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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