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PALMER8A.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER8A
* Problem :
* *********
* A nonlinear least squares problem with bounds
* arising from chemical kinetics.
* model: H-N=C=Se TZVP + MP2
* fitting Y to A0 + A2 X**2 + A4 X**4 + A6 X**6
* + B / ( C + X**2 ), B, C nonnegative.
* Source:
* M. Palmer, Edinburgh, private communication.
* SIF input: Nick Gould, 1992.
* classification SBR2-RN-6-0
* 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
B
C
GROUPS
DO I 12 M
A* XSQR X(I) X(I)
A* XQUART XSQR XSQR
A* XSEXT XQUART XSQR
XN O(I) A0 1.0
ZN O(I) A2 XSQR
ZN O(I) A4 XQUART
ZN O(I) A6 XSEXT
ND
CONSTANTS
DO I 12 M
Z PALMER8A O(I) Y(I)
ND
BOUNDS
FR PALMER8A A0
FR PALMER8A A2
FR PALMER8A A4
FR PALMER8A A6
LO PALMER8A B 0.00001
LO PALMER8A C 0.00001
START POINT
XV PALMER8A 'DEFAULT' 1.0
ELEMENT TYPE
EV QUOT B C
EP QUOT XSQR
ELEMENT USES
DO I 12 M
A* XSQR X(I) X(I)
XT E(I) QUOT
ZV E(I) B B
ZV E(I) C C
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 PALMER8A 0.0
* Solution
*LO SOLTN 4.0606141D-02
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER8A
TEMPORARIES
R DENOM
INDIVIDUALS
T QUOT
A DENOM 1.0 / ( C + XSQR )
F B * DENOM
G B DENOM
G C - B * DENOM * DENOM
H B C - DENOM * DENOM
H C C 2.0 * B * DENOM ** 3
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PALMER8A
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA