FLAGLET  1.0b1
Exact wavelets on the ball
Functions
include/flaglet_axisym.h File Reference
#include <complex.h>

Go to the source code of this file.

Functions

void flaglet_axisym_allocate_f_wav_lmp (complex double **f_wav_lmp, complex double **f_scal_lmp, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_allocate_f_wav_multires_lmp (complex double **f_wav_lmp, complex double **f_scal_lmp, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_allocate_f_wav (complex double **f_wav, complex double **f_scal, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_allocate_f_wav_real (double **f_wav, double **f_scal, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_allocate_f_wav_multires (complex double **f_wav, complex double **f_scal, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_allocate_f_wav_multires_real (double **f_wav, double **f_scal, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_allocate_wav_lmp (double **wav_lmp, double **scal_lmp, int B_l, int B_p, int L, int P)
void flaglet_axisym_wav_lmp (double *wav_lmp, double *scal_lmp, int B_l, int B_p, int J_min_l, int J_min_p, int L, int P)
void flaglet_axisym_wav_analysis_lmp (complex double *f_wav_lmp, complex double *f_scal_lmp, const complex double *flmp, const double *wav_lmp, const double *scal_lmp, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_synthesis_lmp (complex double *flmp, const complex double *f_wav_lmp, const complex double *f_scal_lmp, const double *wav_lmp, const double *scal_lmp, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_analysis_multires_lmp (complex double *f_wav_lmp, complex double *f_scal_lmp, const complex double *flmp, const double *wav_lmp, const double *scal_lmp, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_synthesis_multires_lmp (complex double *flmp, const complex double *f_wav_lmp, const complex double *f_scal_lmp, const double *wav_lmp, const double *scal_lmp, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_analysis (complex double *f_wav, complex double *f_scal, const complex double *f, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_synthesis (complex double *f, const complex double *f_wav, const complex double *f_scal, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_analysis_real (double *f_wav, double *f_scal, const double *f, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_synthesis_real (double *f, const double *f_wav, const double *f_scal, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_analysis_multires (complex double *f_wav, complex double *f_scal, const complex double *f, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_synthesis_multires (complex double *f, const complex double *f_wav, const complex double *f_scal, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_analysis_multires_real (double *f_wav, double *f_scal, const double *f, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
void flaglet_axisym_wav_synthesis_multires_real (double *f, const double *f_wav, const double *f_scal, double R, int B_l, int B_p, int L, int P, int J_min_l, int J_min_p)
int jjlmp2ind (int jl, int jn, int l, int m, int n, int J_l, int J_p, int L, int P)
int lmp2ind (int l, int m, int n, int L)

Function Documentation

void flaglet_axisym_allocate_f_wav ( complex double **  f_wav,
complex double **  f_scal,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Allocates 3D Wavelet transform in real space.

Parameters:
[out]f_wavwavelets contributions of f.
[out]f_scalscaling function contribution of f.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 121 of file flaglet_axisym.c.

void flaglet_axisym_allocate_f_wav_lmp ( complex double **  f_wav_lmp,
complex double **  f_scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Allocates 3D Wavelet transform in FLAG space.

Parameters:
[out]f_wav_lmpFLAG transform of wavelets contributions of f.
[out]f_scal_lmpFLAG transform of scaling function contribution of f.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 100 of file flaglet_axisym.c.

void flaglet_axisym_allocate_f_wav_multires ( complex double **  f_wav,
complex double **  f_scal,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Allocates multiresolution 3D Wavelet transform in real space.

Parameters:
[out]f_wavwavelets contributions of f.
[out]f_scalscaling function contribution of f.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 192 of file flaglet_axisym.c.

void flaglet_axisym_allocate_f_wav_multires_lmp ( complex double **  f_wav_lmp,
complex double **  f_scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Allocates multiresolution 3D Wavelet transform in FLAG space.

Parameters:
[out]f_wav_lmpFLAG transform of wavelets contributions of f.
[out]f_scal_lmpFLAG transform of scaling function contribution of f.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 163 of file flaglet_axisym.c.

void flaglet_axisym_allocate_f_wav_multires_real ( double **  f_wav,
double **  f_scal,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Allocates multiresolution real 3D Wavelet transform in real space.

Parameters:
[out]f_wavwavelets contributions of f.
[out]f_scalscaling function contribution of f.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 221 of file flaglet_axisym.c.

void flaglet_axisym_allocate_f_wav_real ( double **  f_wav,
double **  f_scal,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Allocates real 3D Wavelet transform in real space.

Parameters:
[out]f_wavwavelets contributions of f.
[out]f_scalscaling function contribution of f.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 142 of file flaglet_axisym.c.

void flaglet_axisym_allocate_wav_lmp ( double **  wav_lmp,
double **  scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P 
)

Allocates arrays for the kernels of the wavelets and the scaling functions (in FLAG space).

Parameters:
[out]wav_lmpWavelet kernels.
[out]scal_lmpScaling function kernels.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
Return values:
none

Definition at line 24 of file flaglet_axisym.c.

void flaglet_axisym_wav_analysis ( complex double *  f_wav,
complex double *  f_scal,
const complex double *  f,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Sampling scheme : MW sampling. 3D spherical wavelets : analysis in real space.

Parameters:
[out]f_wavWavelet transform (wavelet contribution in real space).
[out]f_scalWavelet transform (scaling contribution in real space).
[in]fInput function (MW sampling).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 732 of file flaglet_axisym.c.

void flaglet_axisym_wav_analysis_lmp ( complex double *  f_wav_lmp,
complex double *  f_scal_lmp,
const complex double *  flmp,
const double *  wav_lmp,
const double *  scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in FLAG space (from precomputed kernels, gives FLAG coefficients). 3D spherical wavelets : analysis in FLAG-harmonic space.

Parameters:
[out]f_wav_lmpFLAG transform of wavelets contributions of f.
[out]f_scal_lmpFLAG transform of scaling function contribution of f.
[in]flmpFLAG transform of the input function.
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 359 of file flaglet_axisym.c.

void flaglet_axisym_wav_analysis_multires ( complex double *  f_wav,
complex double *  f_scal,
const complex double *  f,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Sampling scheme : MW sampling. 3D spherical wavelets : analysis in real space.

Parameters:
[out]f_wavWavelet transform (wavelet contribution in real space).
[out]f_scalWavelet transform (scaling contribution in real space).
[in]fInput function (MW sampling).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 459 of file flaglet_axisym.c.

void flaglet_axisym_wav_analysis_multires_lmp ( complex double *  f_wav_lmp,
complex double *  f_scal_lmp,
const complex double *  flmp,
const double *  wav_lmp,
const double *  scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform multiresolution wavelet transform in FLAG space (from precomputed kernels, gives FLAG coefficients). 3D spherical wavelets : analysis in FLAG-harmonic space.

Parameters:
[out]f_wav_lmpFLAG transform of wavelets contributions of f.
[out]f_scal_lmpFLAG transform of scaling function contribution of f.
[in]flmpFLAG transform of the input function.
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 254 of file flaglet_axisym.c.

void flaglet_axisym_wav_analysis_multires_real ( double *  f_wav,
double *  f_scal,
const double *  f,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Real input function and real wavelet contributions. Sampling scheme : MW sampling. 3D spherical wavelets : analysis in real space.

Parameters:
[out]f_wavWavelet transform (wavelet contribution in real space).
[out]f_scalWavelet transform (scaling contribution in real space).
[in]fInput function (MW sampling).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 595 of file flaglet_axisym.c.

void flaglet_axisym_wav_analysis_real ( double *  f_wav,
double *  f_scal,
const double *  f,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Real input function and real wavelet contributions. Sampling scheme : MW sampling. 3D spherical wavelets : analysis in real space.

Parameters:
[out]f_wavWavelet transform (wavelet contribution in real space).
[out]f_scalWavelet transform (scaling contribution in real space).
[in]fInput function (MW sampling).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 864 of file flaglet_axisym.c.

void flaglet_axisym_wav_lmp ( double *  wav_lmp,
double *  scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Computes the kernels of the wavelets and the scaling functions (in FLAG space).

Parameters:
[out]wav_lmpWavelet kernels.
[out]scal_lmpScaling function kernels.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 45 of file flaglet_axisym.c.

void flaglet_axisym_wav_synthesis ( complex double *  f,
const complex double *  f_wav,
const complex double *  f_scal,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Sampling scheme : MW sampling. 3D spherical wavelets : synthesis in real space.

Parameters:
[out]fInput function (MW sampling).
[in]f_wavWavelet transform (wavelet contribution in real space).
[in]f_scalWavelet transform (scaling contribution in real space).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 798 of file flaglet_axisym.c.

void flaglet_axisym_wav_synthesis_lmp ( complex double *  flmp,
const complex double *  f_wav_lmp,
const complex double *  f_scal_lmp,
const double *  wav_lmp,
const double *  scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in FLAG space (from precomputed kernels, gives FLAG coefficients). 3D spherical wavelets : synthesis in FLAG-harmonic space.

Parameters:
[out]flmpFLAG transform of the input function.
[in]f_wav_lmpFLAG transform of wavelets contributions of f.
[in]f_scal_lmpFLAG transform of scaling function contribution of f.
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 407 of file flaglet_axisym.c.

void flaglet_axisym_wav_synthesis_multires ( complex double *  f,
const complex double *  f_wav,
const complex double *  f_scal,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Sampling scheme : MW sampling. 3D spherical wavelets : synthesis in real space.

Parameters:
[out]fInput function (MW sampling).
[in]f_wavWavelet transform (wavelet contribution in real space).
[in]f_scalWavelet transform (scaling contribution in real space).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 525 of file flaglet_axisym.c.

void flaglet_axisym_wav_synthesis_multires_lmp ( complex double *  flmp,
const complex double *  f_wav_lmp,
const complex double *  f_scal_lmp,
const double *  wav_lmp,
const double *  scal_lmp,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform multiresolution wavelet transform in FLAG space (from precomputed kernels, gives FLAG coefficients). 3D spherical wavelets : synthesis in FLAG-harmonic space.

Parameters:
[out]flmpFLAG transform of the input function.
[in]f_wav_lmpFLAG transform of wavelets contributions of f.
[in]f_scal_lmpFLAG transform of scaling function contribution of f.
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 305 of file flaglet_axisym.c.

void flaglet_axisym_wav_synthesis_multires_real ( double *  f,
const double *  f_wav,
const double *  f_scal,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Real input function and real wavelet contributions. Sampling scheme : MW sampling. 3D spherical wavelets : synthesis in real space.

Parameters:
[out]fInput function (MW sampling).
[in]f_wavWavelet transform (wavelet contribution in real space).
[in]f_scalWavelet transform (scaling contribution in real space).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 665 of file flaglet_axisym.c.

void flaglet_axisym_wav_synthesis_real ( double *  f,
const double *  f_wav,
const double *  f_scal,
double  R,
int  B_l,
int  B_p,
int  L,
int  P,
int  J_min_l,
int  J_min_p 
)

Perform wavelet transform in real space (from scratch, gives pixel space components). Real input function and real wavelet contributions. Sampling scheme : MW sampling. 3D spherical wavelets : synthesis in real space.

Parameters:
[out]fInput function (MW sampling).
[in]f_wavWavelet transform (wavelet contribution in real space).
[in]f_scalWavelet transform (scaling contribution in real space).
[in]wav_lmpWavelet kernel in FLAG space.
[in]scal_lmpScaling function kernel in FLAG space.
[in]B_lWavelet parameter for angular harmonic space.
[in]B_pWavelet parameter for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
[in]J_min_lFirst wavelet scale to be used in angular space.
[in]J_min_pFirst wavelet scale to be used in radial space.
Return values:
none

Definition at line 931 of file flaglet_axisym.c.

int jjlmp2ind ( int  jl,
int  jp,
int  l,
int  m,
int  n,
int  J_l,
int  J_p,
int  L,
int  P 
)

Indice corresponding to a quintuplet (jl, jp, l, m, n) in the wavelets kernels.

Parameters:
[in]jlAngular scale indice.
[in]jpRadial scale indice.
[in]lMultipole indice.
[in]mOrder indice.
[in]nLaguerre order indice.
[in]J_lMaximum scale for angular harmonic space.
[in]J_pMaximum scale for radial harmonic space.
[in]LAngular harmonic band-limit.
[in]PRadial harmonic band-limit.
Return values:
Indice

Definition at line 992 of file flaglet_axisym.c.

int lmp2ind ( int  l,
int  m,
int  n,
int  L 
)

Indice corresponding to a triplet (l, m, n) in the FLAG basis.

Parameters:
[in]lMultipole indice.
[in]mOrder indice.
[in]nLaguerre order indice.
[in]LAngular harmonic band-limit.
Return values:
Indice

Definition at line 1006 of file flaglet_axisym.c.

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