General about using libraries

It is highly recommended to make use of standard libraries when writing your own code, both to ensure high performance and portability for your codes. Becaue:

• You will always find optmized versions of these libraries on High Performance Computers, beause most serious benchmark programs are using these libraries. However, if you would like to run your program on a computer where these libraries are not installed, you can download them, for free, from NETLIB: http://www.netlib.org/.
• You will never (at least not very often / in general) beat the performance of these libraries by writing your own code.
  
• Most vector-vector, matrix-vector and matrix-matrix operations are available in these common libraries:
• BLAS, BLAS Quick reference, BLAS at Wikipedia
• GotoBLAS
• LAPACK, LAPCK User's Guide, LAPACK at Wikipedia
• ScaLAPACK, ScaLAPACK User's Guide, ScaLAPACK at Wikipedia -- LAPACK routines redesigned for distributed memory MIMD parallel computers

A lot of solvers for various equations and PDE's are also available in various other libraries Therefore it may often be well worth spending some time searching for available libraries. Start out with NETLIB, or even Google or Wikipedia, for instance: SW libraries in general.