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MEYER3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MEYER3
* Problem :
* *********
* A problem arising in the analysis of the resistance of a
* thermistor, as formulated by Meyer.
* This function is a nonlinear least squares with 16 groups. Each
* group has a nonlinear element.
* Source: Problem 28 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.
* See also Buckley #29 (p. 73).
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-RN-3-0
* Number of groups
IE 16 16
* Useful parameters
IE 1 1
VARIABLES
X1 'SCALE' 0.01
X2 'SCALE' 1000.0
X3 'SCALE' 100.0
GROUPS
DO I 1 16
XN G(I)
ND
CONSTANTS
MEYER G1 34780.0
MEYER G2 28610.0
MEYER G3 23650.0
MEYER G4 19630.0
MEYER G5 16370.0
MEYER G6 13720.0
MEYER G7 11540.0
MEYER G8 9744.0
MEYER G9 8261.0
MEYER G10 7030.0
MEYER G11 6005.0
MEYER G12 5147.0
MEYER G13 4427.0
MEYER G14 3820.0
MEYER G15 3307.0
MEYER G16 2872.0
BOUNDS
FR MEYER 'DEFAULT'
START POINT
MEYER X1 0.02
MEYER X2 4000.0
MEYER X3 250.0
ELEMENT TYPE
EV GAUSS V1 V2
EV GAUSS V3
EP GAUSS T
ELEMENT USES
DO I 1 16
IM 5I I 5
IA 45+5I 5I 45
RI TI 45+5I
XT E(I) GAUSS
ZV E(I) V1 X1
ZV E(I) V2 X2
ZV E(I) V3 X3
ZP E(I) T TI
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 16
XT G(I) L2
XE G(I) E(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO MEYER 0.0
* Solution
*LO SOLTN 87.9458
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MEYER3
TEMPORARIES
R TPV3
R TPV3SQ
R EXPA
R V1EXPA
R MG3
R HT
R T33
R H22
M EXP
INDIVIDUALS
* Gaussian function
T GAUSS
A TPV3 T + V3
A EXPA EXP( V2 / TPV3 )
A V1EXPA V1 * EXPA
A TPV3SQ TPV3 * TPV3
A H22 V1EXPA / TPV3SQ
A MG3 - V2 * H22
A HT V2 / TPV3SQ
A T33 HT + 2.0 / TPV3
F V1EXPA
G V1 EXPA
G V2 V1EXPA / TPV3
G V3 MG3
H V1 V2 EXPA / TPV3
H V1 V3 - HT * EXPA
H V2 V2 H22
H V2 V3 - H22 + MG3 / TPV3
H V3 V3 - MG3 * T33
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS MEYER3
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA