diff

Differences and approximate derivatives

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)

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.

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

Examples

Differences Between Vector Elements

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.

Differences Between Matrix Rows

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.

Multiple Differences

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

Differences Between Matrix Columns

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.

Approximate Derivatives with diff

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')

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.

Differences Between Datetime Values

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
   09-Aug-2025 12:09:38   09-Aug-2025 12:11:08   09-Aug-2025 12:12:38   09-Aug-2025 12:14:08

dt = diff(t)

dt = 1×3 duration
   00:01:30   00:01:30   00:01:30

diff returns a duration array.

Input Arguments

X — Input array

vector | matrix | multidimensional array | table | timetable

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

n — Difference order

1 (default) | positive integer scalar | []

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

dim — Dimension to operate along

positive integer scalar

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.

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

Output Arguments

Y — Difference array

scalar | vector | matrix | multidimensional array | table | timetable

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

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function supports tall arrays with the limitations:

You must use the three-input syntax Y = diff(X,N,dim).

For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If used, the dim argument must be a constant at code generation time.

• For input argument X:

  • If you do not specify a dimension, the code generator operates along the first dimension of the input array that is variable size or whose size does not equal 1. If this dimension is variable size at code generation time and is 1 at run time, a run-time error can occur. To avoid this error, specify the dimension.

• Code generation does not support sparse matrix inputs for this function.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The diff function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2025a: Two-input syntax calculates differences along only the first dimension whose size is greater than 1

The two-input syntax diff(X,n) of the diff function now operates along only the first dimension whose size is greater than 1 for all values of n. If n is larger than that dimension, diff returns an empty array. Previously, when n was larger than the first dimension whose size is greater than 1, diff(X,n) reduced the size of that dimension to 1 and then calculated differences along the next dimension whose size is greater than 1.

R2023a: Perform calculations directly on tables and timetables

The diff function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.

R2022a: Improved performance with large number of elements

The diff function shows improved performance when operating on vectors with at least 10⁵ elements or when operating along the first or second dimension of matrices and multidimensional arrays with at least 5 x 10⁵ elements.

For example, this code constructs a double with 2.5 x 10⁷ elements and calculates differences between adjacent elements. The code is approximately 2.4x faster than in the previous release:

function timingDiff
rng default
N = 5000;
A = rand(N);

tic
for k = 1:40
   D = diff(A);
end
toc
end

The approximate execution times are:

R2021b: 2.43 s

R2022a: 1.00 s

The code was timed on a Windows^® 10, Intel^® Xeon^® CPU E5-1650 v4 @ 3.60 GHz test system by calling the timingDiff function.