Numerical Differentiation of Data (derivative)

Numerical differentiation of data (i.e. arrays) over the domain of the data or at specified points.

derivative

Numerical differentiation of data (i.e. arrays).

Syntax

dy = derivative(x,y)
dy = derivative(x,y,x_star)

Description

dy = derivative(x,y) returns the derivative of a set of data, vs. (which are stored in y and x). dy stores the derivative of y vs. x at every point in x.

dy = derivative(x,y,x_star) returns the derivative of a set of data, vs. (which are stored in y and x), at the set of points specified by (x_star). x_star can be a scalar or a vector.

Additional Notes

• This function is the equivalent of trapz and cumtrapz for numerical differentiation and is especially useful for estimating derivatives where the underlying function is unknown (i.e. we have some data set vs. that describes a function , but this underlying function is unknown and so we use the data set to approximate its derivative).
• If we do know the underlying function , then we can still use derivative to estimate its derivative. We can do this by defining a vector of points x and then populating a vector y with evaluations of at every point in x. However, in this case (where the underlying function is known), iderivative and derivest are better functions to use.

Examples and Additional Documentation

• See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.
• See "Basic_Numerical_Calculus.pdf" (also included with download) for the technical documentation.