Calculation error in tropmapf -> mapf ?

[jonathanmuller]

Hi,

There is a common pattern I see in all implementations of the Niell tropo across github :

The implementation is always the same :

(1+a / ... ) / (sinel +b / ...) while I believe it should be (sinel +b / ...) / (1+a / ... ) (the opposite)

For example :

rtklib-py/src/rtkcmn.py

Line 737 in 5d8968d

return (1.0 + a / (1.0 + b / (1.0 + c))) / (sinel + (a / (sinel + b / (sinel + c))))

def mapf(el, a, b, c):
    """ simple tropospheric mapping function """
    sinel = np.sin(el)
    return (1.0 + a / (1.0 + b / (1.0 + c))) / (sinel + (a / (sinel + b / (sinel + c))))

However, original paper ( https://safe.nrao.edu/wiki/pub/Main/RefBendDelayCalc/Niell_Global.pdf ) list "equation 4" as :

So the form is (1/(1+a / ... )) / (1+1/(sinel +b / ...))
As (1/y)/(1/x) can be rewritten as x/y
Then the calculation above can be simplified as (sinel +b / ...) /(1+a / ... )
There can be no ambiguity as later it is used directly as follow, without further division or calculation directly as mapf :

rtklib-py/src/rtkcmn.py

Line 755 in 5d8968d

dm = (1.0 / np.sin(el) - mapf(el, aht[0], aht[1], aht[2])) * pos[2] * 1e-3

This is the same (wrong?) implementation as RTKLib and any other commonly used RTK library I could find on github.
Am I just wrong about the understanding of the calculation, or is everyone copy-pasting the same error ?