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INTEGREQ.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME INTEGREQ
* Problem :
* *********
* The discrete integral problem
* Source: Problem 29 in
* J.J. More', B.S. Garbow and K.E. Hillstrom,
* "Testing Unconstrained Optimization Software",
* ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
* SIF input: Ph. Toint, Feb 1990.
* classification NOR2-AN-V-V
* N+2 is the number of discretization points .
* The number of free variables is N.
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER original value
*IE N 100 $-PARAMETER
IE N 500 $-PARAMETER
* Define useful parameters
IE 0 0
IE 1 1
IA N+1 N 1
RI RN+1 N+1
RD H RN+1 1.0
RM HALFH H 0.5D0
VARIABLES
DO I 0 N+1
X X(I)
ND
GROUPS
DO I 1 N
XE G(I) X(I) 1.0
ND
BOUNDS
FR INTEGREQ 'DEFAULT'
XX INTEGREQ X(0) 0.0
XX INTEGREQ X(N+1) 0.0
START POINT
X INTEGREQ X(0) 0.0
DO I 1 N
RI REALI I
R* IH REALI H
RA IH-1 IH -1.0
R* TI IH IH-1
Z INTEGREQ X(I) TI
ND
X INTEGREQ X(N+1) 0.0
ELEMENT TYPE
EV VBCUBE V
EP VBCUBE B
ELEMENT USES
DO J 1 N
RI REALJ J
R* TJ REALJ H
RA 1+TJ TJ 1.0
XT A(J) VBCUBE
ZV A(J) V X(J)
ZP A(J) B 1+TJ
ND
GROUP USES
DO I 1 N
RI REALI I
R* TI REALI H
RM -TI TI -1.0
RA 1-TI -TI 1.0
R* P1 1-TI HALFH
DO J 1 I
RI REALJ J
R* TJ REALJ H
R* WIL P1 TJ
ZE G(I) A(J) WIL
OD J
IA I+1 I 1
R* P2 TI HALFH
DO J I+1 N
RI REALJ J
R* TJ REALJ H
RM -TJ TJ -1.0
RA 1-TJ -TJ 1.0
R* WIU P2 1-TJ
ZE G(I) A(J) WIU
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS INTEGREQ
* Cube groups
TEMPORARIES
R VPLUSB
INDIVIDUALS
T VBCUBE
A VPLUSB V + B
F VPLUSB**3
G V 3.0 * VPLUSB**2
H V V 6.0 * VPLUSB
ENDATA