nls2.inv - Description of the Inverse of an nls2 Regression Function


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DESCRIPTION
FILE STRUCTURE
SYNTAX
DECLARATION PART
EXPRESSION PART
SEE-ALSO
EXAMPLE





DESCRIPTION:

The regression function, "f", of a model studied by `nls2' being defined by:
y=f(x, theta)+epsilon
its inverse (denoted here by "f-1"):
x=f-1(y, theta)+nu
should be formally described in an operating-system file. This file must contain the expression of the abscissa x in terms of the ordinate y, of the parameters theta and, possibly of second level parameters. The variance of y may also be expressed.

This entry describes the general syntax of this description-file.


FILE STRUCTURE:

The description file is divided into two parts. The first part is the Declaration Part and contains identifier declarations. The second part is the Expression Part and contains the expressions of the inverse function.

The Expression Part is not required if the user provides C or Fortran programs for evaluating the inverse function.

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SYNTAX:

The declarations and the expressions are delimited by a semi-column character (";") and the elements within lists by a comma (",").
Lower and upper case letters are distinguished.
Comments begin with the "" character and end with the new-line character. Lines that contain only the "" character are not accepted. Comments should not be inserted within lists.


DECLARATION PART:

All identifiers that appear in the expressions must be declared. Even if no Expression Part is provided, some identifiers are always required.
An identifier - or a list of identifiers - is declared by naming it after a keyword.
Identifiers must begin with a letter ([a-z, A-Z]) that may be followed by any number of characters among [a-z, A-Z, 0-9,_]. Don't use keywords as identifiers.

The keywords and what they introduce are:

abs
the name of the abscissa x (always required).
ord
the name of the ordinate y (always required).
paract
the names of the parameters theta (always required).
varord
the name of the variance of y.
pbisabs
the names of the second level parameters that occur in the expression of x.
pbisvar
the names of the second level parameters that occur in the expression of the variance of y.
const
the names of the numerical constants used in the expression of x.
aux
the names of the auxiliary variables used in the expressions of x and y. Introducing auxiliary variables may simplify the expressions or avoid calculating the same quantities several times.
filename
the pathname of the C-source file that is generated automatically from the description-file when the Expression Part is provided. By default, the name of the current file followed by a ".c" suffix.

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EXPRESSION PART:

The Expression Part begins with these 2 lines:

   subroutine
   begin
and ends with the line:
   end


The other lines are of the type:
   name=expr
where name is one of the identifiers declared by the keywords "abs", "varord", "aux", "const".
When "const", expr is always a number (for example: 23, -.0e+10, .2).

expr are expressions built with the following operators:
   =, +, -,  *, /, ** 
   log, log10, sin, tg, cos, exp, 
   if then else fi
   ==, !=, >, <, <=, >= (comparison operators)
   and, or, not.
Parentheses can be used.


SEE ALSO:

`calcinvnls2', `calib.nls2', `nls2.myinv', `loadnls2'.

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EXAMPLE:

Example 1:
   ord y; 
   abs x; 
   varord v;
   aux a1,a2; 
   paract a,b; 
   subroutine;
   begin 
   a2=10;
   a1= exp((b*y+a)*log(a2));
   x=a1;
   v=1;
   end 


Example 2: abs x; ord y; varord vy; paract n, d, a, b, g, h; pbisvar lambda; aux a1; subroutine; begin a1=-log10((y-n)/(d-n))/g; x=(log10(-1+exp(a1))-1)/b; vy=exp(lambda*log10(y)); end

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- Mon Sep 30 1996 -