void transpose(mat_zz_pE& X, const mat_zz_pE& 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_pE 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 convert(mat_zz_pE& X, const vector< vector<ZZX> >& A) { long n = A.size(); if (n == 0) { long m = X.NumCols(); X.SetDims(0, m); return; } long m = A[0].size(); X.SetDims(n, m); for (long i = 0; i < n; i++) convert(X[i], A[i]); }
void mul_aux(mat_zz_pE& X, const mat_zz_pE& A, const mat_zz_pE& 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_pX acc, tmp; for (i = 1; i <= n; i++) { for (j = 1; j <= m; j++) { clear(acc); for(k = 1; k <= l; k++) { mul(tmp, rep(A(i,k)), rep(B(k,j))); add(acc, acc, tmp); } conv(X(i,j), acc); } } }
void ident(mat_zz_pE& 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 buildLinPolyMatrix(mat_zz_pE& M, long p) { long d = zz_pE::degree(); M.SetDims(d, d); for (long j = 0; j < d; j++) conv(M[0][j], zz_pX(j, 1)); for (long i = 1; i < d; i++) for (long j = 0; j < d; j++) M[i][j] = power(M[i-1][j], p); }
void diag(mat_zz_pE& X, long n, const zz_pE& d_in) { zz_pE d = d_in; X.SetDims(n, n); long i, j; for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) if (i == j) X(i, j) = d; else clear(X(i, j)); }
void mul(mat_zz_pE& X, const mat_zz_pE& A, const zz_pE& b_in) { zz_pE b = b_in; long n = A.NumRows(); long m = A.NumCols(); X.SetDims(n, m); long i, j; for (i = 0; i < n; i++) for (j = 0; j < m; j++) mul(X[i][j], A[i][j], b); }
void negate(mat_zz_pE& X, const mat_zz_pE& A) { long n = A.NumRows(); long m = A.NumCols(); X.SetDims(n, m); long i, j; for (i = 1; i <= n; i++) for (j = 1; j <= m; j++) negate(X(i,j), A(i,j)); }
void mul(mat_zz_pE& X, const mat_zz_pE& A, long b_in) { newNTL_zz_pRegister(b); b = b_in; long n = A.NumRows(); long m = A.NumCols(); X.SetDims(n, m); long i, j; for (i = 0; i < n; i++) for (j = 0; j < m; j++) mul(X[i][j], A[i][j], b); }
void sub(mat_zz_pE& X, const mat_zz_pE& A, const mat_zz_pE& 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)); }
NTL_START_IMPL void add(mat_zz_pE& X, const mat_zz_pE& A, const mat_zz_pE& B) { long n = A.NumRows(); long m = A.NumCols(); if (B.NumRows() != n || B.NumCols() != m) LogicError("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 kernel(mat_zz_pE& X, const mat_zz_pE& A) { long m = A.NumRows(); long n = A.NumCols(); mat_zz_pE M; long r; transpose(M, A); r = gauss(M); X.SetDims(m-r, m); long i, j, k, s; zz_pX t1, t2; zz_pE T3; vec_long D; D.SetLength(m); for (j = 0; j < m; j++) D[j] = -1; vec_zz_pE inverses; inverses.SetLength(m); j = -1; for (i = 0; i < r; i++) { do { j++; } while (IsZero(M[i][j])); D[j] = i; inv(inverses[j], M[i][j]); } for (k = 0; k < m-r; k++) { vec_zz_pE& v = X[k]; long pos = 0; for (j = m-1; j >= 0; j--) { if (D[j] == -1) { if (pos == k) set(v[j]); else clear(v[j]); pos++; } else { i = D[j]; clear(t1); for (s = j+1; s < m; s++) { mul(t2, rep(v[s]), rep(M[i][s])); add(t1, t1, t2); } conv(T3, t1); mul(T3, T3, inverses[j]); negate(v[j], T3); } } } }
void inv(zz_pE& d, mat_zz_pE& X, const mat_zz_pE& A) { long n = A.NumRows(); if (A.NumCols() != n) Error("inv: nonsquare matrix"); if (n == 0) { set(d); X.SetDims(0, 0); return; } long i, j, k, pos; zz_pX t1, t2; zz_pX *x, *y; const zz_pXModulus& p = zz_pE::modulus(); vec_zz_pX *M = newNTL_NEW_OP vec_zz_pX[n]; for (i = 0; i < n; i++) { M[i].SetLength(2*n); for (j = 0; j < n; j++) { M[i][j].rep.SetMaxLength(2*deg(p)-1); M[i][j] = rep(A[i][j]); M[i][n+j].rep.SetMaxLength(2*deg(p)-1); clear(M[i][n+j]); } set(M[i][n+i]); } zz_pX det; set(det); for (k = 0; k < n; k++) { pos = -1; for (i = k; i < n; i++) { rem(t1, M[i][k], p); M[i][k] = t1; if (pos == -1 && !IsZero(t1)) { pos = i; } } if (pos != -1) { if (k != pos) { swap(M[pos], M[k]); negate(det, det); } MulMod(det, det, M[k][k], p); // make M[k, k] == -1 mod p, and make row k reduced InvMod(t1, M[k][k], p); negate(t1, t1); for (j = k+1; j < 2*n; j++) { rem(t2, M[k][j], p); MulMod(M[k][j], t2, t1, p); } for (i = k+1; i < n; i++) { // M[i] = M[i] + M[k]*M[i,k] t1 = M[i][k]; // this is already reduced x = M[i].elts() + (k+1); y = M[k].elts() + (k+1); for (j = k+1; j < 2*n; j++, x++, y++) { // *x = *x + (*y)*t1 mul(t2, *y, t1); add(*x, *x, t2); } } } else { clear(d); goto done; } } X.SetDims(n, n); for (k = 0; k < n; k++) { for (i = n-1; i >= 0; i--) { clear(t1); for (j = i+1; j < n; j++) { mul(t2, rep(X[j][k]), M[i][j]); add(t1, t1, t2); } sub(t1, t1, M[i][n+k]); conv(X[i][k], t1); } } conv(d, det); done: delete[] M; }