1math::calculus::symdiff(Sny)mbolic differentiation for Tmcalth::calculus::symdiff(n)
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8 math::calculus::symdiff - Symbolic differentiation for Tcl
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11 package require Tcl 8.5
12 package require grammar::aycock 1.0
14 package require math::calculus::symdiff 1.0.1
16 math::calculus::symdiff::symdiff expression variable
18 math::calculus::jacobian variableDict
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24 The math::calculus::symdiff package provides a symbolic differentiation
25 facility for Tcl math expressions. It is useful for providing deriva‐
26 tives to packages that either require the Jacobian of a set of func‐
27 tions or else are more efficient or stable when the Jacobian is pro‐
28 vided.
29
31 The math::calculus::symdiff package exports the two procedures:
32 math::calculus::symdiff::symdiff expression variable
34 Differentiates the given expression with respect to the speci‐
35 fied variable. (See Expressions below for a discussion of the
36 subset of Tcl math expressions that are acceptable to math::cal‐
37 culus::symdiff.) The result is a Tcl expression that evaluates
38 the derivative. Returns an error if expression is not a well-
39 formed expression or is not differentiable.
40 math::calculus::jacobian variableDict
42 Computes the Jacobian of a system of equations. The system is
43 given by the dictionary variableDict, whose keys are the names
44 of variables in the system, and whose values are Tcl expressions
45 giving the values of those variables. (See Expressions below for
46 a discussion of the subset of Tcl math expressions that are
47 acceptable to math::calculus::symdiff. The result is a list of
48 lists: the i'th element of the j'th sublist is the partial de‐
49 rivative of the i'th variable with respect to the j'th variable.
50 Returns an error if any of the expressions cannot be differenti‐
51 ated, or if variableDict is not a well-formed dictionary.
52
54 The math::calculus::symdiff package accepts only a small subset of the
55 expressions that are acceptable to Tcl commands such as expr or if.
56 Specifically, the only constructs accepted are:
57 · Floating-point constants such as 5 or 3.14159e+00.
59 · References to Tcl variable using $-substitution. The variable
61 names must consist of alphanumerics and underscores: the ${...}
62 notation is not accepted.
63 · Parentheses.
65 · The +, -, *, /. and ** operators.
67 · Calls to the functions acos, asin, atan, atan2, cos, cosh, exp,
69 hypot, log, log10, pow, sin, sinh. sqrt, tan, and tanh.
70 Command substitution, backslash substitution, and argument expansion
72 are not accepted.
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75 math::calculus::symdiff::symdiff {($a*$x+$b)*($c*$x+$d)} x
76 ==> (($c * (($a * $x) + $b)) + ($a * (($c * $x) + $d)))
77 math::calculus::symdiff::jacobian {x {$a * $x + $b * $y}
78 y {$c * $x + $d * $y}}
79 ==> {{$a} {$b}} {{$c} {$d}}
80
83 This document, and the package it describes, will undoubtedly contain
84 bugs and other problems. Please report such in the category math ::
85 calculus of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist].
86 Please also report any ideas for enhancements you may have for either
87 package and/or documentation.
88 When proposing code changes, please provide unified diffs, i.e the out‐
90 put of diff -u.
91 Note further that attachments are strongly preferred over inlined
93 patches. Attachments can be made by going to the Edit form of the
94 ticket immediately after its creation, and then using the left-most
95 button in the secondary navigation bar.
96
98 math::calculus, math::interpolate
99
101 Copyright (c) 2010 by Kevin B. Kenny <kennykb@acm.org>
102 Redistribution permitted under the terms of the Open Publication License <http://www.opencontent.org/openpub/>
103tcllib 1.0.1 math::calculus::symdiff(n)