//---------------------
int fdct_wrapping_invwavelet(vector<CpxNumMat>& csc, CpxOffMat& Xhgh)
{
assert(csc.size()==1);
CpxNumMat& C = csc[0];
int N1 = C.m(); int N2 = C.n();
CpxNumMat T(C); //CpxNumMat T(N1, N2); fdct_wrapping_ifftshift(N1, N2, F1, F2, C, T);
fftwnd_plan p = fftw2d_create_plan(N2, N1, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
fftwnd_one(p, (fftw_complex*)T.data(), NULL);
fftwnd_destroy_plan(p);
double sqrtprod = sqrt(double(N1*N2));
for(int j=0; j<N2; j++)
for(int i=0; i<N1; i++)
T(i,j) /= sqrtprod;
Xhgh.resize(N1, N2);
fdct_wrapping_fftshift(T, Xhgh);
return 0;
}
//-------------------------------------------------------------------
int fdct_wrapping(int N1, int N2, int nbscales, int nbangles_coarse, int allcurvelets, CpxNumMat& x, vector< vector<CpxNumMat> >& c)
{
//---------------------------------------------
assert(N1==x.m() && N2==x.n());
int F1 = N1/2; int F2 = N2/2;
// ifft original data
CpxNumMat T(x);
fftwnd_plan p = fftw2d_create_plan(N2, N1, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
fftwnd_one(p, (fftw_complex*)T.data(), NULL);
fftwnd_destroy_plan(p);
double sqrtprod = sqrt(double(N1*N2));
for(int j=0; j<N2; j++) for(int i=0; i<N1; i++) T(i,j) /= sqrtprod;
CpxOffMat O(N1, N2);
fdct_wrapping_fftshift(T, O);
//-----------------------------------------------------------------------------
vector<CpxOffMat> Xhghs;
Xhghs.resize(nbscales);
CpxOffMat X;
//unfold or not
if(allcurvelets==1) {
//--------------------------
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range
int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
IntOffVec t1(XS1);
for(int i=-XF1; i<-XF1+XS1; i++) if( i<-N1/2) t1(i) = i+int(N1); else if(i>(N1-1)/2) t1(i) = i-int(N1); else t1(i) = i;
IntOffVec t2(XS2);
for(int i=-XF2; i<-XF2+XS2; i++) if( i<-N2/2) t2(i) = i+int(N2); else if(i>(N2-1)/2) t2(i) = i-int(N2); else t2(i) = i;
X.resize(XS1, XS2);
for(int j=-XF2; j<-XF2+XS2; j++)
for(int i=-XF1; i<-XF1+XS1; i++)
X(i,j) = O(t1(i), t2(j));
DblOffMat lowpass(XS1,XS2);
fdct_wrapping_lowpasscompute(XL1, XL2, lowpass); //compute the low pass filter
for(int j=-XF2; j<-XF2+XS2; j++)
for(int i=-XF1; i<-XF1+XS1; i++)
X(i,j) *= lowpass(i,j);
} else {
//--------------------------
X = O;
}
//separate
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range
for(int sc=nbscales-1; sc>0; sc--) {
double XL1n = XL1/2; double XL2n = XL2/2;
int XS1n, XS2n; int XF1n, XF2n; double XR1n, XR2n;
fdct_wrapping_rangecompute(XL1n, XL2n, XS1n, XS2n, XF1n, XF2n, XR1n, XR2n);
//computer filter
DblOffMat lowpass(XS1n, XS2n);
fdct_wrapping_lowpasscompute(XL1n, XL2n, lowpass);
DblOffMat hghpass(XS1n, XS2n);
for(int j=-XF2n; j<-XF2n+XS2n; j++)
for(int i=-XF1n; i<-XF1n+XS1n; i++)
hghpass(i,j) = sqrt(1-lowpass(i,j)*lowpass(i,j));
//separate
CpxOffMat Xhgh(X);
for(int j=-XF2n; j<-XF2n+XS2n; j++)
for(int i=-XF1n; i<-XF1n+XS1n; i++)
Xhgh(i,j) *= hghpass(i,j);
CpxOffMat Xlow(XS1n, XS2n);
for(int j=-XF2n; j<-XF2n+XS2n; j++)
for(int i=-XF1n; i<-XF1n+XS1n; i++)
Xlow(i,j) = X(i,j) * lowpass(i,j);
//store and prepare for next level
Xhghs[sc] = Xhgh;
X = Xlow;
XL1 = XL1/2; XL2 = XL2/2;
}
Xhghs[0] = X;
//-----------------------------------------------------------------------------
vector<int> nbangles(nbscales);
if(allcurvelets==1) {
//nbangles
nbangles[0] = 1;
for(int sc=1; sc<nbscales; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) );
//c
c.resize(nbscales);
for(int sc=0; sc<nbscales; sc++) c[sc].resize( nbangles[sc] );
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range
for(int sc=nbscales-1; sc>0; sc--) {
fdct_wrapping_sepangle(XL1, XL2, nbangles[sc], Xhghs[sc], c[sc]);
XL1 /= 2; XL2 /= 2;
}
fdct_wrapping_wavelet(Xhghs[0], c[0]);
} else {
//nbangles
nbangles[0] = 1;
for(int sc=1; sc<nbscales-1; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) );
nbangles[nbscales-1] = 1;
//c
c.resize(nbscales);
for(int sc=0; sc<nbscales; sc++) c[sc].resize( nbangles[sc] );
fdct_wrapping_wavelet(Xhghs[nbscales-1], c[nbscales-1]);
double XL1 = 2.0*N1/3.0; double XL2 = 2.0*N2/3.0; //range
for(int sc=nbscales-2; sc>0; sc--) {
fdct_wrapping_sepangle(XL1, XL2, nbangles[sc], Xhghs[sc], c[sc]);
XL1 /= 2; XL2 /= 2;
}
fdct_wrapping_wavelet(Xhghs[0], c[0]);
}
return 0;
}
//-------------------------------------------------------------------------------
int ifdct_wrapping(int N1, int N2, int nbscales, int nbangles_coarse, int allcurvelets, vector< vector<CpxNumMat> >& c, CpxNumMat& x)
{
assert(nbscales==c.size() && nbangles_coarse==c[1].size());
//int F1 = N1/2; int F2 = N2/2;
//-------------------------------------------angles to Xhgh
vector<int> nbangles(nbscales);
vector<CpxOffMat> Xhghs; Xhghs.resize(nbscales);
if(allcurvelets==1) {
//----
nbangles[0] = 1;
for(int sc=1; sc<nbscales; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) );
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0;
for(int sc=nbscales-1; sc>0; sc--) {
fdct_wrapping_invsepangle(XL1, XL2, nbangles[sc], c[sc], Xhghs[sc]);
XL1 /= 2; XL2 /= 2;
}
fdct_wrapping_invwavelet(c[0], Xhghs[0]);
} else {
//----
nbangles[0] = 1;
for(int sc=1; sc<nbscales-1; sc++) nbangles[sc] = nbangles_coarse * pow2( int(ceil(double(sc-1)/2)) );
nbangles[nbscales-1] = 1;
fdct_wrapping_invwavelet(c[nbscales-1], Xhghs[nbscales-1]);
double XL1 = 2.0*N1/3.0; double XL2 = 2.0*N2/3.0;
for(int sc=nbscales-2; sc>0; sc--) {
fdct_wrapping_invsepangle(XL1, XL2, nbangles[sc], c[sc], Xhghs[sc]);
XL1 /= 2; XL2 /= 2;
}
fdct_wrapping_invwavelet(c[0], Xhghs[0]);
}
//-------------------------------------------xhghs to O
//combine
CpxOffMat X;
if(allcurvelets==1) {
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0; //range
int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
X.resize(XS1, XS2);
} else {
X.resize(N1, N2);
}
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0;
int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
for(int sc=nbscales-1; sc>0; sc--) {
double XL1n = XL1/2; double XL2n = XL2/2;
int XS1n, XS2n; int XF1n, XF2n; double XR1n, XR2n;
fdct_wrapping_rangecompute(XL1n, XL2n, XS1n, XS2n, XF1n, XF2n, XR1n, XR2n);
DblOffMat lowpass(XS1n, XS2n);
fdct_wrapping_lowpasscompute(XL1n, XL2n, lowpass);
DblOffMat hghpass(XS1n, XS2n);
for(int j=-XF2n; j<-XF2n+XS2n; j++)
for(int i=-XF1n; i<-XF1n+XS1n; i++)
hghpass(i,j) = sqrt(1-lowpass(i,j)*lowpass(i,j));
for(int j=-XF2n; j<-XF2n+XS2n; j++)
for(int i=-XF1n; i<-XF1n+XS1n; i++)
Xhghs[sc](i,j) *= hghpass(i,j);
for(int j=-XF2n; j<-XF2n+XS2n; j++)
for(int i=-XF1n; i<-XF1n+XS1n; i++)
Xhghs[sc-1](i,j) *= lowpass(i,j);
CpxOffMat& G = Xhghs[sc];
for(int j=G.t(); j<G.t()+G.n(); j++)
for(int i=G.s(); i<G.s()+G.m(); i++)
X(i,j) += G(i,j);
XL1 = XL1/2; XL2 = XL2/2;
fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
}
for(int j=-XF2; j<-XF2+XS2; j++)
for(int i=-XF1; i<-XF1+XS1; i++)
X(i,j) += Xhghs[0](i,j);
// fold
CpxOffMat O(N1, N2);
if(allcurvelets==1) {
double XL1 = 4.0*N1/3.0; double XL2 = 4.0*N2/3.0;
int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
//times pou;
DblOffMat lowpass(XS1,XS2);
fdct_wrapping_lowpasscompute(XL1, XL2, lowpass);
for(int j=-XF2; j<-XF2+XS2; j++)
for(int i=-XF1; i<-XF1+XS1; i++)
X(i,j) *= lowpass(i,j);
IntOffVec t1(XS1);
for(int i=-XF1; i<-XF1+XS1; i++) if( i<-N1/2) t1(i) = i+int(N1); else if(i>(N1-1)/2) t1(i) = i-int(N1); else t1(i) = i;
IntOffVec t2(XS2);
for(int i=-XF2; i<-XF2+XS2; i++) if( i<-N2/2) t2(i) = i+int(N2); else if(i>(N2-1)/2) t2(i) = i-int(N2); else t2(i) = i;
for(int j=-XF2; j<-XF2+XS2; j++)
for(int i=-XF1; i<-XF1+XS1; i++)
O(t1(i), t2(j)) += X(i,j);
} else {
O = X;
}
//------------------------------------------------------------
CpxNumMat T(N1,N2);
fdct_wrapping_ifftshift(O, T);
fftwnd_plan p = fftw2d_create_plan(N2, N1, FFTW_BACKWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
fftwnd_one(p, (fftw_complex*)T.data(), NULL);
fftwnd_destroy_plan(p);
double sqrtprod = sqrt(double(N1*N2)); //scale
for(int i=0; i<N1; i++) for(int j=0; j<N2; j++) T(i,j) /= sqrtprod;
x = T;
//x.resize(N1, N2);
//fdct_wrapping_fftshift(T, x);
return 0;
}
//---------------------
int fdct_wrapping_invsepangle(double XL1, double XL2, int nbangle, vector<CpxNumMat>& csc, CpxOffMat& Xhgh)
{
typedef pair<int,int> intpair;
map<intpair, fftwnd_plan> planmap;
int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
Xhgh.resize(XS1, XS2);
int nbquadrants = 4;
int nd = nbangle / 4;
int wcnt = 0;
//backup
CpxOffMat Xhghb(Xhgh);
double XL1b = XL1; double XL2b = XL2;
int qvec[] = {2,1,0,3};
for(int qi=0; qi<nbquadrants; qi++) {
int q = qvec[qi];
//ROTATE data to its right position
fdct_wrapping_rotate_forward(q, XL1b, XL2b, XL1, XL2); XL1 = abs(XL1); XL2 = abs(XL2);
fdct_wrapping_rotate_forward(q, Xhghb, Xhgh);
//figure out XS, XF, XR
double XW1 = XL1/nd; double XW2 = XL2/nd;
int XS1, XS2; int XF1, XF2; double XR1, XR2; fdct_wrapping_rangecompute(XL1, XL2, XS1, XS2, XF1, XF2, XR1, XR2);
for(int w=nd-1; w>=0; w--) {
double xs = XR1/4 - (XW1/2)/4;
double xe = XR1;
double ys = -XR2 + (w-0.5)*XW2;
double ye = -XR2 + (w+1.5)*XW2; //x range
int xn = int(ceil(xe-xs)); int yn = int(ceil(ye-ys));
//MAKE THEM ODD
if(xn%2==0) xn++; if(yn%2==0) yn++;
int xf = int(ceil(xs)); //int yf = int(ceil(ys));
//theta
double thts, thtm, thte; //y direction
if(w==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(w==nd-1) {
thts = atan2(-1.0+(2.0*w-1.0)/nd, 1.0);
thtm = atan2(-1.0+(2.0*w+1.0)/nd, 1.0);
thte = atan2(1.0, 1.0-1.0/nd);
} else {
thts = atan2(-1.0+(2.0*w-1.0)/nd, 1.0);
thtm = atan2(-1.0+(2.0*w+1.0)/nd, 1.0);
thte = atan2(-1.0+(2.0*w+3.0)/nd, 1.0);
}
int xh = xn/2; int yh = yn/2; //half length
CpxOffMat wpdata(xn,yn);
{
//load
int xn = csc[wcnt].m(); int yn = csc[wcnt].n();
CpxNumMat tpdata(csc[wcnt]);
//fft
fftwnd_plan p = NULL;
map<intpair, fftwnd_plan>::iterator mit=planmap.find( intpair(xn,yn) );
if(mit!=planmap.end()) {
p = (*mit).second;
} else {
p = fftw2d_create_plan(yn, xn, FFTW_FORWARD, FFTW_ESTIMATE | FFTW_IN_PLACE);
planmap[ intpair(xn, yn) ] = p;
}
fftwnd_one(p, (fftw_complex*)tpdata.data(), NULL);
double sqrtprod = sqrt(double(xn*yn));
for(int i=0; i<xn; i++) for(int j=0; j<yn; j++) tpdata(i,j) /= sqrtprod;
//fftshift
CpxOffMat rpdata;
fdct_wrapping_fftshift(tpdata,rpdata);
//rotate forward
fdct_wrapping_rotate_forward(q, rpdata, wpdata);
}
double R21 = XR2/XR1; //ratio
for(int xcur=xf; xcur<xe; xcur++) { //for each layer
int yfm = (int)ceil( max(-XR2, R21*xcur*tan(thts)) );
int yto = (int)floor( min(XR2, R21*xcur*tan(thte)) );
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;
//partition of unity
double thtcur = atan2(ycur/XR2, xcur/XR1);
double wtht;
if(thtcur<thtm) {
double l,r; fdct_wrapping_window((thtcur-thts)/(thtm-thts), l, r);
wtht = l;
} else {
double l,r; fdct_wrapping_window((thtcur-thtm)/(thte-thtm), l, r);
wtht = r;
}
double pou = wtht;
wpdata(tmpx,tmpy) *= pou;
Xhgh(xcur,ycur) += wpdata(tmpx,tmpy);
}
}
wcnt++;
}//w loop
fdct_wrapping_rotate_backward(q, Xhgh, Xhghb);
} //q loop
Xhgh = Xhghb;
XL1 = XL1b; XL2 = XL2b;
assert(wcnt==nbangle);
for(map<intpair, fftwnd_plan>::iterator mit=planmap.begin(); mit!=planmap.end(); mit++) {
fftwnd_plan p = (*mit).second;
fftwnd_destroy_plan(p);
}
return 0;
}