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HAIRY.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HAIRY
* Problem :
* *********
* A hairy problem in two variables. The surface defined by
* this function has a large number of relatively sharp hills between
* which a valley leads to the minimizer.
* This problem contains a large number of saddle points.
* Dedicated to Meret Oppenheim, creator of the "furry cup" (1936).
* Source:
* Ph. Toint, private communication,
* SIF input: Ph. Toint, Dec 1989.
* classification OUR2-AY-2-0
RE HLENGTH 30.0
RE CSLOPE 100.0
VARIABLES
X1
X2
GROUPS
N FURCUP
BOUNDS
FR HAIRY 'DEFAULT'
START POINT
HAIRY X1 -5.0
HAIRY X2 -7.0
ELEMENT TYPE
EV FUR V1 V2
EP FUR DENS
EV DCUP V1 V2
IV DCUP V
EP DCUP SMOOTH
EV 1CUP V
EP 1CUP SMOOTH
ELEMENT USES
T HAIR FUR
V HAIR V1 X1
V HAIR V2 X2
P HAIR DENS 7.0
T DBOWL DCUP
V DBOWL V1 X1
V DBOWL V2 X2
P DBOWL SMOOTH 0.01
T 1BOWL 1CUP
V 1BOWL V X1
P 1BOWL SMOOTH 0.01
GROUP USES
ZE FURCUP HAIR HLENGTH
ZE FURCUP DBOWL CSLOPE
ZE FURCUP 1BOWL CSLOPE
OBJECT BOUND
* Solution
*LO SOLTN 20.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HAIRY
TEMPORARIES
R DV1
R DV2
R TDV1
R TDV2
R TDL2
R S1SQ
R C2SQ
R STDV1
R STDV2
R VSQ
R ARG
R SQARG
R DEN
M SIN
M COS
INDIVIDUALS
* The fur: a weighted product of sin**2 times cos**2
T FUR
A DV1 DENS * V1
A DV2 DENS * V2
A TDV1 DV1 + DV1
A TDV2 DV2 + DV2
A TDL2 2.0 * DENS * DENS
A S1SQ SIN( DV1 )**2
A C2SQ COS( DV2 )**2
A STDV1 SIN( TDV1 )
A STDV2 SIN( TDV2 )
F S1SQ * C2SQ
G V1 DENS * STDV1 * C2SQ
G V2 -DENS * S1SQ * STDV2
H V1 V1 TDL2 * COS( TDV1) * C2SQ
H V1 V2 -DENS * DENS * STDV1 * STDV2
H V2 V2 -TDL2 * S1SQ * COS( TDV2 )
* The 2D diagonal cup: a smoothed l2-norm
T DCUP
R V V1 1.0 V2 -1.0
A VSQ V * V
A ARG SMOOTH + VSQ
A SQARG SQRT ( ARG )
A DEN 1.0 / SQARG
F SQARG
G V V * DEN
H V V ( 1.0 - VSQ / ARG ) * DEN
* The 1D cup: a smoothed l2-norm
T 1CUP
A VSQ V * V
A ARG SMOOTH + VSQ
A SQARG SQRT ( ARG )
A DEN 1.0 / SQARG
F SQARG
G V V * DEN
H V V ( 1.0 - VSQ / ARG ) * DEN
ENDATA