DISTANCE_TO_POSITION is a FORTRAN90 program which estimates the positions of cities given a city-to-city distance table.
In 2D, the problem is singular. In particular, the position of one city is completely arbitrary, and one component of a second city is completely arbitrary (and a third city's position can be "flipped" about the line connecting cities one and two). To remove some of this singularity, the program assigns city #1 the position (0,0) and city #2 is given a 0 Y coordinate.
In N-dimensional space, a similar set of constraints must be placed on the first N cities, or the least squares solver is likely to fail. (That is, we specify all N components of the first city to be 0, N-1 components of the second one, and so on, up to the N-th city which has a single 0 component).
The computations carried out by this program assume that the cities lie on a plane. If the distance data is for international cities, the effect of spherical geometry may make the planar approximation very bad.
Once the nonlinear least squares problem is set up, the routine UNCMIN from the NMS software package is called to compute a solution.
distance_to_position distance.txtwhere
DISTANCE_TO_POSITION is available in a FORTRAN90 version and a MATLAB version.
CITIES, a dataset directory which contains sets of information about cities and the distances between them;
CITIES, a FORTRAN90 library which handles various problems associated with a set of "cities" on a map.
DISTANCE_TO_POSITION_SPHERE, a MATLAB program which estimates the positions of cities on a sphere (such as the earth) based on a city-to-city distance table.
LAU_NP, a FORTRAN90 library which implements heuristic algorithms for various NP-hard combinatorial problems.
NMS, a FORTRAN90 library which includes a wide variety of numerical software.
PARTIAL_DIGEST, a FORTRAN90 library which solves the partial digest problem.
You can go up one level to the FORTRAN90 source codes.