bugGNU Scientific Library - Bugs: bug #22651, arccosh for complex numbers -...

 
 

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bug #22651: arccosh for complex numbers - branch problem?

Submitted by:  -Deleted Account- <bjg>
Submitted on:  Tue 18 Mar 2008 08:43:04 AM UTC  
 
Category: Accuracy problemSeverity: 3 - Normal
Operating System: Status: Invalid
Assigned to: NoneOpen/Closed: Closed
Release: 1.11

Wed 19 Nov 2008 09:17:18 AM UTC, comment #1:

The information given in the email was incorrect. GSL returns the correct value +0.96 for both real and complex versions of the function.

#include <gsl/gsl_complex_math.h>
#include <math.h>
#include <stdio.h>

int main ()
{
gsl_complex z,f;
double x, y, zero = 0.0;
x = 1.5;
y = acosh(x);
GSL_SET_COMPLEX(&z, x, zero);
f = gsl_complex_arccosh(z);
printf("%.18e\n", x);
printf("%.18e\n", y);
printf("%.18e %.18e\n", GSL_REAL(z), GSL_IMAG(z));
printf("%.18e %.18e\n", GSL_REAL(f), GSL_IMAG(f));
}

$ ./a.out
1.500000000000000000e+00
9.624236501192069415e-01
1.500000000000000000e+00 0.000000000000000000e+00
9.624236501192069415e-01 -0.000000000000000000e+00

-Deleted Account- <bjg>
Tue 18 Mar 2008 08:43:04 AM UTC, original submission:

From: Charles R Harris <charlesr.harris <at> gmail.com>
Subject: arccosh for complex numbers, goofy choice of branch
Newsgroups: gmane.comp.python.numeric.general
Date: 2008-03-17 08:40:19 GMT (1 day ago)

OK,

Which branch do we want to use. As it currently is in numpy and scipy.special

arccosh(1.5) = 0.96242365011920694
arccosh(1.5+0j) = -0.96242365011920705 + 0.0j

This is consistent with gsl, but inconsistent with Mathematica, NAG, Maple, and probably all sensible implementations which use the generally accepted principal value. I've left this inconsistency raising an error in the ufunc tests until we make a decision. It might be nice to know what FORTRAN and MatLab do with this.

Chuck

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-Deleted Account- <bjg>

 

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Follow 3 latest changes.

Date Changed By Updated Field Previous Value => Replaced By
Wed 19 Nov 2008 09:17:18 AM UTCbjgStatusNeed Info=>Invalid
  Open/ClosedOpen=>Closed
  Release=>1.11

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