Element-wise power resulting in imaginary values and NAN

I am using element-wise power .^,which for A.^B should yield a matrix with elements A(i,j) raised to the power B(i,j). However, for the simple example:

A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B

I'm getting

ans =

  -1.0000 + 0.0000i      NaN + 0.0000i
      NaN + 0.0000i  -1.0000 + 0.0000i

If I use a loop, there is no error.

for i=1:2
    for j =1:2
        AB(i,j) = A(i,j)^B(i,j);
    end
end
AB =

    -1     1
     1    -1

I can also select a single power coefficient and get the correct values, such as

A.^B(1,2)
ans =

     1     1
     1     1

What's wrong with the matrix element-wise power? Why is it giving out imaginary numbers and NaN for essentially 0^0, which should equal 1. Thanks.

EDIT: More Information on Replicating the Error

I tried to figure out why others can't replicate the errors I'm getting. After much frustration, I restarted the computer (Windows 10, R2018a) and tried it from a fresh instance, just copying and pasting the code into the Command Window, I get no error. However, if I run it from a script (e.g., script.m with the exact same code), then I get the error, and once it's errored, it can't be undone. Did some system settings change once I run it from an M file? I hope this helps to pinpoint the problem.

>> A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B

ans =

    -1     1
     1    -1

>> script

ans =

  -1.0000 + 0.0000i      NaN + 0.0000i
      NaN + 0.0000i  -1.0000 + 0.0000i

>> A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B

ans =

  -1.0000 + 0.0000i      NaN + 0.0000i
      NaN + 0.0000i  -1.0000 + 0.0000i

[Walter Roberson]

Which MATLAB release are you using? I am getting sensible results when I use A.^B on my Mac

Also, which operating system? And did you happen to set environment variables to force a different MKL or LAPACK to be used?

[MathN00b]

Thanks for your quick reply, Walter. I've tried it on 2 versions of MATLAB, the latest is the R2018a, both on Windows 10. I'm not sure about MKL or LAPACK, I will have to read more on it. Thanks again.

I tried the following command and received the following info:

version('-blas')
ans =
    'Intel(R) Math Kernel Library Version 2017.0.31 Product Build 20170606 for Intel(R) 64 architecture applications, CNR branch AVX2
     '

[Walter Roberson]

I tested on R2018a on Mac, and got sensible answers. My -blas shows the exact same version as yours.

[MathN00b]

Thanks, Walter! I thought I was crazy, when I tried to run the code myself this morning and received sensible answers. Then I did more investigation, and it appears that once I run it from script (M file), the error starts and cannot be undone. I edited the original post to reflect this new discovery.

[Walter Roberson]

Experiment with using

restoredefaultpath

[MathN00b]

>> restoredefaultpath;
A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B
ans =

  -1.0000 + 0.0000i      NaN + 0.0000i
      NaN + 0.0000i  -1.0000 + 0.0000i

I played around restoredefaultpath, but no luck. Not sure what's changed in the script environment.

Anyone else with Windows getting the same complex representation and NaN?

[James Tursa]

WIN64, R2016a:

% command line
>> A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B
ans =
    -1     1
     1    -1
% script file
>> junk88
ans =
    -1     1
     1    -1

WIN64, R2018b:

% command line
>> A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B
ans =
    -1     1
     1    -1
% script file
>> junk88
ans =
    -1     1
     1    -1

Regarding why the erroneous calculation can't be "undone", this may be due to MATLAB parser caching the result in the background as a reference copy. So everytime it sees the calculation expression it pulls the result from the internal cache (the reference copy) rather than redoing the calculation. If you change the syntax of the calculation the reference copy can be avoided and a new calculation will be done. Just a guess on my part ...

BTW, this calculation is not done by any BLAS library code.

[James Tursa]

Have you shadowed the .^ operator? What does this show

which power

[Walter Roberson]

Could you attach the script that is triggering the problem?

[MathN00b]

Thank you for your help, Walter! The script contains the exact same code

 A = [-1, 0; 0, -1];
B = [1, 0; 0, 1];
A.^B

I figured out the problem, thanks to James. One of the libraries contained a directory named @double with an alternative power.m file, which overloaded the default power function. I had no idea this is called when I used .^. It defined

o=power(s,t)

as

o=exp(log(s)*t);

or

o=exp(log(s).*t);

depending on the arguments. Thanks again for your patience and help, I really appreciate it.

Answer 1

[James Tursa]

Looks like the problem calculation is being done in the background as exp(B.*log(A)), but I don't know why it does this sometimes and not other times.

[MathN00b]

Thanks, James! One of the libraries contained a directory named @double with an alternative power.m file, which overloaded the default power function. I had no idea this is called when I used .^. It defined

o=power(s,t)

as

o=exp(log(s)*t);

or

o=exp(log(s).*t);

depending on the arguments. Much thanks!

[Walter Roberson]

Whew!