double num2_VolumeSphere (double pLR, int k)
/* Returns volume of unit sphere in dimension k, norm p */
{
const double eps = 2.0 * DBL_EPSILON;
int p = (int)pLR;
double kLR = (double) k;
double Vol;
int s;
util_Assert (pLR >= 0.0, "num2_VolumeSphere: p < 0");
if (fabs (pLR - p) <= eps) {
switch (p) {
case 0:
return num_TwoExp[k];
break;
case 1:
return num_TwoExp[k] / num2_Factorial (k);
break;
case 2:
if ((k % 2) == 0) {
return pow (num_Pi, kLR / 2.0) / num2_Factorial (k / 2);
} else {
s = (k + 1) / 2;
return pow (num_Pi, (double) (s) - 1.0) * num2_Factorial (s) *
num_TwoExp[2 * s] / num2_Factorial (2 * s);
}
break;
default:
break;
}
}
Vol = kLR * (num_Ln2 + num2_LnGamma (1.0 + 1.0 / pLR)) -
num2_LnGamma (1.0 + kLR / pLR);
return exp (Vol);
}
static void InitFDistMeans (int n, double Coef[])
/*
* Initializes the distribution for svaria_SampleMean by computing the
* coefficients. We shall keep the value of n in element Coef[SAM_LIM],
* since we shall need it to get the value of the distribution at x.
*/
{
int s;
double z;
fmass_INFO Q;
z = num2_Factorial (n);
/* This uses the binomial formulae, but is not the binomial probability
distribution since p + q != 1 */
Q = fmass_CreateBinomial (n, -1.0, 1.0);
for (s = 0; s <= n; s++)
Coef[s] = fmass_BinomialTerm2 (Q, s) / z;
fmass_DeleteBinomial (Q);
Coef[SAM_LIM] = n;
if (swrite_Classes) {
printf ("---------------------------------------\n");
for (s = 0; s <= n; s++) {
printf (" Coeff[%2d] = %14.6g\n", s, Coef[s]);
}
printf ("\n");
}
}
static double ProbabiliteG (int jmin, int j, double g)
/*
* Returns the probability that the minimum number of random U(0,1) whose
* sum is larger than g is j+1. g cannot be too large because the
* calculation here becomes numerically unstable.
*/
{
int s;
double temp;
const double jLR = j;
double signe; /* +1 or -1 */
double somme;
signe = 1.0;
somme = 0.0;
for (s = 0; s <= jmin; s++) {
temp = signe * num2_Combination (j + 1, s);
temp *= pow (g - s, jLR);
somme += temp;
signe = -signe;
}
somme = (jLR + 1.0 - g) * somme / num2_Factorial (j + 1);
return somme;
}
void sknuth_RunIndep (unif01_Gen * gen, sres_Chi2 * res,
long N, long n, int r, lebool Up)
{
long Seq; /* Replication number */
double U;
double UPrec; /* Preceding value of U */
double X2;
long Nb;
long k;
int i;
long Longueur; /* Current length of the sequence */
long *Count;
double *NbExp;
double Prob[7];
char str[LENGTH + 1];
double V[1]; /* Number degrees of freedom for Chi2 */
lebool localRes = FALSE;
chrono_Chrono *Timer;
char *TestName = "sknuth_RunIndep test";
Timer = chrono_Create ();
if (swrite_Basic)
WriteDataRun (gen, TestName, N, n, r, Up);
if (res == NULL) {
localRes = TRUE;
res = sres_CreateChi2 ();
}
sres_InitChi2 (res, N, 6, "sknuth_RunIndep");
NbExp = res->NbExp;
Count = res->Count;
res->jmin = 1;
res->jmax = 6;
sprintf (str, "NumExpected[6] < %.1f", gofs_MinExpected);
for (i = 1; i <= 5; i++) {
Prob[i] = 1.0 / num2_Factorial (i) - 1.0 / num2_Factorial (i + 1);
}
Prob[6] = 1.0 / num2_Factorial (6);
statcoll_SetDesc (res->sVal1,
"The N statistic values (a ChiSquare with 5 degrees of freedom):");
res->degFree = 5;
for (Seq = 1; Seq <= N; Seq++) {
for (i = 1; i <= 6; i++)
Count[i] = 0;
Longueur = 1;
UPrec = unif01_StripD (gen, r);
for (k = 1; k <= n; k++) {
U = unif01_StripD (gen, r);
if ((Up && U < UPrec) || (!Up && U > UPrec)) {
/* The end of a "Run" */
++Count[Longueur];
Longueur = 1;
U = unif01_StripD (gen, r);
} else if (Longueur < 6)
++Longueur;
UPrec = U;
}
++Count[Longueur];
Nb = 0;
for (i = 1; i <= 6; i++)
Nb += Count[i];
for (i = 1; i <= 6; i++)
NbExp[i] = Nb * Prob[i];
if (swrite_Counters) {
tables_WriteTabD (NbExp, 1, 6, 1, 20, 2, 1, "Expected numbers:");
tables_WriteTabL (Count, 1, 6, 1, 17, "Observed numbers:");
}
/* util_Warning (NbExp[6] < gofs_MinExpected, str); */
X2 = gofs_Chi2 (NbExp, Count, 1, 6);
statcoll_AddObs (res->sVal1, X2);
}
V[0] = 5;
gofw_ActiveTests2 (res->sVal1->V, res->pVal1->V, N, wdist_ChiSquare, V,
res->sVal2, res->pVal2);
res->pVal1->NObs = N;
sres_GetChi2SumStat (res);
if (swrite_Collectors)
statcoll_Write (res->sVal1, 5, 14, 4, 3);
if (swrite_Basic) {
swrite_AddStrChi (str, LENGTH, res->degFree);
gofw_WriteActiveTests2 (N, res->sVal2, res->pVal2, str);
swrite_Chi2SumTest (N, res);
swrite_Final (gen, Timer);
}
if (localRes)
sres_DeleteChi2 (res);
chrono_Delete (Timer);
}
