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Conjugate Gradient Solver for Linear Systems

CG implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations in which the matrix A is positive definite (only real, positive eigenvalues) and symmetric.

Usage of the application: cg use_case
 cg 0 (tiny)
 cg 1 (small)
 cg 2 (large)

STEP 0: Create git repository (10%)

Your code should be forked from this repository and hosted on code.it4i.cz as a private project with reporter access for all teachers (bes0030, vys0053, jansik, lriha, mec059, milanjaros, vav0038).

STEP 1: Building the library (10%)

Provide compilation script for your application (the script should run independently on a current path). Script should load all necessary modules and call cmake.

STEP 2: Analysis of the application (10%)

Use Arm map (module Forge) to analyze a sequential run of your application with given use case (large). Identify the most time consuming regions that can be parallelized by OpenMP.

STEP 3: Use OpenMP to run the application in parallel (10%)

Put OpenMP pragmas to a correct positions with appropriate variables visibility in order to utilize more threads effectively.

STEP 4: Test the correctness of the code (10%)

Create script that automatically check correctness of your application for at least 3 different test cases. Comparison can be implemented as comparison of outputs of sequential and parallel runs.

STEP 5: Test the behavior of the code on the Karolina cluster (40%)

  1. Implement time measurement for all parallel regions using omp_get_wtime().
  2. Create script for run strong scalability measurement (PBS script).
  3. Evaluate strong scalability of measured regions up to 128 threads and different thread affinity (compact, scatter, balanced, none).
  4. Prepare charts for all measurements.

STEP 6: Presentation of your project (10%)

Prepare presentation in form of slides (pptx, pdf). The slides should address all topics requested above.

The presentation (pdf) as well as all other modifications, and outputs push to your git repository.