R Under development (unstable) (2024-02-05 r85863 ucrt) -- "Unsuffered Consequences"
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> #### Testing  pcSelect()  _and_  (its main helper) mcor()
> ####          ~~~~~~~~                             ~~~~
> 
> library(pcalg)
> suppressWarnings(RNGversion("3.5.0"))
> p <- 10
> n <- 1000
> 
> set.seed(101)
> myDAG <- randomDAG(p, prob = 0.2)
> d.mat <- rmvDAG(n, myDAG, errDist = "normal")
> y <- d.mat[,10]
> dm <- d.mat[,-10]
> res1 <- pcSelect(y,dm, alpha=0.05)
> if (!all(res1$G == 1:9 %in% c(4,5,6)))
+   stop("Test of pcSelect: Consistency problem 101")
> dput(signif(res1$zMin, 7))
c(0.07643311, 0.6568222, 0.7363025, 11.62001, 6.621493, 18.64382, 
1.447, 1.212824, 1.221812)
> zM.1 <- c(0.07643311, 0.6568222, 0.7363025,
+           11.62001, 6.621493, 18.64382,
+           1.447, 1.212824, 1.221812)
> stopifnot(all.equal(res1$zMin, zM.1, tol = 1e-6))
> 
> ## Now all other methods:
> 
> (corMeths <- eval(formals(mcor)$method))
[1] "standard"     "Qn"           "QnStable"     "ogkScaleTau2" "ogkQn"       
[6] "shrink"      
> ## the other methods (but the default):
> cMeths <- corMeths[-1]
> C. <- zMin. <- setNames(as.list(cMeths), cMeths)
> Cstats <- function(C) {
+     ## numeric symmetric matrix
+     stopifnot(is.matrix(C), is.numeric(C), isSymmetric(C))# , tol = 3e-14
+     cbind(diag = diag(C),
+           colSums = colSums(C),
+           e.values = eigen(C, only.values=TRUE)$values)
+ }
> 
> for(meth in cMeths) {
+     cat(meth,":\n")
+     rr <- pcSelect(y,dm, alpha=0.05, corMethod = meth)
+     iG <- which(as.vector(rr$G))
+     if (!identical(iG, c(4L,5L,6L)))
+         stop(sprintf("pcSelect(dm101.., corMethod=\"%s\"): which(G) = %s\n",
+                      meth, paste(iG, collapse=", ")))
+     zMin.[[meth]] <- rr$zMin
+     C.   [[meth]] <- mcor(d.mat, method=meth)
+ }
Qn :
QnStable :
ogkScaleTau2 :
ogkQn :
shrink :
> 
> C.st <- lapply(C., Cstats)
> stopifnot( sapply(C.st, function(st) st[,"diag"] == 1) )
> 
> C.EVal <- sapply(C.st, function(st) st[,"e.values"])
> C.sums <- sapply(C.st, function(st) st[,"colSums"])
> dns <- list(NULL, c("Qn", "QnStable", "ogkScaleTau2", "ogkQn", "shrink"))
> 
> ## dput(lapply(zMin., signif, digits=7))
> zMin1.Exp <- list(
+     Qn = c(0.5316588, 1.088152, 0.8118473, 11.34048,
+            6.416001, 18.79211, 0.9179979, 0.4779155, 1.346989),
+     QnStable = c(0.9129029, 1.710694, 0.8471604, 10.56123, 6.168661,
+                  18.88213, 0.9710747, 0.4337806, 1.140709),
+     ogkScaleTau2 = c(0.4698467, 0.886344, 0.5731621, 10.94707, 6.335696,
+                      18.60215, 0.9969964, 1.045772, 1.244915),
+     ogkQn = c(0.7588748, 0.6270149, 0.6489765, 11.19786, 6.052107,
+               18.683, 0.8969601, 0.9808662, 1.118423),
+     shrink = c(0.07570146, 0.6493067, 0.7303193, 11.49862, 6.556261,
+                18.45523, 1.433129, 1.199766, 1.211877))
> ##
> dput(signif(C.EVal, digits=7))
structure(c(2.902214, 1.991134, 1.352243, 0.9937615, 0.6887558, 
0.675548, 0.5645716, 0.3164719, 0.3107822, 0.2045182, 2.895631, 
1.980508, 1.3593, 0.9949763, 0.6918006, 0.6710074, 0.5672133, 
0.3192135, 0.3023458, 0.2180048, 2.885849, 1.966942, 1.340686, 
1.003727, 0.7069337, 0.6863926, 0.5652152, 0.3226591, 0.3090602, 
0.2125357, 2.863277, 1.9834, 1.360826, 0.9985534, 0.70277, 0.69042, 
0.5662882, 0.3179164, 0.3060326, 0.2105163, 2.884824, 1.989006, 
1.336554, 1.000628, 0.7192748, 0.6763509, 0.5504135, 0.3225079, 
0.3041295, 0.216311), dim = c(10L, 5L), dimnames = list(NULL, 
    c("Qn", "QnStable", "ogkScaleTau2", "ogkQn", "shrink")))
> C.EV1.Exp <- structure(
+     c(2.902214, 1.991134, 1.352243, 0.9937615, 0.6887558,
+       0.675548, 0.5645716, 0.3164719, 0.3107822, 0.2045182,
+       2.895631, 1.980508, 1.3593, 0.9949763, 0.6918006,
+       0.6710074, 0.5672133, 0.3192135, 0.3023458, 0.2180048,
+       2.885849, 1.966942, 1.340686, 1.003727, 0.7069337,
+       0.6863926, 0.5652152, 0.3226591, 0.3090602, 0.2125357,
+       2.863277, 1.9834, 1.360826, 0.9985534, 0.70277,
+       0.69042, 0.5662882, 0.3179164, 0.3060326, 0.2105163,
+       2.884824, 1.989006, 1.336554, 1.000628, 0.7192748,
+       0.6763509, 0.5504135, 0.3225079, 0.3041295, 0.216311),
+     .Dim = c(10L, 5L), .Dimnames = dns)
> ##
> dput(signif(C.sums, digits=7))
structure(c(2.717515, 3.48909, 2.081151, 3.301211, 2.762732, 
1.388646, 2.721029, 1.384193, 1.71164, 3.184033, 2.712734, 3.508554, 
2.086835, 3.274161, 2.775645, 1.390581, 2.705537, 1.392348, 1.705256, 
3.164881, 2.744097, 3.500246, 2.132502, 3.314979, 2.721613, 1.407829, 
2.675133, 1.376944, 1.696778, 3.147149, 2.720277, 3.471509, 2.125648, 
3.28348, 2.673719, 1.392961, 2.662582, 1.360947, 1.706638, 3.115694, 
2.790109, 3.431366, 2.075317, 3.269821, 2.714512, 1.462898, 2.714256, 
1.337588, 1.736093, 3.192173), dim = c(10L, 5L), dimnames = list(
    NULL, c("Qn", "QnStable", "ogkScaleTau2", "ogkQn", "shrink"
    )))
> C.sum1.Exp <- structure(
+     c(2.717515, 3.48909, 2.081151, 3.301211, 2.762732,
+       1.388646, 2.721029, 1.384193, 1.71164, 3.184033, 2.712734, 3.508554,
+       2.086835, 3.274161, 2.775645, 1.390581, 2.705537, 1.392348, 1.705256,
+       3.164881, 2.744097, 3.500246, 2.132502, 3.314979, 2.721613, 1.407829,
+       2.675133, 1.376944, 1.696778, 3.147149, 2.720277, 3.471509, 2.125648,
+       3.28348, 2.673719, 1.392961, 2.662582, 1.360947, 1.706638, 3.115694,
+       2.790109, 3.431366, 2.075317, 3.269821, 2.714512, 1.462898, 2.714256,
+       1.337588, 1.736093, 3.192173),
+     .Dim = c(10L, 5L), .Dimnames = dns)
> 
> stopifnot(all.equal(zMin. , zMin1.Exp, tol = 1e-6),
+           all.equal(C.EVal, C.EV1.Exp , tol = 1e-6),
+           all.equal(C.sums, C.sum1.Exp, tol = 1e-6),
+           TRUE)
> 
> ###--------------------------------------- Ex. 2 -------------------------------------
> 
> set.seed(456)
> myDAG <- randomDAG(p, prob = 0.2)
> d.mat <- rmvDAG(n, myDAG, errDist = "normal")
> y <- d.mat[,10]
> dm <- d.mat[,-10]
> iG.Exp <- c(5L,8L,9L)
> res2 <- pcSelect(y,dm,alpha=0.05)
> if (!identical(which(as.vector(res2$G)), iG.Exp))
+   stop("Test of pcSelect: Consistency problem 456")
> ## dput(signif(res2$zMin, 7))
> zM.2 <- c(0.1469954, 0.915466, 0.5442373,
+           0.1089084, 14.16709, 1.056202,
+           0.4840786, 17.10435, 14.51551)
> stopifnot(all.equal(res2$zMin, zM.2, tol = 1e-6))
> 
> ## Now all other methods:
> for(meth in cMeths) {
+     cat(meth,":\n")
+     rr <- pcSelect(y,dm, alpha=0.05, corMethod = meth)
+     iG <- which(as.vector(rr$G))
+     if (!identical(iG, iG.Exp))
+         (if(all(iG.Exp %in% iG)) message else stop)(
+             sprintf("pcSelect(dm456.., corMethod=\"%s\"): which(G) = %s\n",
+                     meth, paste(iG, collapse=", ")))
+     zMin.[[meth]] <- rr$zMin
+     C.   [[meth]] <- mcor(d.mat, method=meth)
+ }
Qn :
pcSelect(dm456.., corMethod="Qn"): which(G) = 2, 5, 8, 9

QnStable :
pcSelect(dm456.., corMethod="QnStable"): which(G) = 2, 5, 8, 9

ogkScaleTau2 :
ogkQn :
shrink :
> 
> C.st <- lapply(C., Cstats)
> stopifnot( sapply(C.st, function(st) st[,"diag"] == 1) )
> 
> C.EVal <- sapply(C.st, function(st) st[,"e.values"])
> C.sums <- sapply(C.st, function(st) st[,"colSums"])
> 
> ##
> dput(signif(C.EVal, digits=7))
structure(c(2.395184, 1.686566, 1.280328, 1.094699, 1.002715, 
0.8997931, 0.7362697, 0.5018258, 0.2396817, 0.1629375, 2.414695, 
1.669223, 1.277225, 1.096991, 1.00195, 0.8970272, 0.7380218, 
0.504836, 0.2350952, 0.1649354, 2.386837, 1.679313, 1.309865, 
1.101403, 1.002767, 0.865312, 0.715178, 0.5221997, 0.2352581, 
0.1818661, 2.370872, 1.681723, 1.315575, 1.112341, 1.008541, 
0.8657987, 0.7116331, 0.521083, 0.2312147, 0.1812185, 2.413167, 
1.679511, 1.30454, 1.090105, 1.000066, 0.879334, 0.6960254, 0.5191567, 
0.2335488, 0.1845462), dim = c(10L, 5L), dimnames = list(NULL, 
    c("Qn", "QnStable", "ogkScaleTau2", "ogkQn", "shrink")))
> C.EV2.Exp <- structure(
+     c(2.395184, 1.686566, 1.280328, 1.094699, 1.002715,
+       0.8997931,0.7362697,0.5018258,0.2396817,0.1629375,
+       2.414695, 1.669223, 1.277225, 1.096991, 1.00195,
+       0.8970272,0.7380218,0.504836, 0.2350952,0.1649354,
+       2.386837, 1.679313, 1.309865, 1.101403, 1.002767,
+       0.865312, 0.715178, 0.5221997,0.2352581,0.1818661,
+       2.370872, 1.681723, 1.315575, 1.112341, 1.008541,
+       0.8657987,0.7116331,0.521083, 0.2312147,0.1812185,
+       2.413167, 1.679511, 1.30454,  1.090105, 1.000066,
+       0.879334, 0.6960254,0.5191567,0.2335488,0.1845462),
+     .Dim = c(10L, 5L), .Dimnames = dns)
> ##
> dput(signif(C.sums, digits=7))
structure(c(0.9910661, 1.77166, 1.919368, 1.752008, 2.239346, 
2.056446, 1.496665, 2.717977, 1.909636, 3.079426, 0.9969023, 
1.797362, 1.928749, 1.756807, 2.228714, 2.072544, 1.517333, 2.795068, 
1.921609, 3.127389, 0.9945908, 1.709868, 1.945329, 1.744885, 
2.179677, 2.035526, 1.5155, 2.780851, 1.868081, 3.08998, 1.00944, 
1.692255, 1.943654, 1.754006, 2.144725, 2.019437, 1.490262, 2.764678, 
1.846422, 3.078384, 1.023379, 1.778081, 2.029191, 1.678237, 2.140316, 
2.036679, 1.470303, 2.754962, 1.936074, 3.135426), dim = c(10L, 
5L), dimnames = list(NULL, c("Qn", "QnStable", "ogkScaleTau2", 
"ogkQn", "shrink")))
> C.sum2.Exp <- structure(
+     c(0.9910661,1.77166,  1.919368, 1.752008, 2.239346,
+       2.056446, 1.496665, 2.717977, 1.909636, 3.079426,
+       0.9969023,1.797362, 1.928749, 1.756807, 2.228714,
+       2.072544, 1.517333, 2.795068, 1.921609, 3.127389,
+       0.9945908,1.709868, 1.945329, 1.744885, 2.179677,
+       2.035526, 1.5155,   2.780851, 1.868081, 3.08998,
+       1.00944,  1.692255, 1.943654, 1.754006, 2.144725,
+       2.019437, 1.490262, 2.764678, 1.846422, 3.078384,
+       1.023379, 1.778081, 2.029191, 1.678237, 2.140316,
+       2.036679, 1.470303, 2.754962, 1.936074, 3.135426),
+     .Dim = c(10L, 5L), .Dimnames = dns)
> 
> 
> ## dput(lapply(zMin., signif, digits=7))
> zMin2.Exp <-
+     list(
+         Qn = c(1.055523, 2.555242, 1.691455, 0.7796301, 11.39895,
+                0.8692785, 0.04107331, 14.0156, 14.82198),
+         QnStable = c(0.6208816, 2.475236, 1.831045, 0.9328639, 11.11562,
+                      1.139745, 0.04850462, 14.21195, 14.77496),
+         ogkScaleTau2 = c(0.4164263, 1.092748, 1.689739, 0.4691277, 11.92243,
+                          1.028907, 0.06462646, 13.80103, 14.60776),
+         ogkQn = c(0.237811, 1.916074, 1.704892, 0.3637768, 14.42101,
+                   0.8777305, 0.05152724, 16.72384, 14.60674),
+         shrink = c(0.1459792, 0.902588, 0.540349, 0.1081555, 13.98006,
+                    1.047259, 0.4807316, 16.88456, 14.4006))
> 
> stopifnot(all.equal(zMin. , zMin2.Exp , tol = 1e-6),
+           all.equal(C.EVal, C.EV2.Exp , tol = 1e-6),
+           all.equal(C.sums, C.sum2.Exp, tol = 1e-6),
+           TRUE)
> 
> proc.time()
   user  system elapsed 
   2.10    0.17    2.26