Is there a scaled complementary error function in python available?

Question

In matlab there is a special function which is not available in any of the collections for the Python I know (numpy, scipy, mpmath, ...).

Probably there are other p

Answer 1

The gmpy2 library provides access to the MPFR multiple-precision library. For normal precision, it is almost 5x faster than mpmath.

$ py27 -m timeit -s "import mpmath" -s "def erfcx(x):return mpmath.exp(x**2) * mpmath.erfc(x)" "erfcx(30)"
10000 loops, best of 3: 47.3 usec per loop
$ py27 -m timeit -s "import gmpy2" -s "def erfcx(x):return gmpy2.exp(x**2) * gmpy2.erfc(x)" "erfcx(30)"
100000 loops, best of 3: 10.8 usec per loop

Both libraries return the same result for 30.

>>> import mpmath
>>> import gmpy2
>>> mpmath.exp(30**2) * mpmath.erfc(30)
mpf('0.018795888861416751')
>>> gmpy2.exp(30**2) * gmpy2.erfc(30)
mpfr('0.018795888861416751')
>>> 

Disclaimer: I maintain gmpy2. I'm actively working towards a new release but there shouldn't be any issues with the current release for this calculation.

Edit: I was curious about the overhead of making two functions calls instead of just one so I implemented a gmpy2.erfcx() entirely in C but still using MPFR to perform the calculations. The improvement was less than I expected. If you think erfcx() would be useful, I can add it to the next release.

$ py27 -m timeit -s "import gmpy2" "gmpy2.erfcx(30)"
100000 loops, best of 3: 9.45 usec per loop