Rowmin and rounding issue

[Zakia Nouri]

Hi all! I am sorry for asking this basic question, but I am using egen rowmin to select the minimum value between two variables (v1 and v2). The results from rowmin are not EXACTLY the same as the variable with the minimum value for ALL the observations, with decimal points being the main problem. For example, v1 is 3.916571 while the min value is 3.9165709. I tried the following syntax, but it does not work. I would appreciate your help with this. Thank you!!

*///to simplify, I am rounding my v1 and v2 before creating my min variable.
replace v1=round(v1, 0.000001)
replace v2=round(v2, 0.000001)
egen min=rowmin(v1 v2)
*///because both v1 and v2 are double with %10.0g format, I am trying to recast and reformat the min variable.
recast double min
format %10.0g min
replace min=round(min, 0.000001)

[Nick Cox]

This is a precision issue on several levels. You need to start out generating doubles to preserve detail. A recast double will never restore detail lost in earlier calculations; that is like trying to get spilled milk back into the bottle or toothpaste back into the tube (indeed harder).

Rounding to fractions that are powers of 10 is ultimately either doomed or irrelevant, as almost none of them can be held exactly as binary approximations. Here is what 1 in a million looks like inside Stata, more nearly, (except that this is a decimal display of a number held in binary as an approximation)

. di %27.26f 1e-6
0.00000099999999999999995475

It's not exactly 1 in a million and can't be.

Backing up: If v1 v2 were float then the minimum could be just

gen min = min(v1, v2)

but as both are double you need

gen double min  = min(v1, v2)

and any other approach is wrong or round-about.

egen should do something similar, so long as you insist on double too, but is just a long-winded alternative in this case. Looking inside with

viewsource egen.ado 
viewsource _growmin.ado

will show that you are invoking a lot of code to do something that generate will do in one line.

And naturally comparison should be based on assigning the same display format.

[William Lisowski]

Once you have created a value as float, using recast to convert it to double cannot restore the precision that was lost when the result of Stata's calculations (which are always done in double) was shortened to fit in a float. Instead, don't do any rounding, and replace all the code above with

egen double min=rowmin(v1 v2) 
format %10.0g min

See the output of help precision for more about these issues.

[Zakia Nouri]

Perfect! Thank you both so much for your response and help!

[Anne Shi]

The new command round_exact (available on SSC) will solve this issue. Try this:

clear
input double price
0.3
0.105
2.675
1.005
0.005
end

round_exact1 price, d(2) generate(price_r)
assert price_r[1] == 0.30
assert price_r[2] == 0.11
assert price_r[3] == 2.68
assert price_r[4] == 1.01
assert price_r[5] == 0.01