diff - Differences and approximate derivatives - MATLAB (original) (raw)

Differences and approximate derivatives

Syntax

Description

[Y](#btwmxq8-1-Y) = diff([X](#btwmxq8-1-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, thenY = diff(X) returns a vector of lengthm-1. The elements of Y are the differences between adjacent elements ofX.
Y = [X(2)-X(1) X(3)-X(2) ... X(m)-X(m-1)]
If X is a nonempty, nonvector p-by-m matrix, thenY = diff(X) returns a matrix of size (p-1)-by-m, whose elements are the differences between the rows ofX.
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](#btwmxq8-1-Y) = diff([X](#btwmxq8-1-X),[n](#btwmxq8-1-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](#btwmxq8-1-Y) = diff([X](#btwmxq8-1-X),[n](#btwmxq8-1-n),[dim](#btwmxq8-1-dim)) is the nth difference calculated along the dimension specified bydim. The dim input is a positive integer scalar.

example

Examples

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

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

Note that Y has one fewer element than X.

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 is a 2-by-3 matrix.

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

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

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 is a 3-by-2 matrix.

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.

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 01-Feb-2025 09:02:29 01-Feb-2025 09:03:59 01-Feb-2025 09:05:29 01-Feb-2025 09:06:59

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 is1. When n is larger than the dimension being operated on, diff returns an empty array.

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

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 thann, then this dimension is reduced byn in the output. If this dimension is less thann, it is reduced to zero and the output is empty.

Extended Capabilities

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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.

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.

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).

Version History

Introduced before R2006a

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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, whenn 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.

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.

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 thetimingDiff function.