# Fortran Software Packages

Fortran has many basic mathematical functions as built-in (intrinsic)
functions, standard math
functions like sqrt, sin, exp, etc. (see *Intrinsic functions*)
and also matrix operations such as transpose and matmul
(see *Array storage in Fortran*).

To solve more complex mathematical problems it is generally necessary to
either use some *software package* or write your own code from scratch.
In general it is best to use high-quality software as much as possible, for
several reasons:

- It will take less time to figure out how to use the software than to
write your own version. (Assuming it’s well documented!)
- Good general software has been extensively tested on a wide variety of
problems.
- Often general software is much more sophisticated that what you might
write yourself, for example it may provide error estimates automatically,
or it may be optimized to run fast.

You will probably need to write a main program to call the software, and
often auxiliary functions to describe your problem.

Some software consists of a single subroutine or function that you can
easily download and compile with the rest of your code. Other software is
in the form of a large package that must be installed in some manner before
use.

Often large collections of subroutines are organized into *libraries* that
can be compiled once and stored in a manner that makes it easier to use by
simply *linking* your .o files to the library, which automatically pulls out
the object code for the particular library routines you use in the program.
This frees the user from having to figure out what set of .o or .f files are
required from the software package for each application of the software.
For examples of this, see the sections on *Linear Algebra software*.

## zeroin software

As a very simple example of a single-function piece of software, see the
directory $CLASSHG/codes/fortran/zeroin
This contains code to compute the n‘th root of a by finding a zero of
the function f(x) = x^n - a as in *Homework 3*. But instead
implementing Newton’s method as described in *Special functions*, the
function zeroin is used, which was obtained from
Netlib, a repository of mathematical software.
The version of zeroin used is a slight modification of the Netlib version
http://www.netlib.org/go/zeroin.f, modified to remove the dependence on
d1mach.