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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.         {2.0,  1.0, 2.0,  5.0},
  29.         {3.0, -3.0, 1.0,  6.0},
  30.         {0.0,  1.0, 2.0, 7.0},
  31.         {1.0,  1.0, 3.0,  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("初期ベクトル x(0): [%.1f, %.1f, %.1f, %.1f]\n\n", x[0], x[1], x[2], x[3]);
  42.     printf("%-5s | %-12s | %-12s | %-30s\n", "Iter", "固有値(新)", "差分値", "固有ベクトルx(k)");
  43.     int actual_iters = 0;
  44.     for (int iter = 1; iter <= MAX_ITER; iter++) {
  45.         actual_iters = iter;
  46.         mat_vec_mul(A, x, y, SIZE);
  47.  
  48.         double norm_y = vector_norm(y, SIZE);
  49.         if (norm_y < 1e-12) break;
  50.         for (int i = 0; i < SIZE; i++) {
  51.             y[i] /= norm_y;
  52.         }
  53.  
  54.         mat_vec_mul(A, y, Ax, SIZE);
  55.         double num = 0.0, den = 0.0;
  56.         for (int i = 0; i < SIZE; i++) {
  57.             num += y[i] * Ax[i];
  58.             den += y[i] * y[i];
  59.         }
  60.         lambda_new = num / den;
  61.         double diff = fabs(lambda_new - lambda_old);
  62.  
  63.  
  64.         if (iter <= 5 || iter % 5 == 0) {
  65.             printf("%-5d | %-12.8f | %-12.4e | [%.5f, %.5f, %.5f, %.5f]\n", 
  66.                    iter, lambda_new, diff, y[0], y[1], y[2], y[3]);
  67.         }
  68.  
  69.         if (diff < EPSILON) {
  70.             if (iter % 5 != 0 && iter > 5) { // 最終ステップを確実に表示させる
  71.                 printf("%-5d | %-12.8f | %-12.4e | [%.5f, %.5f, %.5f, %.5f]\n", 
  72.                        iter, lambda_new, diff, y[0], y[1], y[2], y[3]);
  73.             }
  74.             break;
  75.         }
  76.  
  77.         // 次のステップに向けて x を更新
  78.         for (int i = 0; i < SIZE; i++) {
  79.             x[i] = y[i];
  80.         }
  81.         lambda_old = lambda_new;
  82.     }
  83.  
  84.  
  85.     printf("反復回数 %d 回で収束しました。\n", actual_iters);
  86.     printf("\n最大固有値 (λ1)          : %.10f\n", lambda_new);
  87.     printf("対応する固有ベクトル (x1) : [");
  88.     for (int i = 0; i < SIZE; i++) {
  89.         printf("%.10f%s", y[i], (i == SIZE - 1) ? "]\n" : ", ");
  90.     }
  91.  
  92.     printf("\n   検証: Ax と λx の比較   \n");
  93.     mat_vec_mul(A, y, Ax, SIZE); // Axを再計算
  94.     printf("Ax    : [");
  95.     for (int i = 0; i < SIZE; i++) {
  96.         printf("%.6f%s", Ax[i], (i == SIZE - 1) ? "]\n" : ", ");
  97.     }
  98.     printf("λ * x : [");
  99.     for (int i = 0; i < SIZE; i++) {
  100.         printf("%.6f%s", lambda_new * y[i], (i == SIZE - 1) ? "]\n" : ", ");
  101.     }
  102.  
  103.     return 0;
  104. }
  105.  
  106.  
Success #stdin #stdout 0s 5328KB
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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     | 7.58947368   | 7.5895e+00   | [0.59235, 0.41464, 0.59235, 0.35541]
2     | 7.97210119   | 3.8263e-01   | [0.59901, 0.42786, 0.53677, 0.41230]
3     | 7.72878414   | 2.4332e-01   | [0.59682, 0.44176, 0.55001, 0.38228]
4     | 7.86852048   | 1.3974e-01   | [0.60110, 0.42802, 0.54559, 0.39724]
5     | 7.78782087   | 8.0700e-02   | [0.59823, 0.43820, 0.54642, 0.38926]
10    | 7.81916110   | 4.7095e-03   | [0.59949, 0.43391, 0.54638, 0.39217]
15    | 7.81737213   | 2.6407e-04   | [0.59941, 0.43420, 0.54635, 0.39202]
20    | 7.81747243   | 1.4759e-05   | [0.59941, 0.43418, 0.54635, 0.39203]
25    | 7.81746682   | 8.2460e-07   | [0.59941, 0.43418, 0.54635, 0.39203]
30    | 7.81746714   | 4.6068e-08   | [0.59941, 0.43418, 0.54635, 0.39203]
35    | 7.81746712   | 2.5737e-09   | [0.59941, 0.43418, 0.54635, 0.39203]
37    | 7.81746712   | 8.1175e-10   | [0.59941, 0.43418, 0.54635, 0.39203]
反復回数 37 回で収束しました。

最大固有値 (λ1)          : 7.8174671191
対応する固有ベクトル (x1) : [0.5994100822, 0.4341839804, 0.5463547658, 0.3920309865]

   検証: Ax と λx の比較   
Ax    : [4.685869, 3.394219, 4.271110, 3.064689]
λ * x : [4.685869, 3.394219, 4.271110, 3.064689]
https://ideone.com/ticfVi
language:
C (gcc 8.3)
created:
2 days ago
visibility:
public

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