Edwin Woollett woollett at charter.net
Thu Sep 25 15:40:26 CDT 2008

```I get quad_qag(..) error message no. 2
("excessive roundoff error") with
a very simple function f(x) = x.

---------------------------------
1. Why are we getting excessive
roundoff error with such a simple
integrand?

Or is this error message itself an error?

--------------------
2. Why are the SLATEC error messages
progressively disappearing the more
the same function? ("message exhaustion")

===================

(%i1) integrate( x, x, -1, 1 );
(%o1)                                  0

(%i2) for i thru 6 do
(qlist : quad_qag( x, x, -1, 1, i ),
print( "key is ", i ," ", qlist ) )\$

***MESSAGE FROM ROUTINE DQAG IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
*  ABNORMAL RETURN
*  ERROR NUMBER = 2
*
***END OF MESSAGE

key is  1   [0.0, 1.1020760842711039E-14, 15, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  2   [0.0, 1.1060840041517323E-14, 21, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  3   [0.0, 1.108321668765528E-14, 31, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  4   [0.0, 1.1091368685730577E-14, 41, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  5   [0.0, 1.1095211642996757E-14, 51, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  6   [0.0, 1.1097322727621492E-14, 61, 2]

-------------------

(%i3) for i thru 6 do
(qlist : quad_qag( x, x, -1, 1, i ),
print( "key is ", i ," ", qlist ) )\$

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  1   [0.0, 1.1020760842711039E-14, 15, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  2   [0.0, 1.1060840041517323E-14, 21, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  3   [0.0, 1.108321668765528E-14, 31, 2]

[ SAME SLATEC MESSAGE, ERROR N0. 2  ]

key is  4   [0.0, 1.1091368685730577E-14, 41, 2]
key is  5   [0.0, 1.1095211642996757E-14, 51, 2]
key is  6   [0.0, 1.1097322727621492E-14, 61, 2]

--------------------

(%i4) for i thru 6 do
(qlist : quad_qag( x, x, -1, 1, i ),
print( "key is ", i ," ", qlist ) )\$

key is  1   [0.0, 1.1020760842711039E-14, 15, 2]
key is  2   [0.0, 1.1060840041517323E-14, 21, 2]
key is  3   [0.0, 1.108321668765528E-14, 31, 2]
key is  4   [0.0, 1.1091368685730577E-14, 41, 2]
key is  5   [0.0, 1.1095211642996757E-14, 51, 2]
key is  6   [0.0, 1.1097322727621492E-14, 61, 2]

--------------------------
Ted Woollett

```