External matrix libraries

Here we describe how our matrix library makes use of external libraries.


The matrix code in Kaldi is mostly a wrapper on top of the linear-algebra libraries BLAS and LAPACK. The code has been designed to be as flexible as possible in terms of what libraries it can use. Currently it supports four options:

  • Intel MKL, which provides both BLAS and LAPACK (the default)
  • OpenBLAS, which provides BLAS and LAPACK
  • ATLAS, which is an implementation of BLAS plus a subset of LAPACK (with a different interface)
  • Some implementation of BLAS plus CLAPACK (note: this has not been tested recently).

The code has to "know" which of these four options is being used, because although in principle BLAS and LAPACK are standardized, there are some differences in the interfaces. The Kaldi code requires exactly one of the three macros HAVE_ATLAS, HAVE_CLAPACK, HAVE_OPENBLAS or HAVE_MKL to be defined (normally using -DHAVE_ATLAS as an option to the compiler). It must then be linked with the appropriate libraries. The code that deals most directly with including the external libraries and setting up the appropriate typedef's and defines, is in kaldi-blas.h. However, the rest of the matrix code is not completely insulated from these issues because the ATLAS and CLAPACK versions of higher-level routines are called differently (so we have a lot of "#ifdef HAVE_ATLAS" directives and the like). Additionally, some routines are not even available in ATLAS so we have had to implement them ourselves.

The "configure" script in the "src" directory is responsible for setting up Kaldi to use the libraries. It does this by creating the file "kaldi.mk" in the "src" directory, which gives appropriate flags to the compiler. If called with no arguments it will use any Intel MKL installation it can find in "normal" places in your system, but it is configurable. Run the script with the --help option for the complete option list.

Understanding BLAS and LAPACK

Because we refer a lot to BLAS (and more often CBLAS) and LAPACK (or, rarely, CLAPACK) in this section, we briefly explain what it is.

Basic Linear Algebra Subroutines (BLAS)

BLAS is a set of subroutine declarations that correspond to low-level matrix-vector operations. There is BLAS Level 1 (vector-vector), Level 2 (vector-matrix) and Level 3 (matrix-matrix). They have names like daxpy (for "double-precision a x plus y"), and dgemm (for "double-precision general matrix-matrix multiply"). BLAS has various actual implementations. The reference implementation of BLAS originated back in 1979, and has been maintained since by Netlib. The reference implementation lacks any optimization whatsoever, and exists solely as a touchstone to validate the correctness of other implementations. MKL, ATLAS and OpenBLAS provide optimized implementations of BLAS.

CBLAS is just the C language interface to BLAS.

Linear Algebra PACKage (LAPACK)

LAPACK is a set of linear-algebra routines, originally written in Fortran. It includes higher-level routines than BLAS, such as matrix inversion, SVD, etc. The reference implementation of LAPACK was implemented and has been maintained by Netlib. LAPACK internally uses BLAS. It is possible to mix-and-match LAPACK and BLAS implementations (e.g. Netlib's LAPACK with ATLAS's BLAS).

CLAPACK is a version of LAPACK that has been converted from Fortan to C automatically using the f2c utility. Because of this, the f2c library is required during linking with the "original" CLAPACK (usually -lg2c or -lf2c).

MKL provides complete C-callable interfaces for its own BLAS and LAPACK implementations; no additional libraries are required.

Intel Math Kernel Library (MKL)

Intel MKL provides C-language interface to a high-performance implementation of the BLAS and LAPACK routines, and is currently the preferred CBLAS/CLAPACK provider for Kaldi. To use MKL with Kaldi use the -DHAVE_MKL compiler flag.

Previously MKL used to be a paid product. Starting 2017, Intel made MKL freely available and allows royalty-freely runtime redistribution even for commercial application (although, just like, for example, CUDA, it is still a closed-source commercial product).

MKL provides a very highly optimized implementation of linear algebra routines, and especially on Intel CPUs. In fact, the library contains multiple code paths, which are selected at runtime depending on individual features of the CPU it is being loaded on. Thus with MKL you will automatically benefit from all features and instruction sets (such as AVX2 and AVX512) if they are available on your CPU, without any additional configuration. These instructions accelerate linear algebra operations on CPU significantly. It is usually a good idea to use a recent MKL version if your CPU is of a newer architecture.

To simplify MKL setup on Linux, we provide a script tools/extras/install_mkl.sh. We install only 64-bit binaries for MKL, but once the install_mkl.sh script completes successfully once, the Intel repositories are registered on your system, and you can both obtain new versions and 32-bit libraries using your system's package manager.

For Mac and Windows, download the installer from Intel's Web site (registration may be required). Refer to the same page in case the above Linux script does not support your Linux distribution. The Intel installers (Mac, Windows) let you select the 32-bit and 64-bit packages separately. To run Kaldi training recipes only the 64-bit version is required.

We have tested Kaldi extensively with 64-bit libraries under Linux and Windows.

The MKL Link Line Advisor is an interactive Web tool that allows configuring the compiler flags for various systems and compilers, in case our "configure" script does not cover it.
NOTE: Do not use the the multithreaded mode for Kaldi training (select "sequential" as the threading option). Our script and binary setups are designed to run multiple processes on a single machine, presumably maxing out its CPU, and an attempt to multi-thread linear algebra computations will only adversely impact the performance.

Automatically Tuned Linear Algebra Software (ATLAS)

ATLAS is a well known implementation of BLAS plus a subset of LAPACK. The general idea of ATLAS is to tune to the particular processor setup, so the compilation process is quite complex and can take a while. For this reason, it can be quite tricky to compile ATLAS. On UNIX-based systems, you can't even do it unless you are root or are friendly with your system administrator, because to compile it you need to turn off CPU throttling; and on Windows, ATLAS does not compile "natively", only in Cygwin. Sometimes it can be a better bet to find libraries that have been compiled by someone else for your particular platform, but we can't offer much advice on how to do this. ATLAS generally performs better than the "reference BLAS" available from Netlib. ATLAS only includes a few LAPACK routines. These include matrix inversion and Cholesky factorization, but not SVD. For this reason we have implemented a couple more of the LAPACK routines (SVD and eigenvalue decomposition); see the next section.

ATLAS conforms to the BLAS interface, but its interface for the subset of LAPACK routines that it provides is not the same as Netlib's (it's more C-like and less FORTRAN-ish). For this reason, there are quite a number of #ifdef's in our code to switch between the calling styles, depending whether we are linking with ATLAS or CLAPACK.

Installing ATLAS (on Windows)

For instructions on how to install ATLAS on Windows (and note that these instructions require Cygwin), see the file windows/INSTALL.atlas in our source distribution. Note that our Windows setup is not being actively maintained at the moment and we don't anticipate that it will work very cleanly.

Installing ATLAS (on Linux)

If your system does not have ATLAS installed, or there are no pre-built binaries available, you will need to install ATLAS from source. Even if your system has pre-built binaries available, they may not be the best binaries possible for your architecture so it is probably a better idea to compile from source. The easiest way to do this is to cd from "src" to "../tools" and to run ./install_atlas.sh. If this does not work, the detailed installation instructions can be found at: http://math-atlas.sourceforge.net/atlas_install/.

One useful note is that before installing ATLAS you should turn off CPU throttling using "cpufreq-selector -g performance" (cpufreq-selector may be in sbin), if it is enabled (see the ATLAS install page). You can first try running the "install_atlas.sh" script before doing this, to see whether it works– if CPU throttling is enabled, the ATLAS installation scripts will die with an error.


Kaldi now supports linking against the OpenBLAS library, which is an implementation of BLAS and parts of LAPACK. OpenBLAS also automatically compiles Netlib's implementation of LAPACK, so that it can export LAPACK in its entirety. OpenBLAS is a fork of the GotoBLAS project (an assembler-heavy implementation of BLAS) which is no longer being maintained. In order to use GotoBLAS you can cd from "src" to "../tools", type "make openblas", then cd to "../src" and give the correct option to the "configure" script to use OpenBLAS (look at the comments at the top of the configure script to find this option). Thanks to Sola Aina for suggesting this and helping us to get this to work.

Java Matrix Package (JAMA)

JAMA is an implementation of linear-algebra routines for Java, written in collaboration between NIST and MathWorks and put into the public domain (see math.nist.gov/javanumerics/jama). We used some of this code to fill in a couple of holes in ATLAS– specifically, if we're compiling with -DHAVE_ATLAS, we don't have the CLAPACK routines for SVD and eigenvalue decomposition available, so we use code from JAMA that we translated into C++. See the EigenvalueDecomposition class, and the function MatrixBase::JamaSvd. The user of the matrix library should never have to interact with this code directly.

Linking errors you might encounter

To make sure the matrix library is compiling correctly, type "make" in the matrix/ directory and see if it succeeds. A lot of compilation issues will manifest themselves as linking errors. In this section we give a summary of some of the more common linking errors (at least, those that relate specifically to the matrix library).

Depending on the compilation option (-DHAVE_CLAPACK, -DHAVE_LAPACK or -DHAVE_MKL), the code will be expecting to link with different things. When debugging linking errors, bear in mind that the problem could be a mismatch between the compilation options and the libraries that you actually linked.

f2c or g2c errors

The f2c library is often required if you link with CLAPACK, because it was created with f2c and that tool requires you to link with its own library. Not that with recent versions of gcc you have to link with -lg2c not -lf2c.

The symbols that will be missing if this is the problem, include:

s_cat, pow_dd, r_sign, pow_ri, pow_di, s_copy, s_cmp, d_sign

CLAPACK linking errors

You will get these errors if you compiled with -DHAVE_CLAPACK but did not provide the CLAPACK library. The symbols you will be missing are:

sgetrf_, sgetri_, dgesvd_, ssptrf_, ssptri_, dsptrf_, dsptri_, stptri_, dtptri_

This will usually be called something like liblapack.a or if using a dynamic library, you would type -llapack. Be careful– this has the same name as the ATLAS-supplied library "lapack" (see section CLAPACK linking errors), but it supplies different symbols. The native CLAPACK version of liblapack has symbols like those above (e.g. sgesvd_, sgetrf_), but the ATLAS version has symbols like clapack_sgetrf and also ones like ATL_sgetrf.

BLAS linking errors

You will get these errors if you failed to link against an implementation of BLAS. These errors can also occur if libraries are linked in the wrong order. CLAPACK requires BLAS, so you have to link BLAS after CLAPACK.

The symbols you will see if you failed to link with BLAS include:

cblas_sger, cblas_saxpy, cblas_dapy, cblas_ddot, cblas_sdot, cblas_sgemm, cblas_dgemm

To fix these, link with a static library like libcblas.a, or do -lcblas (assuming such a library is on your LD_LIBRARY_PATH). This library may come from ATLAS (which is preferable), or from Netlib (the "reference BLAS"). To the best of my current knowledge they have the same interface.

cblaswrap linking errors

CLAPACK seems to rely on symbols like f2c_sgemm that are some kind of wrapping of symbols like cblas_sgemm and so on. I'm not sure exactly what is being wrapped, and why. Anyway, the effect is that you may need to include a library named libcblaswr.a or dynamically using -lcblaswr, if you are using Netlib's CLAPACK. The cblaswrap library should be invoked before the cblas one. If you are missing cblaswrap, you will see errors about symbols like:

f2c_sgemm, f2c_strsm, f2c_sswap, f2c_scopy, f2c_sspmv, f2c_sdot, f2c_sgemv

and so on (there are a lot of these symbols).

Missing the ATLAS implementation of BLAS

If you linked with an ATLAS implementation of BLAS but only did -lcblas (or compiled with libcblas.a), but did not do -latlas (or compile with libatlas.a), you will have a problem because ATLAS's BLAS routines like cblas_sger internally call things that are in libatlas. If you have this problem you will have undefined references like:

ATL_dgemm, ATL_dsyrk, ATL_dsymm, ATL_daxpy, ATL_ddot, ATL_saxpy, ATL_dgemv, ATL_sgemv

Missing the ATLAS implementation of (parts of) CLAPACK

These errors can only occur if you compiled with the -DHAVE_ATLAS option. Atlas's name for the CLAPACK routines are different from clapack's own (they have clapack_ prepended to indicate the origin, which can be quite confusing).

If you have undefined references to the following symbols:

clapack_sgetrf, clapack_sgetri, clapack_dgetrf, clapack_dgetri

then it means you failed to link with an ATLAS library containing these symbols. This may be variously called liblapack.a, libclapack.a or liblapack_atlas.a, but you can tell that it is the right one if it defines a symbol called ATL_cgetrf (type "nm <library-name> | grep ATL_cgetrf" to see). You may be able to link dynamically with this library using -llapack or some similar option. Watch out, because a library called liblapack.a or liblapack.so could be CLAPACK or it could be ATLAS's version of CLAPACK, and as noted in section f2c or g2c errors, they supply different symbols. The only way to find out is to look inside it using "nm" or "strings".