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.

If X is a vector, then diff(X) returns a vector, one element shorter than X, of differences between adjacent elements:

• [X(2)-X(1) X(3)-X(2) ... X(n)-X(n-1)]
  

If X is a matrix, then diff(X) returns a matrix of row differences:

• [X(2:m,:)-X(1:m-1,:)]
  

In general, diff(X) returns the differences calculated along the first non-singleton (size(X,dim) > 1) dimension of X.

Y = diff(X,n) applies diff recursively n times, resulting in the nth difference. Thus, diff(X,2) is the same as diff(diff(X)).

Y = diff(X,n,dim) is the nth difference function calculated along the dimension specified by scalar dim. If order n equals or exceeds the length of dimension dim, diff returns an empty array.

Remarks

Since each iteration of diff reduces the length of X along dimension dim, it is possible to specify an order n sufficiently high to reduce dim to a singleton (size(X,dim) = 1) dimension. When this happens, diff continues calculating along the next nonsingleton dimension.

Examples

The quantity diff(y)./diff(x) is an approximate derivative.

• x = [1 2 3 4 5];
  y = diff(x)
  y =
       1     1     1     1
  
  z = diff(x,2)
  z =
       0     0     0
  

Given,

• A = rand(1,3,2,4);
  

diff(A) is the first-order difference along dimension 2.

diff(A,3,4) is the third-order difference along dimension 4.