Final Project

1
Final Project

• CAAM 420
• Fall 2004

2
Overview

• This project will exercise your ability to modify
  existing codes and use other libraries.
• The final goal is to create a dense, complex
  valued matrix class object and a sparse,
  complex valued matrix class object.
• i.e. we are extending the ability of the dmat and
  spmat objects to allow for systems of equations
  with complex coefficients and their corresponding
  matrices.

3
Teams

• You may work with at most one other person.
• Each team must complete the full task,
  irregardless of the number of team members.
• There should be no communication of code between
  different teams.
• Students may discuss concepts between teams.

4
Teams cont

• If your partner flakes you may break up the
  group, but must still hand in a complete project
  --- however, you must acknowledge what state the
  code was in at that time.
• If a team breaks up, you must each independently
  inform me by email and explain what happened. In
  this instance each team member will submit a
  separate report and is NOT permitted to join
  another group.
• You MAY NOT switch to another team, under any
  circumstances.

5
Code

• You may use any freely downloadable library
  available on the internet.
• You must cite any code used in your report,
  without exception. A bibliography of web pages
  will be sufficient for this task.
• You should annotate the code with indications of
  which team member coded which functions.
• Minor edits may remain unclaimed.

6
Debugging

• In order to receive assistance from the
  instructor or assistants you must use gdb to
  assertain the cause of the problem first.
• No exceptions.

7
Part 1

• Create two different class types, namely
• double precision complex dense (cmatrix)
• double precision complex sparse (cspmatrix)
• You must equip the classes with the following
  functions
• Default constructor
• Constructor (using a file name)
• Copy constructor
• Destructor
• File input
• File output
• Addition, division operators
• You must create the following algebraic friend
  operators
• cmatrix operator(const cmatrix , const
  cspmatrix )
• cmatrix operator\(const cmatrix , const
  cspmatrix )
• cmatrix operator(const cspmatrix , const
  cmatrix )
• cmatrix operator\(const cspmatrix , const
  cmatrix )

8
File Format

• Do not deviate from the following format.
• The file format for a complex matrix (both sparse
  and dense) should be
• Number of rows, number of columns, number of
  non-zeros
• 3 2 4
• row, column (indexed from 1), real part,
  imaginary part
• 1 1 .3 -.2
• 1 2 .1 0
• 2 2 -.1 .2
• 3 1 0 .1
• Also invoke fileobject.precision(15) before
  writing to file.

This corresponds to

9
Part 1 Hints

• Design your interface, then divide up who codes
  which matrix type.
• Division of the matrices can be done with LAPACK
  (dense) and UMFPACK (sparse) or similar. Each
  package has specific routines for these
  operations.
• Make your storage convention for the dense matrix
  Fortran friendly (i.e. column major).
• Use your previous UMFPACK interface as a starting
  point for the complex sparse matrix.

10
Part 2

• I will provide four downloadable complex
  matrices, in the format described
• Your code must be able to compute the following
• cmatrix A(A.cmat)
• cmatrix B(B.cmat)
• cspmatrix C(C.cspmat)
• cspmatrix D(D.cspmat)
• cmatrix E AC
• cmatrix F A\E
• cmatrix G C\A
• cspmatrix H C\(CD)
• E.output(E.cmat)
• F.output(F.cmat)
• G.output(G.cspmat)
• H.output(H.cspmat)

TEST YOUR CODERESULTS IN MATLAB
11
Extra Credit

• When (and only when) you have completed Parts 1
  2, create an eigenvalue computation functions
  which solves the following
• This is the standard eigenvalue problem for a
  complex matrix, with eigenvectors stored as the
  columns of V and eigenvalues stored as the
  diagonal of L
• For the complex sparse matrix use ARPACK, or
  ARPACK or similar and use extra function
  arguments to determine how many eigenvalues
  should be computed.
• For the complex dense matrix use LAPACK or
  similar.

12
Testing Portability

• You must make sure that your code works with both
  the SUN compiler suite (CC, cc, f77) and with the
  gnu compiler suite (g,gcc,g77)
• i.e. create two versions of Make.opt, i.e.
  Make.gnu and Make.sun. Make sure your code
  compiles and runs without difficulties with both
  sets of compilers.

13
Report

• Standard report format required.
• Include all test results from your code and from
  Matlab.
• ONE REPORT PER GROUP
• ALL TEAM MEMBER NAMES MUST APPEAR ON FRONT PAGE.
• Do not air your team grievances in the report.

14
Deadline

• Deadline midnight 28th November 2004
• Extensions may be granted, on a case by case
  basis, with latest possible submission on 3rd
  December 2004.