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R version 2.6.0 Under development (unstable) (2007-06-23 r42031)
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R version 2.10.0 Under development (unstable) (2009-08-04 r49064)
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Copyright (C) 2007 The R Foundation for Statistical Computing
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Copyright (C) 2009 The R Foundation for Statistical Computing
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ISBN 3-900051-07-0
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ISBN 3-900051-07-0
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R is free software and comes with ABSOLUTELY NO WARRANTY.
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R is free software and comes with ABSOLUTELY NO WARRANTY.
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You are welcome to redistribute it under certain conditions.
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You are welcome to redistribute it under certain conditions.
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Type 'license()' or 'licence()' for distribution details.
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Type 'license()' or 'licence()' for distribution details.
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'help.start()' for an HTML browser interface to help.
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'help.start()' for an HTML browser interface to help.
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Type 'q()' to quit R.
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Type 'q()' to quit R.
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> ### Tests of complex arithemetic.
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> ### Tests of complex arithemetic.
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>
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>
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> Meps <- .Machine$double.eps
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> ## complex
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> ## complex
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> z <- 0i ^ (-3:3)
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> z <- 0i ^ (-3:3)
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> stopifnot(Re(z) == 0 ^ (-3:3))
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> stopifnot(Re(z) == 0 ^ (-3:3))
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> set.seed(123)
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> set.seed(123)
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> z <- complex(real = rnorm(100), imag = rnorm(100))
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> z <- complex(real = rnorm(100), imag = rnorm(100))
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> stopifnot(Mod ( 1 -  sin(z) / ( (exp(1i*z)-exp(-1i*z))/(2*1i) ))
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> stopifnot(Mod ( 1 -  sin(z) / ( (exp(1i*z)-exp(-1i*z))/(2*1i) )) < 20 * Meps)
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+ 	  < 20 * .Machine$double.eps)
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> ## end of moved from complex.Rd
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> ## end of moved from complex.Rd
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>
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>
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>
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>
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> ## powers, including complex ones
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> ## powers, including complex ones
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> a <- -4:12
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> a <- -4:12
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  8  0.354+0.000i 1+0i 2.828+0.000i  8+0i 22.627+0.000i  64+0i
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  8  0.354+0.000i 1+0i 2.828+0.000i  8+0i 22.627+0.000i  64+0i
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  9  0.333+0.000i 1+0i 3.000+0.000i  9+0i 27.000+0.000i  81+0i
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  9  0.333+0.000i 1+0i 3.000+0.000i  9+0i 27.000+0.000i  81+0i
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  10 0.316+0.000i 1+0i 3.162+0.000i 10+0i 31.623+0.000i 100+0i
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  10 0.316+0.000i 1+0i 3.162+0.000i 10+0i 31.623+0.000i 100+0i
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  11 0.302+0.000i 1+0i 3.317+0.000i 11+0i 36.483+0.000i 121+0i
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  11 0.302+0.000i 1+0i 3.317+0.000i 11+0i 36.483+0.000i 121+0i
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  12 0.289+0.000i 1+0i 3.464+0.000i 12+0i 41.569+0.000i 144+0i
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  12 0.289+0.000i 1+0i 3.464+0.000i 12+0i 41.569+0.000i 144+0i
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>
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> stopifnot(m[,as.character(0:2)] == cbind(1,a,a*a),
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+                                         # latter were only approximate
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+           all.equal(unname(m[,"0.5"]),
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+                     sqrt(abs(a))*ifelse(a < 0, 1i, 1),
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+                     tol= 20*Meps))
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> ## fft():
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> ## fft():
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> for(n in 1:30) cat("\nn=",n,":", round(fft(1:n), 8),"\n")
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> for(n in 1:30) cat("\nn=",n,":", round(fft(1:n), 8),"\n")
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n= 1 : 1+0i
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n= 1 : 1+0i
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n= 30 : 465+0i -15+142.7155i -15+70.56945i -15+46.16525i -15+33.69055i -15+25.98076i -15+20.64573i -15+16.65919i -15+13.50606i -15+10.89814i -15+8.66025i -15+6.67843i -15+4.8738i -15+3.18835i -15+1.57656i -15+0i -15-1.57656i -15-3.18835i -15-4.8738i -15-6.67843i -15-8.66025i -15-10.89814i -15-13.50606i -15-16.65919i -15-20.64573i -15-25.98076i -15-33.69055i -15-46.16525i -15-70.56945i -15-142.7155i
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n= 30 : 465+0i -15+142.7155i -15+70.56945i -15+46.16525i -15+33.69055i -15+25.98076i -15+20.64573i -15+16.65919i -15+13.50606i -15+10.89814i -15+8.66025i -15+6.67843i -15+4.8738i -15+3.18835i -15+1.57656i -15+0i -15-1.57656i -15-3.18835i -15-4.8738i -15-6.67843i -15-8.66025i -15-10.89814i -15-13.50606i -15-16.65919i -15-20.64573i -15-25.98076i -15-33.69055i -15-46.16525i -15-70.56945i -15-142.7155i
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>
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>
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>
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>
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> ## Complex Trig.:
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> ## Complex Trig.:
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> Meps <- .Machine$double.eps
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> abs(Im(cos(acos(1i))) -	 1) < 2*Meps
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> abs(Im(cos(acos(1i))) -	 1) < 2*Meps
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[1] TRUE
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[1] TRUE
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> abs(Im(sin(asin(1i))) -	 1) < 2*Meps
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> abs(Im(sin(asin(1i))) -	 1) < 2*Meps
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[1] TRUE
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[1] TRUE
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> ##P (1 - Im(sin(asin(Ii))))/Meps
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> ##P (1 - Im(sin(asin(Ii))))/Meps
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[1] TRUE
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[1] TRUE
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> ##P table(2*abs(Isi-1)	/ Meps)
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> ##P table(2*abs(Isi-1)	/ Meps)
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>
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>
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>
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>
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> ## polyroot():
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> ## polyroot():
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> all(abs(1 + polyroot(choose(8, 0:8))) < 1e-10)# maybe smaller..
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> stopifnot(abs(1 + polyroot(choose(8, 0:8))) < 1e-10)# maybe smaller..
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[1] TRUE
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>
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>
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>
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>
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> ## PR#7781
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> ## PR#7781
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> ## This is not as given by e.g. glibc on AMD64
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> ## This is not as given by e.g. glibc on AMD64
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> (z <- tan(1+1000i)) # 0+1i from R's own code.
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> (z <- tan(1+1000i)) # 0+1i from R's own code.