optiml-transport 0.0.1 (latest)

type mat = (float, Bigarray.float64_elt, Bigarray.c_layout) Bigarray.Array2.t

type vec = (float, Bigarray.float64_elt, Bigarray.c_layout) Bigarray.Array1.t

Low-level interface to the optimal transportation solver.

type result_internal =

| Transport_Infeasible
| Transport_Optimal
| Transport_Unbounded
| Transport_Max_iter_reached

type fref = {

mutable field : float;

}

Only ever useful if you plan to use the stubs directly. This is used to store the cost of the transportation plan produced by kanto_solve.

val kanto_solve : 
  vec ->
  vec ->
  mat ->
  mat ->
  vec ->
  vec ->
  fref ->
  int ->
  result_internal

kanto_solve x y D G u v cost num_iter computes an optimal transportation plan from x to y according to the cost matrix D. The optimal plan is stored in the matrix G, and the dual optimal variables (the "prices") are stored in u and v. Note that D need not satisfy the triangle inequality.

The cost associated to G is stored in the reference cell cost. num_iter specifies the maximum number of iterations of the algorithm. kanto_solve also returns the state of the solver at the end of the process as a value of type result_internal.

NB: kanto_solve does not allocate memory. All matrices and vectors must be preallocated by the user.

High-level interface to the optimal transportation solver.

type result =

| Infeasible
| Unbounded
| Optimal of {
1. cost : float;
2. coupling : mat;
3. u : vec;
4. v : vec;
}
| Max_iter_reached of {
1. cost : float;
2. coupling : mat;
3. u : vec;
4. v : vec;
}

The result type encodes the outcome of solving an instance of the optimal mass transportation problem.

val kantorovich : x:vec -> y:vec -> d:mat -> num_iter:int -> result

kantorovich x y d num_iter is a wrapper around kanto_solve which will allocate all intermediate structures for you. If you plan to perform a lot of calls to the solver for fixed sizes of x and y you might want to consider using the low-level interface, to avoid reallocating those intermediate structures.

package optiml-transport