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THE TRANSFORMATION SECTION
The transformation section is used to define the transformation
equations, to specify which parameters are to be altered and which
are to be held constant during the fitting process, and to assign
initial values to the parameters.
The transformation section begins with the keyword transformation,
followed by the list of parameter declarations, followed by the
transformation equation.
Syntax
transformation
fit parameter = value, parameter = value, ...
constant parameter = value, parameter = value, ...
label : expression = expression
(function) (fit)
The fit keyword begins a list of the parameters to be fit. The
named parameters will be fit if they are present in a
transformation equation. The fit parameter values are used as the
initial guesses for the parameters.
The constant keyword begins a list of the parameters to be held
constant. The named parameters will not be fit. Instead the values
are regarded as constant values in any transformation equation in
which they appear. Constant parameter declarations are used to fix
values if they are known, or to restrict the degrees of freedom of
the fit.
All parameters, both fit and constant, must be declared before the
first equations in which they appear. There may be any number of
fit and constant parameter declaration statements. Redefinitions
are allowed, i.e., it is possible to declare a parameter with the
fit keyword, and redefine it later with the constant keyword. The
inverse is also true.
The transformation equations are composed of three elements: the
equation label, the function expression, and the fit expression.
The label is used to assign a name to the equation and fit
expression. The label can be any name not already in use. The ":"
after the label is necessary to delimit it from the rest of the
transformation equation defintion. Labels are used primarily to
associate the optional error, weight and plot equations with the
appropriate transformation equations. However these labels can
also be used in expressions belonging to subsequent equations, an
action equivalent to replacing them with the fit expression they
reference, before performing the actual evaluation.
The function expression (left hand side of the "=" sign) is used as
a reference expression, i.e. an expression that has no fitting or
constant parameters in it. The function expression contains only
values computed from the input data which are known before the fit
starts.
The fit expression (right hand side of the "=" sign) is an
expression which contains the parameters, both those to be fit and
those that are fixed. If this expression contains names defined in
the catalog section , it will be possible to perform the fit, but
will not be possible to apply the transformations in the forward
sense to program observations that don't have matching catalog
values. If the number of transformations equations is greater than
or equal to the total number of catalog variables used in the
transformation equations, it MAY be possible to invert the system
of equations and so evaluate the catalog variables for program
objects.
Example
# Sample transformation section for the UBV system
transform
# V equation
fit v1 = 25.0, v2=1.03, v3=-0.17
VFIT : V = v1 + v + v2 * (b - v) + v3 * x
# B - V equation
fit b1 = 2.10, b2 = 1.15, b3=-0.12
const b4 = 0.0
BVFIT : BV = b1 + b2 * (b - v) + b3 * x + b4 * (b - v) * x
# U - B equation
fit u1 = 3.45, u2 = 1.063, u3=-0.30
const u4=0.0
UBFIT : UB = u1 + u2 * (u - b) + u3 * x + u4 * (u - b) * x
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