void test_erfc()
{
static_assert((std::is_same<decltype(erfc((double)0)), double>::value), "");
static_assert((std::is_same<decltype(erfcf(0)), float>::value), "");
static_assert((std::is_same<decltype(erfcl(0)), long double>::value), "");
assert(erfc(0) == 1);
}
double JointProb::probparam(double parameter, int thecoord, double maxd0sig ) const
{
double prob = 0;
double resolutionparameters[3][5];
if (_ResolutionParameterRphi.size() != 5 || _ResolutionParameterZ.size() != 5 || _ResolutionParameter3D.size() != 5)
std::cerr << "Warning jointprob.cpp:229 Parameters of wrong length" << std::endl;
for( int iii=0; iii<5; iii++)
{
resolutionparameters[0][iii] = _ResolutionParameterRphi[iii];
resolutionparameters[1][iii] = _ResolutionParameterZ[iii];
resolutionparameters[2][iii] = _ResolutionParameter3D[iii];
}
// The if statement takes into account a different parametrization for different coordinates.
if ( thecoord < 2 )
{
// part one is the gaussian part
// to understand this part better one should look at the meaning of the complementary error function
prob = erfc( parameter / (sqrt( double(2) ) * resolutionparameters[thecoord][0] ))
-erfc( maxd0sig / ( sqrt( double(2) ) * resolutionparameters[thecoord][0] ) );
// part 2 is the added exponential tails
prob += resolutionparameters[thecoord][1]* ( exp(- resolutionparameters[thecoord][2] * parameter )
-exp(- resolutionparameters[thecoord][2] * maxd0sig ) )
+resolutionparameters[thecoord][3]* ( exp(- resolutionparameters[thecoord][4] * parameter )
-exp(- resolutionparameters[thecoord][4] * maxd0sig ) );
}
else
{
//in this view the gaussian part is just squared.
prob = exp(- ( parameter * parameter ) / ( resolutionparameters[thecoord][0] * resolutionparameters[thecoord][0] * double ( 2 ) ) )
-exp(- ( maxd0sig * maxd0sig ) / ( resolutionparameters[thecoord][0] * resolutionparameters[thecoord][0] * double ( 2 ) ) );
prob += resolutionparameters[thecoord][1]* ( ( 1 + resolutionparameters[thecoord][2] * parameter )
*exp ( - resolutionparameters[thecoord][2] * parameter )
- ( 1 + resolutionparameters[thecoord][2] * maxd0sig )
*exp ( - resolutionparameters[thecoord][2] * maxd0sig ))
+resolutionparameters[thecoord][3]* ( ( 1 + resolutionparameters[thecoord][4] * parameter )
*exp ( - resolutionparameters[thecoord][4] * parameter )
- ( 1 + resolutionparameters[thecoord][4] * maxd0sig )
*exp ( - resolutionparameters[thecoord][4] * maxd0sig ));
}
return prob;
}
double operator()(const double time, const Vect3d& r) {
const double x = r[0];
const double alpha = 1.0;
const double beta = sqrt(alpha/D);
const double exact = (mu/(D*beta)) * (
exp(-beta*(1.0-x))
- 0.5*exp(-beta*(1.0-x))*erfc((2.0*beta*D*time-(1.0-x))/sqrt(4.0*D*time))
- 0.5*exp(beta*(1.0-x))*erfc((2.0*beta*D*time+(1.0-x))/sqrt(4.0*D*time))
);
return exact;
}
double energyAndGrad(std::vector<Atom>& atoms) const
{ double eta = sqrt(0.5)/sigma, etaSq=eta*eta;
double sigmaSq = sigma * sigma;
double detR = fabs(det(R)); //cell volume
//Position independent terms:
double Ztot = 0., ZsqTot = 0.;
for(const Atom& a: atoms)
{ Ztot += a.Z;
ZsqTot += a.Z * a.Z;
}
double E
= 0.5 * 4*M_PI * Ztot*Ztot * (-0.5*sigmaSq) / detR //G=0 correction
- 0.5 * ZsqTot * eta * (2./sqrt(M_PI)); //Self-energy correction
//Reduce positions to first centered unit cell:
for(Atom& a: atoms)
for(int k=0; k<3; k++)
a.pos[k] -= floor(0.5 + a.pos[k]);
//Real space sum:
vector3<int> iR; //integer cell number
for(const Atom& a2: atoms)
for(Atom& a1: atoms)
for(iR[0]=-Nreal[0]; iR[0]<=Nreal[0]; iR[0]++)
for(iR[1]=-Nreal[1]; iR[1]<=Nreal[1]; iR[1]++)
for(iR[2]=-Nreal[2]; iR[2]<=Nreal[2]; iR[2]++)
{ vector3<> x = iR + (a1.pos - a2.pos);
double rSq = RTR.metric_length_squared(x);
if(!rSq) continue; //exclude self-interaction
double r = sqrt(rSq);
E += 0.5 * a1.Z * a2.Z * erfc(eta*r)/r;
a1.force += (RTR * x) *
(a1.Z * a2.Z * (erfc(eta*r)/r + (2./sqrt(M_PI))*eta*exp(-etaSq*rSq))/rSq);
}
//Reciprocal space sum:
vector3<int> iG; //integer reciprocal cell number
for(iG[0]=-Nrecip[0]; iG[0]<=Nrecip[0]; iG[0]++)
for(iG[1]=-Nrecip[1]; iG[1]<=Nrecip[1]; iG[1]++)
for(iG[2]=-Nrecip[2]; iG[2]<=Nrecip[2]; iG[2]++)
{ double Gsq = GGT.metric_length_squared(iG);
if(!Gsq) continue; //skip G=0
//Compute structure factor:
complex SG = 0.;
for(const Atom& a: atoms)
SG += a.Z * cis(-2*M_PI*dot(iG,a.pos));
//Accumulate energy:
double eG = 4*M_PI * exp(-0.5*sigmaSq*Gsq)/(Gsq * detR);
E += 0.5 * eG * SG.norm();
//Accumulate forces:
for(Atom& a: atoms)
a.force -= (eG * a.Z * 2*M_PI * (SG.conj() * cis(-2*M_PI*dot(iG,a.pos))).imag()) * iG;
}
return E;
}
double Hypermet::eval_step_tail(double x) {
if (width_.val == 0)
return 0;
double xc = x - center_.val;
double step = step_amplitude.val * erfc( xc/width_.val );
double tail = 0;
double lexp = exp(pow(0.5*width_.val/tail_slope.val, 2) + xc/tail_slope.val);
if ((tail_slope.val != 0) && !isinf(lexp))
tail = tail_amplitude.val * lexp * erfc( 0.5*width_.val/tail_slope.val + xc/width_.val);
return height_.val * 0.5 * (step + tail);
}
int main() {
double x = 1.0;
double y = 1.0;
int i = 1;
acosh(x);
asinh(x);
atanh(x);
cbrt(x);
expm1(x);
erf(x);
erfc(x);
isnan(x);
j0(x);
j1(x);
jn(i,x);
ilogb(x);
logb(x);
log1p(x);
rint(x);
y0(x);
y1(x);
yn(i,x);
# ifdef _THREAD_SAFE
gamma_r(x,&i);
lgamma_r(x,&i);
# else
gamma(x);
lgamma(x);
# endif
hypot(x,y);
nextafter(x,y);
remainder(x,y);
scalb(x,y);
return 0;
}
/** Calculate real space contribution of coulomb pair forces.
If NPT is compiled in, it returns the energy, which is needed for NPT. */
inline double p3m_add_pair_force(double chgfac, double *d,double dist2,double dist,double force[3])
{
int j;
double fac1,fac2, adist, erfc_part_ri;
if(dist < p3m.params.r_cut) {
if (dist > 0.0){ //Vincent
adist = p3m.params.alpha * dist;
#if USE_ERFC_APPROXIMATION
erfc_part_ri = AS_erfc_part(adist) / dist;
fac1 = coulomb.prefactor * chgfac * exp(-adist*adist);
fac2 = fac1 * (erfc_part_ri + 2.0*p3m.params.alpha*wupii) / dist2;
#else
erfc_part_ri = erfc(adist) / dist;
fac1 = coulomb.prefactor * chgfac;
fac2 = fac1 * (erfc_part_ri + 2.0*p3m.params.alpha*wupii*exp(-adist*adist)) / dist2;
#endif
for(j=0;j<3;j++)
force[j] += fac2 * d[j];
ESR_TRACE(fprintf(stderr,"%d: RSE: Pair dist=%.3f: force (%.3e,%.3e,%.3e)\n",this_node,
dist,fac2*d[0],fac2*d[1],fac2*d[2]));
#ifdef NPT
return fac1 * erfc_part_ri;
#endif
}
}
return 0.0;
}
double Frequency(int ** bits, int tailleCollection, int tailleMot)
{
int Sn = 0;
double Sobs = 0;
for(int j = 0; j < tailleCollection; j++)
{
for(int i = 0; i < tailleMot; i ++)
{
if(bits[j][i] == 0)
{
Sn--;
}
else
{
Sn++;
}
}
}
Sobs = fabs(Sn)/ (double) sqrt(tailleCollection*tailleMot);
double result = erfc((double)(Sobs/sqrt(2.0)));
printf("Sn : %d\n", Sn);
printf("Sobs : %lf\n", Sobs);
printf("Pval : %lf\n", result);
return result;
}
static double
l_erfc(char *nm)
{
extern double erfc();
return(erfc(argument(1)));
}
static void
yyerf(void)
{
double d;
p1 = pop();
if (isdouble(p1)) {
d = 1.0 - erfc(p1->u.d);
push_double(d);
return;
}
if (isnegativeterm(p1)) {
push_symbol(ERF);
push(p1);
negate();
list(2);
negate();
return;
}
push_symbol(ERF);
push(p1);
list(2);
return;
}
void Foam::equationReader::evalDimsErfcDimCheck
(
const equationReader * eqnReader,
const label index,
const label i,
const label storageOffset,
label& storeIndex,
dimensionSet& xDims,
dimensionSet sourceDims
) const
{
if
(
!xDims.dimensionless() && dimensionSet::debug
)
{
WarningIn("equationReader::evalDimsErfcDimCheck")
<< "Dimension error thrown for operation ["
<< equationOperation::opName
(
operator[](index)[i].operation()
)
<< "] in equation " << operator[](index).name()
<< ", given by:" << token::NL << token::TAB
<< operator[](index).rawText();
}
dimensionedScalar ds("temp", xDims, 0.0);
xDims.reset(erfc(ds).dimensions());
operator[](index)[i].assignOpDimsFunction
(
&Foam::equationReader::evalDimsErfc
);
}
/* callback function for near field computations */
static inline void
ewald_compute_near(const void *param, fcs_float dist, fcs_float *f, fcs_float *p)
{
fcs_float alpha = *((fcs_float *) param);
fcs_float adist = alpha * dist;
#if FCS_EWALD_USE_ERFC_APPROXIMATION
/* approximate \f$ \exp(d^2) \mathrm{erfc}(d)\f$ by applying a formula from:
Abramowitz/Stegun: Handbook of Mathematical Functions, Dover
(9. ed.), chapter 7 */
fcs_float t = 1.0 / (1.0 + 0.3275911 * adist);
fcs_float erfc_part_ri = exp(-adist*dist) *
(t * (0.254829592 +
t * (-0.284496736 +
t * (1.421413741 +
t * (-1.453152027 +
t * 1.061405429)))))
/ dist;
*p = erfc_part_ri;
*f = -(erfc_part_ri + 2.0*alpha*0.56418958354775627928034964498)
/ dist;
#else
fcs_float erfc_part_ri = erfc(adist) / dist;
*p = erfc_part_ri;
*f = -(erfc_part_ri + 2.0*alpha*0.56418958354775627928034964498*exp(-adist*adist))
/ dist;
#endif
}
double lrchisq(const double *par)
{
// chisq from likelihood ratio
// for more information see Baker and Cousins pg. 439 and Appendix
double yi=0.; // model
double ni=0.; // experiment
double lrchisq = 0.; // likelihood ratio chisq
int i=0;
for (i=startCh[spCurrent]; i<=endCh[spCurrent]; i++)
{
// events in ith bin
ni = expCurrent[i];
// calculate model in the ith bin
yi = par[0]*simCurrent[i] + par[1] + par[2]*erfc(((double)i-sfc[spCurrent])/sfw[spCurrent]);
// evaluate chisq given input parameters
if(ni > 0.)
lrchisq += ( yi - ni + ni*log(ni/yi) );
else
lrchisq += yi; // the log(0) case
}
lrchisq *= 2.;
return lrchisq;
}
double ntail(double zval)
/** normal distribution tail area
uses erfc
*/
{
double pi, t ;
double p, q, d ;
if (zval == 0.0) return 0.5 ;
if (zval<0.0) return (1.0 - ntail(-zval)) ;
if (zval<ZLIM) {
t = zval/sqrt(2.0) ;
q = erfc(t)/2.0 ;
return q ;
}
pi = 2.0*acos(0.0) ;
t = exp(-0.5*zval*zval) ;
t /= (sqrt(2.0*pi) * zval) ;
return t ;
}
double erf(double x)
{
//
// Computation of the error function erf(x).
//
return (1-erfc(x));
}
/*============================================================================*/
double ighmm_rand_get_1overa (double x, double mean, double u)
{
/* Calulates 1/a(x, mean, u), with a = the integral from x til \infty over
the Gauss density function */
# define CUR_PROC "ighmm_rand_get_1overa"
double erfc_value;
if (u <= 0.0) {
GHMM_LOG(LCONVERTED, "u <= 0.0 not allowed\n");
goto STOP;
}
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)
erfc_value = erfc ((x - mean) / sqrt (u * 2));
#else
erfc_value = ighmm_erfc ((x - mean) / sqrt (u * 2));
#endif
if (erfc_value <= DBL_MIN) {
ighmm_mes (MES_WIN, "a ~= 0.0 critical! (mue = %.2f, u =%.2f)\n", mean, u);
return (erfc_value);
}
else
return (2.0 / erfc_value);
STOP:
return (-1.0);
# undef CUR_PROC
} /* ighmm_rand_get_1overa */
/* cumalative distribution function of a-truncated N(mean, u) */
double ighmm_rand_normal_right_cdf (double x, double mean, double u, double a)
{
# define CUR_PROC "ighmm_rand_normal_right_cdf"
if (x <= a)
return (0.0);
if (u <= a) {
GHMM_LOG(LCONVERTED, "u <= a not allowed\n");
goto STOP;
}
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)
/*
Function: int erfc (double x, gsl_sf_result * result)
These routines compute the complementary error function
erfc(x) = 1 - erf(x) = 2/\sqrt(\pi) \int_x^\infty \exp(-t^2).
*/
return 1.0 + (erf ((x - mean) / sqrt (u * 2)) -
1.0) / erfc ((a - mean) / sqrt (u * 2));
#else
return 1.0 + (ighmm_erf ((x - mean) / sqrt (u * 2)) -
1.0) / ighmm_erfc ((a - mean) / sqrt (u * 2));
#endif /* Check for ISO C99 */
STOP:
return (-1.0);
# undef CUR_PROC
} /* double ighmm_rand_normal_cdf */
double Runs(int n, unsigned char *epsilon)
{
int S, k;
double pi, V, erfc_arg, p_value;
S = 0;
for ( k=0; k<n; k++ )
if ( epsilon[k] )
S++;
pi = (double)S / (double)n;
if ( fabs(pi - 0.5) > (2.0 / sqrt(n)) ) {
//PI ESTIMATOR CRITERIA NOT MET!
p_value = -1.0;
}
else {
V = 1;
for ( k=1; k<n; k++ )
if ( epsilon[k] != epsilon[k-1] )
V++;
erfc_arg = fabs(V - 2.0 * n * pi * (1-pi)) / (2.0 * pi * (1-pi) * sqrt(2*n));
p_value = erfc(erfc_arg);
}
return p_value ;
}
double ndtr(double a)
{
double x, y, z;
if (isnan(a)) {
mtherr("ndtr", DOMAIN);
return (NAN);
}
x = a * SQRTH;
z = fabs(x);
if( z < SQRTH )
y = 0.5 + 0.5 * erf(x);
else
{
y = 0.5 * erfc(z);
if( x > 0 )
y = 1.0 - y;
}
return(y);
}
static void add_top_tbl(struct All_variables *E, double age_in_myrs, double mantle_temp)
{
int m, i, j, k, node;
int nox, noy, noz;
double r1, dT, tmp;
nox = E->lmesh.nox;
noy = E->lmesh.noy;
noz = E->lmesh.noz;
dT = (mantle_temp - E->control.TBCtopval);
tmp = 0.5 / sqrt(age_in_myrs / E->data.scalet);
fprintf(stderr, "%e %e\n", dT, tmp);
for(m=1; m<=E->sphere.caps_per_proc; m++)
for(i=1; i<=noy; i++)
for(j=1; j<=nox;j ++)
for(k=1; k<=noz; k++) {
node = k + (j-1)*noz + (i-1)*nox*noz;
r1 = E->sx[m][3][node];
E->T[m][node] -= dT * erfc(tmp * (E->sphere.ro - r1));
}
return;
}
ATF_TC_BODY(erfc_inf_neg, tc)
{
const double x = -1.0L / 0.0L;
if (erfc(x) != 2.0)
atf_tc_fail_nonfatal("erfc(-Inf) != 2.0");
}
/* Implementation of complementary Error function */
double
erfc(double x)
{
static const double one_sqrtpi= 0.564189583547756287;
double a = 1;
double b = x;
double c = x;
double d = x*x+0.5;
double q1;
double q2 = b/d;
double n = 1.0;
double t;
if (fabs(x) < 2.2) {
return 1.0 - erf(x);
}
if (x < 0.0) { /*signbit(x)*/
return 2.0 - erfc(-x);
}
do {
t = a*n+b*x;
a = b;
b = t;
t = c*n+d*x;
c = d;
d = t;
n += 0.5;
q1 = q2;
q2 = b/d;
} while (fabs(q1-q2)/q2 > MATH_TOLERANCE);
return one_sqrtpi*exp(-x*x)*q2;
}
void _sep_3D_ewald_short_bond(sepatom *ptr, double kappa, double cf, sep3D *sys){
double Ucol, rv[3], r2, r, ft, f, erfckr=0, erfkr, zizj, krsq;
int i1, i2, n, k;
const double A = 2*kappa/sqrt(SEP_PI), cf2 = cf*cf;
Ucol = 0.0;
for (i1 = 0; i1 < sys->npart; i1++){
n = 0;
while (1){
i2 = ptr[i1].neighb[n];
if (i2 == -1) break;
r2 = 0.0;
for (k=0; k<3; k++){
rv[k] = ptr[i1].x[k] - ptr[i2].x[k];
if (sys->bound[k] == 'p'){
sep_Wrap( rv[k], sys->length[k] );
}
r2 += rv[k]*rv[k];
}
r = sqrt(r2);
krsq = kappa*kappa*r2;
zizj = ptr[i1].z*ptr[i2].z;
// Not same molecule - short ranged real space contribution
if ( (ptr[i1].molindex == -1 && r2<cf2) ||
(ptr[i1].molindex != ptr[i2].molindex && r2<cf2) ){
erfckr = erfc(kappa*r)/r;
ft = zizj*(erfckr + A*exp(-krsq))/r2;
for ( k=0; k<3; k++ ){
f = ft*rv[k];
ptr[i1].a[k] += f/ptr[i1].m;
ptr[i2].a[k] -= f/ptr[i2].m;
}
Ucol += zizj*erfckr;
}
// Same molecule no real space contribution, but remove
// the self part from the Fourier part
else if ( ptr[i1].molindex == ptr[i2].molindex ){
erfkr = erf(kappa*r)/r;
ft = -zizj*(erfkr - A*exp(-krsq))/r2;
for ( k=0; k<3; k++ ){
f = ft*rv[k];
ptr[i1].a[k] += f/ptr[i1].m;
ptr[i2].a[k] -= f/ptr[i2].m;
}
Ucol -= zizj*erfckr;
}
n++;
}
}
sys->retval[0] = Ucol;
}
//Add energy
inline double ewaldgpu_coulomb_pair_energy(double chgfac, double *d,double dist2,double dist)
{
if (dist < ewaldgpu_params.rcut)
{
return coulomb.prefactor*chgfac*erfc(ewaldgpu_params.alpha*dist)/dist;
}
return 0.0;
}
/* ************************************************** */
double modulate(call_t *c, double snr) {
if (snr == MAX_SNR) {
return 0;
} else {
double bpsk_ber = 0.5 * erfc(sqrt(2*snr));
return (1 - (1 - bpsk_ber) * (1- bpsk_ber));
}
}
ATF_TC_BODY(erfc_inf_pos, tc)
{
const double x = 1.0L / 0.0L;
double y = erfc(x);
if (fabs(y) > 0.0 || signbit(y) != 0)
atf_tc_fail_nonfatal("erfc(+Inf) != +0.0");
}
/////////////////////////////////////////////////////////////////////////////
// Compute the likelihood of superiority
// This function assumes that the covariance matrix and ratings are computed
/////////////////////////////////////////////////////////////////////////////
void CBradleyTerry::ComputeLikelihoodOfSuperiority() {
mLOS.SetSize(crs.GetPlayers(), crs.GetPlayers());
for (int i = mLOS.GetRows(); --i > 0;)
for (int j = i; --j >= 0;) {
double Sigma2 = mCovariance.GetElement(i, i) +
mCovariance.GetElement(j, j) -
mCovariance.GetElement(i, j) -
mCovariance.GetElement(j, i);
double Mu = velo[j] - velo[i];
double x = Mu / std::sqrt(2 * Sigma2);
mLOS.SetElement(i, j, erfc(x) / 2);
mLOS.SetElement(j, i, erfc(-x) / 2);
}
for (int i = mLOS.GetRows(); --i >= 0;)
mLOS.SetElement(i, i, 0.0);
}
void
Math_erfc(void *fp)
{
F_Math_erfc *f;
f = fp;
*f->ret = erfc(f->x);
}
void test_fp_erf( void )
{
#if __STDC_VERSION__ >= 199901L
printf( "Testing C99 error functions...\n" );
VERIFY( CompDbl( erf( 0.0 ), 0.0 ) );
VERIFY( CompDbl( erf( 1.0 ), 0.8427008 ) );
VERIFY( CompDbl( erf( 2.0 ), 0.9953223 ) );
VERIFY( CompDbl( erf( -1.0 ), -0.8427008 ) );
VERIFY( CompDbl( erf( -2.0 ), -0.9953223 ) );
VERIFY( CompDbl( erfc( 0.0 ), 1.0 ) );
VERIFY( CompDbl( erfc( 1.0 ), 0.1572992 ) );
VERIFY( CompDbl( erfc( 2.0 ), 0.0046777 ) );
VERIFY( CompDbl( erfc( -1.0 ), 1.8427008 ) );
VERIFY( CompDbl( erfc( -2.0 ), 1.9953223 ) );
#endif
}
/*
* call-seq:
* Math.erfc(x) -> float
*
* Calculates the complementary error function of x.
*/
static mrb_value
math_erfc(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = erfc(x);
return mrb_float_value(mrb, x);
}