/**
* @brief MathFunctions::normalCDFInverse computes the inverse of the normal cumulative distribution function
* @param p The value on which is applied the function
* @return The inverse of the normal cumulative distribution function value
*/
double MathFunctions::normalCDFInverse(double p) {
if (p <= 0.0 || p >= 1.0) {
QString os;
os = "Invalid input argument (" + QString::number(p) + "); must be larger than 0 but less than 1.";
throw std::invalid_argument(os.toStdString().c_str());
}
if (p < 0.5) {
// F^-1(p) = - G^-1(p)
return -rationalApproximation(qSqrt(-2.0*qLn(p)));
}
else {
// F^-1(p) = G^-1(1-p)
return rationalApproximation(qSqrt(-2.0*qLn(1-p)));
}
}
int maximallyFlat(double beta, double gamma, int *np, double *coefficient)
{
double a[LIMIT+1], c[LIMIT+1], betaMinimum, ac;
int nt, numerator, n, ll, i;
/* INITIALIZE NUMBER OF POINTS */
(*np) = 0;
/* CUT-OFF FREQUENCY MUST BE BETWEEN 0 HZ AND NYQUIST */
if ((beta <= 0.0) || (beta >= 0.5))
return BETA_OUT_OF_RANGE;
/* TRANSITION BAND MUST FIT WITH THE STOP BAND */
betaMinimum = ((2.0 * beta) < (1.0 - 2.0 * beta)) ? (2.0 * beta) :
(1.0 - 2.0 * beta);
if ((gamma <= 0.0) || (gamma >= betaMinimum))
return GAMMA_OUT_OF_RANGE;
/* MAKE SURE TRANSITION BAND NOT TOO SMALL */
nt = (int)(1.0 / (4.0 * gamma * gamma));
if (nt > 160)
return GAMMA_TOO_SMALL;
/* CALCULATE THE RATIONAL APPROXIMATION TO THE CUT-OFF POINT */
ac = (1.0 + cos(TWO_PI * beta)) / 2.0;
rationalApproximation(ac, &nt, &numerator, np);
/* CALCULATE FILTER ORDER */
n = (2 * (*np)) - 1;
if (numerator == 0)
numerator = 1;
/* COMPUTE MAGNITUDE AT NP POINTS */
c[1] = a[1] = 1.0;
ll = nt - numerator;
for (i = 2; i <= (*np); i++) {
int j;
double x, sum = 1.0, y;
c[i] = cos(TWO_PI * ((double)(i-1)/(double)n));
x = (1.0 - c[i]) / 2.0;
y = x;
if (numerator == nt)
continue;
for (j = 1; j <= ll; j++) {
double z = y;
if (numerator != 1) {
int jj;
for (jj = 1; jj <= (numerator - 1); jj++)
z *= 1.0 + ((double)j / (double)jj);
}
y *= x;
sum += z;
}
a[i] = sum * pow((1.0 - x), numerator);
}
/* CALCULATE WEIGHTING COEFFICIENTS BY AN N-POINT IDFT */
for (i = 1; i <= (*np); i++) {
int j;
coefficient[i] = a[1] / 2.0;
for (j = 2; j <= (*np); j++) {
int m = ((i - 1) * (j - 1)) % n;
if (m > nt)
m = n - m;
coefficient[i] += c[m+1] * a[j];
}
coefficient[i] *= 2.0 / (double)n;
}
return 0;
}
