symfun

Create symbolic functions

Syntax

f(inputs) = formula

f = symfun(formula,inputs)

Description

f(inputs) = formula creates the symbolic function f. For example, f(x,y) = x + y. The symbolic variables in inputs are the input arguments. The symbolic expression formula is the body of the function f.

f = symfun(formula,inputs) is the formal way to create a symbolic function.

Examples

Create and Define Symbolic Functions

Define the symbolic function f(x,y) = x + y. First, create the function by using syms. Then define the function.

syms f(x,y)
f(x,y) = x + y

f(x, y) = $$x+y$$

Find the value of f at x = 1 and y = 2.

f(1,2)

ans = $$3$$

Define the function again by using the formal way.

syms x y
f = symfun(x+y,[x y])

f(x, y) = $$x+y$$

Return Body and Arguments of Symbolic Function

Return the body of a symbolic function by using formula. You can use the body for operations such as indexing into the function. Return the arguments of a symbolic function by using argnames.

Index into the symbolic function [x^2, y^4]. Since a symbolic function is a scalar, you cannot directly index into the function. Instead, index into the body of the function.

syms f(x,y)
f(x,y) = [x^2, y^4];
fbody = formula(f);
fbody(1)

ans = $$x^2$$

fbody(2)

ans = $$y^4$$

Return the arguments of the function.

fvars = argnames(f)

fvars = $$\left(\begin{array}{cc}x& y\end{array}\right)$$

Combine Two Symbolic Functions

Create two symbolic functions.

syms f(x) g(x)
f(x) = 2*x^2 - x;
g(x) = 3*x^2 + 2*x;

Combine the two symbolic functions into another symbolic function $$h(x)$$ with the data type symfun.

h(x) = [f(x); g(x)]

h(x) = 
$$\left(\begin{array}{c}2\hspace{0.17em}{x}^2-x\\ 3\hspace{0.17em}{x}^2+2\hspace{0.17em}x\end{array}\right)$$

Evaluate the function $$h(x)$$ at $$x=1$$ and $$x=2$$.

h(1)

ans = 
$$\left(\begin{array}{c}1\\ 5\end{array}\right)$$

h(2)

ans = 
$$\left(\begin{array}{c}6\\ 16\end{array}\right)$$

You can also combine the two functions into an array of symbolic expressions with the data type sym.

h_expr = [f(x); g(x)]

h_expr = 
$$\left(\begin{array}{c}2\hspace{0.17em}{x}^2-x\\ 3\hspace{0.17em}{x}^2+2\hspace{0.17em}x\end{array}\right)$$

Index into h_expr to access the first and the second symbolic expressions.

h_expr(1)

ans = $$2\hspace{0.17em}{x}^2-x$$

h_expr(2)

ans = $$3\hspace{0.17em}{x}^2+2\hspace{0.17em}x$$

Input Arguments

formula — Function body

symbolic expression | vector of symbolic expressions | matrix of symbolic expressions

Function body, specified as a symbolic expression, vector of symbolic expressions, or matrix of symbolic expressions.

Example: x + y

Data Types: sym

inputs — Input argument or arguments of function

symbolic variable | array of symbolic variables

Input argument or arguments of a function, specified as a symbolic variable or an array of symbolic variables, respectively.

Example: [x,y]

Data Types: sym

Output Arguments

f — Function

symbolic function (symfun data type)

Function, returned as a symbolic function.

The data type of the function f is symfun. But the data type of the evaluated function, such as f(1,2), is sym.

Data Types: symfun