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GROWTH.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GROWTH
* Problem :
* *********
* GROWTH problem in 3 variables
* Fit the observed growth g(n) from Gaussian Elimination
* with complete pivoting to a function of the form
*
* U1 * n ** ( U2 + LOG(n) * U3 )
* SIF input: Nick Gould, Nov, 1991.
* classification NOR2-AN-3-12
IE N 3
VARIABLES
U1
U2
U3
GROUPS
E G8
E G9
E G10
E G11
E G12
E G13
E G14
E G15
E G16
E G18
E G20
E G25
CONSTANTS
GROWTH G8 8.0
GROWTH G9 8.4305
GROWTH G10 9.5294
GROWTH G11 10.4627
GROWTH G12 12.0
GROWTH G13 13.0205
GROWTH G14 14.5949
GROWTH G15 16.1078
GROWTH G16 18.0596
GROWTH G18 20.4569
GROWTH G20 24.25
GROWTH G25 32.9863
BOUNDS
FR GROWTH 'DEFAULT'
START POINT
V GROWTH U1 100.0
ELEMENT TYPE
EV FIT U1 U2
EV FIT U3
EP FIT RN
ELEMENT USES
T 'DEFAULT' FIT
V G8 U1 U1
V G8 U2 U2
V G8 U3 U3
P G8 RN 8.0
V G9 U1 U1
V G9 U2 U2
V G9 U3 U3
P G9 RN 9.0
V G10 U1 U1
V G10 U2 U2
V G10 U3 U3
P G10 RN 10.0
V G11 U1 U1
V G11 U2 U2
V G11 U3 U3
P G11 RN 11.0
V G12 U1 U1
V G12 U2 U2
V G12 U3 U3
P G12 RN 12.0
V G13 U1 U1
V G13 U2 U2
V G13 U3 U3
P G13 RN 13.0
V G14 U1 U1
V G14 U2 U2
V G14 U3 U3
P G14 RN 14.0
V G15 U1 U1
V G15 U2 U2
V G15 U3 U3
P G15 RN 15.0
V G16 U1 U1
V G16 U2 U2
V G16 U3 U3
P G16 RN 16.0
V G18 U1 U1
V G18 U2 U2
V G18 U3 U3
P G18 RN 18.0
V G20 U1 U1
V G20 U2 U2
V G20 U3 U3
P G20 RN 20.0
V G25 U1 U1
V G25 U2 U2
V G25 U3 U3
P G25 RN 25.0
GROUP TYPE
GV L2 GVAR
GROUP USES
*T 'DEFAULT' L2
E G8 G8
E G9 G9
E G10 G10
E G11 G11
E G12 G12
E G13 G13
E G14 G14
E G15 G15
E G16 G16
E G18 G18
E G20 G20
E G25 G25
OBJECT BOUND
LO GROWTH 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GROWTH
TEMPORARIES
R LOGRN
R POWER
M LOG
INDIVIDUALS
* Product type elements
T FIT
A LOGRN LOG( RN )
A POWER RN ** ( U2 + LOGRN * U3 )
F U1 * POWER
G U1 POWER
G U2 U1 * POWER * LOGRN
G U3 U1 * POWER * LOGRN ** 2
H U1 U1 0.0
H U1 U2 POWER * LOGRN
H U1 U3 POWER * LOGRN ** 2
H U2 U2 U1 * POWER * LOGRN ** 2
H U2 U3 U1 * POWER * LOGRN ** 3
H U3 U3 U1 * POWER * LOGRN ** 4
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS GROWTH
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA