Prototype numeric matrix library for Ruby via SciRuby
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Fast Numerical Linear Algebra Library for Ruby


NMatrix is a fast numerical linear algebra library for Ruby, written mostly in C and C++. It is part of the SciRuby project.

NMatrix was inspired by and based heavily upon NArray, by Masahiro Tanaka.


For full instructions, please see Generally, you should be able to do

gem install nmatrix

However, you will need to install ATLAS with CBLAS first. Those directions can be found at our website.

NOTE: The above command will not give you 0.0.2, which is not yet complete. To obtain the latest code, you should use the following sequence of commands:

git clone
cd nmatrix/
rake compile
rake repackage
gem install pkg/nmatrix-0.0.4.gem

If you get errors about clapack.h or cblas.h, figure out where your ATLAS headers are using:

locate clapack.h

If you're a Mac user, we recommend you search for cblas.h instead.

Then, tell your system:

export C_INCLUDE_PATH=/usr/local/atlas/include
export CPLUS_INCLUDE_PATH=/usr/local/atlas/include

Finally, try compiling again.



  • LAPACK, probably

  • GCC 4.3

  • Ruby 1.9

  • packable 1.3.5 (used for I/O)


Create a new NMatrix from a ruby array:

>>[2, 3], [0, 1, 2, 3, 4, 5], :int64).pp
  [0, 1, 2]
  [3, 4, 5]
=> nil

Create a new NMatrix using the N shortcut:

	>> m = N[ [2, 3, 4], [7, 8, 9] ]
	=> #<NMatrix:0x007f8e121b6cf8shape:[2,3] dtype:int32 stype:dense> 
	>> m.pp
	  [2, 3, 4]
	  [7, 8, 9]

If you want to learn more about how to create a matrix, read the guide in our wiki.

We will add more examples here soon. :)


Read the instructions in if you want to help NMatrix.


The following features exist in the current version of NMatrix (0.0.2):

  • Matrix storage containers: dense, yale, list (more to come)

  • Data types: uint8, int8, int16, int32, int64, float32, float64, complex64, complex128, rational64, rational128 (incomplete)

  • Conversion between storage and data types (except from-complex, and from-float-to-rational)

  • Element-wise operations and comparisons for dense and yale

  • Matrix-matrix multiplication for dense (using ATLAS) and yale

  • Matrix-vector multiplication for dense (using ATLAS)

  • Dense and list matrix slicing and referencing

  • Native reading and writing of dense and yale matrices

    • Optional compression for dense matrices with symmetry or triangularity: symmetric, skew, hermitian, upper, lower

  • Matlab .MAT v5 file input

  • C and C++ API

  • BLAS internal implementations (no library) and ATLAS (with library) access:

    • Level 1: xROT, xROTG (BLAS dtypes only)

    • Level 2: xGEMV

    • Level 3: xGEMM, xTRSM

  • LAPACK ATLAS access:

    • xGETRF, xGETRI, xGETRS, xGESV (Gaussian elimination)

    • xPOTRF, xPOTRI, xPOTRS, xPOSV (Cholesky factorization)


  • LAPACK-less internal implementations (no LAPACK needed and working on non-BLAS dtypes):

    • xGETRF

    • xLASWP, xSCAL

    • xLAUUM (no LAPACK needed, but BLAS dtypes only)

  • LU decomposition

  • Matrix inversions (requires LAPACK; BLAS dtypes only)

  • Determinant calculation for BLAS dtypes

Planned Features (Short-to-Medium Term)

These are features planned for NMatrix 0.1.0, our first beta.

  • calculation of determinant (LAPACK-free), trace, and eigenvalues (characteristic polynomial) (0.1.0)

  • exponentials and square roots

  • matrix inversions (LAPACK-free)

  • matrix decomposition/factorization

  • calculation of norms

  • tensor products

  • principal component analysis (PCA)

  • improved file I/O

    • compression of yale symmetries in I/O

  • operation scheduling

  • parallelization of some types of operations

  • optimization of non-BLAS data types on BLAS-like operations (e.g., matrix multiplication for rational numbers)

  • Ruby/GSL interoperability


Please be aware that SciRuby and NMatrix are alpha status. If you're thinking of using SciRuby/NMatrix to write mission-critical code, such as for driving a car or flying a space shuttle, you may wish to choose other software for now.

You should also be aware that NMatrix and NArray are incompatible with one another; you should not try to require both at the same time. Unfortunately, that causes problems with Ruby/GSL, which currently depends upon NArray. As such, we are working on a patch for Ruby/GSL.


Copyright © 2012–13, The Ruby Science Foundation.

All rights reserved.

NMatrix, along with SciRuby, is licensed under the BSD 2-clause license. See LICENSE.txt for details.


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