c - 我应该在这段 C 代码中使用指针吗？在哪里？

Question

这是我的代码。它是一个使用高斯消元法和偏枢轴求解线性代数方程组的 C 程序。你能告诉我什么时候使用指针更好吗？

typedef double **Matrix;
typedef double *Row;
typedef double *Col;
typedef double Elem;

Matrix allocate_matrix(int n);
Col allocate_col(int n);
Row allocate_row(int n);
void free_matrix(Matrix M, int n);

void pivot_partial(Matrix A, Col S,Col B, int n);
void forward_elimination(Matrix A,Col B,int n);
Col back_substitution(Matrix A, Col B, int n);
Col scale_factor(Matrix A,int n);
void gauss(Matrix A, Col B, int n);

void swap_rows(Row *r1, Row*r2);
void print_matrix(Matrix M, int n, char * name);
void print_col(Col C, int n, char *name);
void print_row(Row R, int n, char *name);

int main(int argc, char *argv[])
{
 FILE *ifp;
 int n,i,j;
 Matrix A;
 Col B;
 if(argc < 2)
 {
  printf("\nInput filename not passed \n");
  exit(1);
 }

 ifp = fopen(argv[1],"r");

 if(ifp == NULL)
 {
  printf("\nCould not open file %s\n",argv[1]);
  exit(1);
 }
 fscanf(ifp,"%i",&n);
  printf("A * X = B\n");
 printf("\nDimension(A) = %i\n",n);

 A = allocate_matrix(n);
 for( i = 1; i <= n; ++i)
  for(j = 1; j <= n; ++j)
   fscanf(ifp,"%lf", &A[i][j]);

 B = allocate_col(n);

 for(j = 1; j <= n; ++j)
  fscanf(ifp,"%lf",&B[j]);
 fclose(ifp);


 print_matrix(A,n,"A");
 print_col(B,n,"B");

 gauss(A,B,n);

 free_matrix(A,n);
 free(B + 1);

 getchar();
 return 0;
}

void print_matrix(Matrix M, int n, char * name)
{
 int i,j;
 printf("\n[%s] = ",name);
 printf("\n\n");
 for(i = 1; i <= n; i++)
 {
  for(j = 1; j <= n; ++j)
   printf("%6lG ",M[i][j]);
  printf("\n");
 }
}

void print_col(Col C, int n, char * name)
{
 int j;
 printf("\n[%s] = ",name);
 printf("\n\n");
 for(j = 1; j <= n; ++j)
  printf("%6lg\n",C[j]);

}

void print_row(Row R, int n, char * name)
{
 int i;
 printf("\n[%s] = ",name);
 for(i = 1; i <= n; ++i)
  printf("%6lg ",R[i]);
 printf("\n");
}

Matrix allocate_matrix(int n)
{
 Matrix A;
 int i,j;
 A = malloc(n * sizeof(Row));
 if(!A)
 {
  printf("\nError : Could not allocate 
                       memory for matrix\n");
  exit(1);
 }
 --A;

 for(i = 1; i <= n; ++i)
 {
  A[i] = malloc(n * sizeof(Elem));
  if(!A[i])
  {
   printf("\nError : Could not allocate 
                               memory for matrix\n");
   exit(1);
  }
  --A[i];
 }
 return A;
}

void free_matrix(Matrix M, int n)
{
 int i;
 for(i = 1; i <= n; ++i)
   free(M[i] + 1);
 free(M + 1);
}

Col allocate_col(int n)
{
 Col B;

 B = malloc(n * sizeof(Elem));

 if(!B)
 {
  printf("\nError : could not allocate 
                       memory\n");
  exit(1);
 }
 --B;
 return B;
}

Row allocate_row(int n)
{
 Row B;
 B = malloc(n * sizeof(Elem));
 if(!B)
 {
  printf("\nError : could not allocate
                       memory\n");
  exit(1);
 }
 --B;
 return B;
}

Col scale_factor(Matrix A, int n)
{
 int i,j;
 Col S ;
 S = allocate_col(n);

 for(i = 1; i <= n; ++i)
 {
  S[i] = A[i][1];
  for(j = 2; j <= n; ++j)
  {
   if(S[i] < fabs(A[i][j]))
       S[i] = fabs(A[i][j]);
  }

 }
 return S;

}

void pivot_partial(Matrix A, Col S,Col B, int n)
{
 int i,j;
 Elem temp;
 for(j = 1; j <= n; ++j)
 {
  for(i = j + 1; i <= n; ++i)
  {
   if(S[i] == 0)
   {
    if(B[i] == 0)
              printf("\nSystem doesnt
                                   have a unique solution");
    else
       printf("\nSystem is 
                                        inconsistent");
    exit(1);
   }
   if(fabs(A[i][j]/S[i])>fabs(A[j][j]/S[j]))
   {
    swap_rows(&A[i],&A[j]);
    temp = B[i];
    B[i] = B[j];
    B[j] = temp;
   }
  }

  if(A[j][j] == 0)
  {
   printf("\nSingular System Detected\n");
   exit(1);
  }
 }

}

void swap_rows(Row *r1, Row*r2)
{
 Row temp;
 temp = *r1;
 *r1 = *r2;
 *r2 = temp;
}

void forward_elimination(Matrix A,Col B,int n)
{
 int i,j,k;
 double m;

 for(k = 1; k <= n-1; ++k)
 {
  for(i = k + 1; i <= n; ++i)
  {
   m =  A[i][k] / A[k][k];
   for(j = k + 1; j <= n; ++j)
   {
    A[i][j] -= m * A[k][j];
    if(i == j && A[i][j] == 0)
    {
         printf("\nSingular 
                                        system detected");
         exit(1);
    }
   }
   B[i] -= m * B[k];
  }
 }
}

Col back_substitution(Matrix A, Col B, int n)
{
 int i,j;
 Elem sum;
 Col X = allocate_col(n);
 X[n] = B[n]/A[n][n];
 for(i = n - 1; i >= 1; --i)
 {
  sum = 0;
  for(j = i + 1; j <= n; ++j)
   sum += A[i][j] * X[j];
  X[i] = (B[i] - sum) / A[i][i];
 }
 return X;
}

void gauss(Matrix A, Col B, int n)
{
 int i,j;
 Col S, X;
 S = scale_factor(A,n);
 pivot_partial(A,S,B,n);
 forward_elimination(A,B,n);
 X = back_substitution(A,B,n);
 print_col(X,n,"X");

 free(S + 1);
 free(X + 1);
}

Answer 1

如果事先不知道数组(Matrix)的大小，请使用指针。 数组一旦声明为特定大小就无法增长或缩小。

但是，另一方面，指针可以分配内存(使用malloc())、释放内存(使用free())和重新分配内存(使用realloc())。

在您的代码中，这些行

A = allocate_matrix(n);
 for( i = 1; i <= n; ++i)
  for(j = 1; j <= n; ++j)
   fscanf(ifp,"%lf", &A[i][j]);

从文件读取大小后动态分配矩阵 A。对于数组来说这是不可能的。