Mathematics

Finite Differences

MATLAB provides three functions for finite difference calculations.

Function	Description
diff	Difference between successive elements of a vector. Numerical partial derivatives of a vector.
gradient	Numerical partial derivatives a matrix.
del2	Discrete Laplacian of a matrix.

The diff function computes the difference between successive elements in a numeric vector. That is, diff(X) is [X(2)-X(1) X(3)-X(2)...
X(n)-X(n-1)]. So, for a vector A,

• A = [9 -2 3 0 1 5 4];
  diff(A)
  
  ans =
     -11     5    -3     1     4    -1
  

Besides computing the first difference, diff is useful for determining certain characteristics of vectors. For example, you can use diff to determine if a vector is monotonic (elements are always either increasing or decreasing), or if a vector has equally spaced elements. This table describes a few different ways to use diff with a vector x.

Test	Description
diff(x)==0	Tests for repeated elements.
all(diff(x)>0)	Tests for monotonicity.
all(diff(diff(x))==0)	Tests for equally spaced vector elements.

Covariance and Correlation Coefficients

Data Preprocessing