Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

我们为许可用户提供了部分翻译好的中文文档。您只需登录便可查阅这些文档

diff

Differences and Approximate Derivatives

Syntax

Description

example

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.

example

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)).

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.

Examples

collapse all

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

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

     0     1     1     2     3     5     8

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 =

     4     4     4
    20    20    20

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)
Y =

     5     5     5     5     5

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 =

     2     2
     4     2
     2     4

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')

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 array

Columns 1 through 3

   30-Aug-2016 15:14:23   30-Aug-2016 15:15:53   30-Aug-2016 15:17:23

Column 4

   30-Aug-2016 15:18:53

dt = diff(t)
dt = 

  1×3 duration array

   00:01:30   00:01:30   00:01:30

diff returns a duration array.

Input Arguments

collapse all

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

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

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

collapse all

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.

See Also

| | |

Introduced before R2006a


Was this topic helpful?