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ORTHREGB.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ORTHREGB
* Problem :
* *********
* An orthogonal regression problem.
* The problem is to fit (orthogonally) an ellipse to a set of 6 points
* in the 3D space. These points are compatible with this constraint.
* 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.
* correction by Ph. Shott, Jan 1995.
* classification QQR2-AN-27-6
* Parameters for the generation of the data points
RE A 9.0
RE B 6.0
RE C 7.0
RE CX 0.5
RE CY 0.5
RE CZ 0.5
* Constants
IE 1 1
* Computed parameters
RM -A A -1.0
RM -B B -1.0
RM -C C -1.0
* Construct the data points
IE NPTS 1
A= XZ CX
A= YZ CY
A= ZZ CZ
IE NPTS 1
A+ XD(NPTS) XZ A
A+ YD(NPTS) YZ A
A= ZD(NPTS) ZZ
IA NPTS NPTS 1
A+ XD(NPTS) XZ B
A+ YD(NPTS) YZ -B
A= ZD(NPTS) ZZ
IA NPTS NPTS 1
A+ XD(NPTS) XZ -A
A+ YD(NPTS) YZ -A
A= ZD(NPTS) ZZ
IA NPTS NPTS 1
A+ XD(NPTS) XZ -B
A+ YD(NPTS) YZ B
A= ZD(NPTS) ZZ
IA NPTS NPTS 1
A= XD(NPTS) XZ
A= YD(NPTS) YZ
A+ ZD(NPTS) ZZ C
IA NPTS NPTS 1
A= XD(NPTS) XZ
A= YD(NPTS) YZ
A+ ZD(NPTS) ZZ -C
VARIABLES
* Parameters of the ellipse
H11
H12
H13
H22
H23
H33
G1
G2
G3
* Projections of the data points onto the ellipse
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 E(I)
ND
CONSTANTS
DO I 1 NPTS
Z ORTHREGB OX(I) XD(I)
Z ORTHREGB OY(I) YD(I)
Z ORTHREGB OZ(I) ZD(I)
X ORTHREGB E(I) 1.0
ND
BOUNDS
FR ORTHREGB 'DEFAULT'
START POINT
ORTHREGB H11 1.0
ORTHREGB H12 0.0
ORTHREGB H13 0.0
ORTHREGB H22 1.0
ORTHREGB H23 0.0
ORTHREGB H33 1.0
ORTHREGB G1 0.0
ORTHREGB G2 0.0
ORTHREGB G3 0.0
DO I 1 NPTS
Z ORTHREGB X(I) XD(I)
Z ORTHREGB Y(I) YD(I)
Z ORTHREGB Z(I) ZD(I)
ND
ELEMENT TYPE
EV HXX H X
EV HXY H X
EV HXY Y
EV GX G X
ELEMENT USES
DO I 1 NPTS
XT EA(I) HXX
ZV EA(I) H H11
ZV EA(I) X X(I)
XT EB(I) HXY
ZV EB(I) H H12
ZV EB(I) X X(I)
ZV EB(I) Y Y(I)
XT EC(I) HXX
ZV EC(I) H H22
ZV EC(I) X Y(I)
XT ED(I) GX
ZV ED(I) G G1
ZV ED(I) X X(I)
XT EE(I) GX
ZV EE(I) G G2
ZV EE(I) X Y(I)
XT EF(I) HXY
ZV EF(I) H H13
ZV EF(I) X X(I)
ZV EF(I) Y Z(I)
XT EG(I) HXY
ZV EG(I) H H23
ZV EG(I) X Y(I)
ZV EG(I) Y Z(I)
XT EH(I) HXX
ZV EH(I) H H33
ZV EH(I) X Z(I)
XT EI(I) GX
ZV EI(I) G G3
ZV EI(I) X Z(I)
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 E(I) EA(I) EB(I) 2.0
XE E(I) EC(I) ED(I) -2.0
XE E(I) EE(I) -2.0 EF(I) 2.0
XE E(I) EG(I) 2.0 EH(I)
XE E(I) EI(I) -2.0
ND
OBJECT BOUND
LO ORTHREGB 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ORTHREGB
INDIVIDUALS
T HXX
F H * X * X
G H X * X
G X 2.0 * H * X
H H X X + X
H X X H + H
T HXY
F H * X * Y
G H X * Y
G X H * Y
G Y H * X
H H X Y
H H Y X
H X Y H
T GX
F G * X
G G X
G X G
H G X 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS ORTHREGB
* Least-square groups
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA