// "Project" onto cubes that obey uniqueness constraints
cube RC4(const cube& Q){
int n = Q.n_rows;
cube P(n,n,n,fill::zeros);
uvec seq = linspace<uvec>(0,n-1,n), ix(n), order(n);
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++){
ix = seq*n*n + j*n + i;
order = sort_index(Q.elem(ix), "descend");
P(i,j,order(0)) = 1;
}
return 2*P - Q;
}
// "Project" onto cubes that obey column constrains
cube RC2(const cube& Q){
int n = Q.n_rows;
cube P(n,n,n,fill::zeros);
uvec seq = linspace<uvec>(0,n-1,n), ix(n), order(n);
for(int j = 0; j < n; j++)
for(int k = 0; k < n; k++){
ix = k*n*n + j*n + seq;
order = sort_index(Q.elem(ix), "descend");
P(order(0),j,k) = 1;
}
return 2*P - Q;
}
// "Project" onto cubes that obey row constrains
cube RC1(const cube& Q){
int n = Q.n_rows;
cube P(n,n,n,fill::zeros);
uvec seq = linspace<uvec>(0,n-1,n), ix(n), order(n);
for(int i = 0; i < n; i++)
for(int k = 0; k < n; k++){
ix = k*n*n + n*seq + i;
order = sort_index(Q.elem(ix), "descend");
P(i,order(0),k) = 1;
}
return 2*P - Q;
}
// "Project" onto cubes that obey block constaints
cube RC3(const cube& Q){
int n = Q.n_rows;
cube P(n,n,n,fill::zeros);
// a handy tool for indexing later on
int blockSize = sqrt(n);
uvec mask(blockSize*blockSize);
uvec ix(blockSize*blockSize), order;
for(int i = 0; i < blockSize; i++)
for(int j = 0; j < blockSize; j++)
mask(i+blockSize*j) = i + n*j;
// now do the projection
for(int k = 0; k < n; k++)
for(int i = 0; i < blockSize; i++)
for(int j = 0; j < blockSize; j++){
ix = mask + (i*blockSize + j*n*blockSize);
order = sort_index(Q.elem(ix+k*n*n), "descend");
P(ix(order(0)) + k*n*n) = 1;
}
return 2*P - Q;
}