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.\" ========================================================================
.\"
.IX Title "NewtonRaphson 3pm"
.TH NewtonRaphson 3pm "2008-06-13" "perl v5.10.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.SH "NAME"
Math::Calculus::NewtonRaphson \- Algebraic Newton Raphson Implementation
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& use Math::Calculus::NewtonRaphson;
\&
\& # Create an object.
\& my $exp = Math::Calculus::NewtonRaphson\->new;
\&
\& # Set a variable and expression.
\& $exp\->addVariable(\*(Aqx\*(Aq);
\& $exp\->setExpression(\*(Aqx^2 \- 5\*(Aq) or die $exp\->getError;
\&
\& # Apply Newton Raphson.
\& my $result = $exp\->newtonRaphson(2) or die $exp\->getError;
\& print $result; # Prints 1.4142...
.Ve
.SH "DESCRIPTION"
.IX Header "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:\-
.PP
x^2 = 5
.PP
You would need to pass in:\-
.PP
x^2 \- 5
.PP
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.
.SH "EXPORT"
.IX Header "EXPORT"
None by default.
.SH "METHODS"
.IX Header "METHODS"
.IP "new" 4
.IX Item "new"
.Vb 1
\& $exp = Math::Calculus::NewtonRaphson\->new;
.Ve
.Sp
Creates a new instance of the Newton Raphson object, which can hold an individual
expression.
.IP "addVariable" 4
.IX Item "addVariable"
.Vb 1
\& $exp\->addVariable(\*(Aqx\*(Aq);
.Ve
.Sp
Sets a certain named value in the expression as being a variable. A named value must be
an alphabetic chracter.
.IP "setExpression" 4
.IX Item "setExpression"
.Vb 1
\& $exp\->setExpression(\*(Aqx^2 + 5*x);
.Ve
.Sp
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 \s-1BODMAS\s0 precedence
convention. Returns undef on failure and a true value on success.
.IP "getExpression" 4
.IX Item "getExpression"
.Vb 1
\& $expr = $exp\->getExpression;
.Ve
.Sp
Returns a textaul, human readable representation of the expression that is being stored.
.IP "newtonRaphson" 4
.IX Item "newtonRaphson"
.Vb 1
\& $result = $exp\->newtonRaphson($variable, $guess, %mappings);
.Ve
.Sp
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.
.IP "getTraceback" 4
.IX Item "getTraceback"
.Vb 1
\& $exp\->getTraceback;
.Ve
.Sp
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.
.IP "getError" 4
.IX Item "getError"
.Vb 1
\& $exp\->getError;
.Ve
.Sp
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.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
The author of this module has a website at , which has
the latest news about the module and a web-based frontend to allow you to test the module
out for yourself.
.SH "AUTHOR"
.IX Header "AUTHOR"
Jonathan Worthington,
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2004 by Jonathan Worthington
.PP
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.
.SH "POD ERRORS"
.IX Header "POD ERRORS"
Hey! \fBThe above document had some coding errors, which are explained below:\fR
.IP "Around line 65:" 4
.IX Item "Around line 65:"
\&'=item' outside of any '=over'
.IP "Around line 186:" 4
.IX Item "Around line 186:"
You forgot a '=back' before '=head1'