1. Coding FLAME Algorithms with FLAME@lab Example: Cholesky factorization
Robert van de Geijn
Department of Computer Sciences, UT-Austin

2. What is
is the Mscript Application Programming Interface (API) for coding FLAME algorithms.
Mscript is the programming language for Matlab and Octave (which is a public domain version of Matlab).

3. This tutorial assumes that you have already completed the FLaTeX tutorial or that you are at least familiar with the Spark tool

4. Download paper
Step one: download from
Paolo Bientinesi and Robert van de Geijn. " Representing Dense Linear Algebra Algorithms: A Farewell to Indices." FLAME Working Note #17 The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2006-??.
Postscript
PDF
(Actually, you just need Figure 6, which also appears on the next slide)

6. This tutorial will show you how to code the algorithms in Figure 6 with FLAME@lab

7. Download FLAME@lab Download the FLAME@lab files by visiting

8. Translate the Cholesky factorization algorithms to code

9. Start the Spark tool for generating code skeletons at

10. Fill in the form

11. Select FLAME@lab and click
“Generate Code”

12. Click on the right window and Select All

13. Copy

14. Paste into your favorite text editor

15. Translate the update for unblocked variant 1 in Figure 6 into Mscript operations
Save the result in a file called “Chol_unb_var1.m”
From Figure 6

16. Write a simple test routine
% B = rand 5x5 matrix
B = rand( 5, 5 );
% A is Symmetric Positive Definite
A = B * B’
% Use matlab to compute Cholesky factor L.
% Note that chol( A ) computes U s.t. A = U’ * U
% so that L = chol( A )’
L = chol( A )’
% Compute Cholesky factor with your implementation.
% Note that only lower triangular part is updated!
myL = Chol_unb_var1( A )
Diff = L – tril( myL ) % Check the difference
Save the result in a file called “test_chol.m”

17. Test your Cholesky factorization (Variant 1)
Assumption:
The “.m” files are in the same directory as all the files listed below OR you have set the path to where you put them.
You have the following files in the directory
Chol_unb_var1.m
test_chol.m
Start octave (or Matlab):
octave --traditional
test_chol

19. The difference is very small, but nonzero due to roundoff errors

20. Exercises
Before going on, try the following exercises (the answers are in the subsequent slides)
Use the Spark tool to generate a code skeleton for blocked algorithm variant 1 (See Figure 6). Store the result in file “Chol_blk_var1.m”
Note: to test it, change the obvious call to
myL = Chol_blk_var1( A, 2 )
so that a block size of 2 is used.
Repeat for unblocked and blocked variants 2