Should I should use pointers in this C code? Where? [closed]

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Here is my code. It is a C program using Gauss Elimination Method and Partial Pivoting to solve systems of linear algebraic equations. Would you tell me when it is better to use pointers?

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

If you don't know in advance the size of the array (Matrix), use pointers. Arrays once declared with a particular size cannot grow or shrink.

But, pointers on the other hand, can be allocated memory (using malloc()), deallocated memory (using free()) and reallocated memory (using realloc()).

In your code, these lines

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

dynamically allocate a matrix A, after reading the size from file. This isn't possible in case of arrays.