mat_lzz_p.cpp

数值算法库for Windows

#include <NTL/mat_lzz_p.h>

#include <NTL/new.h>

NTL_START_IMPL

NTL_matrix_impl(zz_p,vec_zz_p,vec_vec_zz_p,mat_zz_p)
NTL_io_matrix_impl(zz_p,vec_zz_p,vec_vec_zz_p,mat_zz_p)
NTL_eq_matrix_impl(zz_p,vec_zz_p,vec_vec_zz_p,mat_zz_p)


  
void add(mat_zz_p& X, const mat_zz_p& A, const mat_zz_p& B)  
{  
   long n = A.NumRows();  
   long m = A.NumCols();  
  
   if (B.NumRows() != n || B.NumCols() != m)   
      Error("matrix add: dimension mismatch");  
  
   X.SetDims(n, m);  
  
   long i, j;  
   for (i = 1; i <= n; i++)   
      for (j = 1; j <= m; j++)  
         add(X(i,j), A(i,j), B(i,j));  
}  
  
void sub(mat_zz_p& X, const mat_zz_p& A, const mat_zz_p& B)  
{  
   long n = A.NumRows();  
   long m = A.NumCols();  
  
   if (B.NumRows() != n || B.NumCols() != m)  
      Error("matrix sub: dimension mismatch");  
  
   X.SetDims(n, m);  
  
   long i, j;  
   for (i = 1; i <= n; i++)  
      for (j = 1; j <= m; j++)  
         sub(X(i,j), A(i,j), B(i,j));  
}  
  
void mul_aux(mat_zz_p& X, const mat_zz_p& A, const mat_zz_p& B)  
{  
   long n = A.NumRows();  
   long l = A.NumCols();  
   long m = B.NumCols();  
  
   if (l != B.NumRows())  
      Error("matrix mul: dimension mismatch");  
  
   X.SetDims(n, m);  
  
   long i, j, k;  
   zz_p acc, tmp;  
  
   for (i = 1; i <= n; i++) {  
      for (j = 1; j <= m; j++) {  
         clear(acc);  
         for(k = 1; k <= l; k++) {  
            mul(tmp, A(i,k), B(k,j));  
            add(acc, acc, tmp);  
         }  
         X(i,j) = acc;  
      }  
   }  
}  
  
  
void mul(mat_zz_p& X, const mat_zz_p& A, const mat_zz_p& B)  
{  
   if (&X == &A || &X == &B) {  
      mat_zz_p tmp;  
      mul_aux(tmp, A, B);  
      X = tmp;  
   }  
   else  
      mul_aux(X, A, B);  
}  
  
  
void mul_aux(vec_zz_p& x, const mat_zz_p& A, const vec_zz_p& b)
{
   long n = A.NumRows();
   long l = A.NumCols();

   if (l != b.length())
      Error("matrix mul: dimension mismatch");

   x.SetLength(n);

   long p = zz_p::modulus();
   double pinv = zz_p::ModulusInverse();

   long i, k;
   long acc, tmp;

   const zz_p* bp = b.elts();

   for (i = 0; i < n; i++) {
      acc = 0;
      const zz_p* ap = A[i].elts();

      for (k = 0; k < l; k++) {
         tmp = MulMod(rep(ap[k]), rep(bp[k]), p, pinv);
         acc = AddMod(acc, tmp, p);
      }
 
      x[i].LoopHole() = acc;
   }
}
  
void mul(vec_zz_p& x, const mat_zz_p& A, const vec_zz_p& b)  
{  
   if (&b == &x || A.position(b) != -1) {
      vec_zz_p tmp;
      mul_aux(tmp, A, b);
      x = tmp;
   }
   else
      mul_aux(x, A, b);

}  

static
void mul_aux(vec_zz_p& x, const vec_zz_p& a, const mat_zz_p& B)  
{  
   long n = B.NumRows();  
   long l = B.NumCols();  
  
   if (n != a.length())  
      Error("matrix mul: dimension mismatch");  
  
   x.SetLength(l);  
  
   long i, k;  
   zz_p acc, tmp;  
  
   for (i = 1; i <= l; i++) {  
      clear(acc);  
      for (k = 1; k <= n; k++) {  
         mul(tmp, a(k), B(k,i));
         add(acc, acc, tmp);  
      }  
      x(i) = acc;  
   }  
}  

void mul(vec_zz_p& x, const vec_zz_p& a, const mat_zz_p& B)
{
   if (&a == &x || B.position(a) != -1) {
      vec_zz_p tmp;
      mul_aux(tmp, a, B);
      x = tmp;
   }
   else
      mul_aux(x, a, B);
}

     
  
void ident(mat_zz_p& X, long n)  
{  
   X.SetDims(n, n);  
   long i, j;  
  
   for (i = 1; i <= n; i++)  
      for (j = 1; j <= n; j++)  
         if (i == j)  
            set(X(i, j));  
         else  
            clear(X(i, j));  
} 



void determinant(zz_p& d, const mat_zz_p& M_in)
{
   long k, n;
   long i, j;
   long pos;
   zz_p t1, t2, t3;
   zz_p *x, *y;

   mat_zz_p M;
   M = M_in;

   n = M.NumRows();

   if (M.NumCols() != n)
      Error("determinant: nonsquare matrix");

   if (n == 0) {
      set(d);
      return;
   }

   zz_p det;

   set(det);

   long p = zz_p::modulus();
   double pinv = zz_p::ModulusInverse();

   for (k = 0; k < n; k++) {
      pos = -1;
      for (i = k; i < n; i++) {
         if (!IsZero(M[i][k])) {
            pos = i;
            break;
         }
      }

      if (pos != -1) {
         if (k != pos) {
            swap(M[pos], M[k]);
            negate(det, det);
         }

         mul(det, det, M[k][k]);

         inv(t3, M[k][k]);

         for (i = k+1; i < n; i++) {
            // M[i] = M[i] - M[k]*M[i,k]*t3

            mul(t1, M[i][k], t3);
            negate(t1, t1);

            x = M[i].elts() + (k+1);
            y = M[k].elts() + (k+1);

            long T1 = rep(t1);
            double t1pinv = T1*pinv; 
            long T2;

            for (j = k+1; j < n; j++, x++, y++) {
               // *x = *x + (*y)*t1

               T2 = MulMod2(rep(*y), T1, p, t1pinv);
               x->LoopHole() = AddMod(rep(*x), T2, p); 
            }
         }
      }
      else {
         clear(d);
         return;
      }
   }

   d = det;
}




long IsIdent(const mat_zz_p& A, long n)
{
   if (A.NumRows() != n || A.NumCols() != n)
      return 0;

   long i, j;

   for (i = 1; i <= n; i++)
      for (j = 1; j <= n; j++)
         if (i != j) {
            if (!IsZero(A(i, j))) return 0;
         }
         else {
            if (!IsOne(A(i, j))) return 0;
         }

   return 1;
}
            

void transpose(mat_zz_p& X, const mat_zz_p& A)
{
   long n = A.NumRows();
   long m = A.NumCols();

   long i, j;

   if (&X == & A) {
      if (n == m)
         for (i = 1; i <= n; i++)
            for (j = i+1; j <= n; j++)
               swap(X(i, j), X(j, i));
      else {
         mat_zz_p tmp;
         tmp.SetDims(m, n);
         for (i = 1; i <= n; i++)
            for (j = 1; j <= m; j++)
               tmp(j, i) = A(i, j);
         X.kill();
         X = tmp;
      }
   }
   else {
      X.SetDims(m, n);
      for (i = 1; i <= n; i++)
         for (j = 1; j <= m; j++)
            X(j, i) = A(i, j);
   }
}
   

void solve(zz_p& d, vec_zz_p& X, 
           const mat_zz_p& A, const vec_zz_p& b)

{
   long n = A.NumRows();

   if (A.NumCols() != n)
      Error("solve: nonsquare matrix");


   if (b.length() != n)
      Error("solve: dimension mismatch");

   if (n == 0) {
      set(d);
      X.SetLength(0);
      return;
   }

   long i, j, k, pos;
   zz_p t1, t2, t3;
   zz_p *x, *y;

   mat_zz_p M;
   M.SetDims(n, n+1);
   for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) 
         M[i][j] = A[j][i];
      M[i][n] = b[i];
   }

   zz_p det;
   set(det);

   long p = zz_p::modulus();
   double pinv = zz_p::ModulusInverse();

   for (k = 0; k < n; k++) {
      pos = -1;
      for (i = k; i < n; i++) {
         if (!IsZero(M[i][k])) {
            pos = i;
            break;
         }
      }

      if (pos != -1) {
         if (k != pos) {
            swap(M[pos], M[k]);
            negate(det, det);
         }

         mul(det, det, M[k][k]);

         inv(t3, M[k][k]);
         M[k][k] = t3;


         for (i = k+1; i < n; i++) {
            // M[i] = M[i] - M[k]*M[i,k]*t3

            mul(t1, M[i][k], t3);
            negate(t1, t1);

            x = M[i].elts() + (k+1);
            y = M[k].elts() + (k+1);

            long T1 = rep(t1);
            double t1pinv = T1*pinv;
            long T2;

            for (j = k+1; j <= n; j++, x++, y++) {
               // *x = *x + (*y)*t1

               T2 = MulMod2(rep(*y), T1, p, t1pinv);
               x->LoopHole() = AddMod(rep(*x), T2, p);
            }
         }
      }
      else {
         clear(d);
         return;
      }
   }

   X.SetLength(n);
   for (i = n-1; i >= 0; i--) {
      clear(t1);
      for (j = i+1; j < n; j++) {
         mul(t2, X[j], M[i][j]);
         add(t1, t1, t2);
      }
      sub(t1, M[i][n], t1);
      mul(X[i], t1, M[i][i]);
   }

   d = det;
}

void inv(zz_p& d, mat_zz_p& X, const mat_zz_p& A)
{
   long n = A.NumRows();