`mapSymType`

Applies a function to every subexpression of a given type.

Category: Symbolic Computations in MATLAB > Symbolic Variables, Expressions, Functions, and Preferences

Syntax

R = mapSymType(S, type, f)

Replaces each subexpression of S of type type with f applied to it.

Description

mapSymType walks the expression tree, finds every part of the requested type and replaces it by the value of f on that part. It is a structural rewrite: unlike subs it can act on all occurrences of a whole class of subexpressions, such as every integer or every call of sin.

For example, mapping n -> n + 1 over the integers of x^2 + 3*x produces x^3 + 4*x, since both the exponent and the coefficient are integers.

Input arguments

S: Symbolic expression.
type: Type name string, such as 'variable', 'integer' or a function name like 'sin'.
f: Function handle that takes one subexpression and returns its replacement.

Output arguments

R: The rewritten expression.

Example

Rewriting variables and function calls

syms x
mapSymType(x + 1, 'variable', @(v) v^2)
mapSymType(sin(x) + cos(x), 'sin', @(s) cos(children(s)))
mapSymType(x^2 + 3*x, 'integer', @(n) n + 1)

Output

ans = x^2 + 1
ans = 2*cos(x)
ans = x^3 + 4*x

mapSymType