NAME¶
math::calculus::symdiff - 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 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.
PROCEDURES¶
The
math::calculus::symdiff package exports the two procedures:
- math::calculus::symdiff::symdiff expression
variable
- 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.
- 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 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.
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 Trackers [
http://core.tcl.tk/tcllib/reportlist]. 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/>