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PALMER4B.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER4B
* Problem :
* *********
* A nonlinear least squares problem with bounds
* arising from chemical kinetics.
* model: H-N=C=Se 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 -1.658063
RE X2 -1.570796
RE X3 -1.396263
RE X4 -1.221730
RE X5 -1.047198
RE X6 -0.872665
RE X7 -0.741119
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 0.741119
RE X18 0.872665
RE X19 1.047198
RE X20 1.221730
RE X21 1.396263
RE X22 1.570796
RE X23 1.658063
* Y( KJmol-1)
RE Y1 67.27625
RE Y2 52.8537
RE Y3 30.2718
RE Y4 14.9888
RE Y5 5.5675
RE Y6 0.92603
RE Y7 0.0
RE Y8 0.085108
RE Y9 1.867422
RE Y10 5.014768
RE Y11 8.263520
RE Y12 9.8046208
RE Y13 8.263520
RE Y14 5.014768
RE Y15 1.867422
RE Y16 0.085108
RE Y17 0.0
RE Y18 0.92603
RE Y19 5.5675
RE Y20 14.9888
RE Y21 30.2718
RE Y22 52.8537
RE Y23 67.27625
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 PALMER4B O(I) Y(I)
ND
BOUNDS
FR PALMER4B A2
FR PALMER4B A4
LO PALMER4B B 0.00001
LO PALMER4B C 0.00001
START POINT
XV PALMER4B '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 PALMER4B 0.0
* Solution
*LO SOLTN 6.83513867
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER4B
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 PALMER4B
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA