DEQ
"Centroids" of 2D points
Computes the centroid and geometic median of random 2D points
2025.Sep.22 08:12:43
Points Number of points in region.
Criterion   Minimum cost or distance for exploration.
Width, height Regin width and height.
Power     Power to raise distance to.
Trials (N), seed    → Monte Carlo trials, seed.
Method           Method of multivariable minimization.
Sim. y-, x-axis bounds Simulation: axes bound in plot.
Plot points Simulation: n. of plot points.
Show values Show graph coordinates.

Computes: the centroid (simple average); and the geometric median, by minimum total distance. In Fig. 1, with 10 random points, the two symbols show the two solutions, in a rectangular region.

Minimization methods: (1) NM=Nelder-Mead, (2) Pow=Powell, (3) CG, (4) BFGS, (5) LB=L-BFGS-B, (6) TNC, (7) CL=COBYLA, (8) CQ=COBYQA, (9) SL=SLSQP.

Using numerical minimization (instead of the classical Weiszfeld algorithm) permits to determine the minimum sum of distances raised to several given powers.

Shows the graphical results: (a) region with random points, and centroid as larger circle and g. median as smaller circle; and (b) random behavior of simulated variable.
ODEs Fig. 1
References: Plate: Centroids

• Optimization (scipy.optimize), The SciPy community. • 'minimize' (methods)

• Vászonyi, Andrew (Weiszfeld)

• CISTI'2026, 17–19 June (to be confirmed) 2026, Santiago de Compostela (Spain).

• 1805-08-04: Hamilton, William Rowan (†1865-09-02, 60 yrs.).

 
 
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Created: 2025-08-04 — Last modified: 2025-09-06