diff
Differences and approximate derivatives
Description
calculates
differences between adjacent elements of Y
= diff(X
)X
along
the first array dimension whose size does not equal 1:
If
X
is a vector of lengthm
, thenY = diff(X)
returns a vector of lengthm-1
. The elements ofY
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, thenY = diff(X)
returns a 0-by-0 empty matrix.
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
26-Nov-2022 07:44:36 26-Nov-2022 07:46:06 26-Nov-2022 07:47:36
Column 4
26-Nov-2022 07:49:06
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 you do not specify the dimension, then the default is the first array dimension of size greater than 1.
Consider a two-dimensional p-by-m input array, A
:
diff(A,1,1)
works on successive elements in the columns ofA
and returns a (p-1)-by-m difference matrix.diff(A,1,2)
works on successive elements in the rows ofA
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).
Version History
Introduced before R2006aR2022a: 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.
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