Linear Algebra

BLAS Levels 1, 2, & 3

Applications in high-performance computing, machine learning, and other domains can benefit from highly optimized BLAS and BLAS-like extensions in Intel® Math Kernel Library (Intel® MKL). These low-level linear algebra routines operate on vectors and matrices, and are compatible with industry-standard BLAS operations that include:

  • Level 1: Vector-vector operations
  • Level 2: Matrix-vector operations
  • Level 3: Matrix-matrix operations
benchmark of performance on an Intel Xeon Phi processor

See below for further notes and disclaimers.1


Intel MKL also contains a number of BLAS-like extensions:

  • Triangular GEMM routines: Compute a matrix-matrix product but update only the upper or lower triangular part of the result matrix
  • Batched GEMM routines: Perform multiple GEMM operations in parallel
  • Packed GEMM routines: Amortize internal packing costs across multiple GEMM operations


This package includes highly optimized LU, Cholesky, and QR factorization and driver routines that are compatible with industry-standard APIs. These routines handle real and complex matrices in single and double precision. Eigenvalue and least squares solvers, as well as the latest Netlib LAPACK interfaces and enhancements, are also included.


For cluster computation, Intel MKL implements routines from the industry-standard ScaLAPACK for distributed-memory architectures. The routines include solvers for linear least squares, eigenvalue, and singular value problems for real, complex, dense, and band matrices.

Sparse BLAS (Levels 1, 2, 3) & Solvers

In addition to the standard Sparse BLAS APIs, Intel MKL also supports unique two-stage inspector-executor Sparse BLAS APIs for higher performance. For clusters, use the included implementation of the PARDISO* sparse solver, iterative sparse solver, or a distributed version of the solver. Tackle large-scale sparse eigenvalue problems with the highly robust and scalable Extended Eigensolver (based on the FEAST eigenvalue solver).

Additional Features


1 Benchmark results were obtained prior to implementation of recent software patches and firmware updates that are intended to address exploits referred to as "Spectre" and "Meltdown." Implementation of these updates may make these results inapplicable to your device or system.

Software and workloads used in performance tests may have been optimized for performance only on Intel® microprocessors. Performance tests, such as SYSmark and MobileMark, are measured using specific computer systems, components, software, operations, and functions. Any change to any of those factors may cause the results to vary. You should consult other information and performance tests to assist you in fully evaluating your contemplated purchases, including the performance of that product when combined with other products. For more complete information, visit

Intel’s compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice. Notice revision #20110804