mpz_class latticePaths(mpz_class m, mpz_class n) {
if (m < n) {
return binomialCoefficient(m + n, n);
} else {
return binomialCoefficient(m + n, m);
}
}
void latticePaths(mpz_ptr result, mpz_t m, mpz_t n) {
mpz_t mplusn;
mpz_init(mplusn);
mpz_add(mplusn, m, n);
if (mpz_cmp(m, n) < 1) {
binomialCoefficient(result, mplusn, n);
} else {
binomialCoefficient(result, mplusn, m);
}
mpz_clear(mplusn);
}
static double binomSingle(double const p, uint64_t const k, uint64_t const n)
{
return
binomialCoefficient(k,n) *
slowPow(p,k) *
slowPow(1-p,n-k);
}
int main() {
printf("%d\n", binomial(6, 3));
printf("%d\n", binomial(6, 8));
printf("%d\n", binomial(5, 5));
printf("%d\n", binomial(100, 5));
int a[100];
binomialCoefficient(7, a);
for (int i = 0; i <= 7; i++) printf("%d ", a[i]);
return 0;
}
double nucmath::binomialPMF(double p, size_t n, size_t k)
{
if(k > n)
return 0;
double sum = 0.0;
for(size_t i = 0; i <= k; i++)
sum += binomialCoefficient(n, i) * std::pow(p, i) * std::pow(1.0-p, n-i);
return sum;
}
void w3j_sqrt_sq(mpq_t r, long j1, long j2, long j3, long m1, long m2, long m3)
{
mpz_t n,d,h;
mpz_init(n);
mpz_init(d);
mpz_init(h);
binomialCoefficient(n, 2*j1,j1-j2+j3);
binomialCoefficient(h, 2*j2,j1+j2-j3);
mpz_mul(n,n,h);
binomialCoefficient(h, 2*j3,-j1+j2+j3);
mpz_mul(n,n,h);;
mpq_set_z(r,n);
binomialCoefficient(d, 2*j1,j1+m1);
binomialCoefficient(h, 2*j2,j2+m2);
mpz_mul(d,d,h);
binomialCoefficient(h, 2*j3,j3+m3);
mpz_mul(d,d,h);
mpq_set_den(r,d);
mpq_canonicalize(r);
mpz_clear(d); mpz_clear(h); mpz_clear(n);
}
int main(void){
int n;
int k;
int binKoeff;
printf("\n Berechnung des Binomialkoeffizienten n ueber k \n" );
printf("\n Bitte Wert fuer n eingeben: ");
scanf("%d", &n);
printf("\n Bitte Wert fuer k eingeben: ");
scanf("%d", &k);
binKoeff = binomialCoefficient(n, k);
printf("\n Der Binomialkoeffizienten n ueber k von %d und %d", n, k);
printf(" ist: %d \n", binKoeff);
return 0;
}
BezierPath createBezierPath(const std::vector<Geometry2d::Point>& controls) {
Planning::BezierPath interp;
size_t degree = controls.size();
// generate coefficients
vector<float> coeffs;
for (size_t i = 0; i < degree; ++i) {
coeffs.push_back(binomialCoefficient(degree - 1, i));
}
size_t nrPoints = 20;
float inc = 1.0 / nrPoints;
for (size_t t = 1; t < nrPoints - 1; ++t)
interp.points.push_back(evaluateBezier(t * inc, controls, coeffs));
interp.points.push_back(controls.at(controls.size() - 1));
return interp;
}
vector< vector<T> > combinations(vector<T> &v, unsigned int k) {
unsigned int next = 0;
if(k > v.size())
throw k_GreaterThan_n_Exception();
vector< vector<T> > combs( binomialCoefficient(v.size(), k) );
vector<bool> binary(v.size());
fill(binary.end() - k, binary.end(), true);
do {
for(unsigned int i = 0 ; i < v.size() ; i++) {
if(binary[i])
combs[next].insert(combs[next].end(), v[i]);
}
next++;
} while(next_permutation(binary.begin(), binary.end()));
return combs;
}
float BezierBernsteinCurve::bernsteinPolynomial(const int& n,const int& i,const float& t)const{
return binomialCoefficient(n , i) * std::pow(t , i) * std::pow(1.0f - t , n - i);
}
void w3j_intterm(mpz_t sum, long j1, long j2, long j3, long m1, long m2, long m3)
{
mpz_t term,h;
mpz_init(term);
mpz_init(h);
long I1 = 0;
if(j1-j3+m2>I1) I1=j1-j3+m2;
if(j2-j3-m1>I1) I1=j2-j3-m1;
long I2 = j1+j2-j3;
if(j1-m1<I2) I2=j1-m1;
if(j2+m2<I2) I2=j2+m2;
mpz_set_ui(sum,0);
long sgn=1;
if(iabs(I1)%2==1) sgn=-1;
for(long k=I1; k<=I2; k++)
{
// sum+=sgn*binomialCoefficient(j1+j2-j3,k)*binomialCoefficient(j1-j2+j3,j1-m1-k)
// *binomialCoefficient(-j1+j2+j3,j2+m2-k);
binomialCoefficient(term, j1+j2-j3, k);
binomialCoefficient(h,j1-j2+j3,j1-m1-k);
mpz_mul(term,term,h);
binomialCoefficient(h,-j1+j2+j3,j2+m2-k);
mpz_mul(term,term,h);
mpz_mul_si(term,term,sgn);
mpz_add(sum,sum,term);
sgn*= -1;
}
mpz_clear(h);
mpz_clear(term);
}
