225 lines
7.1 KiB
Plaintext
225 lines
7.1 KiB
Plaintext
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R version 3.6.0 Patched (2019-05-14 r76502) -- "Planting of a Tree"
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Copyright (C) 2019 The R Foundation for Statistical Computing
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Platform: x86_64-pc-linux-gnu (64-bit)
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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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Type 'license()' or 'licence()' for distribution details.
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R is a collaborative project with many contributors.
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Type 'contributors()' for more information and
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'citation()' on how to cite R or R packages in publications.
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Type 'demo()' for some demos, 'help()' for on-line help, or
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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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> library(cluster)
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>
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> tools::assertWarning(eh <- ellipsoidhull(cbind(x=1:4, y = 1:4)), verbose=TRUE) #singular
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Error in Fortran routine computing the spanning ellipsoid,
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probably collinear data
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Asserted warning: algorithm possibly not converged in 5000 iterations
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> eh ## center ok, shape "0 volume" --> Warning
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'ellipsoid' in 2 dimensions:
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center = ( 2.5 2.5 ); squared ave.radius d^2 = 0
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and shape matrix =
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x y
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x 1.25 1.25
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y 1.25 1.25
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hence, area = 0
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** Warning: ** the algorithm did not terminate reliably!
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most probably because of collinear data
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> stopifnot(volume(eh) == 0)
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>
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> set.seed(157)
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> for(n in 4:10) { ## n=2 and 3 still differ -- platform dependently!
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+ cat("n = ",n,"\n")
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+ x2 <- rnorm(n)
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+ print(ellipsoidhull(cbind(1:n, x2)))
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+ print(ellipsoidhull(cbind(1:n, x2, 4*x2 + rnorm(n))))
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+ }
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n = 4
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'ellipsoid' in 2 dimensions:
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center = ( 2.66215 0.82086 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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1.55901 0.91804
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x2 0.91804 0.67732
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hence, area = 2.9008
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'ellipsoid' in 3 dimensions:
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center = ( 2.50000 0.74629 2.95583 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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1.25000 0.72591 1.8427
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x2 0.72591 0.52562 1.5159
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1.84268 1.51588 4.7918
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hence, volume = 3.1969
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n = 5
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'ellipsoid' in 2 dimensions:
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center = ( 3.0726 1.2307 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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2.21414 0.45527
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x2 0.45527 2.39853
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hence, area = 14.194
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'ellipsoid' in 3 dimensions:
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center = ( 2.7989 1.1654 4.6782 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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1.92664 0.40109 1.4317
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x2 0.40109 1.76625 6.9793
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1.43170 6.97928 28.0530
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hence, volume = 26.631
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n = 6
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'ellipsoid' in 2 dimensions:
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center = ( 3.04367 0.97016 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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4.39182 0.30833
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x2 0.30833 0.59967
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hence, area = 10.011
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'ellipsoid' in 3 dimensions:
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center = ( 3.3190 0.7678 3.2037 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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2.786928 -0.044373 -1.1467
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x2 -0.044373 0.559495 1.5496
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-1.146728 1.549620 5.5025
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hence, volume = 24.804
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n = 7
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'ellipsoid' in 2 dimensions:
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center = ( 3.98294 -0.16567 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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4.62064 -0.83135
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x2 -0.83135 0.37030
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hence, area = 6.3453
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'ellipsoid' in 3 dimensions:
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center = ( 4.24890 -0.25918 -0.76499 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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4.6494 -0.93240 -4.0758
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x2 -0.9324 0.39866 1.9725
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-4.0758 1.97253 10.4366
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hence, volume = 16.152
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n = 8
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'ellipsoid' in 2 dimensions:
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center = ( 3.6699 -0.4532 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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9.4327 -2.5269
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x2 -2.5269 3.7270
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hence, area = 33.702
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'ellipsoid' in 3 dimensions:
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center = ( 4.22030 -0.37953 -1.53922 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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7.5211 -1.4804 -6.6587
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x2 -1.4804 2.6972 11.8198
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-6.6587 11.8198 52.6243
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hence, volume = 84.024
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n = 9
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'ellipsoid' in 2 dimensions:
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center = ( 5.324396 -0.037779 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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10.1098 -1.3708
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x2 -1.3708 2.1341
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hence, area = 27.885
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'ellipsoid' in 3 dimensions:
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center = ( 5.44700 -0.12504 -1.13538 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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7.0364 -1.2424 -5.5741
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x2 -1.2424 1.7652 7.3654
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-5.5741 7.3654 31.5558
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hence, volume = 64.161
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n = 10
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'ellipsoid' in 2 dimensions:
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center = ( 4.85439 0.28401 ); squared ave.radius d^2 = 2
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and shape matrix =
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x2
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13.932 0.64900
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x2 0.649 0.95132
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hence, area = 22.508
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'ellipsoid' in 3 dimensions:
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center = ( 5.12537 0.25024 0.86441 ); squared ave.radius d^2 = 3
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and shape matrix =
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x2
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9.29343 0.56973 1.4143
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x2 0.56973 0.76519 1.8941
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1.41427 1.89409 6.3803
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hence, volume = 73.753
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>
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> set.seed(1)
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> x <- rt(100, df = 4)
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> y <- 100 + 5 * x + rnorm(100)
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> ellipsoidhull(cbind(x,y))
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'ellipsoid' in 2 dimensions:
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center = ( -1.3874 93.0589 ); squared ave.radius d^2 = 2
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and shape matrix =
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x y
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x 32.924 160.54
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y 160.543 785.88
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hence, area = 62.993
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> z <- 10 - 8 * x + y + rnorm(100)
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> (e3 <- ellipsoidhull(cbind(x,y,z)))
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'ellipsoid' in 3 dimensions:
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center = ( -0.71678 96.09950 111.61029 ); squared ave.radius d^2 = 3
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and shape matrix =
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x y z
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x 26.005 126.41 -80.284
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y 126.410 616.94 -387.459
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z -80.284 -387.46 254.006
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hence, volume = 301.25
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> d3o <- cbind(x,y + rt(100,3), 2 * x^2 + rt(100, 2))
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> (e. <- ellipsoidhull(d3o, ret.sq = TRUE))
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'ellipsoid' in 3 dimensions:
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center = ( 0.32491 101.68998 39.48045 ); squared ave.radius d^2 = 3
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and shape matrix =
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x
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x 19.655 94.364 48.739
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94.364 490.860 181.022
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48.739 181.022 1551.980
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hence, volume = 21856
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> stopifnot(all.equal(e.$sqdist,
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+ with(e., mahalanobis(d3o, center=loc, cov=cov)),
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+ tol = 1e-13))
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> d5 <- cbind(d3o, 2*abs(y)^1.5 + rt(100,3), 3*x - sqrt(abs(y)))
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> (e5 <- ellipsoidhull(d5, ret.sq = TRUE))
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'ellipsoid' in 5 dimensions:
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center = ( -0.32451 98.54780 37.33619 1973.88383 -10.81891 ); squared ave.radius d^2 = 5
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and shape matrix =
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x
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x 17.8372 87.0277 8.3389 2607.9 49.117
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87.0277 446.9453 -2.0502 12745.4 239.470
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8.3389 -2.0502 1192.8439 2447.8 24.458
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2607.9264 12745.3826 2447.8006 384472.1 7179.239
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49.1172 239.4703 24.4582 7179.2 135.260
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hence, volume = 191410
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> tail(sort(e5$sqdist)) ## 4 values 5.00039 ... 5.0099
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[1] 4.999915 5.000005 5.000010 5.000088 5.001444 5.009849
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>
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> (e5.1e77 <- ellipsoidhull(1e77*d5))
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'ellipsoid' in 5 dimensions:
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center = ( -3.2451e+76 9.8548e+78 3.7336e+78 1.9739e+80 -1.0819e+78 ); squared ave.radius d^2 = 5
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and shape matrix =
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x
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x 1.7837e+155 8.7028e+155 8.3389e+154 2.6079e+157 4.9117e+155
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8.7028e+155 4.4695e+156 -2.0502e+154 1.2745e+158 2.3947e+156
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8.3389e+154 -2.0502e+154 1.1928e+157 2.4478e+157 2.4458e+155
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2.6079e+157 1.2745e+158 2.4478e+157 3.8447e+159 7.1792e+157
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4.9117e+155 2.3947e+156 2.4458e+155 7.1792e+157 1.3526e+156
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hence, volume = exp(898.66)
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> stopifnot(# proof correct scaling c^5
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+ all.equal(volume(e5.1e77, log=TRUE) - volume(e5, log=TRUE),
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+ ncol(d5) * 77* log(10))
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+ )
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>
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> proc.time()
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user system elapsed
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0.117 0.034 0.210
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