Re: [Bug-gsl] gsl_integration_qagiu failure

[Brian Gough]

Manoj Rajagopalan writes:
 >     The result of integration of the square of the radial component of 
 > the normalized hydrogenic bound state wave function (double 
 > gsl_sf_hydrogenicR_1(double Z, double r)  from gsl_sf_coulomb.h) over 
 > range of r from 0 to INFINITY should be 1.0
 >     Using gsl_integration_qagiu to perform this semi-infinite integral 
 > yields the  result 0.0 or core-dumps with an underflow. See file 
 > qagiu.txt (attached)

Thanks for the email.  In this case the library is reporting a
legitimate underflow when gsl_sf_hydrogenicR_1 is called with a very
large first argument.

By default there is an abort() for any underflow, since they could be
important in some circumstances.  Use gsl_set_error_handler_off(); to
avoid seeing underflows.

Working in terms of r/a instead of a dimensionful r would help with
the scaling of the variable since the transformation of the infinite
integral to a finite range used by the QAGIU algorithm is not scale
free.

regards

-- 
Brian Gough