Sorry, but this is completely, absolutely impossible.
The singular vectors are orthogonal to each other. Suppose that you actually have ONE vector in the desired orthant, with all positive elements?
The second vector CANNOT be orthogonal to the first if is it also entirely positive.
You cannot have what is mathematically impossible.
At most, you might have ONE vector with that property. The SVD has no option, no ability to control where even one vector lies, since the vectors are completely based on the matrix itself (unless you have repeated singular values.) There is no such thing as a constrained SVD.
