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EXPFITA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME EXPFITA
* Problem :
* *********
* One sided rational approximation to the exponential function, as
* described by Powell.
* Source:
* M.J.D. Powell,
* "A tolerant algorithm for linearly constrained optimization
* calculations"'
* Mathematical Programming 45(3), pp.561--562, 1989.
* SDIF input: Ph. Toint and N. Gould, May 1990.
* classification OLR2-AN-5-22
* Number of fitting points
IE R 11
* Constants
IE 1 1
RE 5.0 5.0
* Computed parameters
IA R-1 R -1
RI RR-1 R-1
R/ 5/R-1 5.0 RR-1
* Fitting points and their exponentials
DO I 1 R
IA I-1 I -1
RI RI-1 I-1
A* T(I) RI-1 5/R-1
A( ET(I) EXP T(I)
ND
VARIABLES
P0
P1
P2
Q1
Q2
GROUPS
N OBJ
DO I 1 R
AA TM5 T(I) -5.0
R* TM5SQ TM5 TM5
A* QC1 TM5 ET(I)
A* QC2 TM5SQ ET(I)
RM -QC1 QC1 -1.0
RM -QC2 QC2 -1.0
A* 2T T(I) T(I)
XG C(I) P0 1.0
ZG C(I) P1 T(I)
ZG C(I) P2 2T
ZG C(I) Q1 -QC1
ZG C(I) Q2 -QC2
ZG B(I) Q1 TM5
ZG B(I) Q2 TM5SQ
ND
CONSTANTS
DO I 1 R
Z EXPFITA C(I) ET(I)
X EXPFITA B(I) -0.99999
ND
BOUNDS
FR EXPFITA 'DEFAULT'
START POINT
EXPFITA P0 1.0
EXPFITA P1 1.0
EXPFITA P2 6.0
EXPFITA Q1 0.0
EXPFITA Q2 0.0
ELEMENT TYPE
EV FIT P0 P1
EV FIT P2 Q1
EV FIT Q2
EP FIT T
ELEMENT USES
DO I 1 R
XT F(I) FIT
ZV F(I) P0 P0
ZV F(I) P1 P1
ZV F(I) P2 P2
ZV F(I) Q1 Q1
ZV F(I) Q2 Q2
ZP F(I) T T(I)
ND
GROUP USES
DO I 1 R
XE OBJ F(I)
ND
OBJECT BOUND
LO EXPFITA 0.0
* Solution
LO SOLTN 1.1366D-03
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS EXPFITA
TEMPORARIES
R T2
R ET
R QT
R ETQT
R ETQT2
R ETQT3
R PT
R TM5
R TM5SQ
R F
R TWOF
R DFDP0
R DFDP1
R DFDP2
R DFDQ1
R DFDQ2
R D2P0Q1
R D2P0Q2
R D2P1Q1
R D2P1Q2
R D2P2Q1
R D2P2Q2
R D2Q1Q1
R D2Q1Q2
R D2Q2Q2
M EXP
INDIVIDUALS
T FIT
A TM5 T - 5.0
A TM5SQ TM5 * TM5
A T2 T * T
A ET EXP( T )
A QT 1.0 + Q1 * TM5 + Q2 * TM5SQ
A ETQT ET * QT
A ETQT2 ETQT * QT
A ETQT3 ETQT2 * QT
A PT P0 + P1 * T + P2 * T2
A F PT / ETQT - 1.0
A TWOF F + F
A DFDP0 1.0 / ETQT
A DFDP1 T / ETQT
A DFDP2 T2 / ETQT
A DFDQ1 - PT * TM5 / ETQT2
A DFDQ2 - PT * TM5SQ / ETQT2
A D2P0Q1 - TM5 / ETQT2
A D2P0Q2 - TM5SQ / ETQT2
A D2P1Q1 - T * TM5 / ETQT2
A D2P1Q2 - T * TM5SQ / ETQT2
A D2P2Q1 - T2 * TM5 / ETQT2
A D2P2Q2 - T2 * TM5SQ / ETQT2
A D2Q1Q1 2.0 * PT * TM5SQ / ETQT3
A D2Q1Q2 2.0 * PT * TM5SQ * TM5 / ETQT3
A D2Q2Q2 2.0 * PT * TM5SQ * TM5SQ / ETQT3
F F * F
G P0 TWOF * DFDP0
G P1 TWOF * DFDP1
G P2 TWOF * DFDP2
G Q1 TWOF * DFDQ1
G Q2 TWOF * DFDQ2
H P0 P0 2.0 * DFDP0 * DFDP0
H P0 P1 2.0 * DFDP0 * DFDP1
H P0 P2 2.0 * DFDP0 * DFDP2
H P1 P1 2.0 * DFDP1 * DFDP1
H P1 P2 2.0 * DFDP1 * DFDP2
H P2 P2 2.0 * DFDP2 * DFDP2
H P0 Q1 TWOF * D2P0Q1 + 2.0 * DFDP0 * DFDQ1
H P0 Q2 TWOF * D2P0Q2 + 2.0 * DFDP0 * DFDQ2
H P1 Q1 TWOF * D2P1Q1 + 2.0 * DFDP1 * DFDQ1
H P1 Q2 TWOF * D2P1Q2 + 2.0 * DFDP1 * DFDQ2
H P2 Q1 TWOF * D2P2Q1 + 2.0 * DFDP2 * DFDQ1
H P2 Q2 TWOF * D2P2Q2 + 2.0 * DFDP2 * DFDQ2
H Q1 Q1 TWOF * D2Q1Q1 + 2.0 * DFDQ1 * DFDQ1
H Q1 Q2 TWOF * D2Q1Q2 + 2.0 * DFDQ1 * DFDQ2
H Q2 Q2 TWOF * D2Q2Q2 + 2.0 * DFDQ2 * DFDQ2
ENDATA