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PALMER3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER3
* Problem :
* *********
* A nonlinear least squares problem with bounds
* arising from chemical kinetics.
* model: H-N=C=S TZVP + MP2
* fitting Y to A X**2 + B / ( C + X**2 / D ), B, C, D 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 -0.766531
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 0.766531
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 64.87939
RE Y2 50.46046
RE Y3 28.2034
RE Y4 13.4575
RE Y5 4.6547
RE Y6 0.59447
RE Y7 0.0000
RE Y8 0.2177
RE Y9 2.3029
RE Y10 5.5191
RE Y11 8.5519
RE Y12 9.8919
RE Y13 8.5519
RE Y14 5.5191
RE Y15 2.3029
RE Y16 0.2177
RE Y17 0.0000
RE Y18 0.59447
RE Y19 4.6547
RE Y20 13.4575
RE Y21 28.2034
RE Y22 50.46046
RE Y23 64.87939
VARIABLES
A
B
C
D
GROUPS
DO I 1 M
A* XSQR X(I) X(I)
ZN O(I) A XSQR
ND
CONSTANTS
DO I 1 M
Z PALMER3 O(I) Y(I)
ND
BOUNDS
FR PALMER3 A
LO PALMER3 B 0.00001
LO PALMER3 C 0.00001
LO PALMER3 D 0.00001
START POINT
XV PALMER3 'DEFAULT' 1.0
ELEMENT TYPE
EV QUOT B C
EV QUOT D
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
ZV E(I) D D
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 PALMER3 0.0
* Solution
* SOLTN 2265.95822
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER3
TEMPORARIES
R DENOM
INDIVIDUALS
T QUOT
A DENOM 1.0 / ( C + XSQR / D )
F B * DENOM
G B DENOM
G C - B * DENOM * DENOM
G D B * XSQR * ( DENOM / D ) ** 2
H B C - DENOM * DENOM
H B D XSQR * ( DENOM / D ) ** 2
H C C 2.0 * B * DENOM ** 3
H C D - 2.0 * B * XSQR * DENOM *
H+ ( DENOM / D ) ** 2
H D D 2.0 * B * DENOM ** 3 *
H+ ( XSQR / D ** 2 ) ** 2
H+ - 2.0 * B * DENOM ** 2 * XSQR / D ** 3
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PALMER3
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA