# This is a Supplement to the Cleve's Corner Article MATLAB Incorporates LAPACK

This is a supplement to the Cleve's Corner article, MATLAB Incorporates LAPACK

March 29, 2000: Today we are posting versions of the numerics library that correct a bug in earlier versions. The bug involves "balancing" or scaling in eigenvector computations and leads to incorrect eigenvectors for some matrices. Please replace earlier versions with these corrected versions.

This supplement provides access to new versions of the numerics library for use with MATLAB 5.3 (Release 11 of the MathWorks CD).

The new library uses LAPACK and machine-dependent optimized BLAS (Basic Linear Algebra Subprograms) for matrix computations. The built-in functions involved include matrix multiplication (*), linear equation solution (/ and \), `chol, lu, qr, eig, svd, qz, schur, hess, rcond, det and inv`. The command-line and M-file interface to these functions is unchanged, but both execution time performace and numerical results are affected. Expected performance improvments depend upon the matrix size, the function and the machine. We have seen speedups by factors as large as eight for matrix multiplication and Gaussian elimination on matrices of order a few hundred.

Numerical results are affected by changes in floating point round off error and by possibly different determination of quantities that are not uniquely determined mathematically. Eigenvalues and singular values may occur in different orders and eigenvectors and singular vectors may be normalized differently. For example:

```A = pascal(3)
B = hilb(3)
[V,D] = eig(A,B)
```

With previous libraries, the eigenvalues in `diag(D)` can occur in any order and the eigenvectors in the columns of `V` have length one. With the new library, the eigenvalues occur in increasing order and the eigenvectors are normalized so that `V'*B*V` is the identity matrix.

Note that the new library affects only MATLAB itself. The performance and numerical results of other MathWorks products, such as Simulink and the C Math library, will not change.

On Windows, the directory is

```matlab/bin
```

In this directory, you will find a file named `numerics.dll`. Rename this to something like `numerics.bak`. Then download the following Windows self-extracting zip file:

When you execute this in the bin directory, you will produce a new `numerics.dll` and a Fortran support library, `dformd.dll`.

On Unix and Linux, the directory is

```matlab/bin/arch
```

where `arch` is the abbreviation of the particular architecture. In this directory, you will find a file named `libmwnumerics.so`. Rename this to something like `libmwnumerics.bak`. Then download one of the following compressed files:

Uncompress or gunzip this file in the `bin/arch` directory and rename the file to eliminate the prefix up to the underscore. This will produce a new `libmwnumerics.so` shared library that includes LAPACK and the BLAS.

Some Web browsers automatically decompress these files during the download. In one case, the browser decompresses the file, but does not delete the ".gz" suffix in the file name.

If you have any difficulties, or see anything that should be changed before we include this in the next release of MATLAB, please let me know.

Published 2000