/* Value of a blob --------------------------------------------------------- */
double kaiser_value(double r, double a, double alpha, int m)
{
double rda, rdas, arg, w;
rda = r / a;
if (rda <= 1.0)
{
rdas = rda * rda;
arg = alpha * sqrt(1.0 - rdas);
if (m == 0)
{
w = bessi0(arg) / bessi0(alpha);
}
else if (m == 1)
{
w = sqrt (1.0 - rdas);
if (alpha != 0.0)
w *= bessi1(arg) / bessi1(alpha);
}
else if (m == 2)
{
w = sqrt (1.0 - rdas);
w = w * w;
if (alpha != 0.0)
w *= bessi2(arg) / bessi2(alpha);
}
else if (m == 3)
{
w = sqrt (1.0 - rdas);
w = w * w * w;
if (alpha != 0.0)
w *= bessi3(arg) / bessi3(alpha);
}
else if (m == 4)
{
w = sqrt (1.0 - rdas);
w = w * w * w *w;
if (alpha != 0.0)
w *= bessi4(arg) / bessi4(alpha);
}
else
REPORT_ERROR(ERR_VALUE_INCORRECT, "m out of range in kaiser_value()");
}
else
w = 0.0;
return w;
}
/* Value of line integral through Kaiser-Bessel radial function
(n >=2 dimensions) at distance s from center of function.
Parameter m = 0, 1, or 2. */
double kaiser_proj(double s, double a, double alpha, int m)
{
double sda, sdas, w, arg, p;
sda = s / a;
sdas = sda * sda;
w = 1.0 - sdas;
if (w > 1.0e-10)
{
arg = alpha * sqrt(w);
if (m == 0)
{
if (alpha == 0.0)
p = 2.0 * a * sqrt(w);
else
p = (2.0 * a / alpha) * sinh(arg) / bessi0(alpha);
}
else if (m == 1)
{
if (alpha == 0.0)
p = 2.0 * a * w * sqrt(w) * (2.0 / 3.0);
else
p = (2.0 * a / alpha) * sqrt(w) * (cosh(arg) - sinh(arg) / arg)
/ bessi1(alpha);
}
else if (m == 2)
{
if (alpha == 0.0)
p = 2.0 * a * w * w * sqrt(w) * (8.0 / 15.0);
else
p = (2.0 * a / alpha) * w *
((3.0 / (arg * arg) + 1.0) * sinh(arg) - (3.0 / arg) * cosh(arg)) / bessi2(alpha);
}
else
REPORT_ERROR(ERR_VALUE_INCORRECT, "m out of range in kaiser_proj()");
}
else
p = 0.0;
return p;
}
double bessi4(double x)
{
return (x == 0) ? 0 : bessi2(x) - ((2 * 3) / x) * bessi3(x);
}
double bessi3(double x)
{
return (x == 0) ? 0 : bessi1(x) - ((2 * 2) / x) * bessi2(x);
}
