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PALMER5E.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER5E
* Problem :
* *********
* A nonlinear least squares problem
* 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
* + L * EXP( -K X**2 )
* where T_i is the i-th (shifted) Chebyshev polynomial
* Source:
* M. Palmer, Edinburgh, private communication.
* SIF input: Nick Gould, 1992.
* classification SBR2-RN-8-0
* 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
K
L
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 PALMER5E O(I) Y(I)
ND
BOUNDS
FR PALMER5E A0
FR PALMER5E A2
FR PALMER5E A4
FR PALMER5E A6
FR PALMER5E A8
FR PALMER5E A10
*FR PALMER5E A12
*FR PALMER5E A14
FR PALMER5E L
START POINT
XV PALMER5E 'DEFAULT' 1.0
XV PALMER5E A0 1.9264D+01
XV PALMER5E A2 -1.7302D+00
XV PALMER5E A4 4.0794D+01
XV PALMER5E A6 8.3021D-01
XV PALMER5E A8 3.7090D+00
XV PALMER5E A10 -1.7723D-01
XV PALMER5E K 10.0
ELEMENT TYPE
EV PROD K L
EP PROD XSQR
ELEMENT USES
DO I 12 M
A* XSQR X(I) X(I)
XT E(I) PROD
ZV E(I) K K
ZV E(I) L L
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 PALMER5E 0.0
* Solution
*LO SOLTN 1.48003482D-04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER5E
TEMPORARIES
R EXPON
M EXP
INDIVIDUALS
T PROD
A EXPON EXP( - K * XSQR )
F L * EXPON
G K - XSQR * L * EXPON
G L EXPON
H K K XSQR * XSQR * L * EXPON
H K L - XSQR * EXPON
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PALMER5E
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA