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Unexpected behavior from Arg in v13.3

POSTED BY: Martijn Froeling
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ZAQU zaqu
ZAQU zaqu
Posted 3 years ago

Can you check mine too? I recently downloaded 13.3 on my Debian linux and checked there is the same issue as in cloud.
POSTED BY: ZAQU zaqu

I did check. It appears to be simply a bug. I filed a report for it.
POSTED BY: Daniel Lichtblau

Thanks Daniel! For now i know the reason why my code changed outputs and i have a fix for it which works in all versions and i learned some things on the way so I'm happy for now.

POSTED BY: Martijn Froeling

Martijn, I doubt there is anything I can change about this, but I’ll take a look because it does seem suspicious. Your explanation in this recent response, and isolation of clear examples, is a big help.
POSTED BY: Daniel Lichtblau

I am working with version 13.3 on a Mac. The command c = Unitize[arg] gives a list of zeros every time I try it.
POSTED BY: Gianluca Gorni
  • I agree that 0*0.0+0.0 I gives 0.0+0.0 I
  • I also expect that 0 * 0.0 + 10.0^-200 should give 0.0+0.0 I
  • I also expect that Arg[-10.^-200 + (0.)] = Pi and Arg[0.0+0.0 I] = 0.0

But that was not my point, Arg[0 *(-10.0^-200+0.0I)] should and has always evaluated to 0.0 but with Mathematica 13.3 it no longer does. In one case it goes to 0.0 and the other case it goes to Pi which is inconsistent and unexpected.

I found the test case that things are unexpected and they changed from Mathematica 13.2 to 13.3

  • The examples below all go to values i expect => Arg[0 x.] goes to 0.0

    In[347]:= (*define values*)
i = 50; n = 200.;
(*single number - evaluates to 0.0*)
Arg[0 (-10.^-n + (0.)) I]

(*manual list of numbers - all evaluate to 0.0 including negative Re*)
msk = {0, 0, 0, 0, 0};
comp = {(-0.0` 10.^-n + 0.0 I), -5.234654279824674565789` 10.^-n + 
    00. I, -4.32467641324676543243` 10.^-n + 0.0 I, 
   5.234654279824674565789` 10.^-n + 00. I, 
   4.32467641324676543243` 10.^-n + 0.0 I};
val = msk comp;
arg = Arg[val]
Thread[{msk, comp, val, arg}]

Out[348]= 0.

Out[352]= {0., 0., 0., 0., 0.}

Out[353]= {{0, 0. + 0. I, 0. + 0. I, 0.}, {0, -5.23465*10^-200 + 0. I,
   0. + 0. I, 0.}, {0, -4.32468*10^-200 + 0. I, 0. + 0. I, 0.}, {0, 
  5.23465*10^-200 + 0. I, 0. + 0. I, 0.}, {0, 4.32468*10^-200 + 0. I, 
  0. + 0. I, 0.}}

  • But for generated lists they do not, values with small negative Re to to Pi even when multiplied with exact 0 and the actual value that goes into Arg is 0.0+0.0 I the outcome is always Pi. First output is 13.3 second output is 13.2. They are different

    In[364]:= (*define values*)
i = 50; n = 200.;

(*generated list of number  - everything with negative Re evaluates \
to Pi*)
msk = ConstantArray[0, i];
comp = RandomComplex[{-10.^-n, 10.^-n}, i];
val = msk comp;
arg = Arg[val];
Thread[{msk, comp, val, arg}]

(* proof dat all negative numbers in array evaluate to *)
a = UnitStep[-Sign[Re[comp]]]
b = Sign[Re[val]]
c = Unitize[arg]
a == c


Out[369]= {{0, -3.59355*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -8.714-201 + 0. I, 0. + 0. I, 3.14159}, {0, 
  4.51555*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 4.56213*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, -1.73914*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, 2.76678*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -7.29739*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -3.88282*10^-202 + 0. I, 0. + 0. I, 
  3.14159}, {0, -2.38636*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -7.88456*10^-201 + 0. I, 0. + 0. I, 3.14159}, {0, 
  8.5064*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 9.23848*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, -2.09942*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, 6.05198*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  7.35013*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -9.72399*10^-202 + 0. I,
   0. + 0. I, 3.14159}, {0, -2.16232*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -1.72071*10^-201 + 0. I, 0. + 0. I, 3.14159}, {0, 
  2.56238*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -4.72392*10^-202 + 0. I,
   0. + 0. I, 3.14159}, {0, 1.46317*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, 5.45542*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  6.98144*10^-202 + 0. I, 0. + 0. I, 0.}, {0, 7.52893*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, 5.63282*10^-202 + 0. I, 0. + 0. I, 0.}, {0, 
  5.83295*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 8.2813*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, -9.01357*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -7.20074*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -6.65122*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -4.04739*10^-203 + 0. I, 0. + 0. I, 3.14159}, {0, 
  7.55101*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -5.3072*10^-201 + 0. I, 
  0. + 0. I, 3.14159}, {0, 5.01132*10^-201 + 0. I, 0. + 0. I, 0.}, {0,
   2.43361*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 9.98434*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, 5.41462*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  2.51404*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -5.79749*10^-201 + 0. I,
   0. + 0. I, 3.14159}, {0, 3.89775*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -2.98549*10^-201 + 0. I, 0. + 0. I, 3.14159}, {0, 
  5.02625*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 1.49796*10^-203 + 0. I, 
  0. + 0. I, 0.}, {0, 7.29538*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -4.74217*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -3.63903*10^-201 + 0. I, 0. + 0. I, 
  3.14159}, {0, -9.08686*10^-201 + 0. I, 0. + 0. I, 3.14159}, {0, 
  3.00761*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -6.14527*10^-201 + 0. I,
   0. + 0. I, 3.14159}, {0, 6.85878*10^-201 + 0. I, 0. + 0. I, 0.}}

Out[370]= {1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, \
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, \
0, 0, 1, 1, 1, 0, 1, 0}

Out[371]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0}

Out[372]= {1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, \
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, \
0, 0, 1, 1, 1, 0, 1, 0}

Out[373]= True

Now look at the output from the same code in Mathematica 13.2

In[1]:= (*define values*)
i = 50; n = 200.;

(*generated list of number  - everything with negative Re evaluates \
to Pi*)
msk = ConstantArray[0, i];
comp = RandomComplex[{-10.^-n, 10.^-n}, i];
val = msk comp;
arg = Arg[val];
Thread[{msk, comp, val, arg}]

(* proof dat all negative numbers in array evaluate to *)
a = UnitStep[-Sign[Re[comp]]]
b = Sign[Re[val]]
c = Unitize[arg]
a == c


Out[6]= {{0, 4.5418*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  5.69817*10^-202 + 0. I, 0. + 0. I, 0.}, {0, -8.08554*10^-202 + 0. I,
   0. + 0. I, 0.}, {0, -2.50589*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  5.8806*10^-202 + 0. I, 0. + 0. I, 0.}, {0, 2.03054*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, 2.31057*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  7.43712*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -1.32253*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, -4.77195*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  4.58221*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 8.59623*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, 4.82584*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -8.78687*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -2.65764*10^-202 + 0. I, 0. + 0. I, 0.}, {0, 
  2.20168*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 2.74392*10^-202 + 0. I, 
  0. + 0. I, 0.}, {0, -7.233*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  6.18229*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -1.41438*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, 2.30648*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  2.99944*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -9.78346*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, 4.17352*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -5.85227*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -5.58142*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -3.90072*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -2.97276*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  7.29687*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -1.34306*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, 5.24692*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  8.0529*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -2.38566*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, 6.40825*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  6.80501*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -3.68792*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, 3.56694*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  7.03833*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 8.75828*10^-201 + 0. I, 
  0. + 0. I, 0.}, {0, -8.0177*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -4.44713*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -3.30227*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -9.00441*10^-201 + 0. I, 0. + 0. I, 
  0.}, {0, -1.33593*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  5.87783*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -9.87446*10^-202 + 0. I,
   0. + 0. I, 0.}, {0, -9.15533*10^-201 + 0. I, 0. + 0. I, 0.}, {0, 
  5.32573*10^-201 + 0. I, 0. + 0. I, 0.}, {0, -6.20455*10^-201 + 0. I,
   0. + 0. I, 0.}, {0, 6.24134*10^-201 + 0. I, 0. + 0. I, 0.}}

Out[7]= {0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, \
0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, \
1, 0, 1, 1, 0, 1, 0}

Out[8]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0}

Out[9]= {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0}

Out[10]= False

In my opinion the behavior of 13.2 is the correct and expected one and the output of 13.3 is unexpected.
POSTED BY: Martijn Froeling
ZAQU zaqu
ZAQU zaqu
Posted 3 years ago
POSTED BY: ZAQU zaqu

The idea behind having 0*0.0 evaluate to 0.0 is to maintain the type rule int times real equal real. One can question this of course. But it has advantages particularly for type consistency and inferencing, as is needed in Compile and the newer FunctionCompile world.
POSTED BY: Daniel Lichtblau

From the documentation on Numbers:

Whenever you give a number with an explicit decimal point, the Wolfram Language produces an approximate numerical result

Here is what happens by multiplying an approximate number by the exact zero:

In[2]:= 0*0.

Out[2]= 0.
POSTED BY: Gianluca Gorni
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