Sparse Conjugate Gradient shows how to use the Intel® oneAPI Math Kernel Library (oneMKL) sparse linear algebra functionality to solve a sparse, symmetric linear system using the (preconditioned) conjugate gradient method.

For more information on oneMKL and complete documentation of all oneMKL routines, see https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-documentation.html.

Sparse Conjugate Gradient uses oneMKL sparse linear algebra routines to solve a system of linear equations Ax = b, where the A matrix is symmetric and sparse. The symmetric Gauss-Seidel preconditioner is used to accelerate convergence.

This sample performs its computations on the default SYCL* device. You can set the SYCL_DEVICE_TYPE environment variable to cpu or gpu to select the device to use.

oneMKL sparse routines use a two-stage method where the sparse matrix is analyzed to prepare subsequent calculations (the optimize step). Sparse matrix-vector multiplication and triangular solves (gemv and trsv) are used to implement the main loop, along with vector routines from BLAS.

You can use Visual Studio Code (VS Code) extensions to set your environment, create launch configurations, and browse and download samples.

The basic steps to build and run a sample using VS Code include:

• Download a sample using the extension Code Sample Browser for Intel® oneAPI Toolkits.
• Configure the oneAPI environment with the extension Environment Configurator for Intel® oneAPI Toolkits.
• Open a Terminal in VS Code (Terminal>New Terminal).
• Run the sample in the VS Code terminal using the instructions below.
• (Linux only) Debug your GPU application with GDB for Intel® oneAPI toolkits using the Generate Launch Configurations extension.

To learn more about the extensions, see the Using Visual Studio Code with Intel® oneAPI Toolkits User Guide.

Note: If you have not already done so, set up your CLI environment by sourcing the setvars script located in the root of your oneAPI installation.

Linux*:

• For system wide installations: . /opt/intel/oneapi/setvars.sh
• For private installations: . ~/intel/oneapi/setvars.sh
• For non-POSIX shells, like csh, use the following command: $ bash -c 'source <install-dir>/setvars.sh ; exec csh'

Windows*:

• C:\"Program Files (x86)"\Intel\oneAPI\setvars.bat
• For Windows PowerShell*, use the following command: cmd.exe "/K" '"C:\Program Files (x86)\Intel\oneAPI\setvars.bat" && powershell'

For more information on configuring environment variables, see Use the setvars Script with Linux* or MacOS* or Use the setvars Script with Windows*.

If running a sample in the Intel® DevCloud, remember that you must specify the compute node (CPU, GPU, FPGA) and whether to run in batch or interactive mode. For more information, see the Intel® oneAPI Base Toolkit Get Started Guide (https://devcloud.intel.com/oneapi/get-started/base-toolkit/).

Run make to build and run the sample.

You can remove all generated files with make clean.

Run nmake to build and run the sample. nmake clean removes temporary files.

Warning: On Windows, static linking with oneMKL currently takes a very long time due to a known compiler issue. This will be addressed in an upcoming release.

If everything is working correctly, the example program will rapidly converge to a solution and display the solution vector's first few entries. The test will run in both single and double precision (if available on the selected device).

./sparse_cg
########################################################################
# Sparse Conjugate Gradient Solver
#
# Uses the preconditioned conjugate gradient algorithm to
# iteratively solve the symmetric linear system
#
#     A * x = b
#
# where A is a symmetric sparse matrix in CSR format, and
#       x and b are dense vectors.
#
# Uses the symmetric Gauss-Seidel preconditioner.
#
########################################################################

Running tests on Intel(R) Gen9 HD Graphics NEO.
        Running with single precision real data type:
                relative norm of residual on 1 iteration: 0.0856119
                relative norm of residual on 2 iteration: 0.00204826
                relative norm of residual on 3 iterations: 6.68015e-05

                Preconditioned CG process has successfully converged, and
                the following solution has been obtained:

                x[0] = 0.0666633
                x[1] = 0.0835483
                x[2] = 0.0835491
                x[3] = 0.0666627
                ...
        Running with double precision real data type:
                relative norm of residual on 1 iteration: 0.0856119
                relative norm of residual on 2 iteration: 0.00204827
                relative norm of residual on 3 iteration: 6.68017e-05

                Preconditioned CG process has successfully converged, and
                the following solution has been obtained:

                x[0] = 0.0666633
                x[1] = 0.0835483
                x[2] = 0.0835491
                x[3] = 0.0666627
                ...

If an error occurs, troubleshoot the problem using the Diagnostics Utility for Intel® oneAPI Toolkits. Learn more.

Code samples are licensed under the MIT license. See License.txt for details.

Third party program Licenses can be found here: third-party-programs.txt.