Re: [Numpy-discussion] arctan2 with complex args

[David Goldsmith]

Timothy Hochberg wrote:
>
>
> On 4/30/07, *David Goldsmith* <[EMAIL PROTECTED] 
> > wrote:
>
>
> > (hint what is arctan(0+1j)?)
> >
> Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:
>
> arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) =
> -i*log(i)
> = -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2...
>
> Is there some reason I'm forgetting (e.g., a branch cut convention or
> something) why this is wrong?
>
>
> Oops. It may well be OK, I answered too fast (I'd explain my thinking, 
> but ti would be embarassing).
Was it: "pi/2 is outside the range of arctan"? (No worries: I thought of 
this too when I saw what value fell out of the formula, but then, it's 
outside the range of the *real-valued* function, but clearly it's not 
outside the range of the *complex-valued* function.)

DG
> However, I believe atan works in general for complex numbers but it 
> may well have a problem for this specific case.
>
> I should look at this more closely though since the behaviour near 
> zero does seem a little odd. No time right now, but maybe later today.
>  
>
> DG
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Re: [Numpy-discussion] arctan2 with complex args

[David Goldsmith]

lorenzo bolla wrote:
> hold on, david. the formula I posted previously from wolfram is 
> ArcTan[x,y] with x or y complex: its the same of arctan2(x,y). arctan 
> is another function (even though arctan2(y,x) should be "a better" 
> arctan(y/x)).
>
> the correct formula for y = arctan(x), with any x (real or complex), 
> should be (if I still can play with sin and cos...):
>
> y = arctan(x) = 1/(2j) * log((1j-x)/(1j+x))
After a little algebra, they're the same formula (as they must be; hint: 
"rationalize" the denominator inside the log and bring the 1/2 inside 
the log, making it a square root, and finally, rewrite 1/i as -i); I 
have to run my kid to school right now, but if you want me to flesh this 
out, reply and I'll type it out and send it when I get back..

DG
>
> [ you can get it doing: y = arctan(x) --> x = tan(y) = sin(x)/cos(x) = 
> -1j * (exp(1j*y)-exp(-1j*y))/(exp(1j*y)+exp(-1j*y); then let z = 
> exp(1j*y) and solve in z.]
>
> I've tested the formula and it seems ok for different inputs (I've 
> checked that tan(arctan(x)) == x):
> ---
> octave:56> x = 1; tan(1/2/1j*log((1j-x)/(1j+x)))
> ans = 1.
> octave:57> x = 1j; tan(1/2/1j*log((1j-x)/(1j+x)))
> ans = -0 + 1i
> octave:58> x = 2j; tan(1/2/1j*log((1j-x)/(1j+x)))
> ans = 1.8369e-16 + 2.e+00i
> octave:59> x = 1+2j; tan(1/2/1j*log((1j-x)/(1j+x)))
> ans = 1. + 2.i
> ---
>
> hth,
> L.
>
> On 4/30/07, *David Goldsmith* <[EMAIL PROTECTED] 
> > wrote:
>
>
> > (hint what is arctan(0+1j)?)
> >
> Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:
>
> arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) =
> -i*log(i)
> = -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2...
>
> Is there some reason I'm forgetting (e.g., a branch cut convention or
> something) why this is wrong?
>
> DG
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> 
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Re: [Numpy-discussion] arctan2 with complex args

[lorenzo bolla]

hold on, david. the formula I posted previously from wolfram is ArcTan[x,y]
with x or y complex: its the same of arctan2(x,y). arctan is another
function (even though arctan2(y,x) should be "a better" arctan(y/x)).

the correct formula for y = arctan(x), with any x (real or complex), should
be (if I still can play with sin and cos...):

y = arctan(x) = 1/(2j) * log((1j-x)/(1j+x))

[ you can get it doing: y = arctan(x) --> x = tan(y) = sin(x)/cos(x) = -1j *
(exp(1j*y)-exp(-1j*y))/(exp(1j*y)+exp(-1j*y); then let z = exp(1j*y) and
solve in z.]

I've tested the formula and it seems ok for different inputs (I've checked
that tan(arctan(x)) == x):
---
octave:56> x = 1; tan(1/2/1j*log((1j-x)/(1j+x)))
ans = 1.
octave:57> x = 1j; tan(1/2/1j*log((1j-x)/(1j+x)))
ans = -0 + 1i
octave:58> x = 2j; tan(1/2/1j*log((1j-x)/(1j+x)))
ans = 1.8369e-16 + 2.e+00i
octave:59> x = 1+2j; tan(1/2/1j*log((1j-x)/(1j+x)))
ans = 1. + 2.i
---

hth,
L.

On 4/30/07, David Goldsmith <[EMAIL PROTECTED]> wrote:



> (hint what is arctan(0+1j)?)
>
Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:

arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) = -i*log(i)
= -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2...

Is there some reason I'm forgetting (e.g., a branch cut convention or
something) why this is wrong?

DG
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Re: [Numpy-discussion] arctan2 with complex args

[Timothy Hochberg]

On 4/30/07, David Goldsmith <[EMAIL PROTECTED]> wrote:



> (hint what is arctan(0+1j)?)
>
Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:

arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) = -i*log(i)
= -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2...

Is there some reason I'm forgetting (e.g., a branch cut convention or
something) why this is wrong?



Oops. It may well be OK, I answered too fast (I'd explain my thinking, but
ti would be embarassing). However, I believe atan works in general for
complex numbers but it may well have a problem for this specific case.

I should look at this more closely though since the behaviour near zero does
seem a little odd. No time right now, but maybe later today.


DG

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Re: [Numpy-discussion] arctan2 with complex args

[David Goldsmith]

> (hint what is arctan(0+1j)?)
>  
Well, at the risk of embarrassing myself, using arctan(x+iy) = I get:

arctan(0+1i) = -i*log((0+i*1)/sqrt(0^2 + 1^2)) = -i*log(i/1) = -i*log(i) 
= -i*log(exp(i*pi/2)) = -i*i*pi/2 = pi/2...

Is there some reason I'm forgetting (e.g., a branch cut convention or 
something) why this is wrong?

DG
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Re: [Numpy-discussion] arctan2 with complex args

[Timothy Hochberg]

On 4/30/07, David Goldsmith <[EMAIL PROTECTED]> wrote:


lorenzo bolla wrote:
> me!
> I have two cases.
>
>1. I need that arctan2(1+0.0001j,1-0.01j) gives something
>   close to arctan2(1,1): any decent analytic prolungation will do!
>
This is the foreseeable use case described by Anne.

In any event, I stand not only corrected, but embarrassed (for numpy):

Python 2.5 (r25:51918, Sep 19 2006, 08:49:13)
[GCC 4.0.1 (Apple Computer, Inc. build 5341)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
 >>> import numpy as N
 >>> complex(0,1)
1j
 >>> N.arctan(1)
0.78539816339744828
 >>> N.arctan(complex(0,1))
Warning: invalid value encountered in arctan
(nannanj)

I agree that arctan should be implemented for _at least_ *one* complex
argument...



It is, you should look at that error a bit more carefully...

-tim

(hint what is arctan(0+1j)?)


DG

>
>1. if someone of you is familiar with electromagnetic problems, in
>   particular with Snell's law, will recognize that in case of
>   total internal reflection
>    the
>   wavevector tangential to the interface is real, while the normal
>   one is purely imaginary: hence the angle of diffraction is still
>   given by arctan2(k_tangent, k_normal), that, as in Matlab or
>   Octave, should give pi/2 (that physically means no propagation
>   -- total internal reflection, as said).
>
> L.
>
> On 4/30/07, *Anne Archibald* <[EMAIL PROTECTED]
> > wrote:
>
> On 29/04/07, David Goldsmith <[EMAIL PROTECTED]
> > wrote:
> > Far be it from me to challenge the mighty Wolfram, but I'm not
> sure that
> > using the *formula* for calculating the arctan of a *single*
> complex
> > argument from its real and imaginary parts makes any sense if x
> and/or y
> > are themselves complex (in particular, does Lim(formula), as the
> > imaginary part of complex x and/or y approaches zero, approach
> > arctan2(realpart(x), realpart(y)?) - without going to the trouble
to
> > determine it one way or another, I'd be surprised if "their"
> > continuation of the arctan2 function from RxR to CxC is (a. e.)
> > continuous (not that I know for sure that "mine" is...).
>
> Well, yes, in fact, theirs is continuous, and in fact analytic,
except
> along the branch cuts (which they describe). Formulas almost always
> yield continuous functions apart from easy-to-recognize cases. (This
> can be made into a specific theorem if you're determined.)
>
> Their formula is a pretty reasonable choice, given that it's not at
> all clear what arctan2 should mean for complex arguments. But for
> numpy it's tempting to simply throw an exception (which would catch
> quite a few programmer errors that would otherwise manifest as
> nonsense numbers). Still, I suppose defining it on the complex
> numbers
> in a way that is continuous close to the real plane allows people to
> put in almost-real complex numbers and get out pretty much the
answer
> they expect. Does anyone have an application for which they need
> arctan2 of, say, (1+i,1-i)?
>
> Anne
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Re: [Numpy-discussion] arctan2 with complex args

[David Goldsmith]

lorenzo bolla wrote:
> me!
> I have two cases.
>
>1. I need that arctan2(1+0.0001j,1-0.01j) gives something
>   close to arctan2(1,1): any decent analytic prolungation will do!
>
This is the foreseeable use case described by Anne.

In any event, I stand not only corrected, but embarrassed (for numpy):

Python 2.5 (r25:51918, Sep 19 2006, 08:49:13)
[GCC 4.0.1 (Apple Computer, Inc. build 5341)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
 >>> import numpy as N
 >>> complex(0,1)
1j
 >>> N.arctan(1)
0.78539816339744828
 >>> N.arctan(complex(0,1))
Warning: invalid value encountered in arctan
(nannanj)

I agree that arctan should be implemented for _at least_ *one* complex 
argument...

DG
>
>1. if someone of you is familiar with electromagnetic problems, in
>   particular with Snell's law, will recognize that in case of
>   total internal reflection
>    the
>   wavevector tangential to the interface is real, while the normal
>   one is purely imaginary: hence the angle of diffraction is still
>   given by arctan2(k_tangent, k_normal), that, as in Matlab or
>   Octave, should give pi/2 (that physically means no propagation
>   -- total internal reflection, as said).
>
> L.
>
> On 4/30/07, *Anne Archibald* <[EMAIL PROTECTED] 
> > wrote:
>
> On 29/04/07, David Goldsmith <[EMAIL PROTECTED]
> > wrote:
> > Far be it from me to challenge the mighty Wolfram, but I'm not
> sure that
> > using the *formula* for calculating the arctan of a *single*
> complex
> > argument from its real and imaginary parts makes any sense if x
> and/or y
> > are themselves complex (in particular, does Lim(formula), as the
> > imaginary part of complex x and/or y approaches zero, approach
> > arctan2(realpart(x), realpart(y)?) - without going to the trouble to
> > determine it one way or another, I'd be surprised if "their"
> > continuation of the arctan2 function from RxR to CxC is (a. e.)
> > continuous (not that I know for sure that "mine" is...).
>
> Well, yes, in fact, theirs is continuous, and in fact analytic, except
> along the branch cuts (which they describe). Formulas almost always
> yield continuous functions apart from easy-to-recognize cases. (This
> can be made into a specific theorem if you're determined.)
>
> Their formula is a pretty reasonable choice, given that it's not at
> all clear what arctan2 should mean for complex arguments. But for
> numpy it's tempting to simply throw an exception (which would catch
> quite a few programmer errors that would otherwise manifest as
> nonsense numbers). Still, I suppose defining it on the complex
> numbers
> in a way that is continuous close to the real plane allows people to
> put in almost-real complex numbers and get out pretty much the answer
> they expect. Does anyone have an application for which they need
> arctan2 of, say, (1+i,1-i)?
>
> Anne
> ___
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>
> 
>
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Re: [Numpy-discussion] arctan2 with complex args

[lorenzo bolla]

me!
I have two cases.

  1. I need that arctan2(1+0.0001j,1-0.01j) gives something
  close to arctan2(1,1): any decent analytic prolungation will do!
  2. if someone of you is familiar with electromagnetic problems, in
  particular with Snell's law, will recognize that in case of total
  internal reflectionthe
wavevector tangential to the interface is real, while the normal one
is
  purely imaginary: hence the angle of diffraction is still given by
  arctan2(k_tangent, k_normal), that, as in Matlab or Octave, should give pi/2
  (that physically means no propagation -- total internal reflection, as
  said).

L.

On 4/30/07, Anne Archibald <[EMAIL PROTECTED]> wrote:


On 29/04/07, David Goldsmith <[EMAIL PROTECTED]> wrote:
> Far be it from me to challenge the mighty Wolfram, but I'm not sure that
> using the *formula* for calculating the arctan of a *single* complex
> argument from its real and imaginary parts makes any sense if x and/or y
> are themselves complex (in particular, does Lim(formula), as the
> imaginary part of complex x and/or y approaches zero, approach
> arctan2(realpart(x), realpart(y)?) - without going to the trouble to
> determine it one way or another, I'd be surprised if "their"
> continuation of the arctan2 function from RxR to CxC is (a. e.)
> continuous (not that I know for sure that "mine" is...).

Well, yes, in fact, theirs is continuous, and in fact analytic, except
along the branch cuts (which they describe). Formulas almost always
yield continuous functions apart from easy-to-recognize cases. (This
can be made into a specific theorem if you're determined.)

Their formula is a pretty reasonable choice, given that it's not at
all clear what arctan2 should mean for complex arguments. But for
numpy it's tempting to simply throw an exception (which would catch
quite a few programmer errors that would otherwise manifest as
nonsense numbers). Still, I suppose defining it on the complex numbers
in a way that is continuous close to the real plane allows people to
put in almost-real complex numbers and get out pretty much the answer
they expect. Does anyone have an application for which they need
arctan2 of, say, (1+i,1-i)?

Anne
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Re: [Numpy-discussion] arctan2 with complex args

[Anne Archibald]

On 29/04/07, David Goldsmith <[EMAIL PROTECTED]> wrote:
> Far be it from me to challenge the mighty Wolfram, but I'm not sure that
> using the *formula* for calculating the arctan of a *single* complex
> argument from its real and imaginary parts makes any sense if x and/or y
> are themselves complex (in particular, does Lim(formula), as the
> imaginary part of complex x and/or y approaches zero, approach
> arctan2(realpart(x), realpart(y)?) - without going to the trouble to
> determine it one way or another, I'd be surprised if "their"
> continuation of the arctan2 function from RxR to CxC is (a. e.)
> continuous (not that I know for sure that "mine" is...).

Well, yes, in fact, theirs is continuous, and in fact analytic, except
along the branch cuts (which they describe). Formulas almost always
yield continuous functions apart from easy-to-recognize cases. (This
can be made into a specific theorem if you're determined.)

Their formula is a pretty reasonable choice, given that it's not at
all clear what arctan2 should mean for complex arguments. But for
numpy it's tempting to simply throw an exception (which would catch
quite a few programmer errors that would otherwise manifest as
nonsense numbers). Still, I suppose defining it on the complex numbers
in a way that is continuous close to the real plane allows people to
put in almost-real complex numbers and get out pretty much the answer
they expect. Does anyone have an application for which they need
arctan2 of, say, (1+i,1-i)?

Anne
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Re: [Numpy-discussion] arctan2 with complex args

[David Goldsmith]

Far be it from me to challenge the mighty Wolfram, but I'm not sure that 
using the *formula* for calculating the arctan of a *single* complex 
argument from its real and imaginary parts makes any sense if x and/or y 
are themselves complex (in particular, does Lim(formula), as the 
imaginary part of complex x and/or y approaches zero, approach 
arctan2(realpart(x), realpart(y)?) - without going to the trouble to 
determine it one way or another, I'd be surprised if "their" 
continuation of the arctan2 function from RxR to CxC is (a. e.) 
continuous (not that I know for sure that "mine" is...).

DG

lorenzo bolla wrote:
> You make your point, but I would expect a behaviour similar to 
> Mathematica or Matlab.
>
> From http://documents.wolfram.com/mathematica/functions/ArcTan 
> 
> "If x or y is complex, then ArcTan[x , y] gives . When , ArcTan[x, y] 
> gives the number such that and ."
>
> Lorenzo.
>
> On 4/29/07, *David Goldsmith* < [EMAIL PROTECTED] 
> > wrote:
>
> I'll take a stab at this one; if I miss the mark, people, please
> chime in.
>
> What's "strange" here is not numpy's behavior but octave's (IMO).
> Remember that, over R, arctan is used in two different ways: one is
> simply as a map from (-inf, inf) -> (-pi/2,pi/2) - here, let's
> call that
> invtan; the other is as a means to determine "the angle"
> (conventionally
> taken to be between -pi and pi) of a point in the plane - but
> since, for
> example, tan(pi/4) = tan(-3pi/4) (and in general tan(x) =
> tan(x-pi)) to
> uniquely determine said angle, we need to keep track of and take into
> account the quadrant in which the point lies; this is (the only
> reason)
> why arctan2 is a function of two arguments, one representing the
> abscissa, the other the ordinate of the point.  But when the
> argument is
> complex (arctan2, as the inverse of the tangent function, *is* a valid
> function on C), this geometric use no longer makes sense, so there's
> really no reason to implement arctan2(z,w), z, w complex.  If for
> some
> reason, e.g., uniformity of algorithmic expression - I don't see any
> (simple) way to preserve uniformity of code expression - as near as I
> can tell, you're going to have to implement an if/else if you need to
> allow for the invtan of two complex arguments - you need to handle
> arctan2(z,w), implement it as arctan(w/z):
>
> >>> import numpy
> >>> numpy.arctan(1j/1j)
> (0.78539816339744828+0j)
>
> DG
>
> lorenzo bolla wrote:
> > Weird behaviour with arctan2(complex,complex).
> > Take  a look at this:
> >
> > In [11]: numpy.arctan2(1.,1.)
> > Out[11]: 0.785398163397
> >
> > In [12]: numpy.arctan2 (1j,1j)
> >
> 
> ---
> > exceptions.AttributeErrorTraceback (most
> > recent call last)
> >
> > AttributeError: 'complex' object has no attribute 'arctan2'
> >
> > same error for:
> >
> > In [13]: numpy.arctan2(1j,1.)
> > In [14]: numpy.arctan2(1.,1j)
> >
> > But arctan2 is defined for complex arguments, as far as Octave
> knows :-) :
> >
> > octave:7> atan2(1,1)
> > ans = 0.78540
> > octave:8> atan2(1j,1j)
> > ans = 0
> > octave:9> atan2(1j,1)
> > ans = 0
> > octave:10> atan2(1,1j)
> > ans = 1.5708
> >
> > bug or wanted behaviour?
> > Lorenzo.
> >
> 
> >
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Re: [Numpy-discussion] arctan2 with complex args

[lorenzo bolla]

You make your point, but I would expect a behaviour similar to Mathematica
or Matlab.


From http://documents.wolfram.com/mathematica/functions/ArcTan

"If x or y is complex, then ArcTan[x, y] gives . When , ArcTan[x, y] gives
the number such that and ."

Lorenzo.

On 4/29/07, David Goldsmith <[EMAIL PROTECTED]> wrote:


I'll take a stab at this one; if I miss the mark, people, please chime in.

What's "strange" here is not numpy's behavior but octave's (IMO).
Remember that, over R, arctan is used in two different ways: one is
simply as a map from (-inf, inf) -> (-pi/2,pi/2) - here, let's call that
invtan; the other is as a means to determine "the angle" (conventionally
taken to be between -pi and pi) of a point in the plane - but since, for
example, tan(pi/4) = tan(-3pi/4) (and in general tan(x) = tan(x-pi)) to
uniquely determine said angle, we need to keep track of and take into
account the quadrant in which the point lies; this is (the only reason)
why arctan2 is a function of two arguments, one representing the
abscissa, the other the ordinate of the point.  But when the argument is
complex (arctan2, as the inverse of the tangent function, *is* a valid
function on C), this geometric use no longer makes sense, so there's
really no reason to implement arctan2(z,w), z, w complex.  If for some
reason, e.g., uniformity of algorithmic expression - I don't see any
(simple) way to preserve uniformity of code expression - as near as I
can tell, you're going to have to implement an if/else if you need to
allow for the invtan of two complex arguments - you need to handle
arctan2(z,w), implement it as arctan(w/z):

>>> import numpy
>>> numpy.arctan(1j/1j)
(0.78539816339744828+0j)

DG

lorenzo bolla wrote:
> Weird behaviour with arctan2(complex,complex).
> Take  a look at this:
>
> In [11]: numpy.arctan2(1.,1.)
> Out[11]: 0.785398163397
>
> In [12]: numpy.arctan2(1j,1j)
>
---
> exceptions.AttributeErrorTraceback (most
> recent call last)
>
> AttributeError: 'complex' object has no attribute 'arctan2'
>
> same error for:
>
> In [13]: numpy.arctan2(1j,1.)
> In [14]: numpy.arctan2(1.,1j)
>
> But arctan2 is defined for complex arguments, as far as Octave knows :-)
:
>
> octave:7> atan2(1,1)
> ans = 0.78540
> octave:8> atan2(1j,1j)
> ans = 0
> octave:9> atan2(1j,1)
> ans = 0
> octave:10> atan2(1,1j)
> ans = 1.5708
>
> bug or wanted behaviour?
> Lorenzo.
> 
>
> ___
> Numpy-discussion mailing list
> Numpy-discussion@scipy.org
> http://projects.scipy.org/mailman/listinfo/numpy-discussion
>

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Re: [Numpy-discussion] arctan2 with complex args

[David Goldsmith]

I'll take a stab at this one; if I miss the mark, people, please chime in.

What's "strange" here is not numpy's behavior but octave's (IMO).  
Remember that, over R, arctan is used in two different ways: one is 
simply as a map from (-inf, inf) -> (-pi/2,pi/2) - here, let's call that 
invtan; the other is as a means to determine "the angle" (conventionally 
taken to be between -pi and pi) of a point in the plane - but since, for 
example, tan(pi/4) = tan(-3pi/4) (and in general tan(x) = tan(x-pi)) to 
uniquely determine said angle, we need to keep track of and take into 
account the quadrant in which the point lies; this is (the only reason) 
why arctan2 is a function of two arguments, one representing the 
abscissa, the other the ordinate of the point.  But when the argument is 
complex (arctan2, as the inverse of the tangent function, *is* a valid 
function on C), this geometric use no longer makes sense, so there's 
really no reason to implement arctan2(z,w), z, w complex.  If for some 
reason, e.g., uniformity of algorithmic expression - I don't see any 
(simple) way to preserve uniformity of code expression - as near as I 
can tell, you're going to have to implement an if/else if you need to 
allow for the invtan of two complex arguments - you need to handle 
arctan2(z,w), implement it as arctan(w/z):

 >>> import numpy
 >>> numpy.arctan(1j/1j)
(0.78539816339744828+0j)

DG

lorenzo bolla wrote:
> Weird behaviour with arctan2(complex,complex).
> Take  a look at this:
>
> In [11]: numpy.arctan2(1.,1.)
> Out[11]: 0.785398163397
>
> In [12]: numpy.arctan2(1j,1j)
> ---
> exceptions.AttributeErrorTraceback (most 
> recent call last)
>
> AttributeError: 'complex' object has no attribute 'arctan2'
>
> same error for:
>
> In [13]: numpy.arctan2(1j,1.)
> In [14]: numpy.arctan2(1.,1j)
>
> But arctan2 is defined for complex arguments, as far as Octave knows :-) :
>
> octave:7> atan2(1,1)
> ans = 0.78540
> octave:8> atan2(1j,1j)
> ans = 0
> octave:9> atan2(1j,1)
> ans = 0
> octave:10> atan2(1,1j)
> ans = 1.5708
>
> bug or wanted behaviour?
> Lorenzo.
> 
>
> ___
> Numpy-discussion mailing list
> Numpy-discussion@scipy.org
> http://projects.scipy.org/mailman/listinfo/numpy-discussion
>   

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[Numpy-discussion] arctan2 with complex args

[lorenzo bolla]

Weird behaviour with arctan2(complex,complex).
Take  a look at this:

In [11]: numpy.arctan2(1.,1.)
Out[11]: 0.785398163397

In [12]: numpy.arctan2(1j,1j)
---
exceptions.AttributeErrorTraceback (most recent
call last)

AttributeError: 'complex' object has no attribute 'arctan2'

same error for:

In [13]: numpy.arctan2(1j,1.)
In [14]: numpy.arctan2(1.,1j)

But arctan2 is defined for complex arguments, as far as Octave knows :-) :

octave:7> atan2(1,1)
ans = 0.78540
octave:8> atan2(1j,1j)
ans = 0
octave:9> atan2(1j,1)
ans = 0
octave:10> atan2(1,1j)
ans = 1.5708

bug or wanted behaviour?
Lorenzo.
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