Mathematics, MATLAB Version 7.0.1 (R14SP1) Release Notes

Mathematics, MATLAB Version 7.0.1 (R14SP1)

This version introduces the following new features and changes:

• New Function — ordeig

• More Functions Accept Single-Precision Data Inputs

• New Vendor BLAS Used for Linear Algebra in MATLAB

• Overriding the Default BLAS Library on Sun/Solaris Systems

• FDLIBM Version Upgraded

• Different Results When Solving Singular Linear Systems on Intel Systems; Inconsistent NaN Propagation

• funm Returns Status Information; New Output Might Result In Error

New Function — ordeig

The new function ordeig takes a quasitriangular matrix T or matrix pair (A,B) and returns the vector of eigenvalues in the same order that they appear down the diagonal of T or (A,B). You can use ordeig with the functions ordschur and ordqz, which reorder the eigenvalues of a Schur factorization or a QZ factorization, respectively.

More Functions Accept Single-Precision Data Inputs

More MATLAB functions now accept single-precision data inputs in addition to the usual double-precision inputs. To determine whether a function works on single precision inputs, look for the Class support line in the M-file help for the function. For example, to determine whether the function mean accepts single-precision inputs, type

help mean

The Class support line is

float: double, single

which tells you that mean does accept single-precision inputs.

New Vendor BLAS Used for Linear Algebra in MATLAB

MATLAB uses Basic Linear Algebra Subprograms (BLAS) for its vector inner product, matrix-vector product, matrix-matrix product, and triangular solvers in \. MATLAB also uses BLAS behind its core numerical linear algebra routines from Linear Algebra Package (LAPACK), which are used in functions like chol, lu, qr, and within the linear system solver \.

On some platforms, MATLAB continues to use ATLAS BLAS.

Starting in Release 14, MATLAB 7.0 uses vendor BLAS from the vecLib library on the Mac.

Starting in Release 14 with Service Pack 1, MATLAB 7.0.1 uses vendor BLAS from

• The Intel Math Kernel Library (MKL) Version 7.0 on Intel chips running both Windows and Linux. See the MATLAB 7.0 Release Notes for how to use the multi-threaded capabilities of MKL.

• The AMD Core Math Library (ACML) Version 2.0 library on AMD chips, native 64 bit application

Overriding the Default BLAS Library on Sun/Solaris Systems

MATLAB uses the Basic Linear Algebra Subroutines (BLAS) libraries to speed up matrix multiplication and LAPACK-based functions like eig, svd, and \ (mldivide). At start-up, MATLAB selects the BLAS library to use.

For Release 14 with Service Pack 1, MATLAB still uses the ATLAS BLAS libraries on the Sun Microsystems Solaris Operating System. However, you can switch the BLAS library that MATLAB uses to the Sun Performance Library (Sunperf) BLAS, provided by Sun Microsystems.

If you want to take advantage of the potential performance enhancements provided by the Sun BLAS, you can set the value of the environment variable BLAS_VERSION to the name of the Sun Performance Library, libsunperf.so.4. MATLAB uses the BLAS specified by this environment variable, if it exists.

To set the BLAS_VERSION environment variable, enter the following command at the at the UNIX prompt.

% setenv BLAS_VERSION libsunperf.so.4

Then start MATLAB as usual.

To get visual feedback that the BLAS version has changed, also type at the UNIX prompt

% setenv LAPACK_VERBOSITY 1

before starting MATLAB. This will display diagnostic information while MATLAB is starting up, for example:

cpu_id: sun4u
libmwlapack: loading libsunperf.so.4
libmwlapack: loading lapack.so

FDLIBM Version Upgraded

In Release 14, MATLAB used FDLIBM Version 5.2. In R14SP1, MATLAB has been upgraded to use FDLIBM Version 5.3.

Different Results When Solving Singular Linear Systems on Intel Systems; Inconsistent NaN Propagation

In previous releases, when you solved n-by-n linear systems Ax=b using x = A\b, where A is singular or contains NaN, the computed result x often contained NaN. In Version 7.0.1, the same command might return 0 in x, due to the way the Intel Math Kernel Library (MKL) implementation of the BLAS handles this operation.

Compatibility Considerations

Code that relies on the result containing NaN should check for the following warnings instead:

• For singular A, an existing warning is issued.

  x = [1 2; 0 0]\[1; 0]
  Warning: Matrix is singular to working precision.
  x =
       1
       0

• For A that contains NaN, a new warning message is issued.

  x = [1 2; 0 NaN]\[1; 0]
  Warning: Matrix is singular, close to singular or badly scaled.
  Results may be inaccurate. RCOND = NaN.
  x =
       1
       0

funm Returns Status Information; New Output Might Result In Error

Prior to Release 14, the second output of the function funm was an error estimate that was sometimes inaccurate. In Release 14, Version 7.0, the second output was replaced by an exit flag that indicates whether the computation was successful.

Compatibility Considerations

Code that was created prior to Release 14 and that uses the second output of funm, might not work correctly in Version 7.0 or later.

Desktop Tools and Development Environment, MATLAB Version 7.0.1 (R14SP1)

Programming, MATLAB Version 7.0.1 (R14SP1)