ST_GeometricMedian
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## Name

ST_GeometricMedian — Returns the geometric median of a MultiPoint.

## Synopsis

`geometry ST_GeometricMedian (` geometry geom, float8 tolerance = NULL, int max_iter = 10000, boolean fail_if_not_converged = false`)`;

## Description

Computes the approximate geometric median of a MultiPoint geometry using the Weiszfeld algorithm. The geometric median is the point minimizing the sum of distances to the input points. It provides a centrality measure that is less sensitive to outlier points than the centroid (center of mass).

The algorithm iterates until the distance change between successive iterations is less than the supplied `tolerance` parameter. If this condition has not been met after `max_iterations` iterations, the function produces an error and exits, unless `fail_if_not_converged` is set to `false` (the default).

If a `tolerance` argument is not provided, the tolerance value is calculated based on the extent of the input geometry.

If present, the input point M values are interpreted as their relative weights.

Availability: 2.3.0

Enhanced: 2.5.0 Added support for M as weight of points.

This function supports 3d and will not drop the z-index.

This function supports M coordinates.

## Examples

Comparison of the geometric median (red) and centroid (turquoise) of a MultiPoint.

    WITH test AS (
    SELECT 'MULTIPOINT((10 10), (10 40), (40 10), (190 190))'::geometry geom)
    SELECT
      ST_AsText(ST_Centroid(geom)) centroid,
      ST_AsText(ST_GeometricMedian(geom)) median
    FROM test;

          centroid      |                 median
    --------------------+----------------------------------------
       POINT(62.5 62.5) | POINT(25.01778421249728 25.01778421249728)
    (1 row)

## See Also

ST_Centroid

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