Function: SKYFIT
Purpose: SKYFIT is a routine for determining the sky-projection
parameters. It takes a set of grid positions and a set
of sky coordinates to fit the parameters.
The method is a mixture of the steepest descent method and
the Taylor method.
Category: MATH
File: skyfit.c
Author: K.G. Begeman
Use: INTEGER SKYFIT( X , Input DOUBLE PRECISION ARRAY
Y , Input DOUBLE PRECISION ARRAY
A , Input DOUBLE PRECISION ARRAY
D , Input DOUBLE PRECISION ARRAY
N , Input INTEGER
XF , Output DOUBLE PRECISION ARRAY
YF , Output DOUBLE PRECISION ARRAY
FPAR , In/Output DOUBLE PRECISION ARRAY
EPAR , Output DOUBLE PRECISION ARRAY
MPAR , Input INTEGER ARRAY
TOL , Input REAL
ITS , Input INTEGER
LAB , Input REAL
PROJ ) Input INTEGER
SKYFIT Returns number of iterations needed to achieve
convergence according to TOL. When this
number is negative, the fitting was not
continued because a fatal error occurred:
-1 Unknown projection.
-2 No free parameters.
-3 Not enough degrees of freedom.
-4 Maximum number of iterations too small to
obtain a solution which satisfies TOL.
-5 Diagonal of matrix contains elements which
are zero.
-6 Determinant of the coefficient matrix is zero.
-7 Square root of negative number.
X Contains x grid coordinates.
Y Contains y grid coordinates.
XF Contains fitted x grid coordinates.
YF Contains fitted x grid coordinates.
A Contains longitude coordinates.
D Contains latitude coordinates.
N Number of positions.
FPAR On input contains initial estimates of the
parameters, on output the fitted parameters.
There are seven parameters, so the dimension of
FPAR (and EPAR and MPAR) must be seven.
The order of the parameters is the following:
1: longitude projection centre
2: latitude projection centre
3: rotation angle
4: grid size x grid
5: grid size y grid
6: reference x grid position
7: reference y grid position
EPAR Contains estimates of errors in fitted
parameters.
MPAR Logical mask telling which parameters are
free (MPAR(J)=non-zero) and which parameters
are fixed (MPAR(J)=0).
TOL Relative tolerance. LSQFIT stops when
successive iterations fail to produce a
decrement in reduced chi-squared less than
TOL. If TOL is less than the minimum tolerance
possible, TOL will be set to this value. This
means that maximum accuracy can be obtained by
setting TOL=0.0.
ITS Maximum number of iterations.
LAB Mixing parameter, LAB determines the initial
weight of steepest descent method relative to
the Taylor method. LAB should be a small
value (i.e. 0.01).
PROJ Projection type.
2: Cylindrical projection.
3: Flat projection.
4: Gnomonic projection.
5: Orthographic projection.
6: Rectangular projection.
7: Global Sinusoidal projection.
8: North Celestial Pole projection.
9: Stereographic projection.
Updates: Jul 6, 1991: KGB, Document created.
Aug 23, 1993: VOG, Output of fitted grid coordinates.