search for: atan

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

...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. > > > > 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? > > Dunca...

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? --...

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/...

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: > tan(atan(1i)) > # 0+1i > > Inf / 5 > # Inf > > Note: atan(1i) / 5 should have generated 0 + Inf * 1i; even the explicit > complex number fails: &gt...

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)....

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) Also, we are planning to implement a fixed point code for the Vorbis decoder. And as...

...:* Bert Gunter <bgunter.4567 at gmail.com> > *Sent:* Friday, September 6, 2024 1:12 AM > *To:* Duncan Murdoch <murdoch.duncan at gmail.com> > *Cc:* Leo Mada <leo.mada at syonic.eu>; r-help at r-project.org < > r-help at r-project.org> > *Subject:* Re: [R] BUG: atan(1i) / 5 = NaN+Infi ? > > 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> > w...

...______________________________ From: Bert Gunter <bgunter.4567 at gmail.com> Sent: Friday, September 6, 2024 1:12 AM To: Duncan Murdoch <murdoch.duncan at gmail.com> Cc: Leo Mada <leo.mada at syonic.eu>; r-help at r-project.org <r-help at r-project.org> Subject: Re: [R] BUG: atan(1i) / 5 = NaN+Infi ? 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<mailto:murdoch.duncan at gmail.com>> wrote: On 2024-09-0...

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...

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) =...

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 up with different functions that were easier...

...pe and then operate" model is more important than getting good answers, well, it's THEIR language, not mine. But let's not pretend that the answers are *right* in any other sense. On Fri, 6 Sept 2024 at 11:07, Jeff Newmiller via R-help <r-help at r-project.org> wrote: > > 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...

...m on my machine running R 2.9.0. Any suggestions on what might be causing this and what I can do to avoid it would be very gratefully received. Hoping for some insights Marcus ########################## #Problem example #Works fine: integrate(hazard, 0,Inf, v=0.1, gam=pi*232/200, pos=list(r=5,th=atan(3/4)), a=10, b0=10, bt=0.1) #Gives error "...integral probably divergent": integrate(hazard, 0,Inf, v=0.1, gam=pi*231/200, pos=list(r=5,th=atan(3/4)), a=10, b0=10, bt=0.1) #Plot the integrands - doesn't look obviously problematic h <- hazard(seq(0,500,0.1),0.1,pi*231/200,pos=list...

...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) { o=(1/2)*sum(h*atan(lambda*u)+sigma^2*lambda*u/(1+lambda^2*u^2)) - q*u/2 rho=prod((1+lambda^2*u^2)^(h/4))*exp( (1/2)*sum((sigma*lambda*u)^2/(1+lambda^2*u^2)) ) integrand = sin(o)/(u*rho) } #same as above integral2= function(u) { ((1/2)*sum(h*atan(lambda*u)+sigma^2*lambda*u/(1+lambda^2*u^2)) - q*u/2)/ (u*(prod((1...

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....

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....

...rary x and y values y=x*2-rnorm(1:10) plot(x,y,pch=16,xlim=c(0,10)) #create the graph abline(lm(y~x)) #calculate the y coordinate of the text: yval=predict(lm(y~x),list(x=rep(2,length(x))))[1] #calculate the slope: slope=as.numeric(lm(y~x)[[1]][2]) text(2,yval,"Regression",srt=180/pi*atan(slope),adj=0) #### What am I doing wrong here? Many thanks in advance for any help! Best wishes Christoph (using R 2.6.1 on Windows XP)