Recursive LAPACK Collection
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Recursive LAPACK Collection

ReLAPACK offers a collection of recursive algorithms for many of LAPACK's compute kernels. Since it preserves LAPACK's established interfaces, ReLAPACK integrates effortlessly into existing application codes. ReLAPACK's routines not only outperform the reference LAPACK but also improve upon the performance of tuned implementations, such as OpenBLAS and MKL.


For a detailed list of covered operations and an overview of operations to which recursion is not efficiently applicable, see


To compile with the default configuration, simply run make to create the library librelapack.a.

Linking with MKL

Note that to link with MKL, you currently need to set the flag COMPLEX_FUNCTIONS_AS_ROUTINES to 1 to avoid problems in ctrsyl and ztrsyl. For further configuration options see


ReLAPACK builds on top of BLAS and unblocked kernels from LAPACK. There are many optimized and machine specific implementations of these libraries, which are commonly provided by hardware vendors or available as open source (e.g., OpenBLAS).


ReLAPACK's test suite compares its routines numerically with LAPACK's counterparts. To set up the tests (located int test/) you need to specify link flags for BLAS and LAPACK (version 3.5.0 or newer) in; then make test runs the tests. For details on the performed tests, see test/


Since ReLAPACK replaces parts of LAPACK, any LAPACK example involving the covered routines applies directly to ReLAPACK. A few separate examples are given in examples/. For details, see examples/


When referencing ReLAPACK, please cite the preprint of the paper Recursive Algorithms for Dense Linear Algebra: The ReLAPACK Collection:

  author    = {Elmar Peise and Paolo Bientinesi},
  title     = {Recursive Algorithms for Dense Linear Algebra: The ReLAPACK Collection},
  journal   = {CoRR},
  volume    = {abs/1602.06763},
  year      = {2016},
  url       = {},