POWELLSQ.SIF

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* SET UP THE INITIAL DATA *
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NAME          POWELLSQ

*   Problem :
*   *********

*   Source:
*   M.J.D. Powell,
*   " A hybrid method for nonlinear equations",
*   In P. Rabinowitz(ed.) "Numerical Methods for Nonlinear Algebraic
*   Equations", Gordon and Breach, 1970.

*   See also Buckley#217 (p.84.)

*   classification NOR2-AN-2-2

*   SIF input: Ph. Toint, Dec 1989, correction November 2002.
*              NIMG corrected July 2005 (thanks to Roger Fletcher)

VARIABLES

    X1
    X2

GROUPS

 E  G1
 E  G2

BOUNDS

 FR POWELLSQ  'DEFAULT'

START POINT

    POWELLSQ  X1        3.0
    POWELLSQ  X2        1.0

ELEMENT TYPE

 EV SQ        X
 EV A         X

ELEMENT USES

 T  E1        SQ
 V  E1        X                        X1

 T  E2        A
 V  E2        X                        X1

 T  E3        SQ
 V  E3        X                        X2

GROUP USES

 E  G1        E1
 E  G2        E2                       E3        2.0

ENDATA

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

TEMPORARIES

 R  DEN
 R  DEN2
 R  XDEN

INDIVIDUALS

*   Weighted square

 T  SQ
 F                      X * X
 G  X                   X + X
 H  X         X         2.0

*   Type A

 T  A
 A  DEN                 X + 0.1
 A  DEN2                DEN * DEN
 A  XDEN                X / DEN
 F                      10.0 * XDEN
 G  X                   1.0 / DEN2
 H  X         X         - 2.0 / ( DEN2 * DEN )

ENDATA