How to rasterize a point layer with multiple features falling inside a raster cell?

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How to make a raster with values that are the sum of all points inside each raster cell? The burn value is a specific attribute.

Using gdal_rasterize or gdal.RasterizeLayer(), the resulting raster only has the value of a random (or probably the first or last) point inside a raster cell. I’ve already tried gdal_rasterize option ALL_TOUCHED, but it does not change the behaviour.



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