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Why no complex ERF intrinsic?
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Al Greynolds
Oct 19, 2021, 9:53:51 AM10/19/21
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For a simulation I needed the complex Fresnel Integral which can be simply related to an error function with a complex argument. Checking the Fortran 2018 standard I was surprised it only allowed real arguments for ERF. More surprising I found that the plotting package I use with my Fortran codes, the venerable Gnuplot, does support a complex CERF, e.g. a Cornu spiral plot:
fresnel(x) = {1.,1.}*cerf(sqrt(pi)*{1.,-1.}*x/2.)/2.
set parametric
unset key
set samples 1000
plot real(fresnel(t)),imag(fresnel(t))
Didn't check to see how many other useful Fortran math intrinsics only support real and not complex arguments. I'm sure in some cases it doesn't make sense, but not in this one.
Al
fresnel(x) = {1.,1.}*cerf(sqrt(pi)*{1.,-1.}*x/2.)/2.
set parametric
unset key
set samples 1000
plot real(fresnel(t)),imag(fresnel(t))
Didn't check to see how many other useful Fortran math intrinsics only support real and not complex arguments. I'm sure in some cases it doesn't make sense, but not in this one.
Al
gah4
Oct 20, 2021, 2:21:15 AM10/20/21
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On Tuesday, October 19, 2021 at 6:53:51 AM UTC-7, Al Greynolds wrote:
(snip)
LOG_GAMMA, LOG10, and NORM2.
As far as I know, all are defined for complex values.
(snip)
> Didn't check to see how many other useful Fortran math intrinsics only support
> real and not complex arguments. I'm sure in some cases it doesn't make sense,
> but not in this one.
Going down the list, it seems that the BESSEL functions, GAMMA,
> real and not complex arguments. I'm sure in some cases it doesn't make sense,
> but not in this one.
LOG_GAMMA, LOG10, and NORM2.
As far as I know, all are defined for complex values.
Arjen Markus
Oct 20, 2021, 3:33:37 AM10/20/21
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Regards,
Arjen
gah4
Oct 20, 2021, 5:49:32 AM10/20/21
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On Wednesday, October 20, 2021 at 12:33:37 AM UTC-7, arjen.m...@gmail.com wrote:
(snip)
> One reason I can think of for this lack of support is that complex functions add,
> well, a complication that is not easily solved: branch cuts.
> Of course there are conventions for most of these functions that you could
> adhere to, but doing so is less than trivial (see for instance the article by Anton
> Shterenlikht in the Fortran Forum a few years ago) and the features are probably
> of importance to a small group of programmers only.
It seems that gamma is well defined for complex values, other than non-positive
integers.
https://en.wikipedia.org/wiki/Gamma_function
As for erf(z), from: https://en.wikipedia.org/wiki/Error_function
it seems also to be defined for complex values.
It mentions libcerf, which is a broken link, but then:
http://ab-initio.mit.edu/wiki/index.php/Faddeeva_Package
which seems to be C++ with a C wrapper, so should be callable from Fortran.
(snip)
> One reason I can think of for this lack of support is that complex functions add,
> well, a complication that is not easily solved: branch cuts.
> Of course there are conventions for most of these functions that you could
> adhere to, but doing so is less than trivial (see for instance the article by Anton
> Shterenlikht in the Fortran Forum a few years ago) and the features are probably
> of importance to a small group of programmers only.
integers.
https://en.wikipedia.org/wiki/Gamma_function
As for erf(z), from: https://en.wikipedia.org/wiki/Error_function
it seems also to be defined for complex values.
It mentions libcerf, which is a broken link, but then:
http://ab-initio.mit.edu/wiki/index.php/Faddeeva_Package
which seems to be C++ with a C wrapper, so should be callable from Fortran.
Arjen Markus
Oct 20, 2021, 7:46:41 AM10/20/21
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On Wednesday, October 20, 2021 at 11:49:32 AM UTC+2, gah4 wrote:
Hm, might be a nice addition for the Fortran stdlib, as it is being developed at https://github.com/fortran-lang/stdlib/.
Regards,
Arjen
Regards,
Arjen
Rudi Gaelzer
Oct 20, 2021, 9:24:30 AM10/20/21
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The error function is an entire function, so there is a priori reason for the absence of a standard implementation, other than possibly the limited time available to the programmers that maintain the (standard) library of intrinsic functions.
I usually employ the dcerf.f90 function you can download from Alan Miller's repository: https://jblevins.org/mirror/amiller/
I usually employ the dcerf.f90 function you can download from Alan Miller's repository: https://jblevins.org/mirror/amiller/
gah4
Oct 20, 2021, 11:09:51 AM10/20/21
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On Tuesday, October 19, 2021 at 6:53:51 AM UTC-7, Al Greynolds wrote:
> For a simulation I needed the complex Fresnel Integral which can be simply related
> to an error function with a complex argument.
I have the book "Computation of Special Functions" by Zhang and Jin, that I got
> to an error function with a complex argument.
on eBay some years ago.
I was looking for something else, and accidentally found it, maybe in other
items from the same seller. (If I remember, I also bought a tie with pictures
of xenon arc lamps on it, at about that time.)
The price was about $30, which seemed a good deal at the time.
The examples seem to be in, more or less, Fortran 77.
Maybe VAX Fortran, which might have been popular about that time.
It does have a COMPLEX*16 erf().
One that it does have, and that I was using about that time, is elliptic
integrals, which might have been the reason to buy one.
gah4
Oct 21, 2021, 4:14:28 AM10/21/21
to
On Tuesday, October 19, 2021 at 6:53:51 AM UTC-7, Al Greynolds wrote:
> For a simulation I needed the complex Fresnel Integral which can be simply related
> to an error function with a complex argument. Checking the Fortran 2018 standard
> I was surprised it only allowed real arguments for ERF.
There is also libcerf:
> to an error function with a complex argument. Checking the Fortran 2018 standard
> I was surprised it only allowed real arguments for ERF.
https://jugit.fz-juelich.de/mlz/libcerf
which includes Fortran binding.
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