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PALMER8E.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER8E
* Problem :
* *********
* A nonlinear least squares problem
* arising from chemical kinetics.
* model: H-N=C=Se TZVP + MP2
* fitting Y to A0 + A2 X**2 + A4 X**4 + A6 X**6 + A8 X**8 +
* A10 X**10 + L * EXP( -K X**2 )
* Source:
* M. Palmer, Edinburgh, private communication.
* SIF input: Nick Gould, 1992.
* classification SBR2-RN-8-0
* Number of data points
IE M 23
* Other data
IE 1 1
IE 12 12
* X (radians)
RE X12 0.000000
RE X13 0.174533
RE X14 0.314159
RE X15 0.436332
RE X16 0.514504
RE X17 0.610865
RE X18 0.785398
RE X19 0.959931
RE X20 1.134464
RE X21 1.308997
RE X22 1.483530
RE X23 1.570796
* Y( KJmol-1)
RE Y12 4.757534
RE Y13 3.121416
RE Y14 1.207606
RE Y15 0.131916
RE Y16 0.000000
RE Y17 0.258514
RE Y18 3.380161
RE Y19 10.762813
RE Y20 23.745996
RE Y21 44.471864
RE Y22 76.541947
RE Y23 97.874528
VARIABLES
A0
A2
A4
A6
A8
A10
K
L
GROUPS
DO I 12 M
A* XSQR X(I) X(I)
A* XQUART XSQR XSQR
A* X**6 XSQR XQUART
A* X**8 XSQR X**6
A* X**10 XSQR X**8
A* X**12 XSQR X**10
A* X**14 XSQR X**12
XN O(I) A0 1.0
ZN O(I) A2 XSQR
ZN O(I) A4 XQUART
ZN O(I) A6 X**6
ZN O(I) A8 X**8
ZN O(I) A10 X**10
ND
CONSTANTS
DO I 12 M
Z PALMER8E O(I) Y(I)
ND
BOUNDS
FR PALMER8E A0
FR PALMER8E A2
FR PALMER8E A4
FR PALMER8E A6
FR PALMER8E A8
FR PALMER8E A10
FR PALMER8E L
START POINT
XV PALMER8E 'DEFAULT' 1.0
ELEMENT TYPE
EV PROD K L
EP PROD XSQR
ELEMENT USES
DO I 12 M
A* XSQR X(I) X(I)
XT E(I) PROD
ZV E(I) K K
ZV E(I) L L
ZP E(I) XSQR XSQR
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 12 M
XT O(I) L2
XE O(I) E(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO PALMER8E 0.0
* Solution
*LO SOLTN 1.48003482D-04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER8E
TEMPORARIES
R EXPON
M EXP
INDIVIDUALS
T PROD
A EXPON EXP( - K * XSQR )
F L * EXPON
G K - XSQR * L * EXPON
G L EXPON
H K K XSQR * XSQR * L * EXPON
H K L - XSQR * EXPON
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PALMER8E
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA