Calculating sum of Euclidian distances from one point to multiple points within buffer in QGIS

Question

I want to calculate the sum of the inverse distances from one main point to multiple other points within a buffer around the main point in QGIS

I have a point file with multiple home addresses (red points). I have another point file with restaurant locations (blue points). For each home address I want to calculate the sum of the inverse Euclidian distance from the home address to all the restaurants within the neighbourhood (n=all restaurants in 500m buffer). The 500m buffers are often overlapping.

Is it possible to do this calculation in QGIS?

Answer 1

Use this expression with Field Calculator to get 1) an array of all distances to all points on the layer restaurant_layer within max. 900 m (change this value to fit your needs) from each address, then 2) divide 1 by each of the distances and 3) sum up all these values:

array_sum(
    array_foreach (
        overlay_nearest ('restaurant_layer', $geometry, max_distance:=900, limit:=-1),
        1 / distance ($geometry, @element)
    )
)

Answer 2

Here is a pyqgis recipe that will take in points files with centroids (home addresses) and points (restaurants) and a buffer distance, compute the inverse distances and sum them, then write the result as a new file.

Keep in mind the units are tied to the CRS. This example uses decimal degrees (EPSG:4326).

import processing

#specify the buffer size in map units
bdist = 0.45

#specify paths to data
centpath = "C:/path/to/input/centroids.gpkg"
pointpath = "C:/path/to/input/points.gpkg"

#read in data
centroid_layer = QgsVectorLayer(centpath, "centroids", "ogr")
point_layer = QgsVectorLayer(pointpath, "points", "ogr")

#get centroid features
cent_features = centroid_layer.getFeatures()

#add new field for inverse distances if one does not exist
if centroid_layer.dataProvider().fieldNameIndex("sum_inv_dist") == -1:
    centroid_layer.dataProvider().addAttributes([QgsField("sum_inv_dist", QVariant.Double)])
    centroid_layer.updateFields()

#iterate through centroids
for idx, cent in enumerate(cent_features): 
    
    #get point features
    point_features = point_layer.getFeatures()
    
    #initialize sum inverse distance variable
    inv_dist_sum = 0
    
    #buffer centroid point
    buff = cent.geometry().buffer(bdist, 5)
    
    #iterate through points
    for index, point in enumerate(point_features):
        
        #get feature geometry
        pointgeom = point.geometry()
        
        #check if point fall within buffer
        if pointgeom.within(buff):
            
            #Create a measure object
            distance = QgsDistanceArea()
            
            #calculate inverse distance between points
            invdist = 1 / (distance.measureLine([pointgeom.asPoint(),cent.geometry().asPoint()]))
            
            #add inverse distance to sum variable
            inv_dist_sum = inv_dist_sum + invdist
    
    #get column nubmer of new column
    col_id = centroid_layer.dataProvider().fieldNameIndex("sum_inv_dist")
    
    #append inverse distance to layer
    centroid_layer.startEditing()
    centroid_layer.changeAttributeValue(cent.id(), col_id, inv_dist_sum)
    centroid_layer.commitChanges()
    
#write out result
params = {'INPUT': centroid_layer,
        'OUTPUT': 'C:/Path/to/output/points_distances.gpkg',
        'LAYER_NAME': 'points_distances'}
          
processing.run("native:savefeatures", params)