inline int fdct3d_lowpasscompute(float XL1, float XL2, float XL3, DblOffTns& lowpass)
{
int XS1 = 2*int(floor(XL1/2))+1;
int XS2 = 2*int(floor(XL2/2))+1;
int XS3 = 2*int(floor(XL3/2))+1;
//number of samples
int XF1 = int(floor(XL1/2));
int XF2 = int(floor(XL2/2));
int XF3 = int(floor(XL3/2));
//offset on either side
float XR1 = XL1/2;
float XR2 = XL2/2;
float XR3 = XL3/2;
DblOffVec lowpass1(XS1); setvalue(lowpass1,float(1.0));
for(int i=-XF1; i<-XR1/2; i++) {
float x = (i+XR1)/(XR1/2);
float l,r; fdct3d_window(x, l, r);
lowpass1(i) = l;
lowpass1(-i) = l;
} //cerr<<lowpass1;
DblOffVec lowpass2(XS2); setvalue(lowpass2,float(1.0));
for(int i=-XF2; i<-XR2/2; i++) {
float x = (i+XR2)/(XR2/2);
float l,r; fdct3d_window(x, l, r);
lowpass2(i) = l;
lowpass2(-i) = l;
} //cerr<<lowpass2;
DblOffVec lowpass3(XS3); setvalue(lowpass3,float(1.0));
for(int i=-XF3; i<-XR3/2; i++) {
float x = (i+XR3)/(XR3/2);
float l,r; fdct3d_window(x, l, r);
lowpass3(i) = l;
lowpass3(-i) = l;
} //cerr<<lowpass3;
for(int i=-XF1; i<-XF1+XS1; i++)
for(int j=-XF2; j<-XF2+XS2; j++)
for(int k=-XF3; k<-XF3+XS3; k++)
lowpass(i,j,k) = lowpass1(i) * lowpass2(j) * lowpass3(k);
return 0;
}
inline int fdct3d_lowpass(float L1, DblOffVec& lowpass)
{
int S1 = 2*int(floor(L1/2))+1;
int F1 = int(floor(L1/2));
float R1 = L1/2;
assert(lowpass.m()>=S1);
setvalue(lowpass, float(0.0));
for(int i=-F1; i<=0; i++) {
float x = (i+R1)/(R1/2);
float l,r; fdct3d_window(x, l, r);
lowpass(i) = l;
lowpass(-i) = l;
}
return 0;
}
//------------------------------------------------------------------------------------
int fdct3d_inverse_angles(int N1,int N2,int N3,int b, double L1,double L2,double L3, int s,int nd,
CpxCrvletPrtd& C, CpxNumTnsBlkd& W)
{
int mpirank; MPI_Comm_rank(MPI_COMM_WORLD, &mpirank);
int mpisize; MPI_Comm_size(MPI_COMM_WORLD, &mpisize);
vector< vector<int> >& Cowners = C.owners();
vector<int>& crvowners = Cowners[s]; //LEXING: the owner information for wedges in scale s
int nf = 6;
int wcnt = 0;
int S1, S2, S3; int F1, F2, F3; double R1, R2, R3; fdct3d_rangecompute(L1, L2, L3, S1, S2, S3, F1, F2, F3, R1, R2, R3);
DblOffVec big1(S1); fdct3d_lowpass(L1, big1);
DblOffVec big2(S2); fdct3d_lowpass(L2, big2);
DblOffVec big3(S3); fdct3d_lowpass(L3, big3);
double Lh1 = L1/2; double Lh2 = L2/2; double Lh3 = L3/2;
int Sh1, Sh2, Sh3; int Fh1, Fh2, Fh3; double Rh1, Rh2, Rh3; fdct3d_rangecompute(Lh1, Lh2, Lh3, Sh1, Sh2, Sh3, Fh1, Fh2, Fh3, Rh1, Rh2, Rh3);
DblOffVec sma1(S1); fdct3d_lowpass(Lh1, sma1);
DblOffVec sma2(S2); fdct3d_lowpass(Lh2, sma2);
DblOffVec sma3(S3); fdct3d_lowpass(Lh3, sma3);
double W1 = L1/nd; double W2 = L2/nd; double W3 = L3/nd;
typedef pair<int,int> intpair; typedef pair<int, intpair> inttriple;
map<inttriple, fftwnd_plan> planmap;
//face 0: x,y,z
for(int h=0; h<nd; h++) { //(y first z second)
for(int g=0; g<nd; g++) {
if(crvowners[wcnt]==mpirank) {
double xs = R1/4-(W1/2)/4; double xe = R1;
double ys = -R2 + (2*g-1)*W2/2; double ye = -R2 + (2*g+3)*W2/2;
double zs = -R3 + (2*h-1)*W3/2; double ze = -R3 + (2*h+3)*W3/2;
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys)); int zn = int(ceil(ze-zs));
double thts, thtm, thte; //y to x
if(g==0) {
thts = atan2(-1.0, 1.0-1.0/nd); thtm = atan2(-1.0+1.0/nd, 1.0); thte = atan2(-1.0+3.0/nd, 1.0);
} else if(g==nd-1) {
thts = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); thte = atan2(-1.0+(2.0*g+3.0)/nd, 1.0);
}
double phis, phim, phie; //z to x
if(h==0) {
phis = atan2(-1.0, 1.0-1.0/nd); phim = atan2(-1.0+1.0/nd, 1.0); phie = atan2(-1.0+3.0/nd, 1.0);
} else if(h==nd-1) {
phis = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); phie = atan2(1.0, 1.0-1.0/nd);
} else {
phis = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); phie = atan2(-1.0+(2.0*h+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; int zh = zn/2; //half
double R21 = R2/R1; double R31 = R3/R1;
CpxNumTns tpdata(xn,yn,zn);
CpxNumTns& Cblk = C.block(s,wcnt);
tpdata = Cblk;
//fft
fftwnd_plan p = NULL;
map<inttriple, fftwnd_plan>::iterator mit = planmap.find( inttriple(xn, intpair(yn,zn)) );
if(mit!=planmap.end()) { p = (*mit).second;
} else {
p = fftw3d_create_plan(zn, yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ inttriple(xn, intpair(yn,zn)) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL); //cerr<<"wedge s"<<endl;
double sqrtprod = sqrt(double(xn*yn*zn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) for(int k=0; k<zn; k++) tpdata(i,j,k) /= sqrtprod;
CpxOffTns wpdata(xn,yn,zn);
fdct3d_fftshift(xn,yn,zn,tpdata,wpdata);
for(int xcur=(int)ceil(xs); xcur<xe; xcur++) {
int yfm = (int)ceil( max(-R2, R21*xcur*tan(thts)) );
int yto = (int)floor( min(R2, R21*xcur*tan(thte)) );
int zfm = (int)ceil( max(-R3, R31*xcur*tan(phis)) );
int zto = (int)floor( min(R3, R31*xcur*tan(phie)) );
for(int ycur=yfm; ycur<=yto; ycur++)
for(int zcur=zfm; zcur<=zto; zcur++) {
int tmpx = xcur%xn; if(tmpx<-xh) tmpx+=xn; if(tmpx>=-xh+xn) tmpx-=xn;
int tmpy = ycur%yn; if(tmpy<-yh) tmpy+=yn; if(tmpy>=-yh+yn) tmpy-=yn;
int tmpz = zcur%zn; if(tmpz<-zh) tmpz+=zn; if(tmpz>=-zh+zn) tmpz-=zn;
double thtcur = atan2(ycur/R2, xcur/R1);
double phicur = atan2(zcur/R3, xcur/R1);
double glbpou; fdct3d_globalpou(thtcur, phicur, M_PI/4-atan2(1.0-1.0/nd, 1.0), glbpou);
double wtht;
if(thtcur<thtm) {
if(g==0) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thts)/(thtm-thts), l, r); wtht = l; }
} else {
if(g==nd-1) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thtm)/(thte-thtm), l, r); wtht = r; }
}
double wphi;
if(phicur<phim) {
if(h==0) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phis)/(phim-phis), l, r); wphi = l; }
} else {
if(h==nd-1) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phim)/(phie-phim), l, r); wphi = r; }
}
double pou = glbpou * wtht * wphi;
wpdata(tmpx, tmpy, tmpz) *= pou;
double ss = sma1(xcur)*sma2(ycur)*sma3(zcur); double bb = big1(xcur)*big2(ycur)*big3(zcur);
int bi,bj,bk; int oi,oj,ok; fdct3d_position_aux(N1,N2,N3,b, xcur,ycur,zcur, bi,bj,bk,oi,oj,ok);
CpxNumTns& Wblk = W.block(bi,bj,bk);
Wblk(oi,oj,ok) += wpdata(tmpx,tmpy,tmpz) * bb * sqrt(1.0-ss*ss);
}
} //xcur
} //if
wcnt++;
}
} //end of face
//face 1. y z x
for(int f=0; f<nd; f++) {
for(int h=0; h<nd; h++) {
if(crvowners[wcnt]==mpirank) {
double ys = R2/4-(W2/2)/4; double ye = R2;
double zs = -R3 + (2*h-1)*W3/2; double ze = -R3 + (2*h+3)*W3/2;
double xs = -R1 + (2*f-1)*W1/2; double xe = -R1 + (2*f+3)*W1/2;
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys)); int zn = int(ceil(ze-zs));
double thts, thtm, thte; //z to y
if(h==0) {
thts = atan2(-1.0, 1.0-1.0/nd); thtm = atan2(-1.0+1.0/nd, 1.0); thte = atan2(-1.0+3.0/nd, 1.0);
} else if(h==nd-1) {
thts = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); thte = atan2(-1.0+(2.0*h+3.0)/nd, 1.0);
}
double phis, phim, phie; //z to x
if(f==0) {
phis = atan2(-1.0, 1.0-1.0/nd); phim = atan2(-1.0+1.0/nd, 1.0); phie = atan2(-1.0+3.0/nd, 1.0);
} else if(f==nd-1) {
phis = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); phie = atan2(1.0, 1.0-1.0/nd);
} else {
phis = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); phie = atan2(-1.0+(2.0*f+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; int zh = zn/2;
double R32 = R3/R2; double R12 = R1/R2;
CpxNumTns tpdata(xn,yn,zn);
CpxNumTns& Cblk = C.block(s,wcnt);
tpdata = Cblk;
//fft
fftwnd_plan p = NULL;
map<inttriple, fftwnd_plan>::iterator mit = planmap.find( inttriple(xn, intpair(yn,zn)) );
if(mit!=planmap.end()) { p = (*mit).second;
} else {
p = fftw3d_create_plan(zn, yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ inttriple(xn, intpair(yn,zn)) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL); //cerr<<"wedge s"<<endl;
double sqrtprod = sqrt(double(xn*yn*zn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) for(int k=0; k<zn; k++) tpdata(i,j,k) /= sqrtprod;
CpxOffTns wpdata(xn,yn,zn);
fdct3d_fftshift(xn,yn,zn,tpdata,wpdata);
for(int ycur=(int)ceil(ys); ycur<ye; ycur++) {
int zfm = (int)ceil( max(-R3, R32*ycur*tan(thts)) );
int zto = (int)floor( min(R3, R32*ycur*tan(thte)) );
int xfm = (int)ceil( max(-R1, R12*ycur*tan(phis)) );
int xto = (int)floor( min(R1, R12*ycur*tan(phie)) );
for(int zcur=zfm; zcur<=zto; zcur++)
for(int xcur=xfm; xcur<=xto; xcur++) {
int tmpx = xcur%xn; if(tmpx<-xh) tmpx+=xn; if(tmpx>=-xh+xn) tmpx-=xn;
int tmpy = ycur%yn; if(tmpy<-yh) tmpy+=yn; if(tmpy>=-yh+yn) tmpy-=yn;
int tmpz = zcur%zn; if(tmpz<-zh) tmpz+=zn; if(tmpz>=-zh+zn) tmpz-=zn;
double thtcur = atan2(zcur/R3, ycur/R2);
double phicur = atan2(xcur/R1, ycur/R2);
double glbpou; fdct3d_globalpou(thtcur, phicur, M_PI/4-atan2(1.0-1.0/nd, 1.0), glbpou); //CHECK
double wtht;
if(thtcur<thtm) {
if(h==0) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thts)/(thtm-thts), l, r); wtht = l; }
} else {
if(h==nd-1) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thtm)/(thte-thtm), l, r); wtht = r; }
}
double wphi;
if(phicur<phim) {
if(f==0) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phis)/(phim-phis), l, r); wphi = l; }
} else {
if(f==nd-1) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phim)/(phie-phim), l, r); wphi = r; }
}
double pou = glbpou * wtht * wphi;
wpdata(tmpx, tmpy, tmpz) *= pou;
double ss = sma1(xcur)*sma2(ycur)*sma3(zcur); double bb = big1(xcur)*big2(ycur)*big3(zcur);
int bi,bj,bk; int oi,oj,ok; fdct3d_position_aux(N1,N2,N3,b, xcur,ycur,zcur, bi,bj,bk,oi,oj,ok);
CpxNumTns& Wblk = W.block(bi,bj,bk);
Wblk(oi,oj,ok) += wpdata(tmpx,tmpy,tmpz) * bb * sqrt(1.0-ss*ss);
}
} //ycur
}//if
wcnt++;
}
}//end of face
//face 2. z x y
for(int g=0; g<nd; g++) {
for(int f=0; f<nd; f++) {
if(crvowners[wcnt]==mpirank) {
double zs = R3/4-(W3/2)/4; double ze = R3;
double xs = -R1 + (2*f-1)*W1/2; double xe = -R1 + (2*f+3)*W1/2;
double ys = -R2 + (2*g-1)*W2/2; double ye = -R2 + (2*g+3)*W2/2;
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys)); int zn = int(ceil(ze-zs));
double thts, thtm, thte; //y to x
if(f==0) {
thts = atan2(-1.0, 1.0-1.0/nd); thtm = atan2(-1.0+1.0/nd, 1.0); thte = atan2(-1.0+3.0/nd, 1.0);
} else if(f==nd-1) {
thts = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); thte = atan2(-1.0+(2.0*f+3.0)/nd, 1.0);
}
double phis, phim, phie; //z to x
if(g==0) {
phis = atan2(-1.0, 1.0-1.0/nd); phim = atan2(-1.0+1.0/nd, 1.0); phie = atan2(-1.0+3.0/nd, 1.0);
} else if(g==nd-1) {
phis = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); phie = atan2(1.0, 1.0-1.0/nd);
} else {
phis = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); phie = atan2(-1.0+(2.0*g+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; int zh = zn/2;
double R13 = double(F1)/double(F3); double R23 = double(F2)/double(F3);
CpxNumTns tpdata(xn,yn,zn);
CpxNumTns& Cblk = C.block(s,wcnt);
tpdata = Cblk;
//fft
fftwnd_plan p = NULL;
map<inttriple, fftwnd_plan>::iterator mit = planmap.find( inttriple(xn, intpair(yn,zn)) );
if(mit!=planmap.end()) { p = (*mit).second;
} else {
p = fftw3d_create_plan(zn, yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ inttriple(xn, intpair(yn,zn)) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL); //cerr<<"wedge s"<<endl;
double sqrtprod = sqrt(double(xn*yn*zn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) for(int k=0; k<zn; k++) tpdata(i,j,k) /= sqrtprod;
CpxOffTns wpdata(xn,yn,zn);
fdct3d_fftshift(xn,yn,zn,tpdata,wpdata);
for(int zcur=(int)ceil(zs); zcur<ze; zcur++) {
int xfm = (int)ceil( max(-R1, R13*zcur*tan(thts)) );
int xto = (int)floor( min(R1, R13*zcur*tan(thte)) );
int yfm = (int)ceil( max(-R2, R23*zcur*tan(phis)) );
int yto = (int)floor( min(R2, R23*zcur*tan(phie)) );
for(int xcur=xfm; xcur<=xto; xcur++)
for(int ycur=yfm; ycur<=yto; ycur++) {
int tmpx = xcur%xn; if(tmpx<-xh) tmpx+=xn; if(tmpx>=-xh+xn) tmpx-=xn;
int tmpy = ycur%yn; if(tmpy<-yh) tmpy+=yn; if(tmpy>=-yh+yn) tmpy-=yn;
int tmpz = zcur%zn; if(tmpz<-zh) tmpz+=zn; if(tmpz>=-zh+zn) tmpz-=zn;
double thtcur = atan2(xcur/R1, zcur/R3);
double phicur = atan2(ycur/R2, zcur/R3);
double glbpou; fdct3d_globalpou(thtcur, phicur, M_PI/4-atan2(1.0-1.0/nd, 1.0), glbpou);
double wtht;
if(thtcur<thtm) {
if(f==0) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thts)/(thtm-thts), l, r); wtht = l; }
} else {
if(f==nd-1) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thtm)/(thte-thtm), l, r); wtht = r; }
}
double wphi;
if(phicur<phim) {
if(g==0) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phis)/(phim-phis), l, r); wphi = l; }
} else {
if(g==nd-1) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phim)/(phie-phim), l, r); wphi = r; }
}
double pou = glbpou * wtht * wphi;
wpdata(tmpx, tmpy, tmpz) *= pou;
double ss = sma1(xcur)*sma2(ycur)*sma3(zcur); double bb = big1(xcur)*big2(ycur)*big3(zcur);
int bi,bj,bk; int oi,oj,ok; fdct3d_position_aux(N1,N2,N3,b, xcur,ycur,zcur, bi,bj,bk,oi,oj,ok);
CpxNumTns& Wblk = W.block(bi,bj,bk);
Wblk(oi,oj,ok) += wpdata(tmpx,tmpy,tmpz) * bb * sqrt(1.0-ss*ss);
}
}//zcur
}//if
wcnt++;
}
}//end of face
//face 3: -x,-y,-z
for(int h=nd-1; h>=0; h--) {
for(int g=nd-1; g>=0; g--) {
if(crvowners[wcnt]==mpirank) {
double xs = -R1; double xe = -R1/4+(W1/2)/4;
double ys = -R2 + (2*g-1)*W2/2; double ye = -R2 + (2*g+3)*W2/2;
double zs = -R3 + (2*h-1)*W3/2; double ze = -R3 + (2*h+3)*W3/2;
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys)); int zn = int(ceil(ze-zs));
double thts, thtm, thte; //y to x
if(g==0) {
thts = atan2(-1.0, 1.0-1.0/nd); thtm = atan2(-1.0+1.0/nd, 1.0); thte = atan2(-1.0+3.0/nd, 1.0);
} else if(g==nd-1) {
thts = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); thte = atan2(-1.0+(2.0*g+3.0)/nd, 1.0);
}
double phis, phim, phie; //z to x
if(h==0) {
phis = atan2(-1.0, 1.0-1.0/nd); phim = atan2(-1.0+1.0/nd, 1.0); phie = atan2(-1.0+3.0/nd, 1.0);
} else if(h==nd-1) {
phis = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); phie = atan2(1.0, 1.0-1.0/nd);
} else {
phis = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); phie = atan2(-1.0+(2.0*h+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; int zh = zn/2;
double R21 = R2/R1; double R31 = R3/R1;
CpxNumTns tpdata(xn,yn,zn);
CpxNumTns& Cblk = C.block(s,wcnt);
tpdata = Cblk;
//fft
fftwnd_plan p = NULL;
map<inttriple, fftwnd_plan>::iterator mit = planmap.find( inttriple(xn, intpair(yn,zn)) );
if(mit!=planmap.end()) { p = (*mit).second;
} else {
p = fftw3d_create_plan(zn, yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ inttriple(xn, intpair(yn,zn)) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL); //cerr<<"wedge s"<<endl;
double sqrtprod = sqrt(double(xn*yn*zn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) for(int k=0; k<zn; k++) tpdata(i,j,k) /= sqrtprod;
CpxOffTns wpdata(xn,yn,zn);
fdct3d_fftshift(xn,yn,zn,tpdata,wpdata);
for(int xcur=(int)ceil(xs); xcur<xe; xcur++) {
int yfm = (int)ceil( max(-R2, R21*(-xcur)*tan(thts)) );
int yto = (int)floor( min(R2, R21*(-xcur)*tan(thte)) );
int zfm = (int)ceil( max(-R3, R31*(-xcur)*tan(phis)) );
int zto = (int)floor( min(R3, R31*(-xcur)*tan(phie)) );
for(int ycur=yfm; ycur<=yto; ycur++)
for(int zcur=zfm; zcur<=zto; zcur++) {
int tmpx = xcur%xn; if(tmpx<-xh) tmpx+=xn; if(tmpx>=-xh+xn) tmpx-=xn;
int tmpy = ycur%yn; if(tmpy<-yh) tmpy+=yn; if(tmpy>=-yh+yn) tmpy-=yn;
int tmpz = zcur%zn; if(tmpz<-zh) tmpz+=zn; if(tmpz>=-zh+zn) tmpz-=zn;
double thtcur = atan2(ycur/R2, (-xcur)/R1);
double phicur = atan2(zcur/R3, (-xcur)/R1);
double glbpou; fdct3d_globalpou(thtcur, phicur, M_PI/4-atan2(1.0-1.0/nd, 1.0), glbpou);
double wtht;
if(thtcur<thtm) {
if(g==0) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thts)/(thtm-thts), l, r); wtht = l; }
} else {
if(g==nd-1) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thtm)/(thte-thtm), l, r); wtht = r; }
}
double wphi;
if(phicur<phim) {
if(h==0) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phis)/(phim-phis), l, r); wphi = l; }
} else {
if(h==nd-1) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phim)/(phie-phim), l, r); wphi = r; }
}
double pou = glbpou * wtht * wphi;
wpdata(tmpx, tmpy, tmpz) *= pou;
double ss = sma1(xcur)*sma2(ycur)*sma3(zcur); double bb = big1(xcur)*big2(ycur)*big3(zcur);
int bi,bj,bk; int oi,oj,ok; fdct3d_position_aux(N1,N2,N3,b, xcur,ycur,zcur, bi,bj,bk,oi,oj,ok);
CpxNumTns& Wblk = W.block(bi,bj,bk);
Wblk(oi,oj,ok) += wpdata(tmpx,tmpy,tmpz) * bb * sqrt(1.0-ss*ss);
}
} //xcur
} //if
wcnt++;
}
} //end of face
//face 4: -y,-z,-x
for(int f=nd-1; f>=0; f--) {
for(int h=nd-1; h>=0; h--) {
if(crvowners[wcnt]==mpirank) {
double ys = -R2; double ye = -R2/4+(W2/2)/4;
double zs = -R3 + (2*h-1)*W3/2; double ze = -R3 + (2*h+3)*W3/2;
double xs = -R1 + (2*f-1)*W1/2; double xe = -R1 + (2*f+3)*W1/2;
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys)); int zn = int(ceil(ze-zs));
double thts, thtm, thte; //z to y
if(h==0) {
thts = atan2(-1.0, 1.0-1.0/nd); thtm = atan2(-1.0+1.0/nd, 1.0); thte = atan2(-1.0+3.0/nd, 1.0);
} else if(h==nd-1) {
thts = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*h-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*h+1.0)/nd, 1.0); thte = atan2(-1.0+(2.0*h+3.0)/nd, 1.0);
}
double phis, phim, phie; //z to x
if(f==0) {
phis = atan2(-1.0, 1.0-1.0/nd); phim = atan2(-1.0+1.0/nd, 1.0); phie = atan2(-1.0+3.0/nd, 1.0);
} else if(f==nd-1) {
phis = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); phie = atan2(1.0, 1.0-1.0/nd);
} else {
phis = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); phie = atan2(-1.0+(2.0*f+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; int zh = zn/2;
double R32 = double(F3)/double(F2); double R12 = double(F1)/double(F2);
CpxNumTns tpdata(xn,yn,zn);
CpxNumTns& Cblk = C.block(s,wcnt);
tpdata = Cblk;
//fft
fftwnd_plan p = NULL;
map<inttriple, fftwnd_plan>::iterator mit = planmap.find( inttriple(xn, intpair(yn,zn)) );
if(mit!=planmap.end()) { p = (*mit).second;
} else {
p = fftw3d_create_plan(zn, yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ inttriple(xn, intpair(yn,zn)) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL); //cerr<<"wedge s"<<endl;
double sqrtprod = sqrt(double(xn*yn*zn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) for(int k=0; k<zn; k++) tpdata(i,j,k) /= sqrtprod;
CpxOffTns wpdata(xn,yn,zn);
fdct3d_fftshift(xn,yn,zn,tpdata,wpdata);
for(int ycur=(int)ceil(ys); ycur<ye; ycur++) {
int zfm = (int)ceil( max(-R3, R32*(-ycur)*tan(thts)) );
int zto = (int)floor( min(R3, R32*(-ycur)*tan(thte)) );
int xfm = (int)ceil( max(-R1, R12*(-ycur)*tan(phis)) );
int xto = (int)floor( min(R1, R12*(-ycur)*tan(phie)) );
for(int zcur=zfm; zcur<=zto; zcur++)
for(int xcur=xfm; xcur<=xto; xcur++) {
int tmpx = xcur%xn; if(tmpx<-xh) tmpx+=xn; if(tmpx>=-xh+xn) tmpx-=xn;
int tmpy = ycur%yn; if(tmpy<-yh) tmpy+=yn; if(tmpy>=-yh+yn) tmpy-=yn;
int tmpz = zcur%zn; if(tmpz<-zh) tmpz+=zn; if(tmpz>=-zh+zn) tmpz-=zn;
double thtcur = atan2(zcur/R3, (-ycur)/R2);
double phicur = atan2(xcur/R1, (-ycur)/R2);
double glbpou; fdct3d_globalpou(thtcur, phicur, M_PI/4-atan2(1.0-1.0/nd, 1.0), glbpou); //CHECK
double wtht;
if(thtcur<thtm) {
if(h==0) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thts)/(thtm-thts), l, r); wtht = l; }
} else {
if(h==nd-1) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thtm)/(thte-thtm), l, r); wtht = r; }
}
double wphi;
if(phicur<phim) {
if(f==0) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phis)/(phim-phis), l, r); wphi = l; }
} else {
if(f==nd-1) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phim)/(phie-phim), l, r); wphi = r; }
}
double pou = glbpou * wtht * wphi;
wpdata(tmpx, tmpy, tmpz) *= pou;
double ss = sma1(xcur)*sma2(ycur)*sma3(zcur); double bb = big1(xcur)*big2(ycur)*big3(zcur);
int bi,bj,bk; int oi,oj,ok; fdct3d_position_aux(N1,N2,N3,b, xcur,ycur,zcur, bi,bj,bk,oi,oj,ok);
CpxNumTns& Wblk = W.block(bi,bj,bk);
Wblk(oi,oj,ok) += wpdata(tmpx,tmpy,tmpz) * bb * sqrt(1.0-ss*ss);
}
} //ycur
}//if
wcnt++;
}
}//end of face
//face 5.-z,-x,-y
for(int g=nd-1; g>=0; g--) {
for(int f=nd-1; f>=0; f--) {
if(crvowners[wcnt]==mpirank) {
double zs = -R3; double ze = -R3/4+(W3/2)/4;
double xs = -R1 + (2*f-1)*W1/2; double xe = -R1 + (2*f+3)*W1/2;
double ys = -R2 + (2*g-1)*W2/2; double ye = -R2 + (2*g+3)*W2/2;
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys)); int zn = int(ceil(ze-zs));
double thts, thtm, thte; //y to x
if(f==0) {
thts = atan2(-1.0, 1.0-1.0/nd); thtm = atan2(-1.0+1.0/nd, 1.0); thte = atan2(-1.0+3.0/nd, 1.0);
} else if(f==nd-1) {
thts = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*f-1.0)/nd, 1.0); thtm = atan2(-1.0+(2.0*f+1.0)/nd, 1.0); thte = atan2(-1.0+(2.0*f+3.0)/nd, 1.0);
}
double phis, phim, phie; //z to x
if(g==0) {
phis = atan2(-1.0, 1.0-1.0/nd); phim = atan2(-1.0+1.0/nd, 1.0); phie = atan2(-1.0+3.0/nd, 1.0);
} else if(g==nd-1) {
phis = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); phie = atan2(1.0, 1.0-1.0/nd);
} else {
phis = atan2(-1.0+(2.0*g-1.0)/nd, 1.0); phim = atan2(-1.0+(2.0*g+1.0)/nd, 1.0); phie = atan2(-1.0+(2.0*g+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; int zh = zn/2;
double R13 = double(F1)/double(F3); double R23 = double(F2)/double(F3);
CpxNumTns tpdata(xn,yn,zn);
CpxNumTns& Cblk = C.block(s,wcnt);
tpdata = Cblk;
//fft
fftwnd_plan p = NULL;
map<inttriple, fftwnd_plan>::iterator mit = planmap.find( inttriple(xn, intpair(yn,zn)) );
if(mit!=planmap.end()) { p = (*mit).second;
} else {
p = fftw3d_create_plan(zn, yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ inttriple(xn, intpair(yn,zn)) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL); //cerr<<"wedge s"<<endl;
double sqrtprod = sqrt(double(xn*yn*zn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) for(int k=0; k<zn; k++) tpdata(i,j,k) /= sqrtprod;
CpxOffTns wpdata(xn,yn,zn);
fdct3d_fftshift(xn,yn,zn,tpdata,wpdata);
for(int zcur=(int)ceil(zs); zcur<ze; zcur++) {
int xfm = (int)ceil( max(-R1, R13*(-zcur)*tan(thts)) );
int xto = (int)floor( min(R1, R13*(-zcur)*tan(thte)) );
int yfm = (int)ceil( max(-R2, R23*(-zcur)*tan(phis)) );
int yto = (int)floor( min(R2, R23*(-zcur)*tan(phie)) );
for(int xcur=xfm; xcur<=xto; xcur++)
for(int ycur=yfm; ycur<=yto; ycur++) {
int tmpx = xcur%xn; if(tmpx<-xh) tmpx+=xn; if(tmpx>=-xh+xn) tmpx-=xn;
int tmpy = ycur%yn; if(tmpy<-yh) tmpy+=yn; if(tmpy>=-yh+yn) tmpy-=yn;
int tmpz = zcur%zn; if(tmpz<-zh) tmpz+=zn; if(tmpz>=-zh+zn) tmpz-=zn;
double thtcur = atan2(xcur/R1, (-zcur)/R3);
double phicur = atan2(ycur/R2, (-zcur)/R3);
double glbpou; fdct3d_globalpou(thtcur, phicur, M_PI/4-atan2(1.0-1.0/nd, 1.0), glbpou);
double wtht;
if(thtcur<thtm) {
if(f==0) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thts)/(thtm-thts), l, r); wtht = l; }
} else {
if(f==nd-1) wtht = 1;
else { double l,r; fdct3d_window( (thtcur-thtm)/(thte-thtm), l, r); wtht = r; }
}
double wphi;
if(phicur<phim) {
if(g==0) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phis)/(phim-phis), l, r); wphi = l; }
} else {
if(g==nd-1) wphi = 1;
else { double l,r; fdct3d_window( (phicur-phim)/(phie-phim), l, r); wphi = r; }
}
double pou = glbpou * wtht * wphi;
wpdata(tmpx, tmpy, tmpz) *= pou;
double ss = sma1(xcur)*sma2(ycur)*sma3(zcur); double bb = big1(xcur)*big2(ycur)*big3(zcur);
int bi,bj,bk; int oi,oj,ok; fdct3d_position_aux(N1,N2,N3,b, xcur,ycur,zcur, bi,bj,bk,oi,oj,ok);
CpxNumTns& Wblk = W.block(bi,bj,bk);
Wblk(oi,oj,ok) += wpdata(tmpx,tmpy,tmpz) * bb * sqrt(1.0-ss*ss);
}
}//zcur
}//if
wcnt++;
}
}//end of face
iA(wcnt==nd*nd*nf);
//remove plans
for(map<inttriple, fftwnd_plan>::iterator mit=planmap.begin(); mit!=planmap.end(); mit++) {
fftwnd_plan p = (*mit).second;
fftwnd_destroy_plan(p);
}
return 0;
}