qpms/bessel.c

   1 #include <assert.h>
   2 #include "qpms_specfunc.h"
   3 #include <stdlib.h>
   4 #include <stddef.h>
   5 #include <string.h>
   6 #include "kahansum.h"
   7 #include <gsl/gsl_sf_bessel.h>
   8 #include <complex.h>
   9 #include "qpms_error.h"
  10 #include <camos.h>
  11 #include <math.h>
  12
  13 #ifndef M_LN2
  14 #define M_LN2   0.69314718055994530942  /* log_e 2 */
  15 #endif
  16
  17 static inline complex double ipow(int x) {
  18   return cpow(I,x);
  19 }
  20
  21 #if 0
  22 // Inspired by scipy/special/_spherical_bessel.pxd
  23 static inline complex double spherical_jn(qpms_l_t l, complex double z) {
  24   if (isnan(creal(z)) || isnan(cimag(z))) return NAN+I*NAN;
  25   if (l < 0) QPMS_WTF;
  26   if (fpclassify(creal(z)) == FP_INFINITE)
  27     if(0 == cimag(z))
  28       return 0;
  29     else
  30       return INFINITY + I * INFINITY;
  31   if (z == 0)
  32     if (l == 0) return 1;
  33     else return 0;
  34   return csqrt(M_PI_2/z) * zbesj(l + .5, z);
  35 }
  36
  37 static inline complex double spherical_yn(qpms_l_t l, complex double z) {
  38   if (isnan(creal(z)) || isnan(cimag(z))) return NAN+I*NAN;
  39   if (l < 0) QPMS_WTF;
  40   if (fpclassify(creal(z)) == FP_INFINITE)
  41     if(0 == cimag(z))
  42       return 0;
  43     else
  44       return INFINITY + I * INFINITY;
  45   if (z == 0)
  46     return NAN;
  47   return csqrt(M_PI_2/z) * zbesy(l + .5, z);
  48 }
  49 #endif
  50
  51 // There is a big issue with gsl's precision of spherical bessel function; these have to be implemented differently
  52 qpms_errno_t qpms_sph_bessel_realx_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, complex double *result_array) {
  53   int retval;
  54   double tmparr[lmax+1];
  55   switch(typ) {
  56     case QPMS_BESSEL_REGULAR:
  57       retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
  58       for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
  59       return retval;
  60       break;
  61     case QPMS_BESSEL_SINGULAR: //FIXME: is this precise enough? Would it be better to do it one-by-one?
  62       retval = gsl_sf_bessel_yl_array(lmax,x,tmparr);
  63       for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
  64       return retval;
  65       break;
  66     case QPMS_HANKEL_PLUS:
  67     case QPMS_HANKEL_MINUS:
  68       retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
  69       for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
  70       if(retval) return retval;
  71       retval = gsl_sf_bessel_yl_array(lmax, x, tmparr);
  72       if (typ==QPMS_HANKEL_PLUS)
  73         for (int l = 0; l <= lmax; ++l) result_array[l] += I * tmparr[l];
  74       else
  75         for (int l = 0; l <= lmax; ++l) result_array[l] +=-I * tmparr[l];
  76       return retval;
  77       break;
  78     default:
  79       abort();
  80       //return GSL_EDOM;
  81   }
  82   assert(0);
  83 }
  84
  85 // TODO DOC
  86 qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex double x, complex double *res) {
  87   if(!cimag(x))
  88     return qpms_sph_bessel_realx_fill(typ, lmax, creal(x), res);
  89   else if (isnan(creal(x)) || isnan(cimag(x)))
  90     for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = NAN + I*NAN;
  91   else if (lmax < 0) QPMS_WTF;
  92   else if (fpclassify(creal(x)) == FP_INFINITE)
  93     for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = INFINITY + I * INFINITY;
  94   else {
  95 try_again: ;
  96     int retry_counter = 0;
  97     const double zr = creal(x), zi = cimag(x), fnu = 0.5;
  98     const int n = lmax + 1, kode = 1 /* No exponential scaling */;
  99     double cyr[n], cyi[n];
 100     int ierr, nz;
 101     unsigned int kindchar; // Only for error output
 102     const complex double prefac = csqrt(M_PI_2/x);
 103     switch(typ) {
 104       case QPMS_BESSEL_REGULAR:
 105         kindchar = 'j';
 106         ierr = camos_zbesj(zr, zi, fnu, kode, n, cyr, cyi, &nz);
 107         break;
 108       case QPMS_BESSEL_SINGULAR:
 109         kindchar = 'y';
 110         {
 111           double cwrkr[lmax + 1], cwrki[lmax + 1];
 112           ierr = camos_zbesy(zr, zi, fnu, kode, n, cyr, cyi, &nz, cwrkr, cwrki);
 113         }
 114         break;
 115       case QPMS_HANKEL_PLUS:
 116       case QPMS_HANKEL_MINUS:
 117         kindchar = 'h';
 118         {
 119           const int m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2;
 120           ierr = camos_zbesh(zr, zi, fnu, kode, m, n, cyr, cyi, &nz);
 121         }
 122         break;
 123       default:
 124         QPMS_WTF;
 125     }
 126     // TODO check for underflows? (nz != 0)
 127     if (ierr == 0 || ierr == 3) {
 128       for (qpms_l_t l = 0; l <= lmax; ++l)
 129         res[l] = prefac * (cyr[l] + I * cyi[l]);
 130       if (ierr == 3)
 131         QPMS_WARN("Amos's zbes%c computation done but losses of significance "
 132             "by argument reduction produce less than half of machine accuracy.",
 133             kindchar);
 134       return QPMS_SUCCESS; //TODO maybe something else if ierr == 3
 135     }
 136     else {
 137       if (retry_counter < 5) {
 138         QPMS_WARN("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi). Retrying.\n",
 139            kindchar, (int) ierr, lmax, creal(x), cimag(x));
 140         ++retry_counter;
 141         goto try_again;
 142       } else QPMS_PR_ERROR("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi).",
 143            kindchar, (int) ierr, lmax, creal(x), cimag(x));
 144     }
 145   }
 146   return QPMS_SUCCESS;
 147 }
 148
 149 static inline ptrdiff_t akn_index(qpms_l_t n, qpms_l_t k) {
 150   assert(k <= n);
 151   return ((ptrdiff_t) n + 1) * n / 2 + k;
 152 }
 153 static inline ptrdiff_t bkn_index(qpms_l_t n, qpms_l_t k) {
 154   assert(k <= n+1);
 155   return ((ptrdiff_t) n + 2) * (n + 1) / 2 - 1 + k;
 156 }
 157
 158 static inline qpms_errno_t qpms_sbessel_calculator_ensure_lMax(qpms_sbessel_calculator_t *c, qpms_l_t lMax) {
 159   if (lMax <= c->lMax)
 160     return QPMS_SUCCESS;
 161   else {
 162     if ( NULL == (c->akn = realloc(c->akn, sizeof(double) * akn_index(lMax + 2, 0))))
 163       abort();
 164     //if ( NULL == (c->bkn = realloc(c->bkn, sizeof(complex double) * bkn_index(lMax + 1, 0))))
 165     //  abort();
 166     for(qpms_l_t n = c->lMax+1; n <= lMax + 1; ++n)
 167       for(qpms_l_t k = 0; k <= n; ++k)
 168         c->akn[akn_index(n,k)] = exp(lgamma(n + k + 1) - k*M_LN2 - lgamma(k + 1) - lgamma(n - k + 1));
 169     // ... TODO derivace
 170     c->lMax = lMax;
 171     return QPMS_SUCCESS;
 172   }
 173 }
 174
 175 complex double qpms_sbessel_calc_h1(qpms_sbessel_calculator_t *c, qpms_l_t n, complex double x) {
 176   if(QPMS_SUCCESS != qpms_sbessel_calculator_ensure_lMax(c, n))
 177     abort();
 178   complex double z = I/x;
 179   complex double result = 0;
 180   for (qpms_l_t k = n; k >= 0; --k)
 181     // can we use fma for complex?
 182     //result = fma(result, z, c->akn(n, k));
 183     result = result * z + c->akn[akn_index(n,k)];
 184   result *= z * ipow(-n-2) * cexp(I * x);
 185   return result;
 186 }
 187
 188 qpms_errno_t qpms_sbessel_calc_h1_fill(qpms_sbessel_calculator_t * const c,
 189     const qpms_l_t lMax, const complex double x, complex double * const target) {
 190   if(QPMS_SUCCESS != qpms_sbessel_calculator_ensure_lMax(c, lMax))
 191     abort();
 192   memset(target, 0, sizeof(complex double) * lMax);
 193   complex double kahancomp[lMax];
 194   memset(kahancomp, 0, sizeof(complex double) * lMax);
 195   for(qpms_l_t k = 0; k <= lMax; ++k){
 196     double xp = cpow(x, -k-1);
 197     for(qpms_l_t l = k; l <= lMax; ++l)
 198       ckahanadd(target + l, kahancomp + l, c->akn[akn_index(l,k)] * xp * ipow(k-l-1));
 199   }
 200   complex double eix = cexp(I * x);
 201   for (qpms_l_t l = 0; l <= lMax; ++l)
 202     target[l] *= eix;
 203   return QPMS_SUCCESS;
 204 }
 205
 206 qpms_sbessel_calculator_t *qpms_sbessel_calculator_init() {
 207   qpms_sbessel_calculator_t *c = malloc(sizeof(qpms_sbessel_calculator_t));
 208   c->akn = NULL;
 209   //c->bkn = NULL;
 210   c->lMax = -1;
 211   return c;
 212 }
 213
 214 void qpms_sbessel_calculator_pfree(qpms_sbessel_calculator_t *c) {
 215   if(c->akn) free(c->akn);
 216   //if(c->bkn) free(c->bkn);
 217   free(c);
 218 }