Differences and Approximate Derivatives
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.
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
The output Y is a 2-by-3 difference 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
The output Y is a 3-by-2 difference 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.
Input array, specified as a vector, matrix, or multidimensional array.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
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, 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