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  1. #include <stdio.h>
  2. #include <stdlib.h>
  3. #include <math.h>
  4.  
  5. #define SIZE 4
  6. #define EPSILON 1e-9   
  7. #define MAX_ITER 1000  
  8.  
  9. double vector_norm(double *v, int n) {
  10.     double sum = 0.0;
  11.     for (int i = 0; i < n; i++) {
  12.         sum += v[i] * v[i];
  13.     }
  14.     return sqrt(sum);
  15. }
  16.  
  17. void mat_vec_mul(double A[SIZE][SIZE], double *x, double *y, int n) {
  18.     for (int i = 0; i < n; i++) {
  19.         y[i] = 0.0;
  20.         for (int j = 0; j < n; j++) {
  21.             y[i] += A[i][j] * x[j];
  22.         }
  23.     }
  24. }
  25.  
  26. int main() {
  27.     double A[SIZE][SIZE] = {
  28.         {1.0,  2.0, 3.0,  5.0},
  29.         {3.0, -5.0, 1.0,  4.0},
  30.         {5.0,  9.0, 2.0, -6.0},
  31.         {1.0,  7.0, 4.0,  1.0}
  32.     };
  33.  
  34.     double x[SIZE], y[SIZE], Ax[SIZE];
  35.     double lambda_old = 0.0, lambda_new = 0.0;
  36.  
  37.     for (int i = 0; i < SIZE; i++) {
  38.         x[i] = 1.0;
  39.     }
  40.  
  41.     printf("べき乗法による収束状況の確認 \n");
  42.     printf("初期ベクトル x(0): [%.1f, %.1f, %.1f, %.1f]\n\n", x[0], x[1], x[2], x[3]);
  43.     printf("%-5s | %-12s | %-12s | %-30s\n", "Iter", "固有値(新)", "差分値", "固有ベクトルx(k)");
  44.     int actual_iters = 0;
  45.     for (int iter = 1; iter <= MAX_ITER; iter++) {
  46.         actual_iters = iter;
  47.         mat_vec_mul(A, x, y, SIZE);
  48.  
  49.         double norm_y = vector_norm(y, SIZE);
  50.         if (norm_y < 1e-12) break;
  51.         for (int i = 0; i < SIZE; i++) {
  52.             y[i] /= norm_y;
  53.         }
  54.  
  55.         mat_vec_mul(A, y, Ax, SIZE);
  56.         double num = 0.0, den = 0.0;
  57.         for (int i = 0; i < SIZE; i++) {
  58.             num += y[i] * Ax[i];
  59.             den += y[i] * y[i];
  60.         }
  61.         lambda_new = num / den;
  62.         double diff = fabs(lambda_new - lambda_old);
  63.  
  64.  
  65.         if (iter <= 5 || iter % 5 == 0) {
  66.             printf("%-5d | %-12.8f | %-12.4e | [%.5f, %.5f, %.5f, %.5f]\n", 
  67.                    iter, lambda_new, diff, y[0], y[1], y[2], y[3]);
  68.         }
  69.  
  70.         if (diff < EPSILON) {
  71.             if (iter % 5 != 0 && iter > 5) { // 最終ステップを確実に表示させる
  72.                 printf("%-5d | %-12.8f | %-12.4e | [%.5f, %.5f, %.5f, %.5f]\n", 
  73.                        iter, lambda_new, diff, y[0], y[1], y[2], y[3]);
  74.             }
  75.             break;
  76.         }
  77.  
  78.         // 次のステップに向けて x を更新
  79.         for (int i = 0; i < SIZE; i++) {
  80.             x[i] = y[i];
  81.         }
  82.         lambda_old = lambda_new;
  83.     }
  84.  
  85.  
  86.     printf("反復回数 %d 回で収束しました。\n", actual_iters);
  87.     printf("\n=== 計算結果 ===\n");
  88.     printf("最大固有値 (λ1)          : %.10f\n", lambda_new);
  89.     printf("対応する固有ベクトル (x1) : [");
  90.     for (int i = 0; i < SIZE; i++) {
  91.         printf("%.10f%s", y[i], (i == SIZE - 1) ? "]\n" : ", ");
  92.     }
  93.  
  94.     printf("\n=== 検証: Ax と λx の比較 ===\n");
  95.     mat_vec_mul(A, y, Ax, SIZE); // Axを再計算
  96.     printf("Ax    : [");
  97.     for (int i = 0; i < SIZE; i++) {
  98.         printf("%.6f%s", Ax[i], (i == SIZE - 1) ? "]\n" : ", ");
  99.     }
  100.     printf("λ * x : [");
  101.     for (int i = 0; i < SIZE; i++) {
  102.         printf("%.6f%s", lambda_new * y[i], (i == SIZE - 1) ? "]\n" : ", ");
  103.     }
  104.  
  105.     return 0;
  106. }
  107.  
  108.  
Success #stdin #stdout 0.01s 5312KB
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べき乗法による収束状況の確認 
初期ベクトル x(0): [1.0, 1.0, 1.0, 1.0]

Iter  | 固有値(新) | 差分値    | 固有ベクトルx(k)        
1     | 7.06015038   | 7.0602e+00   | [0.55069, 0.15019, 0.50063, 0.65081]
2     | 7.56272200   | 5.0257e-01   | [0.68485, 0.48918, 0.14675, 0.51975]
3     | 7.79665790   | 2.3394e-01   | [0.53345, 0.20811, 0.56744, 0.59172]
4     | 8.36088120   | 5.6422e-01   | [0.66241, 0.41253, 0.25086, 0.57281]
5     | 8.52180634   | 1.6093e-01   | [0.58882, 0.28456, 0.47179, 0.59139]
10    | 8.69758623   | 9.4221e-03   | [0.62524, 0.34192, 0.38099, 0.58908]
15    | 8.69591999   | 7.0277e-04   | [0.62205, 0.33644, 0.39006, 0.58967]
20    | 8.69624282   | 7.2845e-05   | [0.62237, 0.33699, 0.38916, 0.58962]
25    | 8.69621204   | 7.2757e-06   | [0.62234, 0.33693, 0.38925, 0.58962]
30    | 8.69621514   | 7.2934e-07   | [0.62235, 0.33694, 0.38924, 0.58962]
35    | 8.69621483   | 7.3086e-08   | [0.62234, 0.33694, 0.38924, 0.58962]
40    | 8.69621486   | 7.3240e-09   | [0.62234, 0.33694, 0.38924, 0.58962]
45    | 8.69621486   | 7.3395e-10   | [0.62234, 0.33694, 0.38924, 0.58962]
反復回数 45 回で収束しました。

=== 計算結果 ===
最大固有値 (λ1)          : 8.6962148610
対応する固有ベクトル (x1) : [0.6223447229, 0.3369369049, 0.3892384556, 0.5896219066]

=== 検証: Ax と λx の比較 ===
Ax    : [5.412043, 2.930076, 3.384901, 5.127479]
λ * x : [5.412043, 2.930076, 3.384901, 5.127479]
https://ideone.com/X7hzWV
language:
C (gcc 8.3)
created:
1 day ago
visibility:
public

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