NAME

       Math::Calculus::NewtonRaphson - Algebraic Newton Raphson Implementation

SYNOPSIS

         use Math::Calculus::NewtonRaphson;

         # Create an object.
         my $exp = Math::Calculus::NewtonRaphson->new;

         # Set a variable and expression.
         $exp->addVariable('x');
         $exp->setExpression('x^2 - 5') or die $exp->getError;

         # Apply Newton Raphson.
         my $result = $exp->newtonRaphson(2) or die $exp->getError;
         print $result; # Prints 1.4142...

DESCRIPTION

       This module can take an algebraic expression, parses it and then uses the Newton Raphson method to solve
       the it. The Newton Raphson method relies on the fact that the expression you pass in evaluates to zero
       where there is a solution. That is, to solve:-

       x^2 = 5

       You would need to pass in:-

       x^2 - 5

       It understands expressions containing any of the operators +, -, *, / and ^ (raise to power), bracketed
       expressions to enable correct precedence and the functions ln, exp, sin, cos, tan, sec, cosec, cot, sinh,
       cosh, tanh, sech, cosech, coth, asin, acos, atan, asinh, acosh and atanh.

EXPORT

       None by default.

METHODS

       new
             $exp = Math::Calculus::NewtonRaphson->new;

           Creates a new instance of the Newton Raphson object, which can hold an individual expression.

       addVariable
             $exp->addVariable('x');

           Sets a certain named value in the expression as being a variable. A named value must be an alphabetic
           character.

       setExpression
             $exp->setExpression('x^2 + 5*x);

           Takes  an expression in human-readable form and stores it internally as a tree structure, checking it
           is a valid expression that the module can understand in the process. Note that the engine  is  strict
           about  syntax. For example, note above that you must write 5*x and not just 5x. Whitespace is allowed
           in the expression, but does not have any effect on precedence.  If you require control of precedence,
           use brackets; bracketed expressions will always be evaluated first, as you would normally expect. The
           module follows the BODMAS precedence convention. Returns  undef  on  failure  and  a  true  value  on
           success.

       getExpression
             $expr = $exp->getExpression;

           Returns a textaul, human readable representation of the expression that is being stored.

       newtonRaphson
             $result = $exp->newtonRaphson($variable, $guess, %mappings);

           Attempts  to  solve  the expression for the given variable using the Newton Raphson method, using the
           passed value as the first guess. The mappings hash allows  any  other  non-numeric  constants  to  be
           mapped to numeric values - a pre-requisite for solving such equations.

       getTraceback
             $exp->getTraceback;

           When  setExpression  and  newtonRaphson  are  called, a traceback is generated to describe what these
           functions did. If an error occurs, this traceback can be extremely useful in helping track  down  the
           source of the error.

       getError
             $exp->getError;

           When  any method other than getTraceback is called, the error message stored is cleared, and then any
           errors that occur during the execution of the method are stored. If failure occurs, call this  method
           to get a textual representation of the error.

SEE ALSO

       The  author  of  this module has a website at <http://www.jwcs.net/~jonathan/>, which has the latest news
       about the module and a web-based frontend to allow you to test the module out for yourself.

AUTHOR

       Jonathan Worthington, <jonathan@jwcs.net>

COPYRIGHT AND LICENSE

       Copyright (C) 2004 by Jonathan Worthington

       This library is free software; you can redistribute it and/or modify it under  the  same  terms  as  Perl
       itself, either Perl version 5.8.1 or, at your option, any later version of Perl 5 you may have available.

perl v5.36.0                                       2022-12-08                                 NewtonRaphson(3pm)