search for: atane

On 2024-09-05 4:23 p.m., Leo Mada via R-help wrote: > Dear R Users, > > Is this desired behaviour? > I presume it's a bug. > > atan(1i) > # 0+Infi > > tan(atan(1i)) > # 0+1i > > atan(1i) / 5 > # NaN+Infi There's no need to involve atan() and tan() in this: > (0+Inf*1i)/5 [1] NaN+Infi Why do you think this is a bug? Duncan Murdoch

Perhaps > Inf*1i [1] NaN+Infi clarifies why it is *not* a bug. (Boy, did that jog some long dusty math memories :-) ) -- Bert On Thu, Sep 5, 2024 at 2:48?PM Duncan Murdoch <murdoch.duncan at gmail.com> wrote: > On 2024-09-05 4:23 p.m., Leo Mada via R-help wrote: > > Dear R Users, > > > > Is this desired behaviour? > > I presume it's a bug. > >

Dear R Users, Is this desired behaviour? I presume it's a bug. atan(1i) # 0+Infi tan(atan(1i)) # 0+1i atan(1i) / 5 # NaN+Infi There were some changes in handling of complex numbers. But it looks like a bug. Sincerely, Leonard [[alternative HTML version deleted]]

Hi the following gave me a shock: > atan(2) [1] 1.107149 > atan(2+0i) [1] -0.4636476+0i > or, perhaps more of a gotcha: > atan(1.0001+0i) [1] -0.7853482+0i > atan(0.9999+0i) [1] 0.7853482+0i > evidently atan()'s branch cuts aren't where I thought they were. Where do I look for documentation on this? -- Robin Hankin Uncertainty Analyst National

I expect that atan(1i) = (0 + infinity i) and that atan(1i)/5 = (0 + infinity i)/5 = (0 + infinity i). Here's what I get in C: (0,1) = (0, 1) atan((0,1)) = (0, inf) atan((0,1))/5 = (0, inf) Note the difference between I*infinity = (0,1)*infinity = (0*infinity,1*infinity) = (NaN,infinity) and (0,infinity)/5 = (0/5,infinity/5) = (0,infinity). The former involves multiplying 0 by infinity, which

On 2024-09-05 6:12 p.m., Leo Mada wrote: > Dear Duncan, > > Here is also the missing information: > R version 4.4.1 (2024-06-14 ucrt) > Platform: x86_64-w64-mingw32/x64 > Running under: Windows 10 x64 (build 19045) > > Regarding the results: > atan(1i) > #?0+Infi > Re(atan(1i)) > # 0 > Im(atan(1i)) > #? Inf > > 0 + Inf i is a valid complex number:

It seems to me that the documentation of R's complex class & R's atan function do not tell us what to expect, so (as others have suggested), some additional notes are needed. I think that mathematically atan(1i) should be NA_complex_, but R seems not to use any mathematically standard compactification of the complex plane (and I'm not sure that IEEE does either). Incidentally, the

Hi All, I need some clarifications regarding the mismatch I found in the code and the specification. (a) In the specification, the bark(x) equation is given as: bark(x) = 13.1 atan(.00074x) + 2.24 atan(.0000000158(x^2)) + .0001x whereas in the code it is given as: #define toBARK(n) (13.1f*atan(.00074f*(n))+2.24f*atan((n)*(n)*1.85e-8f)+1e-4f*(n)) Which one of these is the proper one ? (b)

> complex(real = 0, imaginary = Inf) [1] 0+Infi > Inf*1i [1] NaN+Infi >> complex(real = 0, imaginary = Inf)/5 [1] NaN+Infi See the Note in ?complex for the explanation, I think. Duncan can correct if I'm wrong. -- Bert On Thu, Sep 5, 2024 at 3:20?PM Leo Mada <leo.mada at syonic.eu> wrote: > Dear Bert, > > These behave like real divisions/multiplications: >

Dear Bert, These behave like real divisions/multiplications: complex(re=Inf, im = Inf) * 5 # Inf+Infi complex(re=-Inf, im = Inf) * 5 # -Inf+Infi The real division / multiplication should be faster and also is well behaved. I was expecting R to do the real division/multiplication on a complex number. Which R actually does for these very particular cases; but not when only Im(x) is Inf.

atan(1i) -> 0 + Inf i complex(1/5) -> 0.2 + 0i atan(1i) -> (0 + Inf i) * (0.2 + 0i) -> 0*0.2 + 0*0i + Inf i * 0.2 + Inf i * 0i infinity times zero is undefined -> 0 + 0i + Inf i + NaN * i^2 -> 0 + 0i + Inf i - NaN -> NaN + Inf i I am not sure how complex arithmetic could arrive at another answer. I advise against messing with infinities... use atan2() if you don't

On 2024-09-06 12:44 a.m., Richard O'Keefe wrote: > I expect that atan(1i) = (0 + infinity i) and that atan(1i)/5 = (0 + > infinity i)/5 = (0 + infinity i). > Here's what I get in C: > (0,1) = (0, 1) > atan((0,1)) = (0, inf) > atan((0,1))/5 = (0, inf) > > Note the difference between I*infinity = (0,1)*infinity = > (0*infinity,1*infinity) = (NaN,infinity) > and

Dear R experts. 'D()' function recognizes some of the analitical functions, such as sin, cos, etc. But I'd like to take analytical derivatives from asin, atan etc. functions. Are there any R packages providing that features? Thanks. -- Timur.

Could someone point me to the BARK/MEL tables that these macros (from vorbis/scales.h) are trying to approximate? #define toBARK(f) (13.1*atan(.00074*(f))+2.24*atan((f)*(f)*1.85e-8)+1e-4*(f)) #define fromBARK(z) (102.*(z)-2.*pow(z,2.)+.4*pow(z,3)+pow(1.46,z)-1.) #define toMEL(f) (log(1.+(f)*.001)*1442.695) #define fromMEL(m) (1000.*exp((m)/1442.695)-1000.) I was wondering if I could come

The thing is that real*complex, complex*real, and complex/real are not "complex arithmetic" in the requisite sense. The complex numbers are a vector space over the reals, and complex*real and real*complex are vector*scalar and scalar*vector. For example, in the Ada programming language, we have function "*" (Left, Right : Complex) return Complex; function "*" (Left :

Hi there I'm trying to construct a model of mortality risk in 2D space that requires numerical integration of a hazard function, for which I'm using the integrate function. I'm occasionally encountering parameter combinations that cause integrate to terminate with error "Error in integrate... the integral is probably divergent", which I'm not sure how to interpret. The

Hi all. I'm trying to numerically invert the characteristic function of a quadratic form following Imhof's (1961, Biometrika 48) procedure. The parameters are: lambda=c(.6,.3,.1) h=c(2,2,2) sigma=c(0,0,0) q=3 I've implemented Imhof's procedure two ways that, for me, should give the same answer: #more legible integral1 = function(u) {

Hi ?atan2 says that atan2(y,x)=atan(y/x) for x and y numeric or complex vectors. Well, I would expect atan2(1,1i) to be equal to atan(-1i), but > atan2(1,1i) Error in atan2(y, x) : Non-numeric argument to mathematical function > R.version _ platform powerpc-apple-darwin8.5.0 arch powerpc os darwin8.5.0 system powerpc, darwin8.5.0

Hi ?atan2 says that atan2(y,x)=atan(y/x) for x and y numeric or complex vectors. Well, I would expect atan2(1,1i) to be equal to atan(-1i), but > atan2(1,1i) Error in atan2(y, x) : Non-numeric argument to mathematical function > R.version _ platform powerpc-apple-darwin8.5.0 arch powerpc os darwin8.5.0 system powerpc, darwin8.5.0

Dear all, I stumbled over a problem recently when trying to use srt with text() on a windows device. What I intended to do was to plot a simple regression line, and to rotate a piece of text such that the text has the same angle as the regression line. However, the text is always plotted in a slightly wrong angle: #### x=1:10 #create arbitrary x and y values y=x*2-rnorm(1:10)