/** \file
The following routines are based on the Fortran program NumSBT written by J.
Talman. The algorithm performs a spherical Bessel transform in O(NlnN) time. If
you adapt this code for any purpose, please cite: Talman, J. Computer Physics
Communications 2009, 180, 332-338. The code is distributed under the Standard
CPC license.
*/

#ifndef SBT_H
#define SBT_H
#include <complex.h>

/**
Contains the parameters for a fast spherical Bessel transform.
*/
typedef struct sbt_descriptor {
  double kmin;     ///< Minimum reciprocal space value
  double kappamin; ///< ln(kmin)
  double rmin;     ///< Minimum real space value
  double rhomin;   ///< ln(rmin)
  double drho;     ///< linear increment of rho = ln(r), drho == dkappa
  double dt;       ///< increment of the multiplication table
  int N;           ///< number of values of r and k
  double complex **mult_table; ///< M_l(t) for l up to lmax
  double *ks;                  ///< Reciprocal space grid
  double *rs;                  ///< Real space grid
  int lmax;
} sbt_descriptor_t;

/**
Creates an sbt_descriptor_t object from the real space and k-space grids.
Extrapolates the radial grid to have N values lower than the initial rmin,
and the reciprocal grid to have N values higher than the initial kmin.
encut+enbuf is the maximum value of k BEFORE extrapolation.
lmax is the maximum l-value used to construct the the mult_table.
N is the size of the grid BEFORE exprapolation (i.e. length of r and ks).
*/
sbt_descriptor_t *spherical_bessel_transform_setup(double encut, double enbuf,
                                                   int lmax, int N, double *r,
                                                   double *ks);

/**
Returns the values of radially defined function f
in reciprocal space in a spherical bessel basis.
f is defined on the grid corresponding to the r
passed into spherical_bessesl_transform_setup.
*/
double *wave_spherical_bessel_transform(sbt_descriptor_t *d, double *f, int l);

/**
Performs the inverse transform of f. Calling this function on the output
of wave_spherical_bessel_transform gives the initial input to
wave_spherical_bessel_transform on the initial radial grid passed to
spherical_bessel_transform_setup
*/
double *inverse_wave_spherical_bessel_transform(sbt_descriptor_t *d, double *f,
                                                int l);

/**
Free all the memory associated with an sbt descriptor.
*/
void free_sbt_descriptor(sbt_descriptor_t *d);

#endif
