raising an element of a vector to a power gives complex number, but it should be real number

Hello guys could you please help me with something, I have a very weird error.

I have a vector of data L_tilda, which I have created by taking logs and the applying HP filter to a vector of raw data. I wanted then to raise this vector element wise to the power 0.35.

The issue is, when I do that the results are complex numbers. But when I raise just the number, identical to the element of the vector, the result is real number.

Below I provide the output of the console, when I try to raise just one element of a vector to the power 0.35

>> L_tilda{end,2}

ans =

-0.007345972038603

>> L_tilda{end,2} ^ 0.35

ans =

0.081313753652337 + 0.159587227160134i

>> -0.007345972038603 ^ 0.35

ans =

-0.179108932233131

Answer 1

[Stephen23]

"Oh okay I guess I got it..."

No guessing is required, this is explained by the rules of operator precedence:

https://www.mathworks.com/help/matlab/matlab_prog/operator-precedence.html

It is clearly shown that matrix power has higher precedence than unary negation, so your code:

-0.007345972038603 ^ 0.35

ans = -0.1791

is exactly equivalent to this:

-(0.007345972038603 ^ 0.35)

ans = -0.1791

This is completely different to

n = -0.007345972038603;
n ^ 0.35

ans = 0.0813 + 0.1596i

which is equivalent to

(-0.007345972038603) ^ 0.35

ans = 0.0813 + 0.1596i

[Martin]

Oh okay I guess I got it, the answer should be complex number, but when i put -0.007345972038603 ^ 0.35 into the console it treats it as -(0.007345972038603 ^ 0.35), which is a real number, but not the correct result, which is 0.081313753652337 + 0.159587227160134i

[Steven Lord]

Yes, that's the expected behavior, as Stephen23 explained.

If you want MATLAB to apply unary minus (to create a negative number) before raising that value to a power, you must either define the negative number as a variable or wrap the negative number in parentheses (which has higher precedence than the power operator.)

In precedence order parentheses are first (level 1), the power operators are the next two (levels 2 and 3), and unary minus (-x) is after that (level 4.) If you remember in school learning the mnemonics PEMDAS or BODMAS, the documentation page Stephen23 linked to is the equivalent in MATLAB.

The two sections of code that create x1a and x1b below behave the same:

format longg
x1a = -0.007345972038603 ^ 0.35 % is the same as

x1a = 
        -0.179108932233131

x1b = uminus(power(0.007345972038603, 0.35))

x1b = 
        -0.179108932233131

while the code that creates x2a, x2b, and x2c behave the same.

x2a = (-0.007345972038603) ^ 0.35 % is the same as

x2a = 
         0.0813137536523356 +     0.159587227160132i

n = -0.007345972038603;
x2b = n^0.35 % and the same as

x2b = 
         0.0813137536523356 +     0.159587227160132i

x2c = power(uminus(0.007345972038603), 0.35)

x2c = 
         0.0813137536523356 +     0.159587227160132i