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ORTHREGE.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ORTHREGE
* Problem :
* *********
* An orthogonal regression problem,
* The problem is to fit (orthogonally) an elliptic helix to a
* set of points in 3D space. This set of points is generated by
* perturbing a first set lying exactly on a predifined helix
* centered at the origin.
* Source:
* M. Gulliksson,
* "Algorithms for nonlinear Least-squares with Applications to
* Orthogonal Regression",
* UMINF-178.90, University of Umea, Sweden, 1990.
* SIF input: Ph. Toint, June 1990.
* classification QOR2-AY-V-V
* Number of data points
* (number of variables = 3 NPTS + 6 )
*IE NPTS 10 $-PARAMETER n= 36 original valu
IE NPTS 2500 $-PARAMETER n= 7506
* True helix parameters (centered at the origin)
RE TP4 1.7
RE TP5 0.8
RE TP6 2.0
* Perturbation parameters
RE PSEED 237.1531
RE PSIZE 0.2
* Constants
IE 1 1
IE 6 6
RE PI 3.1415926535
* Computed parameters
RM 2PI PI 2.0
RI RNPTS NPTS
RD ICR0 RNPTS 1.0
R* INCR ICR0 2PI
* Construct the data points
DO I 1 NPTS
IA I-1 I -1
RI RI-1 I-1
R* THETA RI-1 INCR
R( ST SIN THETA
R( CT COS THETA
R* R1 TP4 CT
R* R2 TP5 ST
R* R3 TP6 THETA
R* XSEED THETA PSEED
R( SSEED COS XSEED
R* PER-1 PSIZE SSEED
RA PERT PER-1 1.0
A* XD(I) R1 PERT
A* YD(I) R2 PERT
A* ZD(I) R3 PERT
ND
VARIABLES
* Parameters of the helix
DO I 1 6
X P(I)
ND
* Projections of the data points onto the helix
DO I 1 NPTS
X X(I)
X Y(I)
X Z(I)
ND
GROUPS
DO I 1 NPTS
XN OX(I) X(I) 1.0
XN OY(I) Y(I) 1.0
XN OZ(I) Z(I) 1.0
XE A(I) X(I) 1.0 P1 -1.0
XE B(I) Y(I) 1.0 P2 -1.0
ND
CONSTANTS
DO I 1 NPTS
Z ORTHREGE OX(I) XD(I)
Z ORTHREGE OY(I) YD(I)
Z ORTHREGE OZ(I) ZD(I)
ND
BOUNDS
FR ORTHREGE 'DEFAULT'
XL ORTHREGE P6 0.001
START POINT
ORTHREGE P1 1.0
ORTHREGE P2 0.0
ORTHREGE P3 1.0
ORTHREGE P4 1.0
ORTHREGE P5 0.0
ORTHREGE P6 0.25
DO I 1 NPTS
Z ORTHREGE X(I) XD(I)
Z ORTHREGE Y(I) YD(I)
Z ORTHREGE Z(I) ZD(I)
ND
ELEMENT TYPE
EV EHX Z A
EV EHX B C
IV EHX AA ZMB
IV EHX CC
ELEMENT USES
DO I 1 NPTS
XT EA(I) EHX
ZV EA(I) Z Z(I)
ZV EA(I) A P4
ZV EA(I) B P3
ZV EA(I) C P6
XT EB(I) EHX
ZV EB(I) Z Z(I)
ZV EB(I) A P5
ZV EB(I) B P3
ZV EB(I) C P6
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 NPTS
XT OX(I) L2
XT OY(I) L2
XT OZ(I) L2
XE A(I) EA(I) -1.0
XE B(I) EB(I) -1.0
ND
OBJECT BOUND
LO ORTHREGE 0.0
* Solution
*LO SOLTN(10) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ORTHREGE
TEMPORARIES
R T
R CT
R ST
R CCSQ
R CCCB
R ACT
R AST
M COS
M SIN
INDIVIDUALS
T EHX
R ZMB Z 1.0 B -1.0
R AA A 1.0
R CC C 1.0
A T ZMB / CC
A CT COS( T )
A ST SIN( T )
A CCSQ CC * CC
A CCCB CCSQ * CC
A ACT AA * CT
A AST AA * ST
F ACT
G AA CT
G ZMB - AST / CC
G CC AST * ZMB / CCSQ
H AA ZMB - ST / CC
H AA CC ST * ZMB / CCSQ
H ZMB ZMB - ACT / CCSQ
H ZMB CC ( AST + ZMB * ACT / CC ) / CCSQ
H CC CC - ZMB * ( ZMB * ACT / CC
H+ + AST + AST ) / CCCB
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS ORTHREGE
* Least-square groups
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA