ARGTRIG.SIF

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* SET UP THE INITIAL DATA *
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NAME          ARGTRIG

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

*   Variable dimension trigonometric problem
*   This problem is a sum of n least-squares groups, each of
*   which has n+1 nonlinear elements.  Its Hessian matrix is dense.

*   Source:  Problem 26 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, Dec 1989.

*   classification NOR2-AN-V-V

*   N is the number of free variables

*IE N                   10             $-PARAMETER
*IE N                   50             $-PARAMETER 
*IE N                   100            $-PARAMETER
 IE N                   200            $-PARAMETER

*   Define useful parameters

 IE 1                   1
 RE 1.0                 1.0

 RI RN        N
 R/ 1OVERN    1.0                      RN

VARIABLES

 DO I         1                        N
 X  X(I)
 ND

GROUPS

 DO I         1                        N
 XE G(I)
 ND

CONSTANTS

 DO I         1                        N
 I+ N+I       N                        I
 RI RN+I      N+I
 Z  ARGTRIG   G(I)                     RN+I
 ND

BOUNDS

 FR ARGTRIG   'DEFAULT'

START POINT

 DO I         1                        N
 Z  ARGTRIG   X(I)                     1OVERN
 ND

ELEMENT TYPE

 EV COSINE    XJ
 EV SINCOS    XI

ELEMENT USES

 DO I         1                        N
 XT C(I)      COSINE
 ZV C(I)      XJ                       X(I)
 XT SC(I)     SINCOS
 ZV SC(I)     XI                       X(I)
 ND

GROUP USES

 DO I         1                        N
 RI REALI     I
 ZE G(I)      SC(I)                    REALI
 DO J         1                        N
 XE G(I)      C(J)
 ND

OBJECT BOUND

*   Solution

*LO SOLTN               0.0

ENDATA

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

ELEMENTS      ARGTRIG

TEMPORARIES

 R  SX
 R  CX
 M  SIN
 M  COS

INDIVIDUALS

*  Cosine type

 T  COSINE
 A  CX                  COS( XJ )
 F                      CX
 G  XJ                  - SIN( XJ )
 H  XJ        XJ        - CX

*   Mixed type

 T  SINCOS
 A  CX                  COS( XI )
 A  SX                  SIN( XI )
 F                      CX + SX
 G  XI                  - SX + CX
 H  XI        XI        - CX - SX

ENDATA