symdiff(n) Symbolic differentiation for Tcl symdiff(n)______________________________________________________________________________NAMEsymdiff - Symbolic differentiation for Tcl
SYNOPSIS
package require Tcl 8.5
package require grammar::aycock 1.0
package require math::calculus::symdiff 1.0
math::calculus::symdiff::symdiff expression variable
math::calculus::jacobian variableDict
_________________________________________________________________DESCRIPTION
The math::calculus::symdiff package provides a symbolic differentiation
facility for Tcl math expressions. It is useful for providing deriva‐
tives to packages that either require the Jacobian of a set of func‐
tions or else are more efficient or stable when the Jacobian is pro‐
vided.
PROCEDURES
The math::calculus::symdiff package exports the two procedures:
math::calculus::symdiff::symdiff expression variable
Differentiates the given expression with respect to the speci‐
fied variable. (See Expressions below for a discussion of the
subset of Tcl math expressions that are acceptable to math::cal‐
culus::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.
math::calculus::jacobian variableDict
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 de‐
rivative of the i'th variable with respect to the j'th variable.
Returns an error if any of the expressions cannot be differenti‐
ated, or if variableDict is not a well-formed dictionary.
EXPRESSIONS
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:
· Floating-point constants such as 5 or 3.14159e+00.
· References to Tcl variable using $-substitution. The variable
names must consist of alphanumerics and underscores: the ${...}
notation is not accepted.
· Parentheses.
· The +, -, *, /. and ** operators.
· Calls to the functions acos, asin, atan, atan2, cos, cosh, exp,
hypot, log, log10, pow, sin, sinh. sqrt, tan, and tanh.
Command substitution, backslash substitution, and argument expansion
are not accepted.
EXAMPLES
math::calculus::symdiff::symdiff {($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}}
BUGS, IDEAS, FEEDBACK
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 SF Trackers [http://source‐
forge.net/tracker/?group_id=12883]. Please also report any ideas for
enhancements you may have for either package and/or documentation.
SEE ALSO
math::calculus, math::interpolate
COPYRIGHT
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/>
math 1.0 symdiff(n)
