function [out] = conv2olam(a,b,mode,siz1,siz2)
%CONV2OLAM Overlap-add method of CONV2 using FFT2.
% Y = CONV2OLAM(A,B) performs the 2-D convolution of matrices
% A and B using the overlap/add method and using internal parameters (FFT2
% size and block length) which guarantee efficient execution.
% If [ma,na] = size(A) and [mb,nb] = size(B), then size(Y) = [ma+mb-1,na+nb-1].
%
%
% Y = CONV2OLAM(A,B,mode,siz1,siz2) allows you to have some control over the
% internal parameters by using a zero padding. If mode is equal to:
% - 0 is the default value, if not specified. This value for
% mode uses overlap/add method. Ex. conv2olam(a,b,0) is equivalent
% to perform conv2olam(a,b).
% - 1 the dimensions of input matrices are zero padded to their nextpow2
% values (type 'help nextpow2' on Matlab prompt) to perform
% FFT2 and IFFT2. No overlap is performed. Ex. conv2olam(a,b,1)
% - 2 the dimensions of input matrices are not zero padded to perform
% these FFT-based operations. No overlap is performed. Ex. conv2olam(a,b,2)
% - 3 the dimensions of matrices are zero padded to fixed values
% which must be specified to perform overlapping.
% Ex. conv2olam(a,b,3,512,512) uses 512 X 512 matrices
% to perform overlap/add method.
%
%
% See also CONV2, FFTFILT, FFT2, IFFT2, FILTFILT.
%
%
% Please contribute if you find this software useful.
% Report bugs to luigi.rosa@tiscali.it
%
%*****************************************************************
% Luigi Rosa
% Via Centrale 27
% 67042 Civita di Bagno
% L'Aquila --- ITALY
% email luigi.rosa@tiscali.it
% mobile +39 340 3463208
% http://utenti.lycos.it/matlab
%*****************************************************************
%
%
[ax,ay]=size(a);
[bx,by]=size(b);
dimx=ax+bx-1;
dimy=ay+by-1;
if (nargin<3)||(mode==0)
% figure out which nfftx, nffty, Lx and Ly to use
%-------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
fftflops=zeros(13);
fftflops(1:10,:)=[14 58 172 440 1038 2358 5264 11644 25594 55946 121644 263136 566438;...
58 178 470 1134 2586 5738 12574 27382 59378 128274 276054 591806 1263946;...
172 470 1170 2730 6098 13330 28858 62186 133602 286242 611498 1302394 2765458;...
440 1134 2730 6242 13762 29794 63986 136914 292290 622658 1323346 2805490 5932322;...
1038 2586 6098 13762 30082 64706 138210 294306 625538 1327234 2810530 5938658 12520002;...
2358 5738 13330 29794 64706 138498 294594 624962 1323778 2799874 5911874 12458946 26203266;...
5264 12574 28858 63986 138210 294594 624386 1320322 2788354 5881346 12386946 26044290 54659330;...
11644 27382 62186 136914 294306 624962 1320322 2783746 5862914 12335106 25918722 54378242 113897986;...
25594 59378 133602 292290 625538 1323778 2788354 5862914 12316674 25851906 54200834 113483266 237249538;...
55946 128274 286242 622658 1327234 2799874 5881346 12335106 25851906 54140930 113275906 236715010 493996034];
fftflops(11:13,:)=1.0e+009 *[0.00012164400000 0.00027605400000 0.00061149800000 0.00132334600000 0.00281053000000 0.00591187400000 0.01238694600000 0.02591872200000 0.05420083400000 0.11327590600000 0.23653990600000 0.49340621000000 1.02794445000000;...
0.00026313600000 0.00059180600000 0.00130239400000 0.00280549000000 0.00593865800000 0.01245894600000 0.02604429000000 0.05437824200000 0.11348326600000 0.23671501000000 0.49340621000000 1.02746521800000 2.13719449800000;...
0.00056643800000 0.00126394600000 0.00276545800000 0.00593232200000 0.01252000200000 0.02620326600000 0.05465933000000 0.11389798600000 0.23724953800000 0.49399603400000 1.02794445000000 2.13719449800000 4.43891712200000];
%.....................................
nx=1:13;
ny=1:13;
validsetx=find(2.^(nx-1)>bx-1);
validsety=find(2.^(ny-1)>by-1);
nx=nx(validsetx);
ny=ny(validsety);
Lx=2.^(nx-1)-bx+1;
Ly=2.^(ny-1)-by+1;
sizex=length(nx);
sizey=length(ny);
matrice=zeros(sizex,sizey);
for ii=1:sizex
for jj=1:sizey
matrice(ii,jj)=ceil(dimx/Lx(ii))*ceil(dimy/Ly(jj))*fftflops(nx(ii),ny(jj));
end
end
[massimo_vettore,posizione_vettore]=min(matrice);
[massimo,posizione]=min(massimo_vettore);
y_max=posizione;
x_max=posizione_vettore(posizione);
massimo;
%.......................................
nx2=1:13;
ny2=1:13;
validsetx2=find(2.^(nx2-1)>ax-1);
validsety2=find(2.^(ny2-1)>ay-1);
nx2=nx2(validsetx2);
ny2=ny2(validsety2);
Lx2=2.^(nx2-1)-ax+1;
Ly2=2.^(ny2-1)-ay+1;
sizex2=length(nx2);
sizey2=length(ny2);
matrice2=zeros(sizex2,sizey2);
for ii=1:sizex2
for jj=1:sizey2
matrice2(ii,jj)=ceil(dimx/Lx2(ii))*ceil(dimy/Ly2(jj))*fftflops(nx2(ii),ny2(jj));
end
end
[massimo_vettore2,posizione_vettore2]=min(matrice2);
[massimo2,posizione2]=min(massimo_vettore2);
y_max2=posizione2;
x_max2=posizione_vettore2(posizione2);
massimo2;
%.......................................
if massimo<massimo2
nfftx=2^(nx(x_max)-1);
nffty=2^(ny(y_max)-1);
Lx=nfftx-bx+1;
Ly=nffty-by+1;
%-------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
B=fft2(b,nfftx,nffty);
out=zeros(dimx,dimy);
a2=a;
a2(dimx,dimy)=0;
xstart=1;
while xstart <= dimx
xend=min(xstart+Lx-1,dimx);
ystart=1;
while ystart <= dimy
yend=min(ystart+Ly-1,dimy);
%---------------------
X=fft2(a2(xstart:xend,ystart:yend),nfftx,nffty);
Y=ifft2(X.*B);
endx=min(dimx,xstart+nfftx-1);
endy=min(dimy,ystart+nffty-1);
out(xstart:endx,ystart:endy)=out(xstart:endx,ystart:endy)+Y(1:(endx-xstart+1),1:(endy-ystart+1));
ystart=ystart+Ly;
%---------------------
end
xstart=xstart+Lx;
end
if ~(any(any(imag(a)))||any(any(imag(b))))
out=real(out);
end
return;
else
nfftx=2^(nx2(x_max2)-1);
nffty=2^(ny2(y_max2)-1);
Lx2=nfftx-ax+1;
Ly2=nffty-ay+1;
%-------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
A=fft2(a,nfftx,nffty);
out=zeros(dimx,dimy);
b2=b;
b2(dimx,dimy)=0;
xstart=1;
while xstart <= dimx
xend=min(xstart+Lx2-1,dimx);
ystart=1;
while ystart <= dimy
yend=min(ystart+Ly2-1,dimy);
%---------------------
X=fft2(b2(xstart:xend,ystart:yend),nfftx,nffty);
Y=ifft2(X.*A);
endx=min(dimx,xstart+nfftx-1);
endy=min(dimy,ystart+nffty-1);
out(xstart:endx,ystart:endy)=out(xstart:endx,ystart:endy)+Y(1:(endx-xstart+1),1:(endy-ystart+1));
ystart=ystart+Ly2;
%---------------------
end
xstart=xstart+Lx2;
end
if ~(any(any(imag(a)))||any(any(imag(b))))
out=real(out);
end
return;
end
else
% mode = 1 ----> nextpow2 for both dimensions
if mode==1
dx=2^(nextpow2(dimx));
dy=2^(nextpow2(dimy));
out=ifft2(fft2(a,dx,dy).*fft2(b,dx,dy));
if ~(any(any(imag(a)))||any(any(imag(b))))
out=real(out);
end
out=out(1:dimx,1:dimy);
return
end
% mode = 2 ----> the same dimensions
if mode==2
out=ifft2(fft2(a,dimx,dimy).*fft2(b,dimx,dimy));
if ~(any(any(imag(a)))||any(any(imag(b))))
out=real(out);
end
return
end
% mode = 3 ----> OverLap Add method with given dimensions siz1 and siz2
if mode==3
nfftx=siz1;
nffty=siz2;
Lx=nfftx-bx+1;
Ly=nffty-by+1;
B=fft2(b,nfftx,nffty);
out=zeros(dimx,dimy);
a2=a;
a2(dimx,dimy)=0;
xstart=1;
while xstart <= dimx
xend=min(xstart+Lx-1,dimx);
ystart=1;
while ystart <= dimy
yend=min(ystart+Ly-1,dimy);
%---------------------
X=fft2(a2(xstart:xend,ystart:yend),nfftx,nffty);
Y=ifft2(X.*B);
endx=min(dimx,xstart+nfftx-1);
endy=min(dimy,ystart+nffty-1);
out(xstart:endx,ystart:endy)=out(xstart:endx,ystart:endy)+Y(1:(endx-xstart+1),1:(endy-ystart+1));
ystart=ystart+Ly;
%---------------------
end
xstart=xstart+Lx;
end
if ~(any(any(imag(a)))||any(any(imag(b))))
out=real(out);
end
return;
end
end