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Copy pathfft_func.cpp
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1110 lines (858 loc) · 33.1 KB
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#include "function.hpp"
#include "fft_kernel.hpp"
/****************************************************************************/
/************************ 1-D kernel selection *******************************/
/****************************************************************************/
/* FFT_3D/iFFT_3D below drive many 1-D transforms over lines of a fixed size.
When the size is a power of two the mixed-radix in-place kernel from
fft_kernel.hpp is used; otherwise (or when built with -DFFT_KERNEL_LEGACY)
the original radix-2 kernel runs unchanged. Both produce the same
transform -- a natural-order DFT_N -- so the zero-padding "half"
convention implemented by the callers does not change. */
static inline const ddafft::plan * fft_plan_for(int N)
{
#ifdef FFT_KERNEL_LEGACY
(void)N;
return NULL;
#else
return ddafft::get_plan(N);
#endif
}
static inline void fft_line_fwd(const ddafft::plan * pl,int lim_NoB,int N,
cplx * cW,cvector * cvIn,cvector * cvOut)
{
if(pl!=NULL) ddafft::fft_line(pl,cvOut,cvIn);
else FFT(lim_NoB,N,cW,cvIn,cvOut);
}
static inline void fft_line_inv(const ddafft::plan * pl,int lim_NoB,int N,
cplx * cW,cvector * cvIn,cvector * cvOut)
{
if(pl!=NULL) ddafft::ifft_line(pl,cvOut,cvIn);
else iFFT(lim_NoB,N,cW,cvIn,cvOut);
}
/****************************************************************************/
/************** Binary inversion of given number (used in FFT) **************/
/****************************************************************************/
void Change_binary_number( int number_old, int number_of_bits, int * number_new )
{ int i,r=0;
/* Bit reversal by bit shifting: no heap allocation and no pow() per call.
This routine is executed once per FFT point, i.e. millions of times per
three-dimensional transform. */
for(i=0;i<number_of_bits;i++)
r=(r<<1)|((number_old>>i)&1);
(* number_new)=r;
return;
}
/****************************************************************************/
/************************* Definition number of bits ************************/
/****************************************************************************/
void Get_number_bits(int number, int * number_of_bits)
{ double d0;
if(number==0) d0=0;
else d0=log((double)number)/log(2.);
(* number_of_bits)=(int)d0+1;
return;
}
/****************************************************************************/
/******************* Calculation the exp(-i((2*PI*j)/(N))) ******************/
/****************************************************************************/
void FourierPhase(int i_max, cplx * cW)
{ int i;
cplx cw=exp_i((real)(-2.*PI/(2*i_max)));
cW[0].r=1.; cW[0].i=0.;
cW[1]=cw;
for(i=2;i<(i_max);i++)
cW[i]=cW[i-1]*cw;
return;
}
/****************************************************************************/
/********************************* FFT base *********************************/
/****************************************************************************/
void FFT(int lim_NoB, int i_max, cplx * cW, cmatrix * cmDATA_ini,
cmatrix * cmDATA)
{ int i,j,l,k,m,i_new,j_new,iNolFFT,iStep;
cmatrix cm0;
/************************* The sorting of initial data **********************/
for(i=0;i<i_max;i++)
{ Change_binary_number(i,lim_NoB,&i_new);
//cmDATA[i]=cmDATA_ini[i_new];
Ccopy(cmDATA_ini[i_new].e00,cmDATA[i].e00);
Ccopy(cmDATA_ini[i_new].e01,cmDATA[i].e01);
Ccopy(cmDATA_ini[i_new].e02,cmDATA[i].e02);
Ccopy(cmDATA_ini[i_new].e11,cmDATA[i].e11);
Ccopy(cmDATA_ini[i_new].e12,cmDATA[i].e12);
Ccopy(cmDATA_ini[i_new].e22,cmDATA[i].e22);
}
/************************ Log2(N) point-to-point FT *************************/
/***************************** Initial step *********************************/
iNolFFT=i_max/2; // number of local FFT at the first step
iStep=i_max/iNolFFT;
for(i=0;i<iNolFFT;i++)
{ i_new=iStep*i;
//cmDATA_ini[i_new] =cmDATA[i_new]+cmDATA[i_new+1];
//cmDATA_ini[i_new+1]=cmDATA[i_new]-cmDATA[i_new+1];
Cadd(cmDATA[i_new].e00,cmDATA[i_new+1].e00,cmDATA_ini[i_new].e00);
Cadd(cmDATA[i_new].e01,cmDATA[i_new+1].e01,cmDATA_ini[i_new].e01);
Cadd(cmDATA[i_new].e02,cmDATA[i_new+1].e02,cmDATA_ini[i_new].e02);
Cadd(cmDATA[i_new].e11,cmDATA[i_new+1].e11,cmDATA_ini[i_new].e11);
Cadd(cmDATA[i_new].e12,cmDATA[i_new+1].e12,cmDATA_ini[i_new].e12);
Cadd(cmDATA[i_new].e22,cmDATA[i_new+1].e22,cmDATA_ini[i_new].e22);
Csub(cmDATA[i_new].e00,cmDATA[i_new+1].e00,cmDATA_ini[i_new+1].e00);
Csub(cmDATA[i_new].e01,cmDATA[i_new+1].e01,cmDATA_ini[i_new+1].e01);
Csub(cmDATA[i_new].e02,cmDATA[i_new+1].e02,cmDATA_ini[i_new+1].e02);
Csub(cmDATA[i_new].e11,cmDATA[i_new+1].e11,cmDATA_ini[i_new+1].e11);
Csub(cmDATA[i_new].e12,cmDATA[i_new+1].e12,cmDATA_ini[i_new+1].e12);
Csub(cmDATA[i_new].e22,cmDATA[i_new+1].e22,cmDATA_ini[i_new+1].e22);
}
/***************************** Others steps *********************************/
for(l=1;l<lim_NoB;l++)
{ iNolFFT/=2; // number of local FFT (At begin iNolFFT=i_max/2)
iStep=i_max/iNolFFT; // number of point in local FFT
for(j=0;j<iNolFFT;j++)
{ j_new=iStep*j;
for(i=0;i<(iStep/2);i++)
{ i_new=j_new+i; k=i*i_max/iStep; m=i_new+(iStep/2);
//cm0=cW[k]*cmDATA_ini[m];
//cmDATA[i_new]=cmDATA_ini[i_new]+cm0;
//cmDATA[m]=cmDATA_ini[i_new]-cm0;
Cmul(cW[k],cmDATA_ini[m].e00,cm0.e00);
Cmul(cW[k],cmDATA_ini[m].e01,cm0.e01);
Cmul(cW[k],cmDATA_ini[m].e02,cm0.e02);
Cmul(cW[k],cmDATA_ini[m].e11,cm0.e11);
Cmul(cW[k],cmDATA_ini[m].e12,cm0.e12);
Cmul(cW[k],cmDATA_ini[m].e22,cm0.e22);
Cadd(cm0.e00,cmDATA_ini[i_new].e00,cmDATA[i_new].e00);
Cadd(cm0.e01,cmDATA_ini[i_new].e01,cmDATA[i_new].e01);
Cadd(cm0.e02,cmDATA_ini[i_new].e02,cmDATA[i_new].e02);
Cadd(cm0.e11,cmDATA_ini[i_new].e11,cmDATA[i_new].e11);
Cadd(cm0.e12,cmDATA_ini[i_new].e12,cmDATA[i_new].e12);
Cadd(cm0.e22,cmDATA_ini[i_new].e22,cmDATA[i_new].e22);
Csub(cmDATA_ini[i_new].e00,cm0.e00,cmDATA[m].e00);
Csub(cmDATA_ini[i_new].e01,cm0.e01,cmDATA[m].e01);
Csub(cmDATA_ini[i_new].e02,cm0.e02,cmDATA[m].e02);
Csub(cmDATA_ini[i_new].e11,cm0.e11,cmDATA[m].e11);
Csub(cmDATA_ini[i_new].e12,cm0.e12,cmDATA[m].e12);
Csub(cmDATA_ini[i_new].e22,cm0.e22,cmDATA[m].e22);
}
}
for(i=0;i<i_max;i++)
{ //cmDATA_ini[i]=cmDATA[i];
Ccopy(cmDATA[i].e00,cmDATA_ini[i].e00);
Ccopy(cmDATA[i].e01,cmDATA_ini[i].e01);
Ccopy(cmDATA[i].e02,cmDATA_ini[i].e02);
Ccopy(cmDATA[i].e11,cmDATA_ini[i].e11);
Ccopy(cmDATA[i].e12,cmDATA_ini[i].e12);
Ccopy(cmDATA[i].e22,cmDATA_ini[i].e22);
}
}
return;
}
void FFT(int lim_NoB, int i_max, cplx * cW, cvector * cvDATA_ini,
cvector * cvDATA)
{ int i,j,l,k,m,i_new,j_new,iNolFFT,iStep;
cvector cv0;
/************************* The sorting of initial data **********************/
for(i=0;i<i_max;i++)
{ Change_binary_number(i,lim_NoB,&i_new);
//cvDATA[i]=cvDATA_ini[i_new];
Ccopy(cvDATA_ini[i_new].x,cvDATA[i].x);
Ccopy(cvDATA_ini[i_new].y,cvDATA[i].y);
Ccopy(cvDATA_ini[i_new].z,cvDATA[i].z);
}
/************************ Log2(N) point-to-point FT *************************/
/***************************** Initial step *********************************/
iNolFFT=i_max/2; // number of local FFT at the first step
iStep=i_max/iNolFFT;
for(i=0;i<iNolFFT;i++)
{ i_new=iStep*i;
//cvDATA_ini[i_new] =cvDATA[i_new]+cvDATA[i_new+1];
//cvDATA_ini[i_new+1]=cvDATA[i_new]-cvDATA[i_new+1];
Cadd(cvDATA[i_new].x,cvDATA[i_new+1].x,cvDATA_ini[i_new].x);
Cadd(cvDATA[i_new].y,cvDATA[i_new+1].y,cvDATA_ini[i_new].y);
Cadd(cvDATA[i_new].z,cvDATA[i_new+1].z,cvDATA_ini[i_new].z);
Csub(cvDATA[i_new].x,cvDATA[i_new+1].x,cvDATA_ini[i_new+1].x);
Csub(cvDATA[i_new].y,cvDATA[i_new+1].y,cvDATA_ini[i_new+1].y);
Csub(cvDATA[i_new].z,cvDATA[i_new+1].z,cvDATA_ini[i_new+1].z);
}
/***************************** Others steps *********************************/
for(l=1;l<lim_NoB;l++)
{ iNolFFT/=2; // number of local FFT (At begin iNolFFT=i_max/2)
iStep=i_max/iNolFFT; // number of point in local FFT
for(j=0;j<iNolFFT;j++)
{ j_new=iStep*j;
for(i=0;i<(iStep/2);i++)
{ i_new=j_new+i; k=i*i_max/iStep; m=i_new+(iStep/2);
//cv0=cW[k]*cvDATA_ini[m];
//cvDATA[i_new]=cvDATA_ini[i_new]+cv0;
//cvDATA[m]=cvDATA_ini[i_new]-cv0;
Cmul(cW[k],cvDATA_ini[m].x,cv0.x);
Cmul(cW[k],cvDATA_ini[m].y,cv0.y);
Cmul(cW[k],cvDATA_ini[m].z,cv0.z);
Cadd(cvDATA_ini[i_new].x,cv0.x,cvDATA[i_new].x);
Cadd(cvDATA_ini[i_new].y,cv0.y,cvDATA[i_new].y);
Cadd(cvDATA_ini[i_new].z,cv0.z,cvDATA[i_new].z);
Csub(cvDATA_ini[i_new].x,cv0.x,cvDATA[m].x);
Csub(cvDATA_ini[i_new].y,cv0.y,cvDATA[m].y);
Csub(cvDATA_ini[i_new].z,cv0.z,cvDATA[m].z);
}
}
for(i=0;i<i_max;i++)
{ //cvDATA_ini[i]=cvDATA[i];
Ccopy(cvDATA[i].x,cvDATA_ini[i].x);
Ccopy(cvDATA[i].y,cvDATA_ini[i].y);
Ccopy(cvDATA[i].z,cvDATA_ini[i].z);
}
}
return;
}
/****************************************************************************/
/**************************** Inverse FFT base ******************************/
/****************************************************************************/
void iFFT(int lim_NoB, int i_max, cplx * cW, cmatrix * cmDATA_ini,
cmatrix * cmDATA)
{ int i;
for(i=0;i<i_max;i++)
{ cmDATA_ini[i].e00=conj(cmDATA_ini[i].e00);
cmDATA_ini[i].e01=conj(cmDATA_ini[i].e01);
cmDATA_ini[i].e02=conj(cmDATA_ini[i].e02);
cmDATA_ini[i].e11=conj(cmDATA_ini[i].e11);
cmDATA_ini[i].e12=conj(cmDATA_ini[i].e12);
cmDATA_ini[i].e22=conj(cmDATA_ini[i].e22);
}
FFT(lim_NoB,i_max,cW,cmDATA_ini,cmDATA);
for(i=0;i<i_max;i++)
{ cmDATA[i].e00=conj(cmDATA[i].e00);
cmDATA[i].e01=conj(cmDATA[i].e01);
cmDATA[i].e02=conj(cmDATA[i].e02);
cmDATA[i].e11=conj(cmDATA[i].e11);
cmDATA[i].e12=conj(cmDATA[i].e12);
cmDATA[i].e22=conj(cmDATA[i].e22);
}
return;
}
void iFFT(int lim_NoB, int i_max, cplx * cW, cvector * cvDATA_ini,
cvector * cvDATA)
{ int i;
for(i=0;i<i_max;i++)
{ cvDATA_ini[i].x=conj(cvDATA_ini[i].x);
cvDATA_ini[i].y=conj(cvDATA_ini[i].y);
cvDATA_ini[i].z=conj(cvDATA_ini[i].z);
}
FFT(lim_NoB,i_max,cW,cvDATA_ini,cvDATA);
for(i=0;i<i_max;i++)
{ cvDATA[i].x=conj(cvDATA[i].x);
cvDATA[i].y=conj(cvDATA[i].y);
cvDATA[i].z=conj(cvDATA[i].z);
}
return;
}
/****************************************************************************/
/********************************** FFT 3D **********************************/
/****************************************************************************/
void FFT_3D(int i_max, int j_max, int l_max, cplx * cW_i, cplx * cW_j,
cplx * cW_l, cmatrix *** cmDATA)
{ int i,j,l,lim_NoB;
real rNorma=1./(i_max*j_max*l_max);
cmatrix * cmWork,* cmResult;
/*********************************** z-FFT **********************************/
cmWork=(cmatrix *)malloc(l_max*sizeof(cmatrix));
if(cmWork==NULL)
{ printf("\n No enough memory for array cmWork[l_max]! ");
exit(1);
}
cmResult=(cmatrix *)malloc(l_max*sizeof(cmatrix));
if(cmResult==NULL)
{ printf("\n No enough memory for array cmResult[l_max]! ");
exit(1);
}
Get_number_bits((l_max-1),&lim_NoB);
for(i=0;i<i_max;i++)
for(j=0;j<j_max;j++)
{ for(l=0;l<l_max;l++)
cmWork[l]=cmDATA[i][j][l];
FFT(lim_NoB,l_max,cW_l,cmWork,cmResult);
for(l=0;l<l_max;l++)
cmDATA[i][j][l]=cmResult[l];
}
free(cmWork); free(cmResult);
/*********************************** y-FFT **********************************/
cmWork=(cmatrix *)malloc(j_max*sizeof(cmatrix));
if(cmWork==NULL)
{ printf("\n No enough memory for array cmWork[j_max]! ");
exit(1);
}
cmResult=(cmatrix *)malloc(j_max*sizeof(cmatrix));
if(cmResult==NULL)
{ printf("\n No enough memory for array cmResult[j_max]! ");
exit(1);
}
Get_number_bits((j_max-1),&lim_NoB);
for(i=0;i<i_max;i++)
for(l=0;l<l_max;l++)
{ for(j=0;j<j_max;j++)
cmWork[j]=cmDATA[i][j][l];
FFT(lim_NoB,j_max,cW_j,cmWork,cmResult);
for(j=0;j<j_max;j++)
cmDATA[i][j][l]=cmResult[j];
}
free(cmWork); free(cmResult);
/*********************************** x-FFT **********************************/
cmWork=(cmatrix *)malloc(i_max*sizeof(cmatrix));
if(cmWork==NULL)
{ printf("\n No enough memory for array cmWork[i_max]! ");
exit(1);
}
cmResult=(cmatrix *)malloc(i_max*sizeof(cmatrix));
if(cmResult==NULL)
{ printf("\n No enough memory for array cmResult[i_max]! ");
exit(1);
}
Get_number_bits((i_max-1),&lim_NoB);
for(j=0;j<j_max;j++)
for(l=0;l<l_max;l++)
{ for(i=0;i<i_max;i++)
cmWork[i]=cmDATA[i][j][l];
FFT(lim_NoB,i_max,cW_i,cmWork,cmResult);
for(i=0;i<i_max;i++)
cmDATA[i][j][l]=cmResult[i];
}
free(cmWork); free(cmResult);
for(i=0;i<i_max;i++)
for(j=0;j<j_max;j++)
for(l=0;l<l_max;l++)
cmDATA[i][j][l]=rNorma*cmDATA[i][j][l];
return;
}
void FFT_3D(int i_max, int j_max, int l_max, cplx * cW_2_i, cplx * cW_2_j,
cplx * cW_2_l, cplx * cW_i, cplx * cW_j, cplx * cW_l,
cvector *** cvDATA)
{ int i,j,l,lim_NoB,i_max_2=i_max/2,j_max_2=j_max/2,l_max_2=l_max/2;
cvector * cvWork,* cvResult;
const ddafft::plan * pl_l=NULL,* pl_j=NULL,* pl_i=NULL;
/*********************************** z-FFT **********************************/
cvWork=(cvector *)malloc(l_max_2*sizeof(cvector));
if(cvWork==NULL)
{ printf("\n No enough memory for array cvWork[l_max]! ");
exit(1);
}
cvResult=(cvector *)malloc(l_max_2*sizeof(cvector));
if(cvResult==NULL)
{ printf("\n No enough memory for array cvResult[l_max]! ");
exit(1);
}
Get_number_bits((l_max_2-1),&lim_NoB);
pl_l=fft_plan_for(l_max_2);
for(i=0;i<i_max_2;i++)
for(j=0;j<j_max_2;j++)
{ for(l=0;l<l_max_2;l++)
cvWork[l]=cvDATA[i][j][l];
fft_line_fwd(pl_l,lim_NoB,l_max_2,cW_2_l,cvWork,cvResult);
/* second (odd-bin) input: built before cvDATA is overwritten */
for(l=0;l<l_max_2;l++)
{ Cmul(cW_l[l],cvDATA[i][j][l].x,cvWork[l].x);
Cmul(cW_l[l],cvDATA[i][j][l].y,cvWork[l].y);
Cmul(cW_l[l],cvDATA[i][j][l].z,cvWork[l].z);
}
for(l=0;l<l_max_2;l++)
cvDATA[i][j][2*l]=cvResult[l];
fft_line_fwd(pl_l,lim_NoB,l_max_2,cW_2_l,cvWork,cvResult);
for(l=0;l<l_max_2;l++)
cvDATA[i][j][2*l+1]=cvResult[l];
}
free(cvWork); free(cvResult);
/*********************************** y-FFT **********************************/
cvWork=(cvector *)malloc(j_max_2*sizeof(cvector));
if(cvWork==NULL)
{ printf("\n No enough memory for array cvWork[j_max]! ");
exit(1);
}
cvResult=(cvector *)malloc(j_max_2*sizeof(cvector));
if(cvResult==NULL)
{ printf("\n No enough memory for array cvResult[j_max]! ");
exit(1);
}
Get_number_bits((j_max_2-1),&lim_NoB);
pl_j=fft_plan_for(j_max_2);
for(i=0;i<i_max_2;i++)
for(l=0;l<l_max;l++)
{ for(j=0;j<j_max_2;j++)
cvWork[j]=cvDATA[i][j][l];
fft_line_fwd(pl_j,lim_NoB,j_max_2,cW_2_j,cvWork,cvResult);
for(j=0;j<j_max_2;j++)
{ Cmul(cW_j[j],cvDATA[i][j][l].x,cvWork[j].x);
Cmul(cW_j[j],cvDATA[i][j][l].y,cvWork[j].y);
Cmul(cW_j[j],cvDATA[i][j][l].z,cvWork[j].z);
}
for(j=0;j<j_max_2;j++)
cvDATA[i][2*j][l]=cvResult[j];
fft_line_fwd(pl_j,lim_NoB,j_max_2,cW_2_j,cvWork,cvResult);
for(j=0;j<j_max_2;j++)
cvDATA[i][2*j+1][l]=cvResult[j];
}
free(cvWork); free(cvResult);
/*********************************** x-FFT **********************************/
cvWork=(cvector *)malloc(i_max_2*sizeof(cvector));
if(cvWork==NULL)
{ printf("\n No enough memory for array cvWork[i_max]! ");
exit(1);
}
cvResult=(cvector *)malloc(i_max_2*sizeof(cvector));
if(cvResult==NULL)
{ printf("\n No enough memory for array cvResult[i_max]! ");
exit(1);
}
Get_number_bits((i_max_2-1),&lim_NoB);
pl_i=fft_plan_for(i_max_2);
for(j=0;j<j_max;j++)
for(l=0;l<l_max;l++)
{ for(i=0;i<i_max_2;i++)
cvWork[i]=cvDATA[i][j][l];
fft_line_fwd(pl_i,lim_NoB,i_max_2,cW_2_i,cvWork,cvResult);
for(i=0;i<i_max_2;i++)
{ Cmul(cW_i[i],cvDATA[i][j][l].x,cvWork[i].x);
Cmul(cW_i[i],cvDATA[i][j][l].y,cvWork[i].y);
Cmul(cW_i[i],cvDATA[i][j][l].z,cvWork[i].z);
}
for(i=0;i<i_max_2;i++)
cvDATA[2*i][j][l]=cvResult[i];
fft_line_fwd(pl_i,lim_NoB,i_max_2,cW_2_i,cvWork,cvResult);
for(i=0;i<i_max_2;i++)
cvDATA[2*i+1][j][l]=cvResult[i];
}
free(cvWork); free(cvResult);
return;
}
/****************************************************************************/
/****************************** Inverse FFT 3D ******************************/
/****************************************************************************/
void iFFT_3D(int i_max, int j_max, int l_max, cplx * cW_i, cplx * cW_j,
cplx * cW_l, cvector *** cvDATA)
{ int i,j,l,lim_NoB,i_max_2=i_max/2,j_max_2=j_max/2;
cvector * cvWork,* cvResult;
const ddafft::plan * pl_l=NULL,* pl_j=NULL,* pl_i=NULL;
/*********************************** x-FFT **********************************/
cvWork=(cvector *)malloc(i_max*sizeof(cvector));
if(cvWork==NULL)
{ printf("\n No enough memory for array cvWork[i_max]! ");
exit(1);
}
cvResult=(cvector *)malloc(i_max*sizeof(cvector));
if(cvResult==NULL)
{ printf("\n No enough memory for array cvResult[i_max]! ");
exit(1);
}
Get_number_bits((i_max-1),&lim_NoB);
pl_i=fft_plan_for(i_max);
for(j=0;j<j_max;j++)
for(l=0;l<l_max;l++)
{ for(i=0;i<i_max;i++)
cvWork[i]=cvDATA[i][j][l];
fft_line_inv(pl_i,lim_NoB,i_max,cW_i,cvWork,cvResult);
for(i=0;i<i_max;i++)
cvDATA[i][j][l]=cvResult[i];
}
free(cvWork); free(cvResult);
/*********************************** y-FFT **********************************/
cvWork=(cvector *)malloc(j_max*sizeof(cvector));
if(cvWork==NULL)
{ printf("\n No enough memory for array cvWork[j_max]! ");
exit(1);
}
cvResult=(cvector *)malloc(j_max*sizeof(cvector));
if(cvResult==NULL)
{ printf("\n No enough memory for array cvResult[j_max]! ");
exit(1);
}
Get_number_bits((j_max-1),&lim_NoB);
pl_j=fft_plan_for(j_max);
for(i=0;i<i_max_2;i++)
for(l=0;l<l_max;l++)
{ for(j=0;j<j_max;j++)
cvWork[j]=cvDATA[i][j][l];
fft_line_inv(pl_j,lim_NoB,j_max,cW_j,cvWork,cvResult);
for(j=0;j<j_max;j++)
cvDATA[i][j][l]=cvResult[j];
}
free(cvWork); free(cvResult);
/*********************************** z-FFT **********************************/
cvWork=(cvector *)malloc(l_max*sizeof(cvector));
if(cvWork==NULL)
{ printf("\n No enough memory for array cvWork[l_max]! ");
exit(1);
}
cvResult=(cvector *)malloc(l_max*sizeof(cvector));
if(cvResult==NULL)
{ printf("\n No enough memory for array cvResult[l_max]! ");
exit(1);
}
Get_number_bits((l_max-1),&lim_NoB);
pl_l=fft_plan_for(l_max);
for(i=0;i<i_max_2;i++)
for(j=0;j<j_max_2;j++)
{ for(l=0;l<l_max;l++)
cvWork[l]=cvDATA[i][j][l];
fft_line_inv(pl_l,lim_NoB,l_max,cW_l,cvWork,cvResult);
for(l=0;l<l_max;l++)
cvDATA[i][j][l]=cvResult[l];
}
free(cvWork); free(cvResult);
return;
}
/***************** FFT functions for Rader-Brenner method *******************/
/****************************************************************************/
/******************* Calculation the exp(-i((2*PI*j)/(N))) ******************/
/****************************************************************************/
void FourierPhase(int i_max, real ** Im_cW, cplx ** cW2)
{ int i,j,N_2=i_max/2;
real rF=2.*PI/i_max;
cplx c0;
for(j=0;j<N_2;j++)
{ Im_cW[0][j]=0.;
cW2[0][j].r=1.; cW2[0][j].i=0.;
}
for(i=1;i<N_2;i++)
for(j=i;j<N_2;j++)
{ Cexp_im((rF*(real)(i*j)),c0);
Cmul(c0,c0,cW2[i][j]);
Im_cW[i][j]=.5/c0.i;
}
for(i=1;i<N_2;i++)
for(j=0;j<i;j++)
{ Im_cW[i][j]=Im_cW[j][i];
cW2[i][j]=cW2[j][i];
}
return;
}
/****************************************************************************/
/********************************* FFT base *********************************/
/****************************************************************************/
void FFT(int i_max, real ** Im_cW, cplx ** cW2, cmatrix * cmDATA_ini,
cmatrix * cmDATA, cmatrix * cA, cmatrix * cB, cmatrix * cC)
{ int i,j,N_2=i_max/2;
cmatrix c0,c1;
Cadd(cmDATA_ini[0].e00,cmDATA_ini[N_2].e00,cB[0].e00);
Cadd(cmDATA_ini[0].e01,cmDATA_ini[N_2].e01,cB[0].e01);
Cadd(cmDATA_ini[0].e02,cmDATA_ini[N_2].e02,cB[0].e02);
Cadd(cmDATA_ini[0].e11,cmDATA_ini[N_2].e11,cB[0].e11);
Cadd(cmDATA_ini[0].e12,cmDATA_ini[N_2].e12,cB[0].e12);
Cadd(cmDATA_ini[0].e22,cmDATA_ini[N_2].e22,cB[0].e22);
cA[0].e00.r=0.; cA[0].e00.i=0.;
cA[0].e01.r=0.; cA[0].e01.i=0.;
cA[0].e02.r=0.; cA[0].e02.i=0.;
cA[0].e11.r=0.; cA[0].e11.i=0.;
cA[0].e12.r=0.; cA[0].e12.i=0.;
cA[0].e22.r=0.; cA[0].e22.i=0.;
for(i=1;i<N_2;i++)
{ Cadd(cmDATA_ini[i].e00,cmDATA_ini[i+N_2].e00,cB[i].e00);
Cadd(cmDATA_ini[i].e01,cmDATA_ini[i+N_2].e01,cB[i].e01);
Cadd(cmDATA_ini[i].e02,cmDATA_ini[i+N_2].e02,cB[i].e02);
Cadd(cmDATA_ini[i].e11,cmDATA_ini[i+N_2].e11,cB[i].e11);
Cadd(cmDATA_ini[i].e12,cmDATA_ini[i+N_2].e12,cB[i].e12);
Cadd(cmDATA_ini[i].e22,cmDATA_ini[i+N_2].e22,cB[i].e22);
Csub(cmDATA_ini[i].e00,cmDATA_ini[i+N_2].e00,c0.e00);
Csub(cmDATA_ini[i].e01,cmDATA_ini[i+N_2].e01,c0.e01);
Csub(cmDATA_ini[i].e02,cmDATA_ini[i+N_2].e02,c0.e02);
Csub(cmDATA_ini[i].e11,cmDATA_ini[i+N_2].e11,c0.e11);
Csub(cmDATA_ini[i].e12,cmDATA_ini[i+N_2].e12,c0.e12);
Csub(cmDATA_ini[i].e22,cmDATA_ini[i+N_2].e22,c0.e22);
cA[i].e00.r=c0.e00.i*Im_cW[i][1]; cA[i].e00.i=-c0.e00.r*Im_cW[i][1];
cA[i].e01.r=c0.e01.i*Im_cW[i][1]; cA[i].e01.i=-c0.e01.r*Im_cW[i][1];
cA[i].e02.r=c0.e02.i*Im_cW[i][1]; cA[i].e02.i=-c0.e02.r*Im_cW[i][1];
cA[i].e11.r=c0.e11.i*Im_cW[i][1]; cA[i].e11.i=-c0.e11.r*Im_cW[i][1];
cA[i].e12.r=c0.e12.i*Im_cW[i][1]; cA[i].e12.i=-c0.e12.r*Im_cW[i][1];
cA[i].e22.r=c0.e22.i*Im_cW[i][1]; cA[i].e22.i=-c0.e22.r*Im_cW[i][1];
}
for(i=0;i<N_2;i++)
{ cmDATA[2*i].e00.r=0.; cmDATA[2*i].e00.i=0.;
cmDATA[2*i].e01.r=0.; cmDATA[2*i].e01.i=0.;
cmDATA[2*i].e02.r=0.; cmDATA[2*i].e02.i=0.;
cmDATA[2*i].e11.r=0.; cmDATA[2*i].e11.i=0.;
cmDATA[2*i].e12.r=0.; cmDATA[2*i].e12.i=0.;
cmDATA[2*i].e22.r=0.; cmDATA[2*i].e22.i=0.;
cC[i].e00.r=0.; cC[i].e00.i=0.;
cC[i].e01.r=0.; cC[i].e01.i=0.;
cC[i].e02.r=0.; cC[i].e02.i=0.;
cC[i].e11.r=0.; cC[i].e11.i=0.;
cC[i].e12.r=0.; cC[i].e12.i=0.;
cC[i].e22.r=0.; cC[i].e22.i=0.;
for(j=0;j<N_2;j++)
{ Cmul(cB[j].e00,cW2[i][j],c0.e00);
Cmul(cB[j].e01,cW2[i][j],c0.e01);
Cmul(cB[j].e02,cW2[i][j],c0.e02);
Cmul(cB[j].e11,cW2[i][j],c0.e11);
Cmul(cB[j].e12,cW2[i][j],c0.e12);
Cmul(cB[j].e22,cW2[i][j],c0.e22);
Cadd(cmDATA[2*i].e00,c0.e00,cmDATA[2*i].e00);
Cadd(cmDATA[2*i].e01,c0.e01,cmDATA[2*i].e01);
Cadd(cmDATA[2*i].e02,c0.e02,cmDATA[2*i].e02);
Cadd(cmDATA[2*i].e11,c0.e11,cmDATA[2*i].e11);
Cadd(cmDATA[2*i].e12,c0.e12,cmDATA[2*i].e12);
Cadd(cmDATA[2*i].e22,c0.e22,cmDATA[2*i].e22);
Cmul(cA[j].e00,cW2[i][j],c0.e00);
Cmul(cA[j].e01,cW2[i][j],c0.e01);
Cmul(cA[j].e02,cW2[i][j],c0.e02);
Cmul(cA[j].e11,cW2[i][j],c0.e11);
Cmul(cA[j].e12,cW2[i][j],c0.e12);
Cmul(cA[j].e22,cW2[i][j],c0.e22);
Cadd(cC[i].e00,c0.e00,cC[i].e00);
Cadd(cC[i].e01,c0.e01,cC[i].e01);
Cadd(cC[i].e02,c0.e02,cC[i].e02);
Cadd(cC[i].e11,c0.e11,cC[i].e11);
Cadd(cC[i].e12,c0.e12,cC[i].e12);
Cadd(cC[i].e22,c0.e22,cC[i].e22);
}
}
cC[N_2]=cC[0];
Csub(cmDATA_ini[0].e00,cmDATA_ini[N_2].e00,c0.e00);
Csub(cmDATA_ini[0].e01,cmDATA_ini[N_2].e01,c0.e01);
Csub(cmDATA_ini[0].e02,cmDATA_ini[N_2].e02,c0.e02);
Csub(cmDATA_ini[0].e11,cmDATA_ini[N_2].e11,c0.e11);
Csub(cmDATA_ini[0].e12,cmDATA_ini[N_2].e12,c0.e12);
Csub(cmDATA_ini[0].e22,cmDATA_ini[N_2].e22,c0.e22);
for(i=0;i<N_2;i++)
{ Csub(cC[i+1].e00,cC[i].e00,c1.e00);
Csub(cC[i+1].e01,cC[i].e01,c1.e01);
Csub(cC[i+1].e02,cC[i].e02,c1.e02);
Csub(cC[i+1].e11,cC[i].e11,c1.e11);
Csub(cC[i+1].e12,cC[i].e12,c1.e12);
Csub(cC[i+1].e22,cC[i].e22,c1.e22);
Cadd(c1.e00,c0.e00,cmDATA[2*i+1].e00);
Cadd(c1.e01,c0.e01,cmDATA[2*i+1].e01);
Cadd(c1.e02,c0.e02,cmDATA[2*i+1].e02);
Cadd(c1.e11,c0.e11,cmDATA[2*i+1].e11);
Cadd(c1.e12,c0.e12,cmDATA[2*i+1].e12);
Cadd(c1.e22,c0.e22,cmDATA[2*i+1].e22);
}
return;
}
void FFT(int i_max, real ** Im_cW, cplx ** cW2, cvector * cvDATA_ini,
cvector * cvDATA, cvector * cA, cvector * cB, cvector * cC)
{ int i,j,N_2=i_max/2;
cvector c0,c1;
Cadd(cvDATA_ini[0].x,cvDATA_ini[N_2].x,cB[0].x);
Cadd(cvDATA_ini[0].y,cvDATA_ini[N_2].y,cB[0].y);
Cadd(cvDATA_ini[0].z,cvDATA_ini[N_2].z,cB[0].z);
cA[0].x.r=0.; cA[0].x.i=0.;
cA[0].y.r=0.; cA[0].y.i=0.;
cA[0].z.r=0.; cA[0].z.i=0.;
for(i=1;i<N_2;i++)
{ Cadd(cvDATA_ini[i].x,cvDATA_ini[i+N_2].x,cB[i].x);
Cadd(cvDATA_ini[i].y,cvDATA_ini[i+N_2].y,cB[i].y);
Cadd(cvDATA_ini[i].z,cvDATA_ini[i+N_2].z,cB[i].z);
Csub(cvDATA_ini[i].x,cvDATA_ini[i+N_2].x,c0.x);
Csub(cvDATA_ini[i].y,cvDATA_ini[i+N_2].y,c0.y);
Csub(cvDATA_ini[i].z,cvDATA_ini[i+N_2].z,c0.z);
cA[i].x.r=c0.x.i*Im_cW[i][1]; cA[i].x.i=-c0.x.r*Im_cW[i][1];
cA[i].y.r=c0.y.i*Im_cW[i][1]; cA[i].y.i=-c0.y.r*Im_cW[i][1];
cA[i].z.r=c0.z.i*Im_cW[i][1]; cA[i].z.i=-c0.z.r*Im_cW[i][1];
}
for(i=0;i<N_2;i++)
{ cvDATA[2*i].x.r=0.; cvDATA[2*i].x.i=0.;
cvDATA[2*i].y.r=0.; cvDATA[2*i].y.i=0.;
cvDATA[2*i].z.r=0.; cvDATA[2*i].z.i=0.;
cC[i].x.r=0.; cC[i].x.i=0.;
cC[i].y.r=0.; cC[i].y.i=0.;
cC[i].z.r=0.; cC[i].z.i=0.;
for(j=0;j<N_2;j++)
{ Cmul(cB[j].x,cW2[i][j],c0.x);
Cmul(cB[j].y,cW2[i][j],c0.y);
Cmul(cB[j].z,cW2[i][j],c0.z);
Cadd(cvDATA[2*i].x,c0.x,cvDATA[2*i].x);
Cadd(cvDATA[2*i].y,c0.y,cvDATA[2*i].y);
Cadd(cvDATA[2*i].z,c0.z,cvDATA[2*i].z);
Cmul(cA[j].x,cW2[i][j],c0.x);
Cmul(cA[j].y,cW2[i][j],c0.y);
Cmul(cA[j].z,cW2[i][j],c0.z);
Cadd(cC[i].x,c0.x,cC[i].x);
Cadd(cC[i].y,c0.y,cC[i].y);
Cadd(cC[i].z,c0.z,cC[i].z);
}
}
cC[N_2]=cC[0];
Csub(cvDATA_ini[0].x,cvDATA_ini[N_2].x,c0.x);
Csub(cvDATA_ini[0].y,cvDATA_ini[N_2].y,c0.y);
Csub(cvDATA_ini[0].z,cvDATA_ini[N_2].z,c0.z);
for(i=0;i<N_2;i++)
{ Csub(cC[i+1].x,cC[i].x,c1.x);
Csub(cC[i+1].y,cC[i].y,c1.y);
Csub(cC[i+1].z,cC[i].z,c1.z);
Cadd(c1.x,c0.x,cvDATA[2*i+1].x);
Cadd(c1.y,c0.y,cvDATA[2*i+1].y);
Cadd(c1.z,c0.z,cvDATA[2*i+1].z);
}
return;
}
/****************************************************************************/
/**************************** Inverse FFT base ******************************/
/****************************************************************************/
void iFFT(int i_max, real ** Im_cW, cplx ** cW2, cvector * cvDATA_ini,
cvector * cvDATA, cvector * cA, cvector * cB, cvector * cC)
{ int i;
for(i=0;i<i_max;i++)
{ cvDATA_ini[i].x=conj(cvDATA_ini[i].x);
cvDATA_ini[i].y=conj(cvDATA_ini[i].y);
cvDATA_ini[i].z=conj(cvDATA_ini[i].z);
}
FFT(i_max,Im_cW,cW2,cvDATA_ini,cvDATA,cA,cB,cC);
for(i=0;i<i_max;i++)
{ cvDATA[i].x=conj(cvDATA[i].x);
cvDATA[i].y=conj(cvDATA[i].y);
cvDATA[i].z=conj(cvDATA[i].z);
}
return;
}
/****************************************************************************/
/********************************** FFT 3D **********************************/
/****************************************************************************/
void FFT_3D(int i_max, int j_max, int l_max, real ** Im_cW_i, real ** Im_cW_j,
real ** Im_cW_l, cplx ** cW2_i, cplx ** cW2_j, cplx ** cW2_l,
cmatrix *** cmDATA)
{ int i,j,l,N;
real rNorma=1./(i_max*j_max*l_max);
cmatrix * cmWork,* cmResult,* cA,* cB,* cC;
i=i_max;
if(i<j_max) i=j_max;
if(i<l_max) i=l_max;
N=i/2;
cA=(cmatrix *)malloc(N*sizeof(cmatrix));
cB=(cmatrix *)malloc(N*sizeof(cmatrix));
cC=(cmatrix *)malloc((N+1)*sizeof(cmatrix));
cmWork=(cmatrix *)malloc(i*sizeof(cmatrix));
cmResult=(cmatrix *)malloc(i*sizeof(cmatrix));
if(cA==NULL||cB==NULL||cC==NULL||cmWork==NULL||cmResult==NULL)
{ printf("\n No memory for array cA, cB, cC, cmWork[] or cmResult[]!");
exit(1);
}
/*********************************** z-FFT **********************************/
for(i=0;i<i_max;i++)
for(j=0;j<j_max;j++)
{ for(l=0;l<l_max;l++)
cmWork[l]=cmDATA[i][j][l];
FFT(l_max,Im_cW_l,cW2_l,cmWork,cmResult,cA,cB,cC);
for(l=0;l<l_max;l++)
cmDATA[i][j][l]=cmResult[l];
}
/*********************************** y-FFT **********************************/
for(i=0;i<i_max;i++)
for(l=0;l<l_max;l++)
{ for(j=0;j<j_max;j++)
cmWork[j]=cmDATA[i][j][l];
FFT(j_max,Im_cW_j,cW2_j,cmWork,cmResult,cA,cB,cC);
for(j=0;j<j_max;j++)
cmDATA[i][j][l]=cmResult[j];
}
/*********************************** x-FFT **********************************/
for(j=0;j<j_max;j++)
for(l=0;l<l_max;l++)
{ for(i=0;i<i_max;i++)
cmWork[i]=cmDATA[i][j][l];
FFT(i_max,Im_cW_i,cW2_i,cmWork,cmResult,cA,cB,cC);
for(i=0;i<i_max;i++)
cmDATA[i][j][l]=cmResult[i];
}
for(i=0;i<i_max;i++)
for(j=0;j<j_max;j++)
for(l=0;l<l_max;l++)
cmDATA[i][j][l]=rNorma*cmDATA[i][j][l];
free(cmWork); free(cmResult); free(cA); free(cB); free(cC);
return;
}
void FFT_3D(int i_max, int j_max, int l_max, real ** Im_cW_i, real ** Im_cW_j,
real ** Im_cW_l, cplx ** cW2_i, cplx ** cW2_j, cplx ** cW2_l,
cvector *** cvDATA)
{ int i,j,l,N,i_max_2=i_max/2,j_max_2=j_max/2;
cvector * cvWork,* cvResult,* cA,* cB,* cC;
i=i_max;
if(i<j_max) i=j_max;
if(i<l_max) i=l_max;
N=i/2;
cA=(cvector *)malloc(N*sizeof(cvector));
cB=(cvector *)malloc(N*sizeof(cvector));
cC=(cvector *)malloc((N+1)*sizeof(cvector));
cvWork=(cvector *)malloc(i*sizeof(cvector));
cvResult=(cvector *)malloc(i*sizeof(cvector));
if(cA==NULL||cB==NULL||cC==NULL||cvWork==NULL||cvResult==NULL)
{ printf("\n No memory for array cA, cB, cC, cvWork[] or cvResult[]!");
exit(1);
}