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FLETCBV3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME FLETCBV3
* Problem :
* *********
* Another Boundary Value problem.
* Source: The first problem given by
* R. Fletcher,
* "An optimal positive definite update for sparse Hessian matrices"
* Numerical Analysis report NA/145, University of Dundee, 1992.
* Scaled version.
* SIF input: Nick Gould, Oct 1992.
* classification OUR2-AN-V-0
* The number of variables is N.
*IE N 10 $-PARAMETER original value
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* KAPPA a parameter.
RE KAPPA 1.0 $-PARAMETER
*RE KAPPA 0.0 $-PARAMETER
RE OBJSCALE 1.0D+8
* Define useful parameters
IE 0 0
IE 1 1
IE 2 2
RE 1.0 1.0
IA N-1 N -1
R/ P 1.0 OBJSCALE
IA N+1 N 1
RI RN+1 N+1
R/ H 1.0 RN+1
R* H2 H H
R* 1/H2 RN+1 RN+1
R* KAPPA/H2 1/H2 KAPPA
RM -KAPPA/H2 KAPPA/H2 -1.0
RM 2/H2 1/H2 2.0
RA 1+2/H2 2/H2 1.0
RM -1-2/H2 1+2/H2 -1.0
R* P*-1-2/H2 1+2/H2 P
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
*ZN G(0) 'SCALE' OBJSCALE
XN G(0) X(1) 1.0
DO I 1 N-1
IA I+1 I 1
*ZN G(I) 'SCALE' OBJSCALE
XN G(I) X(I) 1.0 X(I+1) -1.0
ND
*ZN G(N) 'SCALE' OBJSCALE
XN G(N) X(N) 1.0
DO I 1 N
*ZN L(I) 'SCALE' OBJSCALE
ZN L(I) X(I) P*-1-2/H2
ND
DO I 1 N
*ZN C(I) 'SCALE' OBJSCALE
ZN C(I)
ND
BOUNDS
FR FLETCBV3 'DEFAULT'
START POINT
*V FLETCBV3 'DEFAULT' 0.0
DO I 1 N
RI RI I
R* IH RI H
Z FLETCBV3 X(I) IH
ND
ELEMENT TYPE
EV COS V
EP COS P
ELEMENT USES
T 'DEFAULT' COS
DO I 1 N
ZV C(I) V X(I)
ZP C(I) P P
ND
GROUP TYPE
GV HALFL2 GVAR
GP HALFL2 P
GROUP USES
DO I 0 N
XT G(I) HALFL2
ZP G(I) P P
ND
DO I 1 N
ZE C(I) C(I) -KAPPA/H2
ND
OBJECT BOUND
* Solution
*LO SOLTN ??
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS FLETCBV3
TEMPORARIES
M COS
M SIN
INDIVIDUALS
T COS
F P * COS( V )
G V - P * SIN( V )
H V V - P * COS( V )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS FLETCBV3
INDIVIDUALS
T HALFL2
F 5.0D-1 * P * GVAR * GVAR
G P * GVAR
H P
ENDATA