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SENSORS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME SENSORS
* Problem :
* *********
* A problem arising from two-dimensional optimal sensor placement
* Source:
* H. Zhang and X. Wang,
* "Optimal sensor placement",
* SIAM Review, vol. 35, p. 641, 1993.
* SIF input: Nick Gould, June 1994
* classification SUR2-AN-V-0
* Number of unknowns
*IE N 2 $-PARAMETER
*IE N 3 $-PARAMETER
*IE N 10 $-PARAMETER
IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER
* Other useful parameters
IE 1 1
RI RN N
VARIABLES
DO I 1 N
X THETA(I)
ND
GROUPS
DO J 1 N
DO I 1 N
XN S(I,J)
ND
BOUNDS
FR SENSORS 'DEFAULT'
START POINT
DO I 1 N
RI RI I
R/ I/N RI RN
ZV SENSORS THETA(I) I/N
ND
ELEMENT TYPE
EV SINFUN THETAI THETAJ
ELEMENT USES
T 'DEFAULT' SINFUN
DO J 1 N
DO I 1 N
ZV S(I,J) THETAI THETA(I)
ZV S(I,J) THETAJ THETA(J)
ND
GROUP TYPE
GV -L2 GVAR
GROUP USES
T 'DEFAULT' -L2
DO J 1 N
DO I 1 N
XE S(I,J) S(I,J)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS SENSORS
TEMPORARIES
R TIMJ
R SI
R SJ
R SIMJ
R CI
R CJ
R CIMJ
R CJSIMJ
R CJCIMJ
M SIN
M COS
INDIVIDUALS
T SINFUN
A TIMJ THETAI - THETAJ
A SI SIN( THETAI )
A SJ SIN( THETAJ )
A SIMJ SIN( TIMJ )
A CI COS( THETAI )
A CJ COS( THETAJ )
A CIMJ COS( TIMJ )
A CJSIMJ CJ * SIMJ - SJ * CIMJ
A CJCIMJ CJ * CIMJ + SJ * SIMJ
F SI * SJ * SIMJ
G THETAI SJ * ( CI * SIMJ + SI * CIMJ )
G THETAJ SI * CJSIMJ
H THETAI THETAI 2.0 * SJ * ( CI * CIMJ - SI * SIMJ )
H THETAI THETAJ CI * CJSIMJ + SI * CJCIMJ
H THETAJ THETAJ - 2.0 * SI * CJCIMJ
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS SENSORS
INDIVIDUALS
T -L2
F - GVAR * GVAR
G - GVAR - GVAR
H - 2.0
ENDATA