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SBRYBND.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME SBRYBND
* Problem :
* *********
* Broyden banded system of nonlinear equations, considered in the
* least square sense.
* NB: scaled version of BRYBND
* Source: problem 31 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.
* See also Buckley#73 (p. 41) and Toint#18
* SIF input: Ph. Toint and Nick Gould, Nov 1997.
* classification SUR2-AN-V-0
* N is the number of equations and variables (variable).
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 5000 $-PARAMETER
* Define some problem's parameters (see Buckley)
* Restriction: LB + 1 + UB .le. N
RE ONE 1.0
RE KAPPA1 2.0
RE KAPPA2 5.0
RE KAPPA3 1.0
IE LB 5
IE UB 1
RI RN N
RA RN-1 RN -1
* ratio of smallest to largest scale factors will be exp(scal)
RE SCAL 12.0
* Define useful parameters
IE 1 1
IM MLB LB -1
IM MUB UB -1
IA LB+1 LB 1
I+ N-UB N MUB
IA N-UB-1 N-UB -1
RM -KAPPA3 KAPPA3 -1.0
VARIABLES
DO I 1 N
IA I-1 I -1
RI RI-1 I-1
R/ RAT RI-1 RN-1
R* ARG RAT SCAL
A( SCALE(I) EXP ARG
X X(I)
ND
GROUPS
* Upper left corner
DO I 1 LB
IA I-1 I -1
IA I+1 I 1
I+ I+UB I UB
DO J 1 I-1
A* KAP -KAPPA3 SCALE(J)
ZN G(I) X(J) KAP
OD J
A* KAP KAPPA1 SCALE(I)
ZN G(I) X(I) KAP
DO J I+1 I+UB
A* KAP -KAPPA3 SCALE(J)
ZN G(I) X(J) KAP
ND
* Main (middle) part
DO I LB+1 N-UB-1
I+ I-LB I MLB
IA I-1 I -1
IA I+1 I 1
I+ I+UB I UB
DO J I-LB I-1
A* KAP -KAPPA3 SCALE(J)
ZN G(I) X(J) KAP
OD J
A* KAP KAPPA1 SCALE(I)
ZN G(I) X(I) KAP
DO J I+1 I+UB
A* KAP -KAPPA3 SCALE(J)
ZN G(I) X(J) KAP
ND
* Lower right corner
DO I N-UB N
I+ I-LB I MLB
IA I-1 I -1
IA I+1 I 1
DO J I-LB I-1
A* KAP -KAPPA3 SCALE(J)
ZN G(I) X(J) KAP
OD J
A* KAP KAPPA1 SCALE(I)
ZN G(I) X(I) KAP
DO J I+1 N
A* KAP -KAPPA3 SCALE(J)
ZN G(I) X(J) KAP
ND
BOUNDS
FR SBRYBND 'DEFAULT'
START POINT
DO I 1 N
A/ DIV ONE SCALE(I)
ZV SBRYBND X(I) DIV
ND
ELEMENT TYPE
EV SQ V
EP SQ P
EV CB V
EP CB P
ELEMENT USES
XT 'DEFAULT' CB
DO I 1 N
XT E(I) SQ
ZV E(I) V X(I)
ZP E(I) P SCALE(I)
XT Q(I) CB
ZV Q(I) V X(I)
ZP Q(I) P SCALE(I)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
* Upper left corner
DO I 1 LB
IA I-1 I -1
IA I+1 I 1
I+ I+UB I UB
DO J 1 I-1
ZE G(I) E(J) -KAPPA3
OD J
ZE G(I) Q(I) KAPPA2
DO J I+1 I+UB
ZE G(I) E(J) -KAPPA3
ND
* Main (middle) part
DO I LB+1 N-UB-1
I+ I-LB I MLB
IA I-1 I -1
IA I+1 I 1
I+ I+UB I UB
DO J I-LB I-1
ZE G(I) Q(J) -KAPPA3
OD J
ZE G(I) E(I) KAPPA2
DO J I+1 I+UB
ZE G(I) E(J) -KAPPA3
ND
* Lower right corner
DO I N-UB N
I+ I-LB I MLB
IA I-1 I -1
IA I+1 I 1
DO J I-LB I-1
ZE G(I) E(J) -KAPPA3
OD J
ZE G(I) Q(I) KAPPA2
DO J I+1 N
ZE G(I) E(J) -KAPPA3
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS SBRYBND
TEMPORARIES
R PP
INDIVIDUALS
T SQ
A PP P * P
F PP * V * V
G V PP * ( V + V )
H V V 2.0 * PP
T CB
A PP P * P * P
F PP * V * V * V
G V 3.0 * PP * V * V
H V V 6.0 * PP * V
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS SBRYBND
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA