基本的GMRES基于cpp实现

基本的GMRES基于cpp实现

理论部分和matlab版本可以查看我的其他文章：

1. 基本理论
2. 完整实现

以下为代码，头文件里面有cuda的东西。无视即可。

int main()
{
     
 //time start
 clock_t startTime = clock();
 //load
 FILE *fp;
 static double data[100];
 if (fp = fopen("data.bin", "rb"))
 {
     
  for (int i = 0; i<100; i++)
  {
     
   fread(&data[i], sizeof(double), 100, fp);
  }
 }
 //data
 double *A, *x0, *b;
 A = data;
 x0 = new double[10];
 b = new double[10];
 for (int i = 0; i < 10; i++)
 {
     
  x0[i] = 0;
  b[i] = 0;
 }
 x0[0] = 1;
 //GMRES
 double *y0, *r0, *beta;
 y0 = new double[10];
 r0 = new double[10];
 for (int i = 0; i < 10; i++)
 {
     
  y0[i] = 0;
  r0[i] = 0;
 }
 for (int i = 0; i < 10; i++)
 {
     
  for (int j = 0; j < 10; j++)
  {
     
   y0[i] += A[i * 10 + j] * x0[j];
  }
  r0[i] = b[i] - y0[i];
 }
 beta = new double[1];
 beta[0] = 0;
 double *v = new double[10];
 for (int i = 0; i < 10; i++)
 {
     
  v[i] = 0;
 }
 //V1,单位化
 double temp = 0;
 for (int j = 0; j < 10; j++)
 {
     
  temp = temp + r0[j] * r0[j];
 }
 beta[0] = sqrt(temp);
 for (int j = 0; j < 10; j++)
 {
     
  if (beta[0] == 0)
  {
     
   v[j] = 0;
  }
  else
  {
     
   v[j] = r0[j] / beta[0];
  }
 }
 //data
 double *omiga, *V, *H;
 omiga = new double[10];//vector
 for (int j = 0; j < 10; j++)
 {
     
  omiga[j] = 0;
 }
 V = new double[100];//matrix
 for (int j = 0; j < 100; j++)
 {
     
  V[j] = 0;
 }
 H = new double[110];//matrix
 for (int j = 0; j < 110; j++)
 {
     
  H[j] = 0;
 }
 //V(:,1) = v1
 for (int i = 0; i < 10; i++)
 {
     
  V[10 * i] = v[i];
 }
 //Do
 double resVec[10],resVal;
 for (int j = 0; j < 10; j++)
 {
     
  //Compute omiga(j) := A*v(j)
  for (int i = 0; i < 10; i++)
  {
     
   for (int k = 0; k < 10; k++)
   {
     
    omiga[i] += A[i * 10 + k] * V[k * 10 + j];
   }
  }
  //h(i,j) and res
  for (int i = 0; i <= j; i++)
  {
     
   //h(i,j)
   for (int k = 0; k < 10; k++)
   {
     
    H[i * 10 + j] += omiga[k] * V[10 * k + i];
   }
   //omiga(i,j)
   for (int k = 0; k < 10; k++)
   {
     
    omiga[k] = omiga[k] - H[i * 10 + j] * V[10 * k + i];
   }
  }
  //h(j+1,j)
  for (int i = 0; i < 10; i++)
  {
     
   H[10 * (j + 1) + j] += omiga[i] * omiga[i];
  }
  H[10 * (j + 1) + j] = sqrt(H[10 * (j + 1) + j]);
  //if
  if (H[10 * (j + 1) + j] < 1e-11)//10-10
  {
     
   break;
   printf("done , residual is %d\n", H[10 * (j + 1) + j]);
  }
  v(j+1)
  //for (int i = 0; i <10; i++)
  //{
     
  // v[i] = omiga[i] / H[10 * (j + 1) + j];
  //}
  //V(:,j+1)
  for (int i = 0; i <10; i++)
  {
     
   if (j < 9)
   {
     
    V[10 * i + (j + 1)] = omiga[i] / H[10 * (j + 1) + j];
   }
   else
   {
     
    resVec[i] = omiga[i];
   }
  }
 }
 //visualizion
 //data
 printf("data:\n");
 for (int i = 0; i < 10; i++)
 {
     
  for (int j = 0; j < 10; j++)
  {
     
   cout << data[10*i+j] << "  ";
  }
  cout << endl;
 }
 printf("\n");
 //A
 printf("A:\n");
 for (int i = 0; i < 10; i++)
 {
     
  for (int j = 0; j < 10; j++)
  {
     
   cout << A[10 * i + j] << "  ";
  }
  cout << endl;
 }
 printf("\n");
 //x0
 printf("x0:\n");
 for (int i = 0; i < 10; i++)
 {
     
  cout << x0[i] << "  ";
 }
 printf("\n");
 //b
 printf("b:\n");
 for (int i = 0; i < 10; i++)
 {
     
  cout << b[i] << "  ";
 }
 printf("\n");
 //test
 printf("v:\n");
 for (int i = 0; i < 10; i++)
 {
     
  cout << v[i] << "  ";
 }
 printf("\n");
 //V
 printf("V:\n");
 for (int i = 0; i < 10; i++)
 {
     
  for (int j = 0; j < 10; j++)
  {
     
   cout << V[10 * i + j] << "         ";
  }
  cout << endl;
  cout << "next row" << endl;
 }
 printf("\n");
 //H
 printf("H:\n");
 for (int i = 0; i < 11; i++)
 {
     
  for (int j = 0; j < 10; j++)
  {
     
   cout << H[10 * i + j] << "    ";
  }
  cout << endl;
  cout << "next row" << endl;
 }
 printf("\n");
 //res vector
 printf("res vector:\n");
 for (int i = 0; i < 10; i++)
 {
     
  cout << resVec[i] << "  ";
 }
 printf("\n");
 //res Val
 resVal = 0;
 for (int i = 0; i < 10; i++)
 {
     
  resVal += resVec[i] * resVec[i];
 }
 cout << "残差值为"<<sqrt(resVal) <<endl;;
 //window
 clock_t endTime = clock();
 cout << "整个程序用时：" << double(endTime - startTime) / CLOCKS_PER_SEC << "s" << endl;
 system("PAUSE");
 return 0;
}

其中data是10*10的一个矩阵，然后new出来的空间都没有delete掉，用的时候可以注意一下