5:12 p.m.
Let X be a series of negative numbers. Then the command
series Y = X^(1/3)
(or any other "1/oddnumber" fractional power)
returns a "Warning: pow: Domain error" message, overwrites series "Y"
and returns a "no valid values" if one attempts to view the series.
Why is this happening, considering that X^(1/3) is a real number even if
X is a negative number?
Now, consider series "Z" which has both positive /and/ negative values.
We want to compute
W = Z^(1/3)
Given a recent new feature in gretl, the sign function sgn(), I guess
we can avoid the obvious conditional if-else statement, and compute W
by writing
W = sgn(Z) * (abs(Z)^(1/3))
that covers also the case of Z taking an exact zero value.
Is this the proper/efficient way?
--
Alecos Papadopoulos PhD
Athens University of Economics and Business
web: alecospapadopoulos.wordpress.com/
skype:alecos.papadopoulos
9:45 p.m.
New subject: Negative numbers to fractional powers
Am 12.08.2020 um 19:12 schrieb Alecos Papadopoulos:
Let X be a series of negative numbers. Then the command
series Y = X^(1/3)
(or any other "1/oddnumber" fractional power)
returns a "Warning: pow: Domain error" message, overwrites series
"Y"
and returns a "no valid values" if one attempts to view the series.
Why is this happening, considering that X^(1/3) is a real number even if
X is a negative number?
Good question. I'm noticing that 'eval -1^(1/3)' works fine, in contrast.
Now, consider series "Z" which has both positive /and/
negative values.
We want to compute
W = Z^(1/3)
Given a recent new feature in gretl, the sign function sgn(), I guess
we can avoid the obvious conditional if-else statement, and compute W
by writing
W = sgn(Z) * (abs(Z)^(1/3))
that covers also the case of Z taking an exact zero value.
Is this the proper/efficient way?
Only testing will tell if it's efficient, but my guess would be that the
paper-and-pencil-style multiplication with the sign might not be
optimal. Perhaps like this:
series W = (Z < 0) ? -(abs(Z)^(1/3)) : Z^(1/3)
cheers
sven
6:50 a.m.
New subject: Negative numbers to fractional powers
On 12/08/2020, 23:45, "Sven Schreiber" <svetosch(a)gmx.net> wrote:
Am 12.08.2020 um 19:12 schrieb Alecos Papadopoulos:
Let X be a series of negative numbers. Then the command
series Y = X^(1/3)
(or any other "1/oddnumber" fractional power)
returns a "Warning: pow: Domain error" message, overwrites series
"Y"
and returns a "no valid values" if one attempts to view the series.
Why is this happening, considering that X^(1/3) is a real number even if
X is a negative number?
Good question. I'm noticing that 'eval -1^(1/3)' works fine, in
contrast.
--> I guess that's because exponentiation takes precedence over negation. 'eval
(-1)^(1/3)' results in NaN.
All the best
Jan
7:16 a.m.
New subject: Negative numbers to fractional powers
Am 13.08.2020 um 08:50 schrieb Jan Annaert:
On 12/08/2020, 23:45, "Sven Schreiber"
<svetosch(a)gmx.net> wrote:
Am 12.08.2020 um 19:12 schrieb Alecos Papadopoulos:
> Why is this happening, considering that X^(1/3) is a real number even if
> X is a negative number?
Good question. I'm noticing that 'eval -1^(1/3)' works fine, in
contrast.
--> I guess that's because exponentiation takes precedence over negation.
'eval (-1)^(1/3)' results in NaN.
Of course you're right!
thanks
sven
1:34 a.m.
New subject: Negative numbers to fractional powers
On Wed, 12 Aug 2020, Alecos Papadopoulos wrote:
Let X be a series of negative numbers. Then the command
series Y = X^(1/3)
(or any other "1/oddnumber" fractional power)
returns a "Warning: pow: Domain error" message, overwrites series "Y"
and
returns a "no valid values" if one attempts to view the series.
Why is this happening, considering that X^(1/3) is a real number even if X is
a negative number?
Are you sure of your ground here, Alecos?
We use the C library's pow() function for this job, and here's an
extract from the manual page for pow(), which conforms to the C99
standard:
<quote>
double pow(double x, double y);
RETURN VALUE
On success returns the value of x to the power of y.
If x is a finite value less than 0, and y is a finite
noninteger, a domain error occurs, and a NaN is returned.
</quote>
For reference here's what happens in R:
<input>
x <- -3
y <- 1.0/3
x^y
</input>
<output>
x <- -3
y <- 1.0/3
x^y
[1] NaN
</output>
and in octave:
<input>
x = -3
y = 1.0/3
x^y
</input>
<output>
x = -3
y = 0.33333
ans = 0.72112 + 1.24902i
</output>
Allin
1:55 a.m.
New subject: Negative numbers to fractional powers
On Wed, 12 Aug 2020, Alecos Papadopoulos wrote:
Now, consider series "Z" which has both positive /and/
negative values. We
want to compute
W = Z^(1/3)
Given a recent new feature in gretl, the sign function sgn(), I guess we can
avoid the obvious conditional if-else statement, and compute W by writing
W = sgn(Z) * (abs(Z)^(1/3))
that covers also the case of Z taking an exact zero value.
Is this the proper/efficient way?
My second reply. No, this is not proper!
<gretl>
? Z = -2
Generated scalar Z = -2
? W = sgn(Z) * (abs(Z)^(1.0/4))
Generated scalar W = -1.18921
? eval W^4
2
</gretl>
<octave>
octave:1> Z = -2
Z = -2
octave:2> W = Z^(1.0/4)
W = 0.84090 + 0.84090i
octave:3> W^4
ans = -2.0000e+00 + 1.2561e-15i
<octave>
There's a digital approximation involved in the octave answer, via
complex numbers, but it's basically right, while the answer
according to your proposal is flat wrong.
Allin
2:16 a.m.
New subject: Negative numbers to fractional powers
Well, mathematically, say, (-27)^(1/3) = 3rd root of -27, which is
equal to -3.
But your example below clarifies that my approach with the use of the
sign function (or Sven's conditional statement) are applicable only when
we have as power a rational formed by two odd numbers: 1/3, 3/7, etc.
In such cases, with a negative base the solution will be real-valued and
it will preserve the minus sign of the base.
Certainly, these are special cases, but they are the cases for which a
real-valued solution exists, which is why the "domain error" message
drew my attention.
Alecos Papadopoulos PhD
Athens University of Economics and Business
web: alecospapadopoulos.wordpress.com/
skype:alecos.papadopoulos
On 13/8/2020 04:55, Allin Cottrell wrote:
On Wed, 12 Aug 2020, Alecos Papadopoulos wrote:
> Now, consider series "Z" which has both positive /and/ negative
> values. We want to compute
>
> W = Z^(1/3)
>
> Given a recent new feature in gretl, the sign function sgn(), I guess
> we can avoid the obvious conditional if-else statement, and compute
> W by writing
>
> W = sgn(Z) * (abs(Z)^(1/3))
>
> that covers also the case of Z taking an exact zero value.
>
> Is this the proper/efficient way?
My second reply. No, this is not proper!
<gretl>
? Z = -2
Generated scalar Z = -2
? W = sgn(Z) * (abs(Z)^(1.0/4))
Generated scalar W = -1.18921
? eval W^4
2
</gretl>
<octave>
octave:1> Z = -2
Z = -2
octave:2> W = Z^(1.0/4)
W = 0.84090 + 0.84090i
octave:3> W^4
ans = -2.0000e+00 + 1.2561e-15i
<octave>
There's a digital approximation involved in the octave answer, via
complex numbers, but it's basically right, while the answer according
to your proposal is flat wrong.
Allin
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3:33 a.m.
New subject: Negative numbers to fractional powers
On Thu, 13 Aug 2020, Alecos Papadopoulos wrote:
Well, mathematically, say, (-27)^(1/3) = 3rd root of -27, which is
equal to
-3.
But your example below clarifies that my approach with the use of the sign
function (or Sven's conditional statement) are applicable only when we have
as power a rational formed by two odd numbers: 1/3, 3/7, etc.
In such cases, with a negative base the solution will be real-valued and it
will preserve the minus sign of the base.
Certainly, these are special cases, but they are the cases for which a
real-valued solution exists, which is why the "domain error" message drew my
attention.
Granted, you're right: there's a certain subset of noninteger
floating-point numbers, y, for which there's a real-valued solution
to negative x to the power y. But it seems that no standard pow()
function taking the reals as its domain is willing to identify and
handle that subset.
Allin
7:24 a.m.
New subject: Negative numbers to fractional powers
Am 13.08.2020 um 03:55 schrieb Allin Cottrell:
On Wed, 12 Aug 2020, Alecos Papadopoulos wrote:
> W = sgn(Z) * (abs(Z)^(1/3))
> Is this the proper/efficient way?
My second reply. No, this is not proper!
<gretl>
? Z = -2
Generated scalar Z = -2
? W = sgn(Z) * (abs(Z)^(1.0/4))
There's a digital approximation involved in the octave answer,
via
complex numbers, but it's basically right, while the answer according to
your proposal is flat wrong.
The issue is already largely moot now, but just for the record, notice
how you changed Alecos' example. He hardwired the special case 1/3, and
you responded with 1/4. So depending on how general he wanted to be
(implicitly), he may not have been wrong at all.
cheers
sven
1352
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8 comments
4 participants
participants (4)
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Alecos Papadopoulos -
Allin Cottrell -
Jan Annaert -
Sven Schreiber