fold

Combine (fold) vector elements using function

Syntax

y = fold(fun,x)

y = fold(fun,x,initVal)

Description

y = fold(fun,x) folds the elements of x by using fun. That is, fold applies the function fun on the first two elements of x, and then recursively applies fun on the result and the next element until the last element is combined. Programmatically, this syntax is equivalent to fold(fun,x) = fun(fold(fun,x(1:end-1)),x(end)).

y = fold(fun,x,initVal) folds the elements of x starting from the initial value initVal by using fun. (since R2026a)

Examples

Fold Vector Using Function

Fold a vector of symbolic variables using the power function. The output shows how fold combines elements of the vector from left to right by applying the specified function.

syms a b c d
x = [a b c d];
y = fold(@power,x)

y = $${\left({\left(a^b\right)}^c\right)}^d$$

Assume Variable Belongs to Set of Values

Set an assumption that the variable x belongs to the set of values 1, 2, ..., 10. Applying the or function to the conditions x == 1, ..., x == 10 using fold. Check that the assumption is set by using assumptions.

syms x
cond = fold(@or, x == 1:10);
assume(cond)
assumptions

ans = $$x=1\vee x=2\vee x=3\vee x=4\vee x=5\vee x=6\vee x=7\vee x=8\vee x=9\vee x=10$$

Specify Initial Value

Since R2026a

You can specify an initial value for the fold operation by using the third input argument. For example, apply the power function recursively using the initial value of 100 and the elements [a 2 3]. The result is 100^(6*a), which is equal to ((100^a)^2)^3.

syms a
x = [a 2 3];
y = fold(@power,x,100)

y = $${100}^{6\hspace{0.17em}a}$$

Input Arguments

fun — Function used to fold vector

function handle

Function used to fold the vector, specified as a function handle.

Example: @or

Example: @power

x — Vector to fold

vector | symbolic vector | cell vector

Vector to fold, specified as a vector, symbolic vector, or cell vector. If an element of x is a symbolic function, then the formula or definition of the symbolic function is used by applying formula(x(i)).

initVal — Initial value of fold operation

number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

Initial value of the fold operation, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

Before R2026a: Specify the default value using the third argument. The fold function returns this default value if the input vector to fold is empty.

Output Arguments

y — Result of fold operation

number | symbolic number | symbolic expression

Result of fold operation, returned as a number, symbolic number, or symbolic expression.

Version History

Introduced in R2016b

R2026a: Specify third input argument as initial value instead of default value

When you specify the third input argument of the fold function, specify the initial value instead of the default value for the fold operation. For example, this code returns 100^(6*a), which is equal to ((100^a)^2)^3.

syms a
x = [a 2 3];
y = fold(@power,x,100)

y = 
100^(6*a)

If you specify the second argument as an empty array, then fold returns the initial value as the output.

y = fold(@power,[],100)

y = 
100

Before R2026a, the third input argument of fold specified the default value. If the second argument was not empty, then fold applied the specified operation, ignoring the default value. For example, the same code returned a^6, which is equal to (a^2)^3.

syms a
x = [a 2 3];
y = fold(@power,x,100)

y = 
a^6

If you specified the second argument as an empty array, then fold returned the default value as the output.

y = fold(@power,[],100)

y = 
100