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PALMER5A.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER5A
* Problem :
* *********
* A nonlinear least squares problem with bounds
* arising from chemical kinetics.
* model: H-N=C=Se TZVP + MP2
* fitting Y to A0 T_0 + A2 T_2 + A4 T_4 + A6 T_6 + A8 T_8 +
* A10 T_10 + A12 T_12 + A14 T_14
* + B / ( C + X**2 ), B, C nonnegative.
* where T_i is the i-th (shifted) Chebyshev polynomial
* Source:
* M. Palmer, Edinburgh, private communication.
* classification SBR2-RN-8-0
* SIF input: Nick Gould, 1992.
* Number of data points
IE M 23
* Other data
IE 1 1
IE 2 2
IE 12 12
IE 14 14
* X (radians)
RE X12 0.000000
RE X13 1.570796
RE X14 1.396263
RE X15 1.308997
RE X16 1.221730
RE X17 1.125835
RE X18 1.047198
RE X19 0.872665
RE X20 0.698132
RE X21 0.523599
RE X22 0.349066
RE X23 0.174533
R= B X13
RM A B -1.0D+0
RM DIFF B 2.0D+0
* Y( KJmol-1)
RE Y12 83.57418
RE Y13 81.007654
RE Y14 18.983286
RE Y15 8.051067
RE Y16 2.044762
RE Y17 0.000000
RE Y18 1.170451
RE Y19 10.479881
RE Y20 25.785001
RE Y21 44.126844
RE Y22 62.822177
RE Y23 77.719674
VARIABLES
A0
A2
A4
A6
A8
A10
* A12
* A14
B
C
GROUPS
DO I 12 M
RE T0 1.0D+0
AM Y X(I) 2.0D+0
R- Y Y A
R- Y Y B
R/ Y Y DIFF
R= T1 Y
RM 2Y Y 2.0D+0
DO J 2 14
IA J-1 J -1
IA J-2 J -2
A* T(J) 2Y T(J-1)
A- T(J) T(J) T(J-2)
OD J
ZN O(I) A0 T0
ZN O(I) A2 T2
ZN O(I) A4 T4
ZN O(I) A6 T6
ZN O(I) A8 T8
ZN O(I) A10 T10
*ZN O(I) A12 T12
*ZN O(I) A14 T14
ND
CONSTANTS
DO I 12 M
Z PALMER5A O(I) Y(I)
ND
BOUNDS
FR PALMER5A A0
FR PALMER5A A2
FR PALMER5A A4
FR PALMER5A A6
FR PALMER5A A8
FR PALMER5A A10
*FR PALMER5A A12
*FR PALMER5A A14
*LO PALMER5A B 0.00001
LO PALMER5A C 0.00001
START POINT
XV PALMER5A '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 PALMER5A 0.0
* Solution
*LO SOLTN 4.0606141D-02
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER5A
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 PALMER5A
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA