math::calculus::symdiff(3tcl) Symbolic differentiation for Tcl math::calculus::symdiff(3tcl) 







math::calculus::symdiff - Symbolic differentiation for Tcl








package require Tcl 8.5


package require grammar::aycock 1.0


package require math::calculus::symdiff 1.0.1


math::calculus::symdiff::symdiff expression
    variable


math::calculus::jacobian variableDict












The math::calculus::symdiff package provides a symbolic
    differentiation facility for Tcl math expressions. It is useful for
    providing derivatives to packages that either require the Jacobian of a set
    of functions or else are more efficient or stable when the Jacobian is
    provided.








The math::calculus::symdiff package exports the two
    procedures:



  

  
Differentiates the given expression with respect to the specified
      variable. (See Expressions below for a discussion of the
      subset of Tcl math expressions that are acceptable to
      math::calculus::symdiff.) The result is a Tcl expression that
      evaluates the derivative. Returns an error if expression is not a
      well-formed expression or is not differentiable.

  

  
Computes the Jacobian of a system of equations. The system is given by the
      dictionary variableDict, whose keys are the names of variables in
      the system, and whose values are Tcl expressions giving the values of
      those variables. (See Expressions below for a discussion of the
      subset of Tcl math expressions that are acceptable to
      math::calculus::symdiff. The result is a list of lists: the i'th
      element of the j'th sublist is the partial derivative of the i'th variable
      with respect to the j'th variable. Returns an error if any of the
      expressions cannot be differentiated, or if variableDict is not a
      well-formed dictionary.










The math::calculus::symdiff package accepts only a small
    subset of the expressions that are acceptable to Tcl commands such as
    expr or if. Specifically, the only constructs accepted
  are:



Command substitution, backslash substitution, and argument
    expansion are not accepted.










math::calculus::symdiff::symdiff {($a*$x+$b)*($c*$x+$d)} x
==> (($c * (($a * $x) + $b)) + ($a * (($c * $x) + $d)))
math::calculus::symdiff::jacobian {x {$a * $x + $b * $y}
                         y {$c * $x + $d * $y}}
==> {{$a} {$b}} {{$c} {$d}}











This document, and the package it describes, will undoubtedly
    contain bugs and other problems. Please report such in the category math
    :: calculus of the Tcllib Trackers
    [http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for
    enhancements you may have for either package and/or documentation.


When proposing code changes, please provide unified diffs,
    i.e the output of diff -u.


Note further that attachments are strongly preferred over
    inlined patches. Attachments can be made by going to the Edit form of
    the ticket immediately after its creation, and then using the left-most
    button in the secondary navigation bar.








math::calculus, math::interpolate








Copyright (c) 2010 by Kevin B. Kenny <kennykb@acm.org>
Redistribution permitted under the terms of the Open Publication License <http://www.opencontent.org/openpub/>








  

    1.0.1
    tcllib