int mri(
float* img,
float complex* f,
float* mask,
float lambda,
int N1,
int N2)
{
int i, j;
float complex* f0 = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dx = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dy = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dx_new = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dy_new = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dtildex = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dtildey = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* u_fft2 = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* u = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* fftmul = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* Lap = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* diff = (float complex*) calloc(N1*N2,sizeof(float complex));
float sum = 0;
for(i=0; i<N1; i++)
for(j=0; j<N2; j++)
sum += (SQR(crealf(f(i,j))/N1) + SQR(cimagf(f(i,j))/N1));
float normFactor = 1.f/sqrtf(sum);
float scale = sqrtf(N1*N2);
for(i=0; i<N1; i++) {
for(j=0; j<N2; j++) {
f(i, j) = f(i, j)*normFactor;
f0(i, j) = f(i, j);
}
}
Lap(N1-1, N2-1) = 0.f;
Lap(N1-1, 0) = 1.f;
Lap(N1-1, 1) = 0.f;
Lap(0, N2-1) = 1.f;
Lap(0, 0) = -4.f;
Lap(0, 1) = 1.f;
Lap(1, N2-1) = 0.f;
Lap(1, 0) = 1.f;
Lap(1, 1) = 0.f;
float complex *w1;
float complex *w2;
float complex *buff;
dft_init(&w1, &w2, &buff, N1, N2);
dft(Lap, Lap, w1, w2, buff, N1, N2);
for(i=0;i<N1;i++)
for(j=0;j<N2;j++)
fftmul(i,j) = 1.0/((lambda/Gamma1)*mask(i,j) - Lap(i,j) + Gamma2);
int OuterIter,iter;
for(OuterIter= 0; OuterIter<MaxOutIter; OuterIter++) {
for(iter = 0; iter<MaxIter; iter++) {
for(i=0;i<N1;i++)
for(j=0;j<N2;j++)
diff(i,j) = dtildex(i,j)-dtildex(i,(j-1)>=0?(j-1):0) + dtildey(i,j)- dtildey((i-1)>=0?(i-1):0,j) ;
dft(diff, diff, w1, w2, buff, N1, N2);
for(i=0;i<N1;i++)
for(j=0;j<N2;j++)
u_fft2(i,j) = fftmul(i,j)*(f(i,j)*lambda/Gamma1*scale-diff(i,j)+Gamma2*u_fft2(i,j)) ;
idft(u, u_fft2, w1, w2, buff, N1, N2);
for(i=0;i<N1;i++) {
for(j=0;j<N2;j++) {
float tmp;
float Thresh=1.0/Gamma1;
dx(i,j) = u(i,j<(N2-1)?(j+1):j)-u(i,j)+dx(i,j)-dtildex(i,j) ;
dy(i,j) = u(i<(N1-1)?(i+1):i,j)-u(i,j)+dy(i,j)-dtildey(i,j) ;
tmp = sqrtf(SQR(crealf(dx(i,j)))+SQR(cimagf(dx(i,j))) + SQR(crealf(dy(i,j)))+SQR(cimagf(dy(i,j))));
tmp = max(0,tmp-Thresh)/(tmp+(tmp<Thresh));
dx_new(i,j) =dx(i,j)*tmp;
dy_new(i,j) =dy(i,j)*tmp;
dtildex(i,j) = 2*dx_new(i,j) - dx(i,j);
dtildey(i,j) = 2*dy_new(i,j) - dy(i,j);
dx(i,j) = dx_new(i,j);
dy(i,j) = dy_new(i,j);
}
}
}
for(i=0;i<N1;i++) {
for(j=0;j<N2;j++) {
f(i,j) += f0(i,j) - mask(i,j)*u_fft2(i,j)/scale;
}
}
}
for(i=0; i<N1; i++) {
for(j=0; j<N2; j++) {
img(i, j) = sqrt(SQR(crealf(u(i, j))) + SQR(cimagf(u(i, j))));
}
}
free(w1);
free(w2);
free(buff);
return 0;
}
virtual typename iterative_system_root_base<data_type, N__, NSOL__>::solution_matrix
calculate_delta_factor(const typename iterative_system_root_base<data_type, N__, NSOL__>::solution_matrix &x,
const typename iterative_system_root_base<data_type, N__, NSOL__>::solution_matrix &dx) const
{
size_t i;
typename iterative_system_root_base<data_type, N__, NSOL__>::solution_matrix dx_new(dx);
// Limit constrained values to hit constraint, but allow other terms to remain.
for (i=0; i<N__; ++i)
{
data_type xinew(x(i)+dx(i));
// check if min threshold is hit
switch(xmin_cond[i])
{
case(NRC_EXCLUSIVE):
{
if (xinew<xmin[i])
{
dx_new(i)=xmin[i]-x(i);
}
break;
}
case(NRC_INCLUSIVE):
{
if (xinew<=xmin[i])
{
dx_new(i)=(xmin[i]-x(i))*(1-std::numeric_limits<data_type>::epsilon());
}
break;
}
default:
case(NRC_NOT_USED):
{
break;
}
}
// check if max threshold is hit
switch(xmax_cond[i])
{
case(NRC_EXCLUSIVE):
{
if (xinew>xmax[i])
{
dx_new(i)=xmax[i]-x(i);
}
break;
}
case(NRC_INCLUSIVE):
{
if (xinew>=xmax[i])
{
dx_new(i)=(xmax[i]-x(i))*(1-std::numeric_limits<data_type>::epsilon());
}
break;
}
default:
case(NRC_NOT_USED):
{
break;
}
}
}
// Limit the new dx for periodic conditions.
for (i=0; i<N__; ++i)
{
if (xmin_cond[i]==NRC_PERIODIC)
{
data_type xinew(x[i]+dx_new[i]), period(xmax[i]-xmin[i]);
assert(xmax[i]>xmin[i]);
assert(period>0);
if (xinew<xmin[i])
{
xinew-=period*std::floor((xinew-xmin[i])/period);
assert(xinew>=xmin[i]);
assert(xinew<=xmax[i]);
dx_new[i]=xinew-x[i];
}
}
if (xmax_cond[i]==NRC_PERIODIC)
{
data_type xinew(x[i]+dx_new[i]), period(xmax[i]-xmin[i]);
assert(xmax[i]>xmin[i]);
assert(period>0);
if (xinew>xmax[i])
{
xinew-=period*std::ceil((xinew-xmax[i])/period);
dx_new[i]=fmod(xinew, period)-x[i];
assert(xinew>=xmin[i]);
assert(xinew<=xmax[i]);
dx_new[i]=xinew-x[i];
}
}
}
return dx_new;
}
int mri(
float* img,
float complex* f,
float* mask,
float lambda,
int N1,
int N2)
{
int i, j;
float complex* f0 = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dx = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dy = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dx_new = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dy_new = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dtildex = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* dtildey = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* u_fft2 = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* u = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* fftmul = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* Lap = (float complex*) calloc(N1*N2,sizeof(float complex));
float complex* diff = (float complex*) calloc(N1*N2,sizeof(float complex));
float sum = 0;
float scale = sqrtf(N1*N2);
Lap(N1-1, N2-1) = 0.f;
Lap(N1-1, 0) = 1.f;
Lap(N1-1, 1) = 0.f;
Lap(0, N2-1) = 1.f;
Lap(0, 0) = -4.f;
Lap(0, 1) = 1.f;
Lap(1, N2-1) = 0.f;
Lap(1, 0) = 1.f;
Lap(1, 1) = 0.f;
float complex *w1;
float complex *w2;
float complex *buff;
double lambdaGamma1 = lambda/Gamma1;
double lambdaGamma1Scale = lambda/Gamma1*scale;
float Thresh=1.0/Gamma1;
MPI_Datatype mpi_complexf;
MPI_Type_contiguous(2, MPI_FLOAT, &mpi_complexf);
MPI_Type_commit(&mpi_complexf);
int np, rank;
MPI_Comm_size(MPI_COMM_WORLD ,&np);
MPI_Comm_rank(MPI_COMM_WORLD ,&rank);
int chunksize = N1/np;
int start = rank * chunksize;
int cnt[np];
int disp[np];
for (i = 0 ; i < np - 1; i ++) {
cnt[i] = chunksize * N2 ;
disp[i] = chunksize * i * N2;
}
cnt[i] = (chunksize + N1%np) * N2;
disp[i] = chunksize * i * N2;
if (rank == np - 1)
chunksize += N1%np;
int end = start + chunksize;
for(i=start; i<chunksize; i++)
for(j=0; j<N2; j++)
sum += (SQR(crealf(f(i,j))/N1) + SQR(cimagf(f(i,j))/N1));
MPI_Allreduce(&sum, &sum, 1, MPI_FLOAT, MPI_SUM, MPI_COMM_WORLD);
float normFactor = 1.f/sqrtf(sum);
for(i=0; i<N1; i++) {
for(j=0; j<N2; j++) {
f(i, j) = f(i, j)*normFactor;
f0(i, j) = f(i, j);
}
}
dft_init(&w1, &w2, &buff, N1, N2);
dft(Lap, Lap, w1, w2, buff, N1, N2, start, end, cnt, disp, mpi_complexf, rank);
MPI_Status *status;
for(i=start;i<end;i++)
for(j=0;j<N2;j++)
fftmul(i,j) = 1.0/((lambda/Gamma1)*mask(i,j) - Lap(i,j) + Gamma2);
int OuterIter,iter;
for(OuterIter= 0; OuterIter<MaxOutIter; OuterIter++) {
for(iter = 0; iter<MaxIter; iter++) {
for(i=start;i<end;i++)
for(j=0;j<N2;j++)
diff(i,j) = dtildex(i,j)-dtildex(i,(j-1)>=0?(j-1):0) + dtildey(i,j)- dtildey((i-1)>=0?(i-1):0,j) ;
dft(diff, diff, w1, w2, buff, N1, N2, start, end, cnt, disp, mpi_complexf, rank);
for(i=start;i<end;i++) {
for(j=0;j<N2;j++) {
u_fft2(i,j) = fftmul(i,j)*(f(i,j)*lambdaGamma1Scale-diff(i,j)+Gamma2*u_fft2(i,j)) ;
if (iter == MaxIter - 1)
f(i,j) += f0(i,j) - mask(i,j)*u_fft2(i,j)/scale;
}
}
idft(u, u_fft2, w1, w2, buff, N1, N2, start, end, cnt, disp, mpi_complexf, rank);
//MPI_Allgatherv(u + disp[rank], cnt[rank], mpi_complexf, u, cnt, disp, mpi_complexf, MPI_COMM_WORLD);
if (rank == np - 1)
MPI_Send(u + disp[rank], N2, mpi_complexf, rank - 1, 0, MPI_COMM_WORLD);
else if (rank == 0)
MPI_Recv(u + disp[rank] + cnt[rank], N2, mpi_complexf, rank + 1, 0, MPI_COMM_WORLD, status);
else {
MPI_Recv(u + disp[rank] + cnt[rank], N2, mpi_complexf, rank + 1, 0, MPI_COMM_WORLD, status);
MPI_Send(u + disp[rank], N2, mpi_complexf, rank - 1, 0, MPI_COMM_WORLD);
}
for(i=start;i<end;i++) {
for(j=0;j<N2;j++) {
float tmp;
dx(i,j) = u(i,j<(N2-1)?(j+1):j)-u(i,j)+dx(i,j)-dtildex(i,j) ;
dy(i,j) = u(i<(N1-1)?(i+1):i,j)-u(i,j)+dy(i,j)-dtildey(i,j) ;
tmp = sqrtf(SQR(crealf(dx(i,j)))+SQR(cimagf(dx(i,j))) + SQR(crealf(dy(i,j)))+SQR(cimagf(dy(i,j))));
tmp = max(0,tmp-Thresh)/(tmp+(tmp<Thresh));
dx_new(i,j) =dx(i,j)*tmp;
dy_new(i,j) =dy(i,j)*tmp;
dtildex(i,j) = 2*dx_new(i,j) - dx(i,j);
dtildey(i,j) = 2*dy_new(i,j) - dy(i,j);
dx(i,j) = dx_new(i,j);
dy(i,j) = dy_new(i,j);
}
}
//MPI_Allgatherv(dtildey + disp[rank], cnt[rank], mpi_complexf, dtildey, cnt, disp, mpi_complexf, MPI_COMM_WORLD);
if (rank == np - 1)
MPI_Recv(dtildey + disp[rank] - N2, N2, mpi_complexf, rank - 1, 0, MPI_COMM_WORLD, status);
else if (rank == 0)
MPI_Send(dtildey + disp[rank] + cnt[rank] - N2, N2, mpi_complexf, rank + 1, 0, MPI_COMM_WORLD);
else {
MPI_Recv(dtildey + disp[rank] - N2, N2, mpi_complexf, rank - 1, 0, MPI_COMM_WORLD, status);
MPI_Send(dtildey + disp[rank] + cnt[rank] - N2, N2, mpi_complexf, rank + 1, 0, MPI_COMM_WORLD);
}
}
}
for(i=start; i<end; i++) {
for(j=0; j<N2; j++) {
img(i, j) = sqrt(SQR(crealf(u(i, j))) + SQR(cimagf(u(i, j))));
}
}
MPI_Gatherv(img + disp[rank], cnt[rank], MPI_FLOAT, img, cnt, disp, MPI_FLOAT, 0, MPI_COMM_WORLD);
free(w1);
free(w2);
free(buff);
MPI_Finalize();
if (rank > 0)
exit(0);
return 0;
}