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 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.

Y = diff(X,n) calculates the nth difference by applying the diff(X) operator recursively n times. In practice, this means diff(X,2) is the same as diff(diff(X)).

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 = 1x4 datetime
Columns 1 through 3

   01-Sep-2021 10:29:56   01-Sep-2021 10:31:26   01-Sep-2021 10:32:56

Column 4

   01-Sep-2021 10:34:26

dt = diff(t)

dt = 1x3 duration
   00:01:30   00:01:30   00:01:30

diff returns a duration array.

Input Arguments

X — Input array

vector | matrix | multidimensional array

Input array, specified as a vector, matrix, or multidimensional array. X can be a numeric array, logical array, datetime array, or duration array.

Complex Number Support: Yes

n — Difference order

positive integer scalar | []

Difference order, specified as a positive integer scalar or []. The default value of n is 1.

It is possible to specify n sufficiently large so that dim reduces to a single (size(X,dim) = 1) dimension. When this happens, diff continues calculating along the next array dimension whose size does not equal 1. This process continues until a 0-by-0 empty matrix is returned.

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 no value is specified, 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

Difference array, returned as a scalar, vector, matrix, or multidimensional array. If X is a nonempty array, then the dimension of X acted on by diff is reduced in size by n in the output.

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 supplied, the arguments representing the number of times to apply diff and the dimension along which to calculate the difference must be constants.

• See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

• 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™.

This function fully supports GPU arrays. 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).