diff

Differences and approximate derivatives

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Syntax

Y = diff(X)
Y = diff(X,n)
Y = diff(X,n,dim)

Description

Y = diff(X) calculates differences between adjacent elements of X. By default, diff operates along the first array dimension whose size does not equal 1.

  • If X is a vector of length m, then Y = diff(X) returns a vector of length m-1. The elements of Y are the differences between adjacent elements of X.

    Y = [X(2)-X(1) X(3)-X(2) ... X(m)-X(m-1)]

  • If X is a nonempty, nonvector p-by-m matrix, then Y = diff(X) returns a matrix of size (p-1)-by-m, whose elements are the differences between the rows of X.

    Y = [X(2,:)-X(1,:); X(3,:)-X(2,:); ... X(p,:)-X(p-1,:)]

  • If X is a 0-by-0 empty matrix, then Y = diff(X) returns a 0-by-0 empty matrix.

  • If X is a p-by-m table or timetable, then Y = diff(X) returns a table or timetable of size (p-1)-by-m, whose elements are the differences between the rows of X. If X is a 1-by-m table or timetable, then the size of Y is 0-by-m. (since R2023a)

example

Y = diff(X,n) calculates the nth difference by applying the diff(X) operator recursively n times along the first array dimension whose size does not equal 1.

example

Y = diff(X,n,dim) is the nth difference calculated along the dimension specified by dim. The dim input is a positive integer scalar.

example

Examples

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Open Live Script

Create a vector, then compute the differences between the elements. 

X = [1 1 2 3 5 8 13 21];
Y = diff(X)
Y = 1×7

     0     1     1     2     3     5     8

Note that Y has one fewer element than X.

Open Live Script

Create a 3-by-3 matrix, then compute the first difference between the rows.

X = [1 1 1; 5 5 5; 25 25 25];
Y = diff(X)
Y = 2×3

     4     4     4
    20    20    20

Y is a 2-by-3 matrix.

Open Live Script

Create a vector and compute the second-order difference between the elements.

X = [0 5 15 30 50 75 105];
Y = diff(X,2)
Y = 1×5

     5     5     5     5     5
Open Live Script

Create a 3-by-3 matrix, then compute the first-order difference between the columns. 

X = [1 3 5;7 11 13;17 19 23];
Y = diff(X,1,2)
Y = 3×2

     2     2
     4     2
     2     4

Y is a 3-by-2 matrix.

Open Live Script

Use the diff function to approximate partial derivatives with the syntax Y = diff(f)/h, where f is a vector of function values evaluated over some domain, X, and h is an appropriate step size.

For example, the first derivative of sin(x) with respect to x is cos(x), and the second derivative with respect to x is -sin(x). You can use diff to approximate these derivatives.

h = 0.001;       % step size
X = -pi:h:pi;    % domain
f = sin(X);      % range
Y = diff(f)/h;   % first derivative
Z = diff(Y)/h;   % second derivative
plot(X(:,1:length(Y)),Y,'r',X,f,'b', X(:,1:length(Z)),Z,'k')

Figure contains an axes object. The axes object contains 3 objects of type line.

In this plot the blue line corresponds to the original function, sin. The red line corresponds to the calculated first derivative, cos, and the black line corresponds to the calculated second derivative, -sin.

Open Live Script

Create a sequence of equally-spaced datetime values, and find the time differences between them.

t1 = datetime('now');
t2 = t1 + minutes(5);
t = t1:minutes(1.5):t2
t = 1×4 datetime
   13-Jul-2025 19:29:05   13-Jul-2025 19:30:35   13-Jul-2025 19:32:05   13-Jul-2025 19:33:35


dt = diff(t)
dt = 1×3 duration
   00:01:30   00:01:30   00:01:30

diff returns a duration array.

Input Arguments

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Input array, specified as a vector, matrix, multidimensional array, table, or timetable. X can be a numeric array, logical array, datetime array, or duration array, or a table or timetable whose variables have any of these data types.

Complex Number Support: Yes

Difference order, specified as a positive integer scalar or []. The default value of n is 1. When n is larger than the dimension being operated on, diff returns an empty array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Dimension to operate along, specified as a positive integer scalar. If you do not specify the dimension, then the default is the first array dimension whose size does not equal 1.

Consider a two-dimensional p-by-m input array, A:

  • diff(A,1,1) works on successive elements in the columns of A and returns a (p-1)-by-m difference matrix.

  • diff(A,1,2) works on successive elements in the rows of A and returns a p-by-(m-1) difference matrix.

diff(A,1,1) column-wise computation and diff(A,1,2) row-wise computation

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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Difference array, returned as a scalar, vector, matrix, multidimensional array, table, or timetable. If the dimension of X acted on by diff has size greater than n, then this dimension is reduced by n in the output. If this dimension is less than n, it is reduced to zero and the output is empty.

Extended Capabilities

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Version History

Introduced before R2006a

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See Also

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