ARTIF.SIF

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* SET UP THE INITIAL DATA *
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NAME          ARTIF

*   Problem :
*   *********
*   An artificial nonlinear system.

*   Source:
*   K.M. Irani, M.P. Kamat, C.J. Ribbens, H.F.Walker and L.T. Watson,
*   "Experiments with conjugate gradient algoritms for homotopy curve
*    tracking" ,
*   SIAM Journal on Optimization, May 1991, pp. 222-251, 1991.

*   SIF input: Ph. Toint, May 1990.

*   classification NOR2-AN-V-V

*   Number of variables

*IE N                   10             $-PARAMETER     original value
*IE N                   50             $-PARAMETER 
*IE N                   100            $-PARAMETER
*IE N                   500            $-PARAMETER
*IE N                   1000           $-PARAMETER
 IE N                   5000           $-PARAMETER

*   Constants

 IE 0                   0
 IE 1                   1

*   Computed parameters

 IA N+1       N         1

VARIABLES

 DO I         0                        N+1
 X  X(I)
 ND

GROUPS

 DO I         1                        N

 IA I-1       I         -1
 IA I+1       I         1

 XE EQ(I)     X(I)      -0.05          X(I+1)    -0.05
 XE EQ(I)     X(I-1)    -0.05

 ND

BOUNDS

 FR ARTIF     'DEFAULT'

 XX ARTIF     X(0)      0.0
 XX ARTIF     X(N+1)    0.0

START POINT

 XV ARTIF     'DEFAULT' 1.0

ELEMENT TYPE

 EV TRIG      X
 EP TRIG      PAR

ELEMENT USES

 T  'DEFAULT' TRIG

 DO I         1                        N
 RI RI        I
 ZV E(I)      X                        X(I)
 ZP E(I)      PAR                      RI
 ND

GROUP USES

 DO I         1                        N
 XE EQ(I)     E(I)
 ND

OBJECT BOUND

*   Solution

*LO SOLTN               0.0

ENDATA

***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
***********************

ELEMENTS      ARTIF

TEMPORARIES

 R  FACT
 R  S
 R  DSDX
 R  D2SDX2
 R  D
 R  THAT
 M  ATAN
 M  SIN
 M  COS
 M  MOD

INDIVIDUALS

*   Trigonometric

 T  TRIG

 A  THAT                100.0
 A  FACT                MOD( PAR, THAT )
 A  S                   SIN( FACT * X )
 A  DSDX                FACT * COS( FACT * X )
 A  D2SDX2              - FACT * FACT * S
 A  D                   1.0 + S * S

 F                      ATAN( S )
 G  X                   DSDX / D
 H  X         X         ( D2SDX2 * D - 2.0 * S * DSDX**2 ) /D**2

ENDATA