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PALMER1A.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PALMER1A
* Problem :
* *********
* A nonlinear least squares problem with bounds
* arising from chemical kenetics.
* model: H-N=N=N TZVP+MP2
* fitting Y to A0 + A2 X**2 + A4 X**4 + A6 X**6
* + B / ( C + X**2 ), B, C nonnegative.
* Source:
* M. Palmer, Edinburgh, private communication.
* SIF input: Nick Gould, 1990.
* classification SBR2-RN-6-0
* Number of data points
IE M 35
* Other data
IE 1 1
* X (radians)
RE X1 -1.788963
RE X2 -1.745329
RE X3 -1.658063
RE X4 -1.570796
RE X5 -1.483530
RE X6 -1.396263
RE X7 -1.308997
RE X8 -1.218612
RE X9 -1.134464
RE X10 -1.047198
RE X11 -0.872665
RE X12 -0.698132
RE X13 -0.523599
RE X14 -0.349066
RE X15 -0.174533
RE X16 0.0000000
RE X17 1.788963
RE X18 1.745329
RE X19 1.658063
RE X20 1.570796
RE X21 1.483530
RE X22 1.396263
RE X23 1.308997
RE X24 1.218612
RE X25 1.134464
RE X26 1.047198
RE X27 0.872665
RE X28 0.698132
RE X29 0.523599
RE X30 0.349066
RE X31 0.174533
RE X32 -1.8762289
RE X33 -1.8325957
RE X34 1.8762289
RE X35 1.8325957
* Y( KJmol-1)
RE Y1 78.596218
RE Y2 65.77963
RE Y3 43.96947
RE Y4 27.038816
RE Y5 14.6126
RE Y6 6.2614
RE Y7 1.538330
RE Y8 0.000000
RE Y9 1.188045
RE Y10 4.6841
RE Y11 16.9321
RE Y12 33.6988
RE Y13 52.3664
RE Y14 70.1630
RE Y15 83.4221
RE Y16 88.3995
RE Y17 78.596218
RE Y18 65.77963
RE Y19 43.96947
RE Y20 27.038816
RE Y21 14.6126
RE Y22 6.2614
RE Y23 1.538330
RE Y24 0.000000
RE Y25 1.188045
RE Y26 4.6841
RE Y27 16.9321
RE Y28 33.6988
RE Y29 52.3664
RE Y30 70.1630
RE Y31 83.4221
RE Y32 108.18086
RE Y33 92.733676
RE Y34 108.18086
RE Y35 92.733676
VARIABLES
A0
A2
A4
A6
B
C
GROUPS
DO I 1 M
A* XSQR X(I) X(I)
A* XQUART XSQR XSQR
A* XSEXT XQUART XSQR
XN O(I) A0 1.0
ZN O(I) A2 XSQR
ZN O(I) A4 XQUART
ZN O(I) A6 XSEXT
ND
CONSTANTS
DO I 1 M
Z PALMER1A O(I) Y(I)
ND
BOUNDS
FR PALMER1A A0
FR PALMER1A A2
FR PALMER1A A4
FR PALMER1A A6
LO PALMER1A B 0.00001
LO PALMER1A C 0.00001
START POINT
XV PALMER1A '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 PALMER1A 0.0
* Solution
*LO SOLTN 8.98830D-02
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PALMER1A
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 PALMER1A
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA