FreeMat
EXP Exponential Function

Section: Mathematical Functions

Usage

Computes the exp function for its argument. The general syntax for its use is

   y = exp(x)

where x is an n-dimensional array of numerical type. Integer types are promoted to the double type prior to calculation of the exp function. Output y is of the same size and type as the input x, (unless x is an integer, in which case y is a double type).

Internals

Mathematically, the exp function is defined for all real valued arguments x as

\[ \exp x \equiv e^{x}, \]

where

\[ e = \sum_{0}^{\infty} \frac{1}{k!} \]

and is approximately 2.718281828459045 (returned by the function e). For complex values z, the famous Euler formula is used to calculate the exponential

\[ e^{z} = e^{|z|} \left[ \cos \Re z + i \sin \Re z \right] \]

Example

The following piece of code plots the real-valued exp function over the interval [-1,1]:

--> x = linspace(-1,1);
--> plot(x,exp(x))
expplot1.png
In the second example, we plot the unit circle in the complex plane e^{i 2 pi x} for x in [-1,1].

--> x = linspace(-1,1);
--> plot(exp(-i*x*2*pi))
expplot2.png