LAPACK

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LAPACK#

Our program currently relies on custom matrix-solver primitives, but in practice you should always first seek existing, highly optimized libraries rather than reinvent the wheel. The Linear Algebra PACKage (LAPACK) is the standard for matrix problems: it offers a wide range of efficient, well-implemented algorithms for solving matrix equations and is used extensively in scientific software.

If you need fast, reliable linear-algebra routines, LAPACK should be your first choice. To demonstrate how to integrate it, we’ll add a new command-line flag (for example, --lapack-cholesky) that tells the program to use LAPACK’s Cholesky decomposition routine.

We use two LAPACK functions: ``LAPACKE_dpotrf`` and ``LAPACKE_dpotrs``. Their documentation can be found on the official LAPACK website and on Intel oneAPI.

E.g.:

int info = LAPACKE_dpotrf(LAPACK_ROW_MAJOR, 'U', n_row, A_lapack_1d, n_row);

  • The first argument specifies whether matrix storage layout is row-major (LAPACK_ROW_MAJOR) or column-major (LAPACK_COL_MAJOR).

  • 'U' indicates the upper triangle of A is stored.

  • n_row is the order (number of rows) of the matrix A.

  • A_lapack_1d is a pointer to the first element of the 1D array storing the matrix; this array will be overwritten.

  • On exit, the upper triangular factor U overwrites the upper triangle of A_lapack_1d, and the routine computes A = U^T * U.

  • Return value: if info == 0, the factorization succeeded; if info > 0, the leading minor of order info is not positive definite.

Exercises#

  1. In ``linear-algebra-lapack.c``, after performing Cholesky factorisation with ``LAPACKE_dpotrf``, call ``LAPACKE_dpotrs`` to solve the system. Fill in all required arguments: matrix layout, triangle indicator, dimensions, pointers to U and the right-hand side. See the manual on potrs.

2. Compile, include linking the LAPACK library (the library you need is libmkl_rt), and run the program with the new flag. On Gadi, LAPACK is shipped with Intel MKL. To load the library modules, run:

module load intel-compiler-llvm/2025.0.4
module load intel-mkl/2025.0.1
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