/usr/include/vigra/bessel.hxx is in libvigraimpex-dev 1.9.0+dfsg-10+b2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 | /************************************************************************/
/* */
/* Copyright 2010-2011 by Ullrich Koethe */
/* */
/* This file is part of the VIGRA computer vision library. */
/* The VIGRA Website is */
/* http://hci.iwr.uni-heidelberg.de/vigra/ */
/* Please direct questions, bug reports, and contributions to */
/* ullrich.koethe@iwr.uni-heidelberg.de or */
/* vigra@informatik.uni-hamburg.de */
/* */
/* Permission is hereby granted, free of charge, to any person */
/* obtaining a copy of this software and associated documentation */
/* files (the "Software"), to deal in the Software without */
/* restriction, including without limitation the rights to use, */
/* copy, modify, merge, publish, distribute, sublicense, and/or */
/* sell copies of the Software, and to permit persons to whom the */
/* Software is furnished to do so, subject to the following */
/* conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the */
/* Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES */
/* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND */
/* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT */
/* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, */
/* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING */
/* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR */
/* OTHER DEALINGS IN THE SOFTWARE. */
/* */
/************************************************************************/
#ifndef VIGRA_BESSEL_HXX
#define VIGRA_BESSEL_HXX
#include "mathutil.hxx"
#ifdef HasBoostMath
#include <boost/math/special_functions/bessel.hpp>
#endif
namespace vigra {
/** \addtogroup MathFunctions
*/
//@{
namespace detail {
template <class REAL>
int msta1(REAL x, int mp)
{
double a0,f0,f1,f;
int i,n0,n1,nn;
a0 = abs(x);
n0 = (int)(1.1*a0)+1;
f0 = 0.5*std::log10(6.28*n0) - n0*std::log10(1.36*a0/n0)-mp;
n1 = n0+5;
f1 = 0.5*std::log10(6.28*n1) - n1*std::log10(1.36*a0/n1)-mp;
for(i=0;i<20;i++)
{
nn = int(n1-(n1-n0)/(1.0-f0/f1));
f = 0.5*std::log10(6.28*nn) - nn*std::log10(1.36*a0/nn)-mp;
if(abs(nn-n1) < 1)
break;
n0 = n1;
f0 = f1;
n1 = nn;
f1 = f;
}
return nn;
}
template <class REAL>
int msta2(REAL x, int n, int mp)
{
double a0,ejn,hmp,f0,f1,f,obj;
int i,n0,n1,nn;
a0 = abs(x);
hmp = 0.5*mp;
ejn = 0.5*std::log10(6.28*n) - n*std::log10(1.36*a0/n);
if (ejn <= hmp)
{
obj = mp;
n0 = (int)(1.1*a0);
if (n0 < 1)
n0 = 1;
}
else
{
obj = hmp+ejn;
n0 = n;
}
f0 = 0.5*std::log10(6.28*n0) - n0*std::log10(1.36*a0/n0)-obj;
n1 = n0+5;
f1 = 0.5*std::log10(6.28*n1) - n1*std::log10(1.36*a0/n1)-obj;
for (i=0;i<20;i++)
{
nn = int(n1-(n1-n0)/(1.0-f0/f1));
f = 0.5*std::log10(6.28*nn) - nn*std::log10(1.36*a0/nn)-obj;
if (abs(nn-n1) < 1)
break;
n0 = n1;
f0 = f1;
n1 = nn;
f1 = f;
}
return nn+10;
}
//
// INPUT:
// double x -- argument of Bessel function of 1st and 2nd kind.
// int n -- order
//
// OUPUT:
//
// int nm -- highest order actually computed (nm <= n)
// double jn[] -- Bessel function of 1st kind, orders from 0 to nm
// double yn[] -- Bessel function of 2nd kind, orders from 0 to nm
//
// Computes Bessel functions of all order up to 'n' using recurrence
// relations. If 'nm' < 'n' only 'nm' orders are returned.
//
// code has been adapted from C.R. Bond's implementation
// see http://www.crbond.com/math.htm
//
template <class REAL>
void bessjyn(int n, REAL x,int &nm, double *jn, double *yn)
{
double t1,t2,f,f1,f2,bj0,bj1,bjk,by0,by1,cu,s0,su,sv;
double ec,bs,byk,p0,p1,q0,q1;
static double a[] = {
-0.7031250000000000e-1,
0.1121520996093750,
-0.5725014209747314,
6.074042001273483};
static double b[] = {
0.7324218750000000e-1,
-0.2271080017089844,
1.727727502584457,
-2.438052969955606e1};
static double a1[] = {
0.1171875,
-0.1441955566406250,
0.6765925884246826,
-6.883914268109947};
static double b1[] = {
-0.1025390625,
0.2775764465332031,
-1.993531733751297,
2.724882731126854e1};
int i,k,m;
nm = n;
if (x < 1e-15)
{
for (i=0;i<=n;i++)
{
jn[i] = 0.0;
yn[i] = -1e308;
}
jn[0] = 1.0;
return;
}
if (x <= 300.0 || n > (int)(0.9*x))
{
if (n == 0)
nm = 1;
m = msta1(x,200);
if (m < nm)
nm = m;
else
m = msta2(x,nm,15);
bs = 0.0;
su = 0.0;
sv = 0.0;
f2 = 0.0;
f1 = 1.0e-100;
for (k = m;k>=0;k--)
{
f = 2.0*(k+1.0)/x*f1 - f2;
if (k <= nm)
jn[k] = f;
if ((k == 2*(int)(k/2)) && (k != 0))
{
bs += 2.0*f;
su += (-1)*((k & 2)-1)*f/(double)k;
}
else if (k > 1)
{
sv += (-1)*((k & 2)-1)*(double)k*f/(k*k-1.0);
}
f2 = f1;
f1 = f;
}
s0 = bs+f;
for (k=0;k<=nm;k++)
{
jn[k] /= s0;
}
ec = std::log(0.5*x) + M_EULER_GAMMA;
by0 = M_2_PI*(ec*jn[0]-4.0*su/s0);
yn[0] = by0;
by1 = M_2_PI*((ec-1.0)*jn[1]-jn[0]/x-4.0*sv/s0);
yn[1] = by1;
}
else
{
t1 = x-M_PI_4;
p0 = 1.0;
q0 = -0.125/x;
for (k=0;k<4;k++)
{
p0 += a[k]*std::pow(x,-2*k-2);
q0 += b[k]*std::pow(x,-2*k-3);
}
cu = std::sqrt(M_2_PI/x);
bj0 = cu*(p0*std::cos(t1)-q0*std::sin(t1));
by0 = cu*(p0*std::sin(t1)+q0*std::cos(t1));
jn[0] = bj0;
yn[0] = by0;
t2 = x-0.75*M_PI;
p1 = 1.0;
q1 = 0.375/x;
for (k=0;k<4;k++)
{
p1 += a1[k]*std::pow(x,-2*k-2);
q1 += b1[k]*std::pow(x,-2*k-3);
}
bj1 = cu*(p1*std::cos(t2)-q1*std::sin(t2));
by1 = cu*(p1*std::sin(t2)+q1*std::cos(t2));
jn[1] = bj1;
yn[1] = by1;
for (k=2;k<=nm;k++)
{
bjk = 2.0*(k-1.0)*bj1/x-bj0;
jn[k] = bjk;
bj0 = bj1;
bj1 = bjk;
}
}
for (k=2;k<=nm;k++)
{
byk = 2.0*(k-1.0)*by1/x-by0;
yn[k] = byk;
by0 = by1;
by1 = byk;
}
}
} // namespace detail
/*! Bessel function of the first kind.
Computes the value of BesselJ of integer order <tt>n</tt> and argument <tt>x</tt>.
Negative <tt>x</tt> are unsupported and will result in a <tt>std::domain_error</tt>.
This function wraps a number of existing implementations and falls back to
a rather slow algorithm if none of them is available. In particular,
it uses boost::math when <tt>HasBoostMath</tt> is \#defined, or native
implementations on gcc and MSVC otherwise.
<b>\#include</b> \<vigra/bessel.hxx\><br>
Namespace: vigra
*/
inline double besselJ(int n, double x)
{
if(x < 0.0)
throw std::domain_error("besselJ(n, x): x cannot be negative");
if(x < 1e-15)
return n == 0 ? 1.0 : 0.0;
#if defined(HasBoostMath)
return boost::math::cyl_bessel_j((double)n, x);
#elif defined(__GNUC__)
return ::jn(n, x);
#elif defined(_MSC_VER)
return _jn(n, x);
#else
int an = abs(n), nr = n, s = an+2;
ArrayVector<double> t(2*s);
detail::bessjyn(an, x, nr, &t[0], &t[s]);
if(n < 0 && odd(an))
return -t[an];
else
return t[an];
#endif
}
/*! Bessel function of the second kind.
Computes the value of BesselY of integer order <tt>n</tt> and argument <tt>x</tt>.
Negative <tt>x</tt> are unsupported and will result in a <tt>std::domain_error</tt>.
This function wraps a number of existing implementations and falls back to
a rather slow algorithm if none of them is available. In particular,
it uses boost::math when <tt>HasBoostMath</tt> is \#defined, or native
implementations on gcc and MSVC otherwise.
<b>\#include</b> \<vigra/bessel.hxx\><br>
Namespace: vigra
*/
inline double besselY(int n, double x)
{
if(x < 0.0)
throw std::domain_error("besselY(n, x): x cannot be negative");
if(x == 0.0 )
return -std::numeric_limits<double>::infinity();
#if defined(HasBoostMath)
return boost::math::cyl_neumann((double)n, x);
#elif defined(__GNUC__)
return ::yn(n, x);
#elif defined(_MSC_VER)
return _yn(n, x);
#else
int an = abs(n), nr = n, s = an+2;
ArrayVector<double> t(2*s);
detail::bessjyn(an, x, nr, &t[0], &t[s]);
if(n < 0.0 && odd(n))
return -t[an+s];
else
return t[an+s];
#endif
}
//@}
} // namespace vigra
#endif // VIGRA_BESSEL_HXX
|