1 As Integer = 0 To r-1
    			For i2 As Integer = 0 To r-1
    				w(i1,i2)   = C(i1,i2)
    				C11(i1,i2) = C(i1,i2)
    			Next
    			For i2 As Integer = r To 2*r-1
    				w(i1,i2) = 0.0
    			Next
    			w(i1,i1+r) = 1.0
    		Next
    
    		Dim sw1 As Integer = gauss(w, r, r, 1.0e-10)
    
    		If sw1 = 0
    			For i1 As Integer = 0 To r-1
    				For i2 As Integer = 0 To r-1
    					C11i(i1,i2) = w(i1,i2+r)
    				Next
    			Next
    		Else
    			sw = 1
    		End If
    						' C22とその逆行列
    		For i1 As Integer = 0 To s-1
    			For i2 As Integer = 0 To s-1
    				w(i1,i2)   = C(i1+r,i2+r)
    				C22(i1,i2) = C(i1+r,i2+r)
    			Next
    			For i2 As Integer = s To 2*s-1
    				w(i1,i2) = 0.0
    			Next
    			w(i1,i1+s) = 1.0
    		Next
    
    		sw1 = gauss(w, s, s, eps)
    
    		If sw1 = 0
    			For i1 As Integer = 0 To s-1
    				For i2 As Integer = 0 To s-1
    					C22i(i1,i2) = w(i1,i2+s)
    				Next
    			Next
    		Else
    			sw = 1
    		End If
    					' 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 As Integer = 0 To s-1
    				For i2 As Integer = 0 To r-1
    					A(i1,i2) = 0.0
    					For i3 As Integer = 0 To s-1
    						A(i1,i2) += C22i(i1,i3) * C21(i3,i2)
    					Next
    				Next
    			Next
    
    			For i1 As Integer = 0 To r-1
    				For i2 As Integer = 0 To s-1
    					w(i1,i2) = 0.0
    					For i3 As Integer = 0 To s-1
    						w(i1,i2) += C12(i1,i3) * A(i3,i2)
    					Next
    				Next
    			Next
    
    			For i1 As Integer = 0 To r-1
    				For i2 As Integer = 0 To r-1
    					A(i1,i2) = 0.0
    					For i3 As Integer = 0 To r-1
    						A(i1,i2) += C11i(i1,i3) * w(i3,i2)
    					Next
    				Next
    			Next
    						' 固有値と固有ベクトル(べき乗法)
    			For i1 As Integer = 0 To r-1
    				For i2 As Integer = 0 To r-1
    					B(i1,i2) = 0.0
    				Next
    				B(i1,i1) = 1.0
    			Next
    
    			sw = power(0, r, m, ct, eps, A, B, C, ryz, ab, v0, v1, v2)
    
    			If sw > 0
    
    				For i1 As Integer = 0 To r-1
    							' 相関係数
    					ryz(i1) = Math.Sqrt(ryz(i1))
    							' 大きさの調整(a)
    					For i2 As Integer = 0 To r-1
    						w1(i2) = 0.0
    						For i3 As Integer = 0 To r-1
    							w1(i2) += C11(i2,i3) * ab(i1,i3)
    						Next
    					Next
    					Dim len As Double = 0.0
    					For i2 As Integer = 0 To r-1
    						len += ab(i1,i2) * w1(i2)
    					Next
    					len = Math.Sqrt(len)
    					For i2 As Integer = 0 To r-1
    						ab(i1,i2) /= len
    					Next
    							' bの計算
    					For i2 As Integer = 0 To s-1
    						w1(i2) = 0.0
    						For i3 As Integer = 0 To r-1
    							w1(i2) += C21(i2,i3) * ab(i1,i3)
    						Next
    					Next
    					For i2 As Integer = 0 To s-1
    						ab(i1,i2+r) = 0.0
    						For i3 As Integer = 0To s-1
    							ab(i1,i2+r) += C22i(i2,i3) * w1(i3)
    						Next
    					Next
    					For i2 As Integer = 0 To s-1
    						ab(i1,i2+r) /= ryz(i1)
    					Next
    							' 大きさの調整(b)
    					For  i2 As Integer = 0 To s-1
    						w1(i2) = 0.0
    						For i3 As Integer = 0 To s-1
    							w1(i2) += C22(i2,i3) * ab(i1,i3+r)
    						Next
    					Next
    					len = 0.0
    					For i2 As Integer = 0 To s-1
    						len += ab(i1,i2+r) * w1(i2)
    					Next
    					len = Math.Sqrt(len)
    					For i2 As Integer = 0 To s-1
    						ab(i1,i2+r) /= len
    					Next
    				Next
    			End If
    		Else
    			sw = 0
    		End If
    
    		Return sw
    
    	End Function
    
    	''''''''''''''''''''''''''''''''''''''''
    	' 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             '
    	''''''''''''''''''''''''''''''''''''''''
    	Function power(i As Integer, n As Integer, m As Integer, ct As Integer,
    	               eps As Double, A(,) As Double, B(,) As Double, C(,) As Double,
    	               r() As Double, v(,) As Double, v0() As Double, v1() As Double,
    	               v2() As Double)
    					' 初期設定
    		Dim ind As Integer = i
    		Dim k As Integer   = 0
    		Dim l1 As Double   = 0.0
    		For i1 As Integer = 0 To n-1
    			l1     += v0(i1) * v0(i1)
    			v1(i1)  = v0(i1)
    		Next
    		l1 = Math.Sqrt(l1)
    					' 繰り返し計算
    		Do While k < ct
    						' 丸め誤差の修正
    			Dim l2 As Double
    			If (k Mod m) = 0
    				l2 = 0.0
    				For i1 As Integer = 0 To n-1
    					v2(i1) = 0.0
    					For i2 As Integer = 0 To n-1
    						v2(i1) += B(i1,i2) * v1(i2)
    					Next
    					l2 += v2(i1) * v2(i1)
    				Next
    				l2 = Math.Sqrt(l2)
    				For i1 As Integer = 0 To n-1
    					v1(i1) = v2(i1) / l2
    				Next
    			End If
    						' 次の近似
    			l2 = 0.0
    			For i1 As Integer = 0 To n-1
    				v2(i1) = 0.0
    				For i2 As Integer = 0 To n-1
    					v2(i1) += A(i1,i2) * v1(i2)
    				Next
    				l2 += v2(i1) * v2(i1)
    			Next
    			l2 = Math.Sqrt(l2)
    			For i1 As Integer = 0 To n-1
    				v2(i1) /= l2
    			Next
    						' 収束判定
    							' 収束した場合
    			If Math.Abs((l2-l1)/l1) < eps
    				Dim k1 As Integer = -1
    				Dim ii As Integer = 0
    				Do While ii < n and k1 < 0
    					If Math.Abs(v2(ii)) > 0.001
    						k1 = ii
    						If v2(k1)*v1(k1) < 0.0
    							l2 = -l2
    						End If
    					End If
    					ii += 1
    				Loop
    				k    = ct
    				r(i) = l2
    				For i1 As Integer = 0 To n-1
    					v(i,i1) = v2(i1)
    				Next
    				If i = n-1
    					ind = i + 1
    				Else
    					For i1 As Integer = 0 To n-1
    						For i2 As Integer = 0 To n-1
    							C(i1,i2) = 0.0
    							For i3 As Integer = 0 To n-1
    								Dim x As Double = A(i1,i3) - l2
    								If i1 <> i3
    									x = A(i1,i3)
    								End If
    								C(i1,i2) += x * B(i3,i2)
    							Next
    						Next
    					Next
    					For i1 As Integer = 0 To n-1
    						For i2 As Integer = 0 To n-1
    							B(i1,i2) = C(i1,i2)
    						Next
    					Next
    					For i1 As Integer = 0 To n-1
    						v1(i1) = 0.0
    						For i2 As Integer = 0 To n-1
    							v1(i1) += B(i1,i2) * v0(i2)
    						Next
    					Next
    					For i1 As Integer = 0 To n-1
    						v0(i1) = v1(i1)
    					Next
    					ind = power(i+1, n, m, ct, eps, A, B, C, r, v, v0, v1, v2)
    				End If
    							' 収束しない場合
    			Else
    				For i1 As Integer = 0 To n-1
    					v1(i1) = v2(i1)
    				Next
    				l1 = l2
    				k += 1
    			End If
    		Loop
    
    		Return ind
    
    	End Function
    
    	''''''''''''''''''''''''''''''''''''''''''
    	' 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  '
    	''''''''''''''''''''''''''''''''''''''''''
    	Function gauss(w(,) As Double, n As Integer, m As Integer, eps As Double) As Integer
    
    		Dim ind As Integer = 0
    		Dim nm As Integer  = n + m
    
    		Dim i1 As Integer = 0
    		Do While i1 < n and ind = 0
    
    			Dim y1 As Double  = 0.0
    			Dim m1 As Integer = i1 + 1
    			Dim m2 As Integer = 0
    						' ピボット要素の選択
    			For i2 As Integer = i1 To n-1
    				Dim y2 As Double = Math.Abs(w(i2,i1))
    				If y1 < y2
    					y1 = y2
    					m2 = i2
    				End If
    			Next
    						' 逆行列が存在しない
    			If y1 < eps
    				ind = 1
    						' 逆行列が存在する
    			Else
    							' 行の入れ替え
    				For i2 As Integer = i1 To nm-1
    					y1       = w(i1,i2)
    					w(i1,i2) = w(m2,i2)
    					w(m2,i2) = y1
    				Next
    							' 掃き出し操作
    				y1 = 1.0 / w(i1,i1)
    
    				For i2 As Integer = m1 To nm-1
    					w(i1,i2) *= y1
    				Next
    
    				For i2 As Integer = 0 To n-1
    					If i2 <> i1
    						For i3 As Integer = m1 To nm-1
    							w(i2,i3) -= w(i2,i1) * w(i1,i3)
    						Next
    					End If
    				Next
    			End If
    			i1 += 1
    		Loop
    
    		Return ind
    
    	End Function
    
    End Module
    
    /*
    ---------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
    */
    			

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