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PALMER2B.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER2B
* Problem :
* *********
* A nonlinear least squares problem with bounds
* arising from chemical kinetics.
* model: H-N=C=O TZVP + MP2
* fitting Y to A2 X**2 + A4 X**4
* + B / ( C + X**2 ), B, C nonnegative.
* Source:
* M. Palmer, Edinburgh, private communication.
* SIF input: Nick Gould, 1990.
* classification SBR2-RN-4-0
* Number of data points
IE M 23
* Other data
IE 1 1
* X (radians)
RE X1 -1.745329
RE X2 -1.570796
RE X3 -1.396263
RE X4 -1.221730
RE X5 -1.047198
RE X6 -0.937187
RE X7 -0.872665
RE X8 -0.698132
RE X9 -0.523599
RE X10 -0.349066
RE X11 -0.174533
RE X12 0.0
RE X13 0.174533
RE X14 0.349066
RE X15 0.523599
RE X16 0.698132
RE X17 0.872665
RE X18 0.937187
RE X19 1.047198
RE X20 1.221730
RE X21 1.396263
RE X22 1.570796
RE X23 1.745329
* Y( KJmol-1)
RE Y1 72.676767
RE Y2 40.149455
RE Y3 18.8548
RE Y4 6.4762
RE Y5 0.8596
RE Y6 0.00000
RE Y7 0.2730
RE Y8 3.2043
RE Y9 8.1080
RE Y10 13.4291
RE Y11 17.7149
RE Y12 19.4529
RE Y13 17.7149
RE Y14 13.4291
RE Y15 8.1080
RE Y16 3.2053
RE Y17 0.2730
RE Y18 0.00000
RE Y19 0.8596
RE Y20 6.4762
RE Y21 18.8548
RE Y22 40.149455
RE Y23 72.676767
VARIABLES
A2
A4
B
C
GROUPS
DO I 1 M
A* XSQR X(I) X(I)
A* XQUART XSQR XSQR
ZN O(I) A2 XSQR
ZN O(I) A4 XQUART
ND
CONSTANTS
DO I 1 M
Z PALMER2B O(I) Y(I)
ND
BOUNDS
FR PALMER2B A2
FR PALMER2B A4
LO PALMER2B B 0.00001
LO PALMER2B C 0.00001
START POINT
XV PALMER2B 'DEFAULT' 1.0
ELEMENT TYPE
EV QUOT B C
EP QUOT XSQR
ELEMENT USES
DO I 1 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 1 M
XT O(I) L2
XE O(I) E(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO PALMER2B 0.0
* Solution
*LO SOLTN 0.62326690
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER2B
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 PALMER2B
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA