void sub(vec_RR& x, const vec_RR& a, const vec_RR& b) { long n = a.length(); if (b.length() != n) Error("vector sub: dimension mismatch"); x.SetLength(n); long i; for (i = 0; i < n; i++) sub(x[i], a[i], b[i]); }
void add(vec_RR& x, const vec_RR& a, const vec_RR& b) { long n = a.length(); if (b.length() != n) LogicError("vector add: dimension mismatch"); x.SetLength(n); long i; for (i = 0; i < n; i++) add(x[i], a[i], b[i]); }
RR computeAverageRR (vec_RR &result){ RR average = 0; for (int i = 1; i <= result.length() ; i++){ average += result(i); } return average/result.length(); }
void InnerProduct(RR& xx, const vec_RR& a, const vec_RR& b) { RR t1, x; long n = min(a.length(), b.length()); long i; clear(x); for (i = 1; i <= n; i++) { mul(t1, a(i), b(i)); add(x, x, t1); } xx = x; }
void clear(vec_RR& x) { long n = x.length(); long i; for (i = 0; i < n; i++) clear(x[i]); }
void negate(vec_RR& x, const vec_RR& a) { long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) negate(x[i], a[i]); }
void mul(vec_RR& x, const vec_RR& a, const RR& b_in) { RR b = b_in; long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) mul(x[i], a[i], b); }
void mul(vec_RR& x, const vec_RR& a, double b_in) { static RR b; conv(b, b_in); long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) mul(x[i], a[i], b); }
long IsZero(const vec_RR& a) { long n = a.length(); long i; for (i = 0; i < n; i++) if (!IsZero(a[i])) return 0; return 1; }
void VectorCopy(vec_RR& x, const vec_RR& a, long n) { if (n < 0) Error("VectorCopy: negative length"); if (NTL_OVERFLOW(n, 1, 0)) Error("overflow in VectorCopy"); long m = min(n, a.length()); x.SetLength(n); long i; for (i = 0; i < m; i++) x[i] = a[i]; for (i = m; i < n; i++) clear(x[i]); }
static void mul_aux(vec_RR& x, const mat_RR& A, const vec_RR& b) { long n = A.NumRows(); long l = A.NumCols(); if (l != b.length()) Error("matrix mul: dimension mismatch"); x.SetLength(n); long i, k; RR acc, tmp; for (i = 1; i <= n; i++) { clear(acc); for (k = 1; k <= l; k++) { mul(tmp, A(i,k), b(k)); add(acc, acc, tmp); } x(i) = acc; } }
static void mul_aux(vec_RR& x, const vec_RR& a, const mat_RR& B) { long n = B.NumRows(); long l = B.NumCols(); if (n != a.length()) Error("matrix mul: dimension mismatch"); x.SetLength(l); long i, k; RR 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 solve(RR& d, vec_RR& X, const mat_RR& A, const vec_RR& 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; RR t1, t2; RR *x, *y; mat_RR 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]; } RR det; set(det); RR maxval; for (k = 0; k < n; k++) { pos = -1; clear(maxval); for (i = k; i < n; i++) { abs(t1, M[i][k]); if (t1 > maxval) { pos = i; maxval = t1; } } if (pos != -1) { if (k != pos) { swap(M[pos], M[k]); negate(det, det); } mul(det, det, M[k][k]); // make M[k, k] == -1 inv(t1, M[k][k]); negate(t1, t1); for (j = k+1; j <= n; j++) { mul(M[k][j], M[k][j], t1); } for (i = k+1; i < n; i++) { // M[i] = M[i] + M[k]*M[i,k] t1 = M[i][k]; x = M[i].elts() + (k+1); y = M[k].elts() + (k+1); for (j = k+1; j <= n; j++, x++, y++) { // *x = *x + (*y)*t1 mul(t2, *y, t1); add(*x, *x, t2); } } } 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, t1, M[i][n]); X[i] = t1; } d = det; }