R Under development (unstable) (2024-08-15 r87022 ucrt) -- "Unsuffered Consequences"
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> ## Copyright (C) 2012 Marius Hofert, Ivan Kojadinovic, Martin Maechler, and Jun Yan
> ##
> ## This program is free software; you can redistribute it and/or modify it under
> ## the terms of the GNU General Public License as published by the Free Software
> ## Foundation; either version 3 of the License, or (at your option) any later
> ## version.
> ##
> ## This program is distributed in the hope that it will be useful, but WITHOUT
> ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
> ## FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
> ## details.
> ##
> ## You should have received a copy of the GNU General Public License along with
> ## this program; if not, see <http://www.gnu.org/licenses/>.
> 
> require(copula)
Loading required package: copula
> source(system.file("Rsource", "utils.R",     package="copula", mustWork=TRUE))
Loading required package: tools
> ##-> assertError(), assert.EQ(), ... showProc.time()  +  comparederiv()
> showProc.time()
Time (user system elapsed): 0.01 0 0.02 
> 
> (doExtras <- copula:::doExtras())
[1] FALSE
> 
> 
> tC2.F <- tCopula(df=2, df.fixed=TRUE)
> (cm <- setTheta(tC2.F, value=-0.5, freeOnly=TRUE)) ## setTheta() had failed
t-copula, dim. d = 2 
Dimension:  2 
Parameters (partly fixed, see ':='):
  rho.1   = -0.5
  df     :=  2.0
> (cp <- setTheta(tC2.F, value= 0.5, freeOnly=TRUE))
t-copula, dim. d = 2 
Dimension:  2 
Parameters (partly fixed, see ':='):
  rho.1   = 0.5
  df     := 2.0
> (c2 <- setTheta(tC2.F, value=c(0.5,3), freeOnly=FALSE)) ## had failed
t-copula, dim. d = 2 
Dimension:  2 
Parameters (partly fixed, see ':='):
  rho.1   = 0.5
  df     := 3.0
> stopifnot(all.equal(getTheta(cm), -0.5), all.equal(getTheta(cp), +0.5),
+           all.equal(getTheta(cm, freeOnly=FALSE, named=TRUE),
+                     c(rho.1 = -0.5, df = 2)),
+           all.equal(getTheta(cp, freeOnly=FALSE), c(0.5, 2)),
+           all.equal(getTheta(c2, freeOnly=FALSE, named=TRUE),
+                     c(rho.1 = 0.5, df = 3)))
> 
> (N3 <- normalCopula(c(0.5,0.3,0.2), dim=3, dispstr = "un"))
Normal copula, dim. d = 3 
Dimension:  3 
Parameters:
  rho.1   = 0.5
  rho.2   = 0.3
  rho.3   = 0.2
dispstr:  un 
> fixedParam(N3) <- c(TRUE, FALSE, FALSE); N3
Normal copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.5
  rho.2   = 0.3
  rho.3   = 0.2
dispstr:  un 
> (N3.2 <- setTheta(N3,     c( 0.4, 0.2) -> t2)) # partially fixed: works since 2017-02-11
Normal copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.5
  rho.2   = 0.4
  rho.3   = 0.2
dispstr:  un 
> (N3.3 <- setTheta(N3, c(0.6, 0.4, 0.2) -> t3, freeOnly=FALSE))
Normal copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.6
  rho.2   = 0.4
  rho.3   = 0.2
dispstr:  un 
> stopifnot(all.equal(getTheta(N3.2), t2),
+ 	  all.equal(getTheta(N3.3), t3[-1]),
+ 	  all.equal(getTheta(N3.2, freeOnly=FALSE), c(0.5, t2)),
+ 	  all.equal(getTheta(N3.3, freeOnly=FALSE), t3))
> 
> (tC3 <- tCopula(c(0.5,0.3,0.2), dim=3, dispstr = "un")) # df = 4 is not fixed
t-copula, dim. d = 3 
Dimension:  3 
Parameters:
  rho.1   = 0.5
  rho.2   = 0.3
  rho.3   = 0.2
  df      = 4.0
dispstr:  un 
> fixedParam(tC3) <- c(TRUE, FALSE, FALSE, TRUE); tC3 #-> df fixed, too
t-copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.5
  rho.2   = 0.3
  rho.3   = 0.2
  df     := 4.0
dispstr:  un 
> (tC3.2 <- setTheta(tC3,     c( 0.4, 0.1)    -> t2)) # partially fixed: works since 2017-02-11
t-copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.5
  rho.2   = 0.4
  rho.3   = 0.1
  df     := 4.0
dispstr:  un 
> (tC3.3 <- setTheta(tC3, c(0.6, 0.4, 0.1, 3) -> t3, freeOnly=FALSE))
t-copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.6
  rho.2   = 0.4
  rho.3   = 0.1
  df     := 3.0
dispstr:  un 
> stopifnot(all.equal(getTheta(tC3.2), t2),
+ 	  all.equal(getTheta(tC3.3), t3[-c(1,4)]),
+ 	  all.equal(getTheta(tC3.2, freeOnly=FALSE), c(0.5, t2, 4)),
+ 	  all.equal(getTheta(tC3.3, freeOnly=FALSE), t3))
> 
> fixedParam(tC3) <- c(TRUE, FALSE, FALSE, FALSE); tC3 # df remains free
t-copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.5
  rho.2   = 0.3
  rho.3   = 0.2
  df      = 4.0
dispstr:  un 
> (tC3u.2 <- setTheta(tC3,     c( 0.4, 0.2, 5) -> t2)) # partially fixed: works since 2017-02-11
t-copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.5
  rho.2   = 0.4
  rho.3   = 0.2
  df      = 5.0
dispstr:  un 
> (tC3u.3 <- setTheta(tC3, c(0.6, 0.4, 0.2, 3) -> t3, freeOnly=FALSE))
t-copula, dim. d = 3 
Dimension:  3 
Parameters (partly fixed, see ':='):
  rho.1  := 0.6
  rho.2   = 0.4
  rho.3   = 0.2
  df      = 3.0
dispstr:  un 
> stopifnot(all.equal(getTheta(tC3u.2), t2),
+ 	  all.equal(getTheta(tC3u.3), t3[-1]),
+ 	  all.equal(getTheta(tC3u.2, freeOnly=FALSE), c(0.5, t2)),
+ 	  all.equal(getTheta(tC3u.3, freeOnly=FALSE), t3))
> 
> 
> 
> ### TEST FITTING ##########################################################
> 
>     n <- 100
>     ## with normal copulas
>     nc3  <- normalCopula(dim = 3, c(.6,.3,.2), dispstr = "un")
>     nc3@parameters
[1] 0.6 0.3 0.2
>     set.seed(4521)
>     x <- rCopula(n, nc3)
>     u <- pobs(x)
> 
>     fitCopula(nc3, data = u)
Call: fitCopula(nc3, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5715 0.3498 0.2391 
The maximized loglikelihood is 23.6 
Optimization converged
>     fitCopula(nc3, data = u, estimate.variance = FALSE)
Call: fitCopula(nc3, data = u, ... = pairlist(estimate.variance = FALSE))
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5715 0.3498 0.2391 
The maximized loglikelihood is 23.6 
Optimization converged
>     fitCopula(nc3, data = x, method = "ml")
Call: fitCopula(nc3, data = x, ... = pairlist(method = "ml"))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5793 0.3277 0.2552 
The maximized loglikelihood is 24.08 
Optimization converged
>     fitCopula(nc3, data = x, method = "ml", estimate.variance = FALSE)
Call: fitCopula(nc3, data = x, ... = pairlist(method = "ml", estimate.variance = FALSE))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5793 0.3277 0.2552 
The maximized loglikelihood is 24.08 
Optimization converged
>     fitCopula(nc3, data = u, method = "itau")
Call: fitCopula(nc3, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5697 0.3805 0.2308 
>     fitCopula(nc3, data = u, method = "itau", estimate.variance = FALSE)
Call: fitCopula(nc3, data = u, ... = pairlist(method = "itau", estimate.variance = FALSE))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5697 0.3805 0.2308 
>     fitCopula(nc3, data = u, method = "irho")
Call: fitCopula(nc3, data = u, ... = pairlist(method = "irho"))
Fit based on "inversion of Spearman's rho" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5780 0.3878 0.2395 
>     fitCopula(nc3, data = u, method = "irho", estimate.variance = FALSE)
Call: fitCopula(nc3, data = u, ... = pairlist(method = "irho", estimate.variance = FALSE))
Fit based on "inversion of Spearman's rho" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.1  rho.2  rho.3 
0.5780 0.3878 0.2395 
> 
> showProc.time()
Time (user system elapsed): 0.36 0.03 0.39 
> 
>     nc2  <- normalCopula(dim = 3, fixParam(c(.6,.3,.2), c(TRUE, FALSE, FALSE)),
+                          dispstr = "un")
>     nc2@parameters
[1] 0.6 0.3 0.2
attr(,"fixed")
[1]  TRUE FALSE FALSE
> 
>     fitCopula(nc2, data = u)
Call: fitCopula(nc2, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3512 0.2484 
The maximized loglikelihood is 23.47 
Optimization converged
>     fitCopula(nc2, data = u, estimate.variance = FALSE)
Call: fitCopula(nc2, data = u, ... = pairlist(estimate.variance = FALSE))
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3512 0.2484 
The maximized loglikelihood is 23.47 
Optimization converged
>     fitCopula(nc2, data = x, method = "ml")
Call: fitCopula(nc2, data = x, ... = pairlist(method = "ml"))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3294 0.2607 
The maximized loglikelihood is 24.01 
Optimization converged
>     fitCopula(nc2, data = x, method = "ml", estimate.variance = FALSE)
Call: fitCopula(nc2, data = x, ... = pairlist(method = "ml", estimate.variance = FALSE))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3294 0.2607 
The maximized loglikelihood is 24.01 
Optimization converged
>     fitCopula(nc2, data = u, method = "itau")
Call: fitCopula(nc2, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3805 0.2308 
>     fitCopula(nc2, data = u, method = "itau", estimate.variance = FALSE)
Call: fitCopula(nc2, data = u, ... = pairlist(method = "itau", estimate.variance = FALSE))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3805 0.2308 
>     fitCopula(nc2, data = u, method = "irho")
Call: fitCopula(nc2, data = u, ... = pairlist(method = "irho"))
Fit based on "inversion of Spearman's rho" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3878 0.2395 
>     fitCopula(nc2, data = u, method = "irho", estimate.variance = FALSE)
Call: fitCopula(nc2, data = u, ... = pairlist(method = "irho", estimate.variance = FALSE))
Fit based on "inversion of Spearman's rho" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.2  rho.3 
0.3878 0.2395 
> 
> showProc.time()
Time (user system elapsed): 0.16 0 0.16 
> 
> 
>     nc1  <- normalCopula(dim = 3, fixParam(c(.6,.3,.2), c(TRUE, TRUE, FALSE)),
+                          dispstr = "un")
>     nc1@parameters
[1] 0.6 0.3 0.2
attr(,"fixed")
[1]  TRUE  TRUE FALSE
> 
>     fitCopula(nc1, data = u)
Call: fitCopula(nc1, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.3 
0.2164 
The maximized loglikelihood is 23.31 
Optimization converged
>     fitCopula(nc1, data = x, method = "ml")
Call: fitCopula(nc1, data = x, ... = pairlist(method = "ml"))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.3 
0.2437 
The maximized loglikelihood is 23.96 
Optimization converged
>     fitCopula(nc1, data = u, method = "itau")
Call: fitCopula(nc1, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.3 
0.2308 
>     fitCopula(nc1, data = u, method = "irho")
Call: fitCopula(nc1, data = u, ... = pairlist(method = "irho"))
Fit based on "inversion of Spearman's rho" and 100 3-dimensional observations.
Copula: normalCopula 
 rho.3 
0.2395 
> 
> showProc.time()
Time (user system elapsed): 0.06 0 0.06 
> 
> 
>     ## with t copulas (df.fixed = FALSE)
>     tc3df  <- tCopula(dim = 3, c(.6,.3,.2), dispstr = "un")
>     tc3df@parameters
[1] 0.6 0.3 0.2 4.0
attr(,"fixed")
[1] FALSE FALSE FALSE FALSE
>     set.seed(4521)
>     x <- rCopula(n, tc3df)
>     u <- pobs(x)
>     fitCopula(tc3df, data = u)
Call: fitCopula(tc3df, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3     df 
0.5878 0.4266 0.2695 6.3232 
The maximized loglikelihood is 31.68 
Optimization converged
Warning message:
In var.mpl(copula, u) :
  the covariance matrix of the parameter estimates is computed as if 'df.fixed = TRUE' with df = 6.32321437509388
>     fitCopula(tc3df, data = x, method = "ml")
Call: fitCopula(tc3df, data = x, ... = pairlist(method = "ml"))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3     df 
0.6080 0.4443 0.2896 5.7102 
The maximized loglikelihood is 35.56 
Optimization converged
>     fitCopula(tc3df, data = u, method = "itau")
Call: fitCopula(tc3df, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3 
0.5960 0.4241 0.2370 
Warning message:
In fitCopula.icor(copula, x = data, method = method, estimate.variance = estimate.variance,  :
  "itau" fitting ==> copula coerced to 'df.fixed=TRUE'
>     fitCopula(tc3df, data = u, estimate.variance = FALSE)
Call: fitCopula(tc3df, data = u, ... = pairlist(estimate.variance = FALSE))
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3     df 
0.5878 0.4266 0.2695 6.3232 
The maximized loglikelihood is 31.68 
Optimization converged
>     fitCopula(tc3df, data = x, method = "ml", estimate.variance = FALSE)
Call: fitCopula(tc3df, data = x, ... = pairlist(method = "ml", estimate.variance = FALSE))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3     df 
0.6080 0.4443 0.2896 5.7102 
The maximized loglikelihood is 35.56 
Optimization converged
>     fitCopula(tc3df, data = u, method = "itau", estimate.variance = FALSE)
Call: fitCopula(tc3df, data = u, ... = pairlist(method = "itau", estimate.variance = FALSE))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3 
0.5960 0.4241 0.2370 
Warning message:
In fitCopula.icor(copula, x = data, method = method, estimate.variance = estimate.variance,  :
  "itau" fitting ==> copula coerced to 'df.fixed=TRUE'
>     fitCopula(tc3df, data = u, method = "itau.mpl")
Call: fitCopula(tc3df, data = u, ... = pairlist(method = "itau.mpl"))
Fit based on "itau for dispersion matrix P and maximum likelihood for df" and 100 3-dimensional observations.
Copula: tCopula 
 rho.1  rho.2  rho.3     df 
0.5960 0.4241 0.2370 6.6540 
The maximized loglikelihood is 31.59 
Optimization converged
> 
> showProc.time()
Time (user system elapsed): 0.86 0.01 0.87 
> 
> 
>     tc2df  <- tCopula(dim = 3, fixParam(c(.6,.3,.2), c(TRUE, FALSE, FALSE)),
+                     dispstr = "un")
>     tc2df@parameters
[1] 0.6 0.3 0.2 4.0
attr(,"fixed")
[1]  TRUE FALSE FALSE FALSE
> 
>     fitCopula(tc2df, data = u)
Call: fitCopula(tc2df, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3     df 
0.4279 0.2752 6.5069 
The maximized loglikelihood is 31.66 
Optimization converged
Warning message:
In var.mpl(copula, u) :
  the covariance matrix of the parameter estimates is computed as if 'df.fixed = TRUE' with df = 6.50688878741488
>     fitCopula(tc2df, data = x, method = "ml")
Call: fitCopula(tc2df, data = x, ... = pairlist(method = "ml"))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3     df 
0.4432 0.2854 5.6182 
The maximized loglikelihood is 35.55 
Optimization converged
>     fitCopula(tc2df, data = u, method = "itau")
Call: fitCopula(tc2df, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3 
0.4241 0.2370 
Warning message:
In fitCopula.icor(copula, x = data, method = method, estimate.variance = estimate.variance,  :
  "itau" fitting ==> copula coerced to 'df.fixed=TRUE'
>     fitCopula(tc2df, data = u, estimate.variance = FALSE)
Call: fitCopula(tc2df, data = u, ... = pairlist(estimate.variance = FALSE))
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3     df 
0.4279 0.2752 6.5069 
The maximized loglikelihood is 31.66 
Optimization converged
>     fitCopula(tc2df, data = x, method = "ml", estimate.variance = FALSE)
Call: fitCopula(tc2df, data = x, ... = pairlist(method = "ml", estimate.variance = FALSE))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3     df 
0.4432 0.2854 5.6182 
The maximized loglikelihood is 35.55 
Optimization converged
>     fitCopula(tc2df, data = u, method = "itau", estimate.variance = FALSE)
Call: fitCopula(tc2df, data = u, ... = pairlist(method = "itau", estimate.variance = FALSE))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3 
0.4241 0.2370 
Warning message:
In fitCopula.icor(copula, x = data, method = method, estimate.variance = estimate.variance,  :
  "itau" fitting ==> copula coerced to 'df.fixed=TRUE'
>     fitCopula(tc2df, data = u, method = "itau.mpl")
Call: fitCopula(tc2df, data = u, ... = pairlist(method = "itau.mpl"))
Fit based on "itau for dispersion matrix P and maximum likelihood for df" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3     df 
0.4241 0.2370 6.7515 
The maximized loglikelihood is 31.57 
Optimization converged
>     ## fitCopula(tc2df, data = u, method = "irho")
> showProc.time()
Time (user system elapsed): 0.56 0 0.57 
> 
> 
>     tc1df  <- tCopula(dim = 3, fixParam(c(.6,.3,.2), c(TRUE, TRUE, FALSE)),
+                     dispstr = "un")
>     tc1df@parameters
[1] 0.6 0.3 0.2 4.0
attr(,"fixed")
[1]  TRUE  TRUE FALSE FALSE
> 
>     fitCopula(tc1df, data = u)
Call: fitCopula(tc1df, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.3     df 
0.1947 5.9244 
The maximized loglikelihood is 30.76 
Optimization converged
Warning message:
In var.mpl(copula, u) :
  the covariance matrix of the parameter estimates is computed as if 'df.fixed = TRUE' with df = 5.924446341239
>     fitCopula(tc1df, data = x, method = "ml")
Call: fitCopula(tc1df, data = x, ... = pairlist(method = "ml"))
Fit based on "maximum likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.3     df 
0.2015 4.9538 
The maximized loglikelihood is 34.51 
Optimization converged
>     fitCopula(tc1df, data = u, method = "itau")
Call: fitCopula(tc1df, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
rho.3 
0.237 
Warning message:
In fitCopula.icor(copula, x = data, method = method, estimate.variance = estimate.variance,  :
  "itau" fitting ==> copula coerced to 'df.fixed=TRUE'
>     fitCopula(tc1df, data = u, method = "itau.mpl")
Call: fitCopula(tc1df, data = u, ... = pairlist(method = "itau.mpl"))
Fit based on "itau for dispersion matrix P and maximum likelihood for df" and 100 3-dimensional observations.
Copula: tCopula 
rho.3    df 
0.237 5.812 
The maximized loglikelihood is 30.64 
Optimization converged
>     ## fitCopula(tc1df, data = u, method = "irho")
> showProc.time()
Time (user system elapsed): 0.28 0.02 0.29 
> 
> 
>     ## with t copulas (df.fixed = TRUE)
>     tc2  <- tCopula(dim = 3, fixParam(c(.6,.3,.2), c(TRUE, FALSE, FALSE)),
+                     dispstr = "un", df.fixed = TRUE)
>     tc2@parameters
[1] 0.6 0.3 0.2 4.0
attr(,"fixed")
[1]  TRUE FALSE FALSE  TRUE
> 
>     fitCopula(tc2, data = u)
Call: fitCopula(tc2, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3 
0.4161 0.2731 
The maximized loglikelihood is 31.14 
Optimization converged
>     fitCopula(tc2, data = u, method = "itau")
Call: fitCopula(tc2, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
 rho.2  rho.3 
0.4241 0.2370 
>     ## fitCopula(tc2, data = u, method = "irho")
> showProc.time()
Time (user system elapsed): 0.07 0 0.07 
> 
> 
>     tc1  <- tCopula(dim = 3, fixParam(c(.6,.3,.2), c(TRUE, TRUE, FALSE)),
+                     dispstr = "un", df.fixed = TRUE)
>     tc1@parameters
[1] 0.6 0.3 0.2 4.0
attr(,"fixed")
[1]  TRUE  TRUE FALSE  TRUE
> 
>     fitCopula(tc1, data = u)
Call: fitCopula(tc1, data = u)
Fit based on "maximum pseudo-likelihood" and 100 3-dimensional observations.
Copula: tCopula 
rho.3 
0.199 
The maximized loglikelihood is 30.4 
Optimization converged
>     fitCopula(tc1, data = u, method = "itau")
Call: fitCopula(tc1, data = u, ... = pairlist(method = "itau"))
Fit based on "inversion of Kendall's tau" and 100 3-dimensional observations.
Copula: tCopula 
rho.3 
0.237 
>     ##fitCopula(tc1, data = u, method = "irho")
> showProc.time()
Time (user system elapsed): 0.04 0 0.04 
> 
> ### TEST dC-dc functions #####################################################
> 
>     ## d*du functions should return the same result as when unfixed
>     ## d*dtheta functions should return "columns" corresponding to free params
>     testdCdc <- function(cop, v, cop.unfixed) {
+         fixed <- attr(cop@parameters, "fixed")
+         if (.hasSlot(cop, "df.fixed")) fixed <- fixed[-length(fixed)]
+         stopifnot(all.equal(copula:::dCdu(cop, v), copula:::dCdu(cop.unfixed, v)),
+                   all.equal(copula:::dCdtheta(cop, v),
+                             copula:::dCdtheta(cop.unfixed, v)[, !fixed, drop = FALSE]),
+                   all.equal(copula:::dlogcdu(cop, v), copula:::dlogcdu(cop.unfixed, v)),
+                   all.equal(copula:::dlogcdtheta(cop, v),
+                             copula:::dlogcdtheta(cop.unfixed, v)[, !fixed, drop = FALSE]))
+     }
> 
>     ## random points in unit cube
>     set.seed(7615)
>     v <- matrix(runif(15), 5, 3)
> 
>     ## normal
>     testdCdc(nc2, v, nc3)
>     testdCdc(nc1, v, nc3)
> 
>     ## t with df.fixed = TRUE
>     tc3  <- tCopula(dim = 3, c(.6,.3,.2), dispstr = "un", df.fixed = TRUE)
>     testdCdc(tc2, v, tc3)
>     testdCdc(tc1, v, tc3)
> 
> showProc.time()
Time (user system elapsed): 0.08 0 0.08 
> 
> cD <- rbind(## comparederiv() <<-- ../inst/Rsource/utils.R
+     Nc2 = comparederiv(nc2, v),
+     Nc1 = comparederiv(nc1, v),
+     tc2 = comparederiv(tc2, v),
+     tc1 = comparederiv(tc1, v))
> cD
           dCdu     dCdtheta      dlogcdu  dlogcdtheta
Nc2 0.001703269 3.291936e-14 3.886333e-08 7.434494e-09
Nc1 0.001703269 3.291936e-14 3.886333e-08 6.431659e-09
tc2 0.001605088 4.199505e-14 3.426593e-08 1.102597e-08
tc1 0.001605088 4.199505e-14 3.426593e-08 1.102597e-08
> stopifnot(
+     cD[,"dCdu"    ] < 0.3, # max: 0.2357 for 'tc2'
+     cD[,"dCdtheta"] < 0.2, # max: 0.1529 for 'tc2'
+     ## bug the dlog* are "good":
+     cD[,"dlogcdu"    ] < 7e-8, # see 3.886e-8 for both 'Nc'
+     cD[,"dlogcdtheta"] < 4e-8) # max: 1.54e-8 for 'tc2'
> showProc.time()
Time (user system elapsed): 0.73 0.01 0.75 
> 
> if (doExtras) {## ~ 7 secs
+ 
+ ### Multiplier GOF #####################################################
+ 
+     ## check size of mult GOF test briefly
+     do1 <- function(n, cop) {
+         u <- pobs(rCopula(n, cop))
+         gofCopula(cop, pobs(u), sim = "mult")$p.value
+     }
+     n <- 100
+     M <- 10 #1000
+     mM <- sapply(list(nc2=nc2, nc1=nc1, tc2=tc2, tc1=tc1
+                     ## , tc2df, tc1df
+                       ), function(COP) mean(replicate(M, do1(n, COP))))
+     print(mM)
+     print(mM < 0.05)
+ 
+ showProc.time()
+ }
> 
> 
> proc.time()
   user  system elapsed 
   4.35    0.32    4.62