double Polynomial_Root(int n,double c[], double a, double b, double eps){
int newton(double x0, double *r,double c[], double d[], int n, double a, double b, double eps);
double d[MAXN];
int i;
double root = 0.0;
for (i=n-1; i>=0; i--) {
d[i] = (i+1)*c[i+1];
}
if (a>b) {
root = a; a = b; b = root;
}
double average = 0.0;
int k = 0;
int t = newton(a, &root, c, d, n, a, b, eps);
if (t == 1){
average += root;
k++;
}
int s = newton(b, &root, c, d, n, a, b, eps);
if (s == 1){
average += root;
k++;
}
int u = newton((a+b)*0.5, &root, c, d, n, a, b, eps);
if (u == 1){
average += root;
k++;
}
average /= k;
if (fabs(root)<eps) return fabs(root);
else return root;
}
int newton(int n, int k)
{
if (k == 0 || k == n)
return 1;
else
return newton(n - 1, k - 1) + newton(n - 1, k);
}
int newton(int n,int k)
{
if(k==0 || k==n)
return 1;
if(k>0 && k<n)
return newton(n-1,k-1)+newton(n-1,k);
}
void main_train(int iter,void* dat,void *vector){
printf("starting train\n");
Data data;
int t;
//init constant
do{
Int* buffer=(Int*)dat;
dat+=sizeof(Int)*3;
data.ndata=buffer[0];
data.cust.n=buffer[1];
data.movie.n=buffer[2];
data.ndim=10;
data.cust.p=(Int*)dat;
dat+=sizeof(Int)*(data.cust.n+1);
data.movie.p=(Int*)dat;
dat+=sizeof(Int)*(data.movie.n+1);
data.cust.i=(Int*)dat;
dat+=sizeof(Int)*data.ndata;
data.movie.i=(Int*)dat;
dat+=sizeof(Int)*data.ndata;
}while(0);
printf("(ndata: %d)(ncust: %d)(nmovie: %d)\n",data.ndata,data.cust.n,data.movie.n);
//data.ndata=10000000;
for(t=0;t<10;t++){
printf("p2[%d]=%d\n",t,data.movie.p[t]);
}
if(vector==0){
int size=(data.cust.n+data.movie.n)*data.ndim;
vector=malloc(sizeof(Double)*size);
for(size--;size>=0;size--){
((Double*)vector)[size]=((Double)rand()/RAND_MAX-0.5)/10;
}
}
//init vector
Double* v1=(Double*)vector;
vector+=sizeof(Double)*data.cust.n*data.ndim;
Double* v2=(Double*)vector;
vector+=sizeof(Double)*data.cust.n*data.ndim;
printf("starting iteration\n");
time_t time0,time1;
time(&time0);
int iterleft=iter;
while(iterleft!=0){
newton(v1,v2,data,data.cust,data.movie);
request_judge(v1);
newton(v2,v1,data,data.movie,data.cust);
request_judge(v1);
printf("iterleft: %d\n",iterleft);
time(&time1);
printf("time elapsed: %lu\n",time1-time0);
iterleft--;
}
}
int main(void)
{
double a1 = 0.0, b1 = 1.0;
double a2 = 1.0, b2 = 3.0;
double eps = 0.000001;
double d1 = dichotomy(f1, eps, a1, b1);
double i1 = iteration(f1_it, eps, a1, b1);
double n1 = newton(f1, f1_pr, eps, a1, b1);
double d2 = dichotomy(f2, eps, a2, b2);
double i2 = iteration(f2_it, eps, a2, b2);
double n2 = newton(f2, f2_pr, eps, a2, b2);
printf("Точность: %.6f\n", eps);
printf("+-----------+----------+---------------+-----------------------+-----------+----------+---------+\n");
printf("| Уравнение | Отрезок | Базовый метод | Прибл. значение корня | Дихотомии | Итераций | Ньютона |\n");
printf("+-----------+----------+---------------+-----------------------+-----------+----------+---------+\n");
printf("| 1 | [0, 1] | Ньютона | 0.8814 |%.9f|%.8f|%.7f|\n", d1, i1, n1);
printf("+-----------+----------+---------------+-----------------------+-----------+----------+---------+\n");
printf("| 2 | [1, 3] | Дихотомии | 1.3749 |%.9f| - |%.7f|\n", d2, n2);
printf("+-----------+----------+---------------+-----------------------+-----------+----------+---------+\n");
return 0;
}
int newton(int n, int k) {
if (n == 0 || n == k) {
return 1;
}
if (n > 0 && k > 0 && n > k) {
return newton(n - 1, k - 1) + newton(n - 1, k);
}
}
int newton(int n,int k)
{
if(k==0 || k==n)
{
return 1;
}
if(n>k && k>0)
{
return newton(n-1,k-1)+newton(n-1,k);
}
}
void CtcNewton::contract(IntervalVector& box, ContractContext& context) {
if (!(box.max_diam()<=ceil)) return;
else {
if (!vars)
newton(f,box,prec,gauss_seidel_ratio);
else
newton(f,*vars,box,prec,gauss_seidel_ratio);
}
if (box.is_empty()) {
context.output_flags.add(FIXPOINT);
}
}
int main() {
// Create coarse mesh, set Dirichlet BC, enumerate
// basis functions
Mesh *mesh = new Mesh(A, B, N_elem, P_init, N_eq);
mesh->set_bc_left_dirichlet(0, Val_dir_left_0);
mesh->set_bc_right_dirichlet(0, Val_dir_right_0);
mesh->set_bc_left_dirichlet(1, Val_dir_left_1);
mesh->set_bc_right_dirichlet(1, Val_dir_right_1);
printf("N_dof = %d\n", mesh->assign_dofs());
// Register weak forms
DiscreteProblem *dp = new DiscreteProblem();
dp->add_matrix_form(0, 0, jacobian_0_0);
dp->add_matrix_form(0, 1, jacobian_0_1);
dp->add_matrix_form(1, 0, jacobian_1_0);
dp->add_matrix_form(1, 1, jacobian_1_1);
dp->add_vector_form(0, residual_0);
dp->add_vector_form(1, residual_1);
// Newton's loop
newton(dp, mesh, NULL, NEWTON_TOL, NEWTON_MAXITER);
// Plot the solution
Linearizer l(mesh);
l.plot_solution("solution.gp");
printf("Done.\n");
return 1;
}
int main() {
// Create coarse mesh, set Dirichlet BC, enumerate
// basis functions
Mesh *mesh = new Mesh(A, B, N_elem, P_init, N_eq);
printf("N_dof = %d\n", mesh->assign_dofs());
// Register weak forms
DiscreteProblem *dp = new DiscreteProblem();
dp->add_matrix_form(0, 0, jacobian_vol);
dp->add_vector_form(0, residual_vol);
dp->add_matrix_form_surf(0, 0, jacobian_surf_left, BOUNDARY_LEFT);
dp->add_vector_form_surf(0, residual_surf_left, BOUNDARY_LEFT);
dp->add_matrix_form_surf(0, 0, jacobian_surf_right, BOUNDARY_RIGHT);
dp->add_vector_form_surf(0, residual_surf_right, BOUNDARY_RIGHT);
// Newton's loop
newton(dp, mesh, NULL, NEWTON_TOL, NEWTON_MAXITER);
// Plot the solution
Linearizer l(mesh);
l.plot_solution("solution.gp");
printf("Done.\n");
return 1;
}
void main () {
double x[2], fx[2], tol;
int iter, maxIter;
// INPUT
cout << "Enter tolerance: ";
cin >> tol;
cout << "Enter max iterations: ";
cin >> maxIter;
cout << "Enter an initial guess: ";
cin >> x[0] >> x[1];
// NEWTON SOLVER
int state = newton(x, f, df, iter, tol, maxIter);
f(x,fx);
// STATUS AND OUTPUT
switch(state) {
case SUCCESS:
cout << "An approximate root is (" << x[0] << ", " << x[1] <<")\n";
cout << "f(approximate root) is (" << fx[0] << ", " << fx[1] <<")\n";
cout << "The number of iterations is " << iter << endl;
break;
case WONT_STOP:
default:
cout << "ERROR: Failed to converge in "<<maxIter<<" iterations!" << endl;
break;
}
}
void NewtonEqualitySelfTest()
{
cout<<"Testing equality-constrained Newton solver..."<<endl;
Matrix A(2,2);
Vector b(2);
Real c;
A.setIdentity(); A *= -Two;
b.setZero();
c=10;
QuadraticScalarFieldFunction c1(A,b,c);
ComponentVectorFieldFunction C;
C.functions.resize(1); C.functions[0] = &c1;
Vector p(2);
p(0) = -1; p(1) = 0;
Real q=0;
LinearScalarFieldFunction f(p,q);
NonlinearProgram nlp(&f,&C);
nlp.minimize = true;
nlp.inequalityLess = false;
NewtonSolver newton(nlp);
newton.x.resize(2); newton.x(0) = -1; newton.x(1) = -1;
newton.verbose=1;
newton.Init();
int iters=100;
ConvergenceResult res=newton.Solve(iters);
cout<<"Result "<<res<<" iters "<<iters<<endl;
cout<<"x = "<<VectorPrinter(newton.x)<<endl;
cout<<"done."<<endl;
}
void OGProjection<Scalar>::project_internal(Hermes::vector<Space<Scalar>*> spaces, WeakForm<Scalar>* wf,
Scalar* target_vec, Hermes::MatrixSolverType matrix_solver_type)
{
_F_;
// Instantiate a class with global functions.
Global<Scalar> hermes2d;
unsigned int n = spaces.size();
// sanity checks
if (n <= 0 || n > 10) error("Wrong number of projected functions in project_internal().");
for (unsigned int i = 0; i < n; i++) if(spaces[i] == NULL) error("this->spaces[%d] == NULL in project_internal().", i);
if (spaces.size() != n) error("Number of spaces must match number of projected functions in project_internal().");
// this is needed since spaces may have their DOFs enumerated only locally.
int ndof = Space<Scalar>::assign_dofs(spaces);
// Initialize DiscreteProblem.
DiscreteProblem<Scalar> dp(wf, spaces);
// Initial coefficient vector for the Newton's method.
Scalar* coeff_vec = new Scalar[ndof];
memset(coeff_vec, 0, ndof*sizeof(Scalar));
// Perform Newton's iteration.
NewtonSolver<Scalar> newton(&dp, matrix_solver_type);
if (!newton.solve(coeff_vec))
error("Newton's iteration failed.");
delete [] coeff_vec;
if (target_vec != NULL)
for (int i = 0; i < ndof; i++)
target_vec[i] = newton.get_sln_vector()[i];
}
int main() {
double a, b, e;
int status;
char chce_podac_x[2];
do {
printf("Podaj a: ");
scanf("%lf", &a);
printf("Podaj b: ");
scanf("%lf", &b);
if(a < b) {
if (f(a) * f(b) < 0) {
do {
printf("Podaj przybliżenie: ");
status = scanf("%lf", &e);
if(e > 0 && e < 1) {
bisection(a, b, e);
newton(a, e);
}
do {
printf("Chcesz podać kolejne przybliżenie? (tak/nie): ");
scanf("%s", chce_podac_x);
if(strcmp(chce_podac_x, "tak") == 0 || strcmp(chce_podac_x, "nie") == 0) break;
} while(1);
} while (strcmp(chce_podac_x, "tak") == 0);
} else {
printf("błąd: f(a) i f(b) muszą mieć różny znak\n");
}
} else {
printf("błąd: a musi być mniejsze od b\n");
}
} while(a >= b || f(a) * f(b) >= 0);
return 0;
}
int main()
{
printf("\n Dla równania f(x) = 0, gdzie f(x) = 3x + 2 - e^x, wczytać a, b należące");
printf("\n do zbioru liczb rzeczywistych takie, by a < b oraz f(a) * f(b) < 0. Następnie,");
printf("\n dopóki \"użytownik się nie znudzi\", wczytywać wartości 0 < E < 1 i metodą");
printf("\n połowienia na [a, b] przybliżyc z dokładnością E rozwiązanie tego równania.");
printf("\n Rozwiązanie to przybliżyc również metodą Newtona z x_0 = a, przy czym, x_k");
printf("\n będzie dobrym przybliżeniem, gdy |x_k - x_(k - 1)| <= E. Porównać ilość");
printf("\n kroków wykonanych metodą połowienia i metodą Newtona.\n");
double a, b;
printf("\n Podaj a należące do zbioru liczb rzeczywistych:\n a = ");
scanf("%lf", &a);
b = a;
while(a >= b || equation(a) * equation(b) >= 0)
{
printf("\n Podaj b należące do zbioru liczb rzeczywistych,\n takie by b > a oraz f(b) * f(a) < 0\n b = ");
scanf("%lf", &b);
}
double epsilon, rB, rN;
int choice;
while (1)
{
printf("\n 1 - Przybliż rozwiązanie równania z dokładnością E metodą połowienia i Newtona");
printf("\n 2 - Zakoncz program");
printf("\n Twoj wybor: ");
scanf("%i", &choice);
switch (choice)
{
case 1:
epsilon = 0;
while (epsilon <= 0 || epsilon >= 1)
{
printf("\n Podaj E, takie by 0 < E < 1:\n E = ");
scanf("%lf", &epsilon);
}
rB = bisection(a, b, epsilon);
rN = newton(a, epsilon);
printf("\n Metoda połowienia:\n %lf - przybliżone rozwiązanie\n %i - ilość kroków\n", rB, iB);
printf("\n Metoda Newtona:\n %lf - przybliżone rozwiązanie\n %i - ilość kroków\n", rN, iN);
iB = iN = 0;
break;
case 2:
printf("\n");
return 0;
}
}
}
int main() {
double x_0; /* Initial guess */
double x; /* Approximate solution */
double tol; /* Maximum error */
int max_iters; /* Maximum number of iterations */
int iters; /* Actual number of iterations */
int converged; /* Whether iteration converged */
printf("Enter x_0, tol, and max_iters\n");
scanf("%lf %lf %d", &x_0, &tol, &max_iters);
x = newton(x_0, tol, max_iters, &iters, &converged);
if (converged) {
printf("Newton algorithm converged after %d steps.\n",
iters);
printf("The approximate solution is %19.16e\n", x);
printf("f(%19.16e) = %19.16e\n", x, f(x));
} else {
printf("Newton algorithm didn't converge after %d steps.\n",
iters);
printf("The final estimate was %19.16e\n", x);
printf("f(%19.16e) = %19.16e\n", x, f(x));
}
return 0;
} /* main */
int main()
{
newton();
//--gnuplotによるグラフ作成--//
FILE *gp;
gp=popen("gnuplot -persist","w");
fprintf(gp, "set title 'df(x)=-1/x^2+1/x'\n");
fprintf(gp, "set size ratio 1.0\n");
fprintf(gp, "set border lw 2.5\n");
fprintf(gp, "set mxtics 5\n");
fprintf(gp, "set mytics 5\n");
fprintf(gp, "set nokey\n");
fprintf(gp, "set xl 'x' font 'Arial'\n");
fprintf(gp, "set yl 'df(x)' font 'Arial'\n");
fprintf(gp, "set parametric\n");
fprintf(gp, "const=0\n");
fprintf(gp, "set trange[-5:5]\n");
fprintf(gp, "set xr [0:5]\n");
fprintf(gp, "set yr [-5:1]\n");
fprintf(gp, "plot const+1.5,t dt(5,5) lw 2.5 lt 1 lc rgb 'black'\n");
fprintf(gp, "replot t,const dt(5,5) lw 2.5 lt 1 lc rgb 'black'\n");
fprintf(gp, "replot t,t*4/27 dt(5,5) lw 2.5 lt 1 lc rgb 'navy'\n");
fprintf(gp, "replot t,-1/(t*t)+1/t w l lw 3 lt 1 lc rgb 'red'\n");
pclose(gp);
//--gnuplot終了--//
return 0;
}
void CtcNewton::contract(IntervalVector& box) {
if (!(box.max_diam()<=ceil)) return;
else newton(f,box,prec,gauss_seidel_ratio);
if (box.is_empty()) {
set_flag(FIXPOINT);
}
}
int main(void){
double x;
double eps=pow(2.0,-30.0);
printf("Please input x0:");
scanf("%lf",&x);
newton(x,eps);
return 0;
}
int inexact_newton(int , char **)
{
typedef double value_type;
typedef std::string key_type;
typedef std::map<key_type,std::vector<value_type> > stats_type;
stats_type stats;
const int size = 2;
InexactNewtonMethod<value_type,1000,100> newton(size);
function_type<2> F;
value_type x[size] = {1,1};
newton ( F,x,1e-16f,1e-13f, &stats );
display_stats(stats);
return 0;
}
int main()
{
printf("%d\n",newton(15,8));
}
int main()
{
mpc mycase = loadcase();
//mycase.print();
newton(mycase);
return 0;
}
bool PicardSolver<Scalar>::solve(double tol, int max_iter)
{
int it = 0;
NewtonSolver<Scalar> newton(static_cast<DiscreteProblem<Scalar>*>(this->dp),
this->matrix_solver_type);
while (true)
{
// Delete the old solution vector, if there is any.
if(this->sln_vector != NULL)
{
delete [] this->sln_vector;
this->sln_vector = NULL;
}
// Project the previous solution in order to get a vector of coefficient.
this->sln_vector = new Scalar[static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_space(0)->get_num_dofs()];
memset(this->sln_vector, 0, static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_space(0)->get_num_dofs() * sizeof(Scalar));
// Perform Newton's iteration to solve the linear problem.
// Translate the resulting coefficient vector into the Solution sln_new.
Solution<Scalar> sln_new;
if (!newton.solve(this->sln_vector, tol, max_iter))
{
warn("Newton's iteration in the Picard's method failed.");
return false;
}
else
Solution<Scalar>::vector_to_solution(newton.get_sln_vector(),
static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_space(0), &sln_new);
double rel_error = Global<Scalar>::calc_rel_error(sln_prev_iter, &sln_new,
HERMES_L2_NORM);
if (this->verbose_output)
info("---- Picard iter %d, ndof %d, rel. error %g%%",
it+1, static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_space(0)->get_num_dofs(),
rel_error);
// Stopping criterion.
if (rel_error < tol)
{
for (int i = 0; i < static_cast<DiscreteProblem<Scalar>*>(this->dp)->get_space(0)->get_num_dofs(); i++)
this->sln_vector[i] = newton.get_sln_vector()[i];
return true;
}
if (it++ >= max_iter)
{
if (this->verbose_output)
info("Maximum allowed number of Picard iterations exceeded, returning false.");
return false;
}
// Copy the solution into the previous iteration.
sln_prev_iter->copy(&sln_new);
}
}
inline long long int solve(const long long int &n, const long long int &k)
{
long long int result = 0;
std::sort(number, number + numbers);
for(long long int i = 1; i <= n - k + 1; ++ i)
result = (result + number[numbers - i] * newton(n - i, k - 1)) % MOD;
return result;
}
int main() {
/*
* Вычисляем ширину эпсилон.
*/
int epswidth = ceil(-log10(REAL_EPSILON));
printf(
"target_1 = 0, x = %.*f; dichotomy, x ∈ [%f, %f]\n",
epswidth,
dichotomy(target_1, TARGET_1_A, TARGET_1_B),
TARGET_1_A, TARGET_1_B
);
printf(
"target_1 = 0, x = %.*f; iterations, x ∈ [%f, %f]\n",
epswidth,
iterations(target_1_xfx, TARGET_1_A, TARGET_1_B),
TARGET_1_A, TARGET_1_B
);
printf(
"target_1 = 0, x = %.*f; newton, x ∈ [%f, %f]\n",
epswidth,
newton(target_1, target_1_derivative, TARGET_1_A, TARGET_1_B),
TARGET_1_A, TARGET_1_B
);
printf(
"target_2 = 0, x = %.*f; dichotomy, x ∈ [%f, %f]\n",
epswidth,
dichotomy(target_2, TARGET_2_A, TARGET_2_B),
TARGET_2_A, TARGET_2_B
);
printf(
"target_2 = 0, x = %.*f; iterations, x ∈ [%f, %f]\n",
epswidth,
iterations(target_2_xfx, TARGET_2_A, TARGET_2_B),
TARGET_2_A, TARGET_2_B
);
printf(
"target_2 = 0, x = %.*f; newton, x ∈ [%f, %f]\n",
epswidth,
newton(target_2, target_2_derivative, TARGET_2_A, TARGET_2_B),
TARGET_2_A, TARGET_2_B
);
return (0);
}
main()
{
double user_number;
printf("Please enter the number you want the square root of\r\n");
scanf("%lf",&user_number);
//squareroot(user_number);
newton(user_number);
}
int main() {
double x;
double a = 0.0;
for (int i=0; i<100000; i++) {
x = newton(i % 10);
a += x;
// cout << x << endl;
}
printf("%g\n", a);
}
int
main() {
FILE *file = fopen("result/newtonDROB.txt", "w+");
for (i=0; i < 5; i++) {
printf("Iteration %d with e = %lf\n", i+1, e[i]);
newton(file);
}
fclose (file);
return 0;
}
int main() {
int n, k, out;
printf("Podaj wartość n: ");
scanf("%d", &n);
printf("Podaj wartość k: ");
scanf("%d", &k);
wynik = newton(n, k);
printf("%d\n", out);
}
int main(void)
{
int x, y;
printf("Podaj liczbe x: ");
scanf("%d", &x);
printf("Podaj liczbe y: ");
scanf("%d", &y);
printf("%d \n", newton(x, y));
return 0;
}
