Matlab exponent bug?

Hello MatLabers

I have encountered a problem when calculating a non integer exponent/power of a variable.

example:

>>  -3.^(1.3)
>> ans = -4.1712

thats exactly what I aim to calculate. However, if I do the exact same thing with a variable - the result gets complex:

>> a = -3
>> a.^(1.3)
>> ans = -2.4518 - 3.3745i

is this an known issue or am I doing somehting wrong? (tested on R2010a, R2011b)

[Jonas Reber]

see also:

http://www.mathworks.com/support/solutions/en/data/1-15M1N/index.html

Answer 1

[Daniel Shub]

This is a precedence issue: http://www.mathworks.com/help/releases/R2011a/techdoc/matlab_prog/f0-40063.html#f0-38155

Try

(-3).^(1.3)

[Jan]

@Daniel: Fast!

[Daniel Shub]

and I got the documentation link ...

[Jan]

then you get the credits. +1

Answer 2

[Jan]

The POWER operation has a higher precedence than the unary minus. Try this:

-3 .^ (1.3)
(-3) .^ (1.3)

[Jonas Reber]

Jan&Daniel - thanks for the fast replies

>> (-3).^(1.3)

didn't realize that.

Answer 3

[Edgar An]

The problem is not about precedence. The problem occurs when we use variables instead of numbers. Just like the person who posted.

-0.685^1.5 gives a correct answer

but a = -0.685, b = 1.5, and then a^b gives wrong answer

i am using R2020b version

[Bruno Luong]

"wrong" answer? Rather not what YOU expect.

>> a = -0.685; b = 1.5;
>> a^b

ans =

  0.000000000000000 - 0.566938378485705i

>> exp(log(a)*b)

ans =

 -0.000000000000000 - 0.566938378485705i
 
 >> -(abs(a)^b) % You expect this but you miss how power function is defined

ans =

  -0.566938378485705
  
  >> -0.685^1.5

ans =

  -0.566938378485705

[Walter Roberson]

In MATLAB, a^b is defined to be equivalent to exp(log(a)*b). When a is negative the log is complex with a πι component and if b is not an integer then the exp() of the πι*b is going to be complex.

In practice you can tell from timings that for at least some integer values a^b is not implemented through logs: for example a^2 has timing the same as a*a, but the principle is the same.

[Bruno Luong]

To be precise for z complex (including negarive real)

log(z)

is defined in term of real-argument function log and atan2

log(abs(z)) + 1i*angle(z)

where abs(z) is

sqrt(imag(z)^2+real(z)^2) % the square "x^2" here is interpreted as (x*x)

angle(z) is

atan2(imag(z),real(z))

with all the rule we discuss recently, notably discontinuity when real(z) is negative and numeriral sign of imag(z).

The definition of

exp(z)

has no ambiguity.