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I know how to calculate the latitude-longitude coordinates of a given pixel of a TIFF file using rasterio. Methods based on importing external functions (from within rasterio or GDAL for example) appear often, ie here: How to speed up rasterio.transform.xy.

How can I perform these calculations after extracting relevant values from the TIFF file using numpy only?

My aim with using numpy only is to have a better understanding of what's going on under the hood. Here is an example tiff file, a Sentinel image of Oslo area, in case you want to play around with it.