void
test_f (const gsl_root_fsolver_type * T, const char * description, gsl_function *f,
double lower_bound, double upper_bound, double correct_root)
{
int status;
size_t iterations = 0;
double r, a, b;
double x_lower, x_upper;
gsl_root_fsolver * s;
x_lower = lower_bound;
x_upper = upper_bound;
s = gsl_root_fsolver_alloc(T);
gsl_root_fsolver_set(s, f, x_lower, x_upper) ;
do
{
iterations++ ;
gsl_root_fsolver_iterate (s);
r = gsl_root_fsolver_root(s);
a = gsl_root_fsolver_x_lower(s);
b = gsl_root_fsolver_x_upper(s);
if (a > b)
gsl_test (GSL_FAILURE, "interval is invalid (%g,%g)", a, b);
if (r < a || r > b)
gsl_test (GSL_FAILURE, "r lies outside interval %g (%g,%g)", r, a, b);
status = gsl_root_test_interval (a,b, EPSABS, EPSREL);
}
while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
gsl_test (status, "%s, %s (%g obs vs %g expected) ",
gsl_root_fsolver_name(s), description,
gsl_root_fsolver_root(s), correct_root);
if (iterations == MAX_ITERATIONS)
{
gsl_test (GSL_FAILURE, "exceeded maximum number of iterations");
}
/* check the validity of the returned result */
if (!WITHIN_TOL (r, correct_root, EPSREL, EPSABS))
{
gsl_test (GSL_FAILURE, "incorrect precision (%g obs vs %g expected)",
r, correct_root);
}
gsl_root_fsolver_free(s);
}
double fzero( function<double(double)> fun, double x_lo, double x_hi,
int max_iter, double epsabs, double epsrel )
{
// Allocate
gsl_function F = { gsl::sfunction_proxy, &fun };
const gsl_root_fsolver_type *T = gsl_root_fsolver_brent;
gsl_root_fsolver *s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set( s, &F, x_lo, x_hi );
// Main loop
int status;
double rv;
int iter = 0;
do {
iter++;
status = gsl_root_fsolver_iterate(s);
rv = gsl_root_fsolver_root(s);
x_lo = gsl_root_fsolver_x_lower(s);
x_hi = gsl_root_fsolver_x_upper(s);
status = gsl_root_test_interval( x_lo, x_hi, epsabs, epsrel );
} while (status == GSL_CONTINUE && iter < max_iter);
if( iter == max_iter )
warning("bealab::fzero - maximum number of iterations reached");
// Free
gsl_root_fsolver_free (s);
return rv;
}
//_______________________________________________________________________________________________________________________
///
/// \brief Calculate chemical potential 'mu' such that FermiDirac distribution gives exactly 'nelec' electrons
///
static double CalculateChemicalPotential(const en_levels_t *levels, const int nelec, const bool spinpol, const double kBT)
{
int m, n, i;
const int maxiter = 128;
gsl_FD_params_t params;
params.nelec = nelec;
params.nlevels = (levels->m_max+1)*levels->num;
params.en = malloc(params.nlevels * sizeof(double));
params.occ = malloc(params.nlevels * sizeof(int));
params.kBT = kBT;
// fill energy levels and occupancies
for (m = 0; m <= levels->m_max; m++)
{
for (n = 0; n < levels->num; n++)
{
params.en [n + m*levels->num] = levels->en[n + m*levels->num];
params.occ[n + m*levels->num] = GetMaxOccupancy(m, spinpol);
}
}
// first interval used in interval bisection method
double mu_lo = 0.0;
double mu_hi = levels->en[(levels->m_max+1)*levels->num-1]; // use "last" energy level as upper bound
gsl_function F;
F.function = &NumParticleDifference;
F.params = ¶ms;
const gsl_root_fsolver_type *T = gsl_root_fsolver_brent;
gsl_root_fsolver *s = gsl_root_fsolver_alloc(T);
gsl_root_fsolver_set(s, &F, mu_lo, mu_hi);
double mu = 0;
int status = GSL_CONTINUE;
for (i = 0; i < maxiter && status == GSL_CONTINUE; i++)
{
status = gsl_root_fsolver_iterate(s);
if (status != GSL_SUCCESS) {
fprintf(stderr, "CalculateOccupancy() warning: gsl_root_fsolver_iterate() returned with status code %i\n", status);
}
mu = gsl_root_fsolver_root(s);
mu_lo = gsl_root_fsolver_x_lower(s);
mu_hi = gsl_root_fsolver_x_upper(s);
status = gsl_root_test_interval(mu_lo, mu_hi, 0, 1e-8);
}
if (status != GSL_SUCCESS) {
fprintf(stderr, "CalculateOccupancy() warning: not converged after %i iterations, status: %i\n", maxiter, status);
}
// clean up
free(params.occ);
free(params.en);
gsl_root_fsolver_free(s);
return mu;
}
//----------------------------------------------------------------------------
int f_root4p(REAL p1,REAL p2,REAL p3,REAL a,REAL b,REAL (*fp)(REAL, void*),
REAL * result){
struct f_params_3 alpha = {p1,p2,p3};
int status;
int iter = 0, max_iter = 1000;
REAL r = 0.0;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
gsl_function F;
F.function = fp;
F.params = α
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc(T);
gsl_root_fsolver_set(s,&F,a,b);
do{
iter++;
status = gsl_root_fsolver_iterate(s);
r = gsl_root_fsolver_root(s);
a = gsl_root_fsolver_x_lower(s);
b = gsl_root_fsolver_x_upper(s);
status = gsl_root_test_interval(a,b,0,0.001);
}while (status == GSL_CONTINUE && iter < max_iter);
*result=r;
gsl_root_fsolver_free (s);
return 0;
}
/* this function returns the solution to f (x) = 0 */
int f_root (double x_min, double x_max, double *root, struct f_root_params *par) {
size_t iter;
int status;
double x_lo, x_hi;
gsl_root_fsolver *s;
/* defines the function to pass to the solver */
gsl_function func;
func.function = par->f;
func.params = par->p;
/* allocates and initializes the minimizer */
s = gsl_root_fsolver_alloc (par->type);
gsl_root_fsolver_set (s, &func, x_min, x_max);
/* start the iteration to find the root */
iter = 0;
do {
iter++;
status = gsl_root_fsolver_iterate (s);
*root = gsl_root_fsolver_root (s);
x_lo = gsl_root_fsolver_x_lower (s);
x_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (x_lo, x_hi, par->eps_abs, par->eps_rel);
if (par->verbose)
fprintf (stderr, "%lu: x = %f\n", iter, *root);
}
while (status==GSL_CONTINUE && iter<par->max_iter);
/* free the memory and return the found root */
gsl_root_fsolver_free (s);
return status;
}
double f_eq_hyper(vec n_small, set_const *C){
int status;
int iter = 0, max_iter = 3000;
double x = 0.0, x_expect = 0.5;
double xmin = -0.001, xmax = 1.0;
gsl_function F;
F.function = &func_f_eq_multi;
func_f_eq_multi_params params = { n_small, C };
F.params = ¶ms;
gsl_root_fsolver_set(s_f_eq, &F, xmin, xmax);
do {
iter++;
status = gsl_root_fsolver_iterate(s_f_eq);
x = gsl_root_fsolver_root(s_f_eq);
xmin = gsl_root_fsolver_x_lower(s_f_eq);
xmax = gsl_root_fsolver_x_upper(s_f_eq);
status = gsl_root_test_interval(xmin, xmax, 0, 1e-9);
} while (status == GSL_CONTINUE && iter < max_iter);
if (status != 0) {
cout << "error, status = " << status << endl;
}
return x;
}
int np_eq_solve(double n, vec n_ext, double xmin, double xmax, set_const * C, double & res){
int status;
int iter = 0, max_iter = 1000;
double x = 0.0, x_expect = (xmax - xmin)/2.0;
gsl_function F;
F.function = &func_np;
func_np_params par = { n, C, n_ext };
F.params = ∥
status = gsl_root_fsolver_set(s_np_eq, &F, xmin, xmax);
if (status != 0){
return status;
}
do {
iter++;
status = gsl_root_fsolver_iterate(s_np_eq);
x = gsl_root_fsolver_root(s_np_eq);
xmin = gsl_root_fsolver_x_lower(s_np_eq);
xmax = gsl_root_fsolver_x_upper(s_np_eq);
status = gsl_root_test_interval(xmin, xmax, 0, 1e-10);
} while (status == GSL_CONTINUE && iter < max_iter);
;
if (status != 0) {
cout << "error, status = " << status << endl;
}
res = x;
return status;
}
double root_finder( double (*f)(double), double a, double b, double epsrel, double epsabs ) {
int status,i;
double root;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
gsl_function F;
F.function = gsl_function_wrapper;
F.params = (void *)f;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, a, b);
for ( i = 0; i < MAX_ITER; i++ ) {
status = gsl_root_fsolver_iterate (s);
status = gsl_root_test_interval (gsl_root_fsolver_x_lower(s),
gsl_root_fsolver_x_upper(s),
epsrel, epsabs);
if (status == GSL_SUCCESS) {
root = gsl_root_fsolver_root(s);
gsl_root_fsolver_free(s);
return root;
}
}
cart_error("Did not reach root after %u iterations!", MAX_ITER);
return 0.0;
}
double root(double begin) {
int status;
int iter = 0, max_iter = 100000;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double x_lo = begin / 2, x_hi = begin - e, r;
gsl_function F;
F.function = &f;
F.params = &begin;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, x_lo, x_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
r = gsl_root_fsolver_root (s);
x_lo = gsl_root_fsolver_x_lower (s);
x_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (x_lo, x_hi,
0, e);
}
while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return r;
}
void Spectrometer::calibrate(){
if(calibration.size()!=2)
return;
double a=1e3; // grating step in nm
double l1 = calibration[0].wavelength;
double x1 = calibration[0].pixelNum-imageWidth/2.;
double l2 = calibration[1].wavelength;
double x2 = calibration[1].pixelNum-imageWidth/2.;
struct calcFParams params = {l1,l2,x1,x2,a};
double f_lo= 200;
double f_hi= 3000;
gsl_function F;
F.function = &Spectrometer::calcFFunc;
F.params = ¶ms;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
//T = gsl_root_fsolver_brent;
T = gsl_root_fsolver_bisection;
s = gsl_root_fsolver_alloc(T);
gsl_root_fsolver_set (s, &F, f_lo, f_hi); //f in pixels guessed to be between 300 and 5000
double r=500;
int iter=0;
int max_iter=100;
int status;
do{
iter++;
status = gsl_root_fsolver_iterate(s);
r = gsl_root_fsolver_root(s);
f_lo = gsl_root_fsolver_x_lower(s);
f_hi = gsl_root_fsolver_x_upper(s);
status = gsl_root_test_interval (f_lo, f_hi,
0, 0.001);
} while (status == GSL_CONTINUE && iter < max_iter);
if(status==GSL_SUCCESS) {
focal = r;
pas = a;
sin_angle_i = l1/pas + x1/sqrt(r*r+x1*x1);
isXCalibrated = true;
qDebug()<<"Calibration finished !";
qDebug()<<"focal : "<< focal;
qDebug()<<"angle i : "<< 180/3.1415*asin(sin_angle_i);
qDebug()<<"angle i2 : "<< 180/3.1415*asin( l2/pas + x2/sqrt(r*r+x2*x2));
}
gsl_root_fsolver_free (s);
}
double Chevalier::MachNumber(double r)
{
double Mx;
double x = r/R;
gsl_function func;
int status;
int iter = 0;
int max_iter = 100;
double M_lo = 1.0e-6;
double M_hi = 5.;
double answer;
double fp[2];
fp[0] = gamma;
fp[1] = x;
//choose which solution to use
if(x<=1.0)
{
M_lo = 1.0e-6;
M_hi = 1.0;
func.function = &mach_crossing_A;
}else{
M_lo = 1.0;
M_hi = 100.0;
func.function = &mach_crossing_B;
}
func.params = &fp[0];
gsl_root_fsolver_set(grsolve, &func, M_lo, M_hi);
do{
iter++;
status = gsl_root_fsolver_iterate(grsolve);
Mx = gsl_root_fsolver_root(grsolve);
M_lo = gsl_root_fsolver_x_lower(grsolve);
M_hi = gsl_root_fsolver_x_upper(grsolve);
status = gsl_root_test_interval(M_lo,M_hi,0,1.0e-5);
if(status==GSL_SUCCESS)
{
answer = Mx;
}
}
while(status==GSL_CONTINUE && iter<max_iter);
//return the answer
return answer;
}
int
main (void)
{
int status;
int iter = 0, max_iter = 100;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double r = 0, r_expected = sqrt (5.0);
double x_lo = 0.0, x_hi = 5.0;
gsl_function F;
struct quadratic_params params = {1.0, 0.0, -5.0};
F.function = &quadratic;
F.params = ¶ms;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, x_lo, x_hi);
printf ("using %s method\n",
gsl_root_fsolver_name (s));
printf ("%5s [%9s, %9s] %9s %10s %9s\n",
"iter", "lower", "upper", "root",
"err", "err(est)");
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
r = gsl_root_fsolver_root (s);
x_lo = gsl_root_fsolver_x_lower (s);
x_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (x_lo, x_hi,
0, 0.001);
if (status == GSL_SUCCESS)
printf ("Converged:\n");
printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
iter, x_lo, x_hi,
r, r - r_expected,
x_hi - x_lo);
}
while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return status;
}
/// Get the cDel for a given cvir
double cosmology::getcDel(double cvir, double z, double Delta)
{
int status;
int iter = 0, max_iter = 100;
double res;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double c_lo = 0.01*cvir, c_hi = 10.0*cvir;
gsl_function F;
cDel_params p;
p.cptr = this;
p.cvir = &cvir;
double omz=Omega(z);
double dcz=Delta_crit(z);
p.omegaz=&omz;
p.dcz=&dcz;
p.Delta=Δ
F.function = &findcDel;
F.params = &p;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, c_lo, c_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
res = gsl_root_fsolver_root (s);
c_lo = gsl_root_fsolver_x_lower (s);
c_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (c_lo, c_hi,0, 1e-6);
if (status == GSL_SUCCESS)
{
//std::cout<<"# "<<"zcollapse:Brent converged after "<< iter<<" iterations"<<std::endl;
}
}while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return res;
}
int UnidimensionalRootFinder(gsl_function *F,
double lower_bound,
double upper_bound,
double abs_error,
double rel_error,
int max_iterations,
double *return_result)
{
const gsl_root_fsolver_type * T = gsl_root_fsolver_bisection;
gsl_root_fsolver * s = gsl_root_fsolver_alloc(T);
// Test if the limits straddle the root,
// if they don't, we will return -1.
if (GSL_SIGN(GSL_FN_EVAL(F, lower_bound)) == GSL_SIGN(GSL_FN_EVAL(F, upper_bound)))
return -1;
gsl_root_fsolver_set(s, F, lower_bound, upper_bound);
int i = 0;
double x_lower;
double x_upper;
do{
i++;
int status = gsl_root_fsolver_iterate(s);
if (status != GSL_SUCCESS){
printf("ERROR: No solution to the gap equation was found!\n");
exit(EXIT_FAILURE);
}
x_lower = gsl_root_fsolver_x_lower(s);
x_upper = gsl_root_fsolver_x_upper(s);
} while(GSL_CONTINUE == gsl_root_test_interval(x_lower,
x_upper,
abs_error,
rel_error)
&& i <= max_iterations);
double result = gsl_root_fsolver_root(s);
void gsl_root_fsolver_free(gsl_root_fsolver * S);
*return_result = result;
return 0;
}
/* compute the first N roots alpha_k of the equation
((A-1)/(A+1)) cos((H - Z B) alpha) = cos((H + Z B) alpha)
where H and B are heights and A, Z are defined in terms of material
constants */
int print_alpha_k(const int N) {
int status, iter, k, max_iter = 200;
double Z, A;
double alpha, alpha_lo, alpha_hi, temp_lo;
const gsl_root_fsolver_type *solvT;
gsl_root_fsolver *solv;
gsl_function F;
struct coscross_params params;
Z = sqrt((rho_BR * c_p_BR * k_ICE) / (rho_ICE * c_p_ICE * k_BR));
A = (k_BR / k_ICE) * Z;
params.Afrac = (A - 1.0) / (A + 1.0);
params.HZBsum = H0 + Z * B0;
params.HZBdiff = H0 - Z * B0;
F.function = &coscross;
F.params = ¶ms;
solvT = gsl_root_fsolver_brent; /* faster than bisection but still bracketing */
solv = gsl_root_fsolver_alloc(solvT);
for (k = 0; k < N; k++) {
/* these numbers bracket exactly one solution */
alpha_lo = (double(k) * pi) / params.HZBsum;
alpha_hi = (double(k + 1) * pi) / params.HZBsum;
gsl_root_fsolver_set(solv, &F, alpha_lo, alpha_hi);
iter = 0;
do {
iter++;
status = gsl_root_fsolver_iterate(solv);
alpha = gsl_root_fsolver_root(solv);
alpha_lo = gsl_root_fsolver_x_lower(solv);
alpha_hi = gsl_root_fsolver_x_upper(solv);
temp_lo = (alpha_lo > 0) ? alpha_lo : (alpha_hi/2.0);
status = gsl_root_test_interval(temp_lo, alpha_hi, 0, ALPHA_RELTOL);
} while ((status == GSL_CONTINUE) && (iter < max_iter));
if (iter >= max_iter) {
printf("!!!ERROR: root finding iteration reached maximum iterations; QUITING!\n");
return ITER_MAXED_OUT;
}
printf("%19.15e,\n",alpha);
/* DEBUG: printf("%19.15e (in orig bracket [%19.15e,%19.15e])\n",alpha,
(double(k) * pi) / params.HZBsum, (double(k+1) * pi) / params.HZBsum); */
}
gsl_root_fsolver_free(solv);
return status;
}
/// Get the Mvir for a given MDel
double cosmology::getMvir(double M, double z,double Delta)
{
int status;
int iter = 0, max_iter = 100;
double res;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double m_lo = 0.1*M, m_hi = 5.0*M;
gsl_function F;
mvir_params p;
p.cptr = this;
p.mDel = &M;
p.z=&z;
p.Delta=Δ
F.function = &findmvir;
F.params = &p;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, m_lo, m_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
res = gsl_root_fsolver_root (s);
m_lo = gsl_root_fsolver_x_lower (s);
m_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (m_lo, m_hi,0, 1.e-6);
if (status == GSL_SUCCESS)
{
//std::cout<<"# "<<"zcollapse:Brent converged after "<< iter<<" iterations"<<std::endl;
}
}while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return res;
}
static VALUE rb_gsl_function_rootfinder(int argc, VALUE *argv, VALUE obj)
{
int status, iter = 0, max_iter = 1000;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s = NULL;
gsl_function *F = NULL;
double r, a, b, epsabs = 0.0, epsrel = 1e-6;
Data_Get_Struct(obj, gsl_function, F);
switch (argc) {
case 2:
a = NUM2DBL(argv[0]);
b = NUM2DBL(argv[1]);
break;
case 1:
switch (TYPE(argv[0])) {
case T_ARRAY:
a = NUM2DBL(rb_ary_entry(argv[0], 0));
b = NUM2DBL(rb_ary_entry(argv[0], 1));
break;
default:
rb_raise(rb_eTypeError, "interval must be given by an array [a, b]");
}
break;
default:
rb_raise(rb_eArgError, "interval must be given");
break;
}
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, F, a, b);
do {
iter++;
status = gsl_root_fsolver_iterate (s);
r = gsl_root_fsolver_root (s);
a = gsl_root_fsolver_x_lower (s);
b = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (a, b, epsabs, epsrel);
if (status == GSL_SUCCESS) break;
} while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free(s);
if (status == GSL_SUCCESS) {
return rb_ary_new3(3, rb_float_new(r), INT2FIX(iter), INT2FIX(status));
} else {
printf("not converged\n");
return Qfalse;
}
}
/// Get the c200 for a given cvir
double cosmology::getcDeltap_from_cDelta(double cDelta, double Delta, double Deltap)
{
int status;
int iter = 0, max_iter = 100;
double res;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double c_lo = 0.01*cDelta, c_hi = 10.0*cDelta;
gsl_function F;
cDelta_params p;
double frac=Delta/Deltap;
p.cDelta = &cDelta;
p.frac = &frac;
F.function = &findcDelp;
F.params = &p;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, c_lo, c_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
res = gsl_root_fsolver_root (s);
c_lo = gsl_root_fsolver_x_lower (s);
c_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (c_lo, c_hi,0, 1e-6);
if (status == GSL_SUCCESS)
{
//std::cout<<"# "<<"zcollapse:Brent converged after "<< iter<<" iterations"<<std::endl;
}
}while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return res;
}
/// Get the M which has N_{+} number of haloes above mass M.
double cosmology::getM(double Np,double z)
{
int status;
int iter = 0, max_iter = 100;
double res;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
// m is in log_{10}(m)
double xm_lo = 9.0, xm_hi = 15.5;
gsl_function F;
np_params p;
p.cptr = this;
p.z = &z;
p.Np = &Np;
F.function = &findM;
F.params = &p;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, xm_lo, xm_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
res = gsl_root_fsolver_root (s);
xm_lo = gsl_root_fsolver_x_lower (s);
xm_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (xm_lo, xm_hi,0, 1e-6);
if (status == GSL_SUCCESS)
{
std::cout<<"# "<<"getM:Brent converged after "<< iter<<" iterations"<<std::endl;
}
}while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return pow(10.,res);
}
double iterate(Args *args, gsl_root_fsolver *s, double xLo, double xHi){
int iter;
double r;
int status;
iter = 0;
do{
iter++;
status = gsl_root_fsolver_iterate(s);
r = gsl_root_fsolver_root(s);
xLo = gsl_root_fsolver_x_lower(s);
xHi = gsl_root_fsolver_x_upper(s);
status = gsl_root_test_interval(xLo, xHi, 0, args->t);
}while(status == GSL_CONTINUE && iter < args->i);
return r;
}
/// Get the collapse redshift for a given variance
double cosmology::getzcoll(double sigma)
{
int status;
int iter = 0, max_iter = 100;
double res;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double z_lo = 0.0, z_hi = 10.0;
gsl_function F;
coll_params p;
p.cptr = this;
p.sig = σ
F.function = &findzcoll;
F.params = &p;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, z_lo, z_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
res = gsl_root_fsolver_root (s);
z_lo = gsl_root_fsolver_x_lower (s);
z_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (z_lo, z_hi,0, 1e-6);
if (status == GSL_SUCCESS)
{
//std::cout<<"# "<<"zcollapse:Brent converged after "<< iter<<" iterations"<<std::endl;
}
}while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return res;
}
int f_eq_solve(vec n, set_const *C, double lo, double hi, double * res){
int status;
int iter = 0, max_iter = 3000;
double x = 0.0, x_expect = 0.5;
double xmin = lo, xmax = hi;
gsl_function F;
F.function = &func_f_eq_multi;
func_f_eq_multi_params params = { n, C };
F.params = ¶ms;
//Like there is no root if function values have the same sign:
double fmin = F.function(xmin, ¶ms);
double fmax = F.function(xmax, ¶ms);
if (fmin*fmax > 0){
return -10;
}
gsl_root_fsolver_set(s_f_eq, &F, xmin, xmax);
do {
iter++;
status = gsl_root_fsolver_iterate(s_f_eq);
//printf("status = %i\n", status);
x = gsl_root_fsolver_root(s_f_eq);
xmin = gsl_root_fsolver_x_lower(s_f_eq);
xmax = gsl_root_fsolver_x_upper(s_f_eq);
status = gsl_root_test_interval(xmin, xmax, 0, 1e-9);
//printf("status = %i\n", status);
} while (status == GSL_CONTINUE && iter < max_iter);
if (status != 0) {
cout << "error, status = " << status << endl;
}
//printf("func_feq_vec: nn = %f, np = %f, res = %f \n", n[0], n[1], x);
*res = x;
return status;
}
double raytrace_free_distance(scope_ray ray, raytrace_geom geom, int surf){
/* Variable declarations */
/* Variables needed for GSL's root-finder algorithms */
int status;
int iter = 0, max_iter = 100;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double r = 0;
double x_lo = 0.0, x_hi = 5.0;
gsl_function F;
scope_root_params params = {ray, geom, surf};
/* If w/in Rowland Circle, reduce x_hi to 2.1 */
if(surf == OPTIC_SF) x_hi = 2.1;
F.function = &raytrace_distroot;
F.params = ¶ms;
/* Solve using GSL's Brent's Method Solver */
// T = gsl_root_fsolver_brent;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc(T);
gsl_root_fsolver_set(s, &F, x_lo, x_hi);
do{
iter++;
status = gsl_root_fsolver_iterate(s);
r = gsl_root_fsolver_root(s);
x_lo = gsl_root_fsolver_x_lower(s);
x_hi = gsl_root_fsolver_x_upper(s);
status = gsl_root_test_interval(x_lo, x_hi, 0, 1.e-14);
} while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
return r;
}
int
main ()
{
int status;
int iterations = 0, max_iterations = 100;
gsl_root_fsolver *s;
double r = 0, r_expected = sqrt (5.0);
double x_lower x = 0.0, x_upper = 5.0;
gsl_function F;
struct quadratic_params params =
{1.0, 0.0, -5.0};
F.function = &quadratic;
F.params = ¶ms;
s = gsl_root_fsolver_alloc (gsl_root_fsolver_bisection);
gsl_root_fsolver_set (s, &F, x);
printf ("using %s method\n", gsl_root_fsolver_name (s));
printf ("%5s [%9s, %9s] %9s %9s %10s %9s\n",
"iter", "lower", "upper", "root", "actual", "err", "err(est)");
do
{
iterations++;
status = gsl_root_fsolver_iterate (s);
r = gsl_root_fsolver_root (s);
x_lower = gsl_root_fsolver_x_lower (s);
x_upper = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (x, 0, 0.001);
if (status == GSL_SUCCESS)
printf ("Converged:\n");
printf ("%5d [%.7f, %.7f] %.7f %.7f %+.7f %.7f\n",
iterations, x_lower, x_upper,
r, r_expected, r - r_expected, x_upper - x_lower);
}
while (status == GSL_CONTINUE && iterations < max_iterations);
}
void
test_f_e (const gsl_root_fsolver_type * T,
const char * description, gsl_function *f,
double lower_bound, double upper_bound, double correct_root)
{
int status;
size_t iterations = 0;
double x_lower, x_upper;
gsl_root_fsolver * s;
x_lower = lower_bound;
x_upper = upper_bound;
s = gsl_root_fsolver_alloc(T);
status = gsl_root_fsolver_set(s, f, x_lower, x_upper) ;
gsl_test (status != GSL_EINVAL, "%s (set), %s", T->name, description);
if (status == GSL_EINVAL)
{
gsl_root_fsolver_free(s);
return ;
}
do
{
iterations++ ;
gsl_root_fsolver_iterate (s);
x_lower = gsl_root_fsolver_x_lower(s);
x_upper = gsl_root_fsolver_x_lower(s);
status = gsl_root_test_interval (x_lower, x_upper,
EPSABS, EPSREL);
}
while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
gsl_test (!status, "%s, %s", gsl_root_fsolver_name(s), description,
gsl_root_fsolver_root(s) - correct_root);
gsl_root_fsolver_free(s);
}
static VALUE rb_gsl_fsolver_solve(int argc, VALUE *argv, VALUE *obj)
{
gsl_root_fsolver *s = NULL;
gsl_function *F = NULL;
double x, xl, xh, epsabs = 0.0, epsrel = 1e-6;
int status, iter = 0, max_iter = 100;
switch (argc) {
case 3:
Check_Type(argv[2], T_ARRAY);
epsabs = NUM2DBL(rb_ary_entry(argv[2], 0));
epsrel = NUM2DBL(rb_ary_entry(argv[2], 1));
/* no break */
case 2:
Check_Type(argv[1], T_ARRAY);
xl = NUM2DBL(rb_ary_entry(argv[1], 0));
xh = NUM2DBL(rb_ary_entry(argv[1], 1));
break;
default:
rb_raise(rb_eArgError,
"Usage: solve(f = Function, range = Array, eps = Array)");
break;
}
CHECK_FUNCTION(argv[0]);
Data_Get_Struct(argv[0], gsl_function, F);
Data_Get_Struct(obj, gsl_root_fsolver, s);
gsl_root_fsolver_set(s, F, xl, xh);
do {
iter++;
status = gsl_root_fsolver_iterate (s);
x = gsl_root_fsolver_root (s);
xl = gsl_root_fsolver_x_lower (s);
xh = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (xl, xh, epsabs, epsrel);
if (status == GSL_SUCCESS) break;
} while (status == GSL_CONTINUE && iter < max_iter);
return rb_ary_new3(3, rb_float_new(x), INT2FIX(iter), INT2FIX(status));
}
double f_eq(double nn, double np, set_const * C) {
int status;
int iter = 0, max_iter = 3000;
double x = 0.0, x_expect = 0.5;
double xmin = 1e-5, xmax = 1.0;
gsl_function F;
F.function = &func_f_eq;
func_f_eq_params params = { nn, np, C };
F.params = ¶ms;
//for (int i = 0; i < 100; i++){
// if (func_f_eq(0.01*i, ¶ms) < 0){
// xmin = 0.01*i;
// }
//}
gsl_root_fsolver_set(s_f_eq, &F, xmin, xmax);
do {
iter++;
status = gsl_root_fsolver_iterate(s_f_eq);
x = gsl_root_fsolver_root(s_f_eq);
xmin = gsl_root_fsolver_x_lower(s_f_eq);
xmax = gsl_root_fsolver_x_upper(s_f_eq);
status = gsl_root_test_interval(xmin, xmax, 0, 1e-9);
} while (status == GSL_CONTINUE && iter < max_iter);
if (status != 0) {
cout << "error, status = " << status << endl;
}
//printf("func_feq_orig: nn = %f, np = %f, res = %f \n", nn, np, x);
return x;
}
/**
* Function: get_xvalue_from_tlength
* The function computes the x-offset position from the reference point
* for a given tracelength in a given beam.
* The solution is numerically derived and therefore
* does work for any reasonable tracefunction.
*
* Parameters:
* @param actbeam - the beam to compute the x-offset
* @param tlength - tracelength
*
* Returns:
* @return xdiff - the x-offset
*/
double
get_xvalue_from_tlength(beam *actbeam, double tlength)
{
int iter=0;
int status;
double xdiff=0.0;
d_point x_interv;
// define and initialize the solver
const gsl_root_fsolver_type *T = gsl_root_fsolver_brent;
gsl_root_fsolver *s = gsl_root_fsolver_alloc (T);
gsl_function F;
tlength_pars *tpars;
// derive the x-interval from the beam boundaries
x_interv = get_xinterv_from_beam(actbeam);
// fprintf(stdout, "xpos: %f, ypos: %f\n", x_interv.x, x_interv.y);
// allocate and fill the parameters
tpars = (tlength_pars *) malloc(sizeof(tlength_pars));
tpars->actbeam = actbeam;
tpars->tlength = tlength;
// fille the GSL-function
F.function = &zero_tlength;
F.params = tpars;
// set the boundaries for the solver
gsl_root_fsolver_set (s, &F, x_interv.x, x_interv.y);
// iterate to find the zeropoint
do
{
// increment the iteration counter
iter++;
// iterate on the solver
status = gsl_root_fsolver_iterate (s);
// get a new guess from the solver
xdiff = gsl_root_fsolver_root (s);
// derive and set new boundaries
x_interv.x = gsl_root_fsolver_x_lower (s);
x_interv.y = gsl_root_fsolver_x_upper (s);
// check the accuracy
status = gsl_root_test_interval (x_interv.x, x_interv.y,
0, 0.0001);
//--------------CAVEAT---------------------------------------
// until March 28th 08 the code, wriongly was:
//status = gsl_root_test_interval (x_interv.x, x_interv.x,
// 0, 0.0001);
// somehow this made no difference.....
//-----------------------------------------------------------
}
// check for the break condition
while (status == GSL_CONTINUE && iter < MAX_ITER);
// free the memory
free(tpars);
// free the memory
gsl_root_fsolver_free (s);
// return the result
return xdiff;
}
double eta(double q[2], double qdot[2], double t, double eta0) {
// calculates the auxiliary variable eta by solving Kepler's equation
// the equation is solved by searching for a root
// using the brent's algorithm root bracketer in GSL
// definitions for root solver
const gsl_root_fsolver_type *T = gsl_root_fsolver_brent;
gsl_root_fsolver *s;
gsl_function keq;
// iteration limits for root solver
double epsabs=0.0;
double epsrel = 1e-10;
size_t max_iter=100;
size_t iter=0;
int status;
double xlo,xhi;
double r;
//compute e, c, omega3, initial theta3
double e = eccentricity(q, qdot);
double c = c_aux(q, qdot);
double omega3 = Omega3(q,qdot);
double theta30 = theta3(eta0,q,qdot);
// set up function parameters
keplerEquationParamsType pkeq={ e * c / (c + B_ISO), omega3 * t + theta30};
//set up function for rootfinding
keq.function = &keplerEquation;
keq.params = &pkeq;
//initialize rootfinder
s=gsl_root_fsolver_alloc(T);
//set it to bracket root of kepler eqn. The initial guess should be near eta=Omega3*t + theta30
xlo = omega3 * t + theta30 - M_PI;
xhi = omega3 * t + theta30 + M_PI;
gsl_root_fsolver_set(s, &keq, xlo, xhi);
//iterate till root is solved
do {
iter++;
status=gsl_root_fsolver_iterate(s);
xlo=gsl_root_fsolver_x_lower(s);
xhi=gsl_root_fsolver_x_upper(s);
status=gsl_root_test_interval(xlo,xhi,epsabs,epsrel);
} while (status==GSL_CONTINUE && iter<max_iter);
r = gsl_root_fsolver_root(s);
gsl_root_fsolver_free(s);
return r;
}
void cosmology::pevolve_fixed(double cdel, int opt, double z, double
&cdelz, double &fdelz, double zstart){
double fac;
if(opt==1){
fac=pow(cdel*(1.+zstart)/(1.+z),3)/mu(cdel);
}else if(opt==2){
fac=pow(cdel,3)/mu(cdel);
fac=fac*pow(Eofz(zstart)/Eofz(z),2);
fac=fac*Delta_crit(zstart)/Delta_crit(z);
}else if(opt==3){
fac=pow(cdel,3)/mu(cdel);
fac=fac*pow(Eofz(zstart)/Eofz(z),2);
}else{
fprintf(stderr,"Option %d not supported yet, bailing out...",opt);
exit(100);
}
int status;
int iter = 0, max_iter = 100;
double res;
const gsl_root_fsolver_type *T;
gsl_root_fsolver *s;
double c_lo = 0.01*cdel, c_hi = 100000.0*cdel;
gsl_function F;
march_params p;
p.fac = fac;
F.function = &findcmarch;
F.params = &p;
T = gsl_root_fsolver_brent;
s = gsl_root_fsolver_alloc (T);
gsl_root_fsolver_set (s, &F, c_lo, c_hi);
do
{
iter++;
status = gsl_root_fsolver_iterate (s);
res = gsl_root_fsolver_root (s);
c_lo = gsl_root_fsolver_x_lower (s);
c_hi = gsl_root_fsolver_x_upper (s);
status = gsl_root_test_interval (c_lo, c_hi,0, 1e-6);
if (status == GSL_SUCCESS)
{
//std::cout<<"# "<<"zcollapse:Brent converged after "<< iter<<" iterations"<<std::endl;
}
}while (status == GSL_CONTINUE && iter < max_iter);
gsl_root_fsolver_free (s);
cdelz=res;
fdelz=mu(cdelz)/mu(cdel);
}