Different svd results with R2015b and R2016a

I'm trying to figure out why I'm seeing different results with the same code for R2015b and R2016a on Windows and Linux. Mac 2015b and R2016a match R2015b on Windows and Linux. Windows and Linux R2016a results match.

Any ideas on where to look to figure out why I'm getting different results?

>> ver
----------------------------------------------------------------------------------------------------
MATLAB Version: 8.6.0.267246 (R2015b)
MATLAB License Number: XXXXXXX
Operating System: Microsoft Windows 10 Pro Version 10.0 (Build 10586)
Java Version: Java 1.7.0_60-b19 with Oracle Corporation Java HotSpot(TM) 64-Bit Server VM mixed mode
----------------------------------------------------------------------------------------------------
MATLAB                                                Version 8.6         (R2015b)
Database Toolbox                                      Version 6.0         (R2015b)
MATLAB Compiler                                       Version 6.1         (R2015b)
Optimization Toolbox                                  Version 7.3         (R2015b)
Parallel Computing Toolbox                            Version 6.7         (R2015b)
Statistics and Machine Learning Toolbox               Version 10.1        (R2015b)

>> ver
----------------------------------------------------------------------------------------------------
MATLAB Version: 9.0.0.341360 (R2016a)
MATLAB License Number: XXXXXXX
Operating System: Microsoft Windows 10 Pro Version 10.0 (Build 10586)
Java Version: Java 1.7.0_60-b19 with Oracle Corporation Java HotSpot(TM) 64-Bit Server VM mixed mode
----------------------------------------------------------------------------------------------------
MATLAB                                                Version 9.0         (R2016a)
Database Toolbox                                      Version 6.1         (R2016a)
MATLAB Compiler                                       Version 6.2         (R2016a)
Optimization Toolbox                                  Version 7.4         (R2016a)
Parallel Computing Toolbox                            Version 6.8         (R2016a)
Statistics and Machine Learning Toolbox               Version 10.2        (R2016a)

[Cameron Taggart]

My first inclination was to look to see if the random seed generator had changed, but the first three numbers are not different. Probably cold use a bigger test.

rng(25346954, 'twister');
r = rand(1, 3);

[Walter Roberson]

What does the code do ?

[Cameron Taggart]

After a few hours of debugging, I've narrowed it down to: http://www.mathworks.com/help/matlab/ref/svd.html

[Cameron Taggart]

Why don't these produce the same results? Is one correct and the other not?

R2015b

>> format long;
m = [   0.020000000000000   3.162340905089140   5.099058736668955   5.000039999840001; ...
        3.162340905089140   0.020000000000000   8.246235504762158   5.000039999840001; ...
        5.099058736668955   8.246235504762158   0.020000000000000   8.544027153514904; ...
        5.000039999840001   5.000039999840001   8.544027153514904   0.020000000000000; ];
svd(m)

ans =

    17.972498059668290
     9.629925976510560
     5.567459858959232
     2.695112224198502

R2016a

>> format long;
m = [   0.020000000000000   3.162340905089140   5.099058736668955   5.000039999840001; ...
        3.162340905089140   0.020000000000000   8.246235504762158   5.000039999840001; ...
        5.099058736668955   8.246235504762158   0.020000000000000   8.544027153514904; ...
        5.000039999840001   5.000039999840001   8.544027153514904   0.020000000000000; ];
svd(m)

ans =

    17.972498059668293
     9.629925976510558
     5.567459858959231
     2.695112224198502

[Christine Tobler]

Both results are correct up to machine precision. The reason for the difference between MATLAB versions is that the MKL library (containing the BLAS and LAPACK libraries which are used for the linear algebra computations) has been updated between releases.

To check the version of the MKL used in MATLAB, type

>> version -blas

The reason that the results changed is likely due to a difference in the order of operations. This will affect the results in small ways, without there necessarily being a better or worse result. Such small changes are likely to happen between any two MATLAB versions, as the MKL version is updated regularly.

[Cameron Taggart]

Thanks Christine! This makes sense.

For my notes, `version -blas`

R2015b Mac

Intel® Math Kernel Library Version 11.1.1 Product Build 20131010 for Intel® 64 architecture applications

R2016a Mac

Intel® Math Kernel Library Version 11.2.3 Product Build 20150409 for Intel® 64 architecture applications, CNR branch AVX2

R2015b Windows

Intel® Math Kernel Library Version 11.1.1 Product Build 20131010 for Intel® 64 architecture applications

R2016a Windows

Intel® Math Kernel Library Version 11.2.3 Product Build 20150413 for Intel® 64 architecture applications, CNR branch AVX2