Nothing
R/ddst.norm.test.R
In ddst: Data Driven Smooth Tests
Defines functions
`ddst.norm.test`
`ddst.norm.test` <-
function(x, base = ddst.base.legendre, c = 100, B=1000, compute.p = F, Dmax = 5, ...) {
# method.name = as.character(substitute(base))
# only Legendre is implemented yet
base = ddst.base.legendre
method.name = "ddst.base.legendre"
n = length(x)
if(n<5)
stop("length(x) should be at least 5")
er1 = mean(x)
sx = sort(x)
H = qnorm((1:n - 3/8)/(n+1/4))
er2 = mean((sx[-1] - sx[-n])/(H[-1] - H[-n]))
pp = (x-er1)/er2
tmpp = c(mean(pp), (mean(pp^2) - 1)/2)
maxN = max(min(Dmax, length(x)-2, 20),1)
u = numeric(maxN)
for (j in 1:maxN)
u[j] = ddst.phi(pnorm(x,er1,er2), j, base)
coord = numeric(Dmax)
for (k in 1:Dmax) {
korekta = u[1:k] - t(MMnorm12[[k]]) %*% tmpp
coord[k] = t(korekta) %*% MMnorm[[k]] %*% korekta * n
}
l = ddst.IIC(coord, n, c)
attr(l, "names") = "n. coord"
t = coord[l]
attr(t, "names") = "WT*"
result = list(statistic = t, parameter = l, method = "Data Driven Smooth Test for Normality")
result$data.name = paste(paste(as.character(substitute(x)), collapse=""), ", base: ", method.name, ", c: ", c, sep="")
class(result) = "htest"
if (compute.p) {
ns <- as.numeric(rownames(tabNorm))
ts <- as.numeric(colnames(tabNorm))
n1 <- min(nrow(tabNorm), nrow(tabNorm) + 1 - sum(ns >= n))
n2 <- max(1, sum(ns <= n))
t1 <- min(ncol(tabNorm), ncol(tabNorm) + 1 - sum(ts >= t))
t2 <- max(1, sum(ts <= t))
del1 <- (t - ts[t1])/min(diff(ts[c(t1,t2)]),-10^-6)
del2 <- (n - ns[n1])/min(diff(ns[c(n1,n2)]),-10^-6)
tmpwt <- tabNorm[n1,t1] + del2 * diff(tabNorm[c(n1,n2),t1]) + del1 * diff(tabNorm[n1,c(t1,t2)])
p.val =10^(-tmpwt*(t^0.71*log(n)))
# tmp = numeric(B)
# for (i in 1:B) {
# y = rnorm(n)
# tmpC = ddst.norm.Nk(y, base, Dmax = Dmax, n=length(y))
# l = ddst.IIC(tmpC, n, c)
# tmp[i] = tmpC[l]
# }
# p.val = mean(tmp > t)
result$p.value = p.val
}
result
}
#
# data
#
`MMnorm` <-
list(structure(22.1875398382093, .Dim = c(1L, 1L)), structure(c(22.1875398382093,
2.01931363023228e-08, 2.01931363023228e-08, 4.16508527502846), .Dim = c(2L,
2L)), structure(c(83.4756259149887, 7.8604632343874e-08, 15.4458059238418,
7.8604632343874e-08, 4.16508527502846, 1.47208485259075e-08,
15.4458059238418, 1.47208485259075e-08, 3.89264759121555), .Dim = c(3L,
3L)), structure(c(83.4756259149887, -3.11486631106693e-07, 15.4458059238418,
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-5.83343698116557e-08, 3.0796351270439, 15.4458059238418, -5.83343698116557e-08,
3.89264759121555, -5.46034419676308e-08, -2.91564738982522e-07,
3.0796351270439, -5.46034419676308e-08, 2.30180241422338), .Dim = c(4L,
4L)), structure(c(195.740517005162, -2.07574657321328e-06, 36.4704626100170,
-1.25498828263742e-06, 16.28123440358, -2.07574657321328e-06,
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3.04910431425500, -1.39720658808408e-07, 2.36118871296460), .Dim = c(5L,
5L)), structure(c(195.74051700562, -5.3817963869213e-05, 36.4704626101029,
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1.48523202547124, -2.18384459466602e-06, 1.86769120771211), .Dim = c(7L,
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0.00264560246232048, 4.20381674777824e-09, 3.96063626340037e-10,
-7.51192885672936e-10, 7.18518577969007e-11, -3.23222337783591e-10,
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6.02142335992539e-10, -1.14118847704958e-09, 7.03948899172246e-09,
0.014051283323416), .Dim = c(20L, 20L)))
`MMnorm12` <-
list(structure(c(0.977205023723124, 0), .Dim = c(2L, 1L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427), .Dim = c(2L, 2L)),
structure(c(0.977205023723124, 0, 2.23606816251288e-10, 1.23280888807427,
0.183008240031890, -3.30454577584812e-15), .Dim = 2:3), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013
), .Dim = c(2L, 4L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08), .Dim = c(2L, 5L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136), .Dim = c(2L, 6L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08), .Dim = c(2L,
7L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692), .Dim = c(2L, 8L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06), .Dim = c(2L, 9L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819
), .Dim = c(2L, 10L)), structure(c(0.977205023723124, 0,
2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05), .Dim = c(2L, 11L
)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043
), .Dim = c(2L, 12L)), structure(c(0.977205023723124, 0,
2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05, 0.00147644047823897,
0.11694220725043, 0.0137470668940847, -0.00303574979864906
), .Dim = c(2L, 13L)), structure(c(0.977205023723124, 0,
2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05, 0.00147644047823897,
0.11694220725043, 0.0137470668940847, -0.00303574979864906,
-0.00928615179284165, 0.103085593678959), .Dim = c(2L, 14L
)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412), .Dim = c(2L,
15L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412,
-1.98978137872651, -0.806390449226108), .Dim = c(2L, 16L)),
structure(c(0.977205023723124, 0, 2.23606816251288e-10, 1.23280888807427,
0.183008240031890, -3.30454577584812e-15, -1.79998266292003e-09,
0.521124588000013, 0.081698992568508, -1.3929854269323e-08,
-7.7519022437197e-08, 0.3045144998136, 0.0477295778133786,
8.9464549897464e-08, 2.22665619947903e-07, 0.205587566336692,
0.0318733652194164, 9.47446740454069e-06, 5.68335880297501e-05,
0.150729840706819, 0.0227469480714439, 8.52261690623742e-05,
0.00147644047823897, 0.11694220725043, 0.0137470668940847,
-0.00303574979864906, -0.00928615179284165, 0.103085593678959,
0.234330805463596, 0.0465189445727412, -1.98978137872651,
-0.806390449226108, 14.0490612099788, 7.9137204989213), .Dim = c(2L,
17L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412,
-1.98978137872651, -0.806390449226108, 14.0490612099788,
7.9137204989213, -87.5203589925242, -54.7276872419126), .Dim = c(2L,
18L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412,
-1.98978137872651, -0.806390449226108, 14.0490612099788,
7.9137204989213, -87.5203589925242, -54.7276872419126, 503.59029517106,
320.39056589639), .Dim = c(2L, 19L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05, 0.00147644047823897,
0.11694220725043, 0.0137470668940847, -0.00303574979864906,
-0.00928615179284165, 0.103085593678959, 0.234330805463596,
0.0465189445727412, -1.98978137872651, -0.806390449226108,
14.0490612099788, 7.9137204989213, -87.5203589925242, -54.7276872419126,
503.59029517106, 320.39056589639, 4131932941.74848, 4305467590.14660
), .Dim = c(2L, 20L)))
`ddst.polynomial.fun` <-
list(function (x)
{
w <- 0
w <- 1 + x * w
w
}, function (x)
{
w <- 0
w <- 3.46410161513775 + x * w
w <- -1.73205080756888 + x * w
w
}, function (x)
{
w <- 0
w <- 13.4164078649987 + x * w
w <- -13.4164078649987 + x * w
w <- 2.23606797749979 + x * w
w
}, function (x)
{
w <- 0
w <- 52.9150262212918 + x * w
w <- -79.3725393319377 + x * w
w <- 31.7490157327751 + x * w
w <- -2.64575131106459 + x * w
w
}, function (x)
{
w <- 0
w <- 210 + x * w
w <- -420 + x * w
w <- 270 + x * w
w <- -60 + x * w
w <- 3 + x * w
w
}, function (x)
{
w <- 0
w <- 835.78944716956 + x * w
w <- -2089.4736179239 + x * w
w <- 1857.30988259902 + x * w
w <- -696.491205974634 + x * w
w <- 99.498743710662 + x * w
w <- -3.3166247903554 + x * w
w
}, function (x)
{
w <- 0
w <- 3331.52937852873 + x * w
w <- -9994.58813558618 + x * w
w <- 11357.4865177116 + x * w
w <- -6057.3261427795 + x * w
w <- 1514.33153569488 + x * w
w <- -151.433153569488 + x * w
w <- 3.60555127546399 + x * w
w
}, function (x)
{
w <- 0
w <- 13292.0788441839 + x * w
w <- -46522.2759546435 + x * w
w <- 64415.4590141218 + x * w
w <- -44732.9576486957 + x * w
w <- 16266.5300540712 + x * w
w <- -2927.97540973281 + x * w
w <- 216.887067387615 + x * w
w <- -3.87298334620742 + x * w
w
}, function (x)
{
w <- 0
w <- 53064.3694016993 + x * w
w <- -212257.477606797 + x * w
w <- 346687.213424435 + x * w
w <- -297160.468649516 + x * w
w <- 142865.609927652 + x * w
w <- -38097.4959807072 + x * w
w <- 5195.11308827826 + x * w
w <- -296.863605044472 + x * w
w <- 4.12310562561767 + x * w
w
}, function (x)
{
w <- 0
w <- 211929.666634948 + x * w
w <- -953683.499857264 + x * w
w <- 1795168.94090779 + x * w
w <- -1832568.29384337 + x * w
w <- 1099540.97630602 + x * w
w <- -392693.205823580 + x * w
w <- 80552.4524766317 + x * w
w <- -8630.61990821054 + x * w
w <- 392.300904918661 + x * w
w <- -4.35889894354068 + x * w
w
}, function (x)
{
w <- 0
w <- 846658.355097261 + x * w
w <- -4233291.77548631 + x * w
w <- 9023595.6266945 + x * w
w <- -10694631.8538601 + x * w
w <- 7706425.89469334 + x * w
w <- -3467891.652612 + x * w
w <- 963303.236836668 + x * w
w <- -157273.997850885 + x * w
w <- 13610.2498140189 + x * w
w <- -504.083326445142 + x * w
w <- 4.58257569495585 + x * w
w
}, function (x)
{
w <- 0
w <- 3383133.02315354 + x * w
w <- -18607231.6273445 + x * w
w <- 44302932.4460583 + x * w
w <- -59808958.8021787 + x * w
w <- 50365438.9913083 + x * w
w <- -27421183.4508234 + x * w
w <- 9678064.74734945 + x * w
w <- -2160282.30967622 + x * w
w <- 288037.641290162 + x * w
w <- -20574.1172350116 + x * w
w <- 633.049761077279 + x * w
w <- -4.79583152331273 + x * w
w
}, function (x)
{
w <- 0
w <- 13520780 + x * w
w <- -81124680 + x * w
w <- 213393180 + x * w
w <- -323323000 + x * w
w <- 311775750 + x * w
w <- -199536480 + x * w
w <- 85765680 + x * w
w <- -24504480 + x * w
w <- 4504500 + x * w
w <- -500500 + x * w
w <- 30030.0000000000 + x * w
w <- -780 + x * w
w <- 5.00000000000002 + x * w
w
}, function (x)
{
w <- 0
w <- 54043102.8876026 + x * w
w <- -351280168.769417 + x * w
w <- 1011686886.05592 + x * w
w <- -1700196016.84398 + x * w
w <- 1848039148.74345 + x * w
w <- -1360828827.71109 + x * w
w <- 691214642.646902 + x * w
w <- -241925124.926416 + x * w
w <- 57298055.9036248 + x * w
w <- -8842292.57771988 + x * w
w <- 832215.772020695 + x * w
w <- -42556.4883419674 + x * w
w <- 945.699740932607 + x * w
w <- -5.19615242270665 + x * w
w
}, function (x)
{
w <- 0
w <- 216034502.501892 + x * w
w <- -1512241517.51324 + x * w
w <- 4732755860.36552 + x * w
w <- -8737395434.52097 + x * w
w <- 10572248475.7704 + x * w
w <- -8810207063.14198 + x * w
w <- 5171208493.58333 + x * w
w <- -2149073659.67100 + x * w
w <- 626813150.737374 + x * w
w <- -125362630.147475 + x * w
w <- 16495082.9141414 + x * w
w <- -1332935.99306193 + x * w
w <- 58805.9996939088 + x * w
w <- -1130.88460949825 + x * w
w <- 5.38516480713452 + x * w
w
}, function (x)
{
w <- 0
w <- 863657799.906573 + x * w
w <- -6477433499.2993 + x * w
w <- 21889258032.1149 + x * w
w <- -44039102469.374 + x * w
w <- 58718803292.4986 + x * w
w <- -54653655372.2487 + x * w
w <- 36435770248.1658 + x * w
w <- -17567246369.6514 + x * w
w <- 6110346563.357 + x * w
w <- -1512156472.74997 + x * w
w <- 259226823.899994 + x * w
w <- -29457593.6249993 + x * w
w <- 2067199.55263153 + x * w
w <- -79507.6751012128 + x * w
w <- 1336.26344707920 + x * w
w <- -5.56776436283004 + x * w
w
}, function (x)
{
w <- 0
w <- 3452943955.96051 + x * w
w <- -27623551647.6841 + x * w
w <- 100246760011.757 + x * w
w <- -218315166247.826 + x * w
w <- 318062612895.539 + x * w
w <- -327150116121.126 + x * w
w <- 244352864510.224 + x * w
w <- -134259815664.958 + x * w
w <- 54375225344.3081 + x * w
w <- -16111177879.795 + x * w
w <- 3432381374.39111 + x * w
w <- -510602187.92595 + x * w
w <- 50654978.9609077 + x * w
w <- -3117229.4745174 + x * w
w <- 105470.170190438 + x * w
w <- -1562.52103985834 + x * w
w <- 5.74456264653804 + x * w
w
}, function (x)
{
w <- 0
w <- 13805800579.8575 + x * w
w <- -117349304928.789 + x * w
w <- 455173061541.969 + x * w
w <- -1066811862988.99 + x * w
w <- 1686251009240.66 + x * w
w <- -1899842803744.48 + x * w
w <- 1572283699650.60 + x * w
w <- -970644528865.934 + x * w
w <- 449372467067.562 + x * w
w <- -155552007831.079 + x * w
w <- 39821314004.7563 + x * w
w <- -7391077220.57976 + x * w
w <- 964053550.510404 + x * w
w <- -84270415.2544059 + x * w
w <- 4586145.04785882 + x * w
w <- -137584.351435765 + x * w
w <- 1810.32041362848 + x * w
w <- -5.91607978309963 + x * w
w
}, function (x)
{
w <- 0
w <- 55201892960.2267 + x * w
w <- -496817036642.04 + x * w
w <- 2051144622707.85 + x * w
w <- -5147970817776.57 + x * w
w <- 8774950257573.7 + x * w
w <- -10749314065527.8 + x * w
w <- 9766849876742.99 + x * w
w <- -6697268486909.48 + x * w
w <- 3492971926362.27 + x * w
w <- -1386099970778.68 + x * w
w <- 415829991233.604 + x * w
w <- -93052865171.156 + x * w
w <- 15198634644.6222 + x * w
w <- -1753688612.84102 + x * w
w <- 136155948.201942 + x * w
w <- -6601500.51888205 + x * w
w <- 176825.906755769 + x * w
w <- -2080.30478536199 + x * w
w <- 6.08276253029823 + x * w
w
}, function (x)
{
w <- 0
w <- 220731101683.863 + x * w
w <- -2096945465996.7 + x * w
w <- 9181220688958.53 + x * w
w <- -24568266473231.6 + x * w
w <- 44924830122480.7 + x * w
w <- -59459333985636.2 + x * w
w <- 58858734652448 + x * w
w <- -44406813197605.9 + x * w
w <- 25784601211513.1 + x * w
w <- -11555321283678.1 + x * w
w <- 3984593546095.89 + x * w
w <- -1047896354655.09 + x * w
w <- 206991872524.462 + x * w
w <- -30007697496.1498 + x * w
w <- 3086506028.17541 + x * w
w <- -214340696.40107 + x * w
w <- 9319160.71309 + x * w
w <- -224257.878122487 + x * w
w <- 2373.09923939139 + x * w
w <- -6.24499799839841 + x * w
w
}, function (x)
{
w <- 0
w <- 882648449733.328 + x * w
w <- -8826484497333.28 + x * w
w <- 40850780814580.9 + x * w
w <- -116102219157230 + x * w
w <- 226713117138105 + x * w
w <- -322436433263082 + x * w
w <- 345467607067588 + x * w
w <- -284502735232131 + x * w
w <- 182124857023599 + x * w
w <- -91062428511799.6 + x * w
w <- 35543722096541.1 + x * w
w <- -10770824877739.7 + x * w
w <- 2507002342232.53 + x * w
w <- -440791620612.312 + x * w
w <- 57139654523.8183 + x * w
w <- -5274429648.35246 + x * w
w <- 329651853.022028 + x * w
w <- -12927523.6479227 + x * w
w <- 281033.122780928 + x * w
w <- -2689.31217972179 + x * w
w <- 6.40312423743286 + x * w
w
})
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ddst documentation built on May 2, 2019, 7:57 a.m.
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Defines functions `ddst.norm.test`
`ddst.norm.test` <-
function(x, base = ddst.base.legendre, c = 100, B=1000, compute.p = F, Dmax = 5, ...) {
# method.name = as.character(substitute(base))
# only Legendre is implemented yet
base = ddst.base.legendre
method.name = "ddst.base.legendre"
n = length(x)
if(n<5)
stop("length(x) should be at least 5")
er1 = mean(x)
sx = sort(x)
H = qnorm((1:n - 3/8)/(n+1/4))
er2 = mean((sx[-1] - sx[-n])/(H[-1] - H[-n]))
pp = (x-er1)/er2
tmpp = c(mean(pp), (mean(pp^2) - 1)/2)
maxN = max(min(Dmax, length(x)-2, 20),1)
u = numeric(maxN)
for (j in 1:maxN)
u[j] = ddst.phi(pnorm(x,er1,er2), j, base)
coord = numeric(Dmax)
for (k in 1:Dmax) {
korekta = u[1:k] - t(MMnorm12[[k]]) %*% tmpp
coord[k] = t(korekta) %*% MMnorm[[k]] %*% korekta * n
}
l = ddst.IIC(coord, n, c)
attr(l, "names") = "n. coord"
t = coord[l]
attr(t, "names") = "WT*"
result = list(statistic = t, parameter = l, method = "Data Driven Smooth Test for Normality")
result$data.name = paste(paste(as.character(substitute(x)), collapse=""), ", base: ", method.name, ", c: ", c, sep="")
class(result) = "htest"
if (compute.p) {
ns <- as.numeric(rownames(tabNorm))
ts <- as.numeric(colnames(tabNorm))
n1 <- min(nrow(tabNorm), nrow(tabNorm) + 1 - sum(ns >= n))
n2 <- max(1, sum(ns <= n))
t1 <- min(ncol(tabNorm), ncol(tabNorm) + 1 - sum(ts >= t))
t2 <- max(1, sum(ts <= t))
del1 <- (t - ts[t1])/min(diff(ts[c(t1,t2)]),-10^-6)
del2 <- (n - ns[n1])/min(diff(ns[c(n1,n2)]),-10^-6)
tmpwt <- tabNorm[n1,t1] + del2 * diff(tabNorm[c(n1,n2),t1]) + del1 * diff(tabNorm[n1,c(t1,t2)])
p.val =10^(-tmpwt*(t^0.71*log(n)))
# tmp = numeric(B)
# for (i in 1:B) {
# y = rnorm(n)
# tmpC = ddst.norm.Nk(y, base, Dmax = Dmax, n=length(y))
# l = ddst.IIC(tmpC, n, c)
# tmp[i] = tmpC[l]
# }
# p.val = mean(tmp > t)
result$p.value = p.val
}
result
}
#
# data
#
`MMnorm` <-
list(structure(22.1875398382093, .Dim = c(1L, 1L)), structure(c(22.1875398382093,
2.01931363023228e-08, 2.01931363023228e-08, 4.16508527502846), .Dim = c(2L,
2L)), structure(c(83.4756259149887, 7.8604632343874e-08, 15.4458059238418,
7.8604632343874e-08, 4.16508527502846, 1.47208485259075e-08,
15.4458059238418, 1.47208485259075e-08, 3.89264759121555), .Dim = c(3L,
3L)), structure(c(83.4756259149887, -3.11486631106693e-07, 15.4458059238418,
-2.91564738982522e-07, -3.11486631106693e-07, 8.28540092728336,
-5.83343698116557e-08, 3.0796351270439, 15.4458059238418, -5.83343698116557e-08,
3.89264759121555, -5.46034419676308e-08, -2.91564738982522e-07,
3.0796351270439, -5.46034419676308e-08, 2.30180241422338), .Dim = c(4L,
4L)), structure(c(195.740517005162, -2.07574657321328e-06, 36.4704626100170,
-1.25498828263742e-06, 16.28123440358, -2.07574657321328e-06,
8.2854009272834, -3.88740066799939e-07, 3.07963512704392, -2.55862089985123e-07,
36.4704626100170, -3.88740066799939e-07, 7.83008684296238, -2.35030724727411e-07,
3.04910431425500, -1.25498828263742e-06, 3.07963512704392, -2.35030724727411e-07,
2.30180241422338, -1.39720658808408e-07, 16.28123440358, -2.55862089985123e-07,
3.04910431425500, -1.39720658808408e-07, 2.36118871296460), .Dim = c(5L,
5L)), structure(c(195.74051700562, -5.3817963869213e-05, 36.4704626101029,
-2.31271064442009e-05, 16.2812344036189, -2.87527480450007e-05,
-5.3817963869213e-05, 14.1151813391882, -1.00788786846730e-05,
5.54396025048634, -4.64763013466494e-06, 3.23956366968714, 36.4704626101029,
-1.00788786846730e-05, 7.83008684297847, -4.33118021209071e-06,
3.04910431426229, -5.38473472458586e-06, -2.31271064442009e-05,
5.54396025048634, -4.33118021209071e-06, 3.34350516886373, -1.99617897527181e-06,
1.36940631998744, 16.2812344036189, -4.64763013466494e-06, 3.04910431426229,
-1.99617897527181e-06, 2.36118871296791, -2.44047137250392e-06,
-2.87527480450007e-05, 3.23956366968714, -5.38473472458586e-06,
1.36940631998744, -2.44047137250391e-06, 1.80020035549295), .Dim = c(6L,
6L)), structure(c(364.715151396685, -8.36073153539962e-05, 68.1155623580781,
-3.60470490628969e-05, 30.4083183463369, -4.95248263314955e-05,
17.7649215866143, -8.36073153539962e-05, 14.1151813391934, -1.56577456108281e-05,
5.54396025048862, -7.1381617493137e-06, 3.23956366969081, -3.13186351993226e-06,
68.1155623580781, -1.56577456108281e-05, 13.7564931445402, -6.75079114588642e-06,
5.69478531914434, -9.27487179585528e-06, 3.32696512496847, -3.60470490628969e-05,
5.54396025048861, -6.75079114588642e-06, 3.34350516886471, -3.07634769152424e-06,
1.36940631998903, -1.35832084118318e-06, 30.4083183463369, -7.1381617493137e-06,
5.69478531914434, -3.07634769152424e-06, 3.54228019124693, -4.17711601550329e-06,
1.48523202547124, -4.95248263314955e-05, 3.23956366969081, -9.27487179585528e-06,
1.36940631998903, -4.17711601550329e-06, 1.80020035549551, -2.18384459466602e-06,
17.7649215866143, -3.13186351993226e-06, 3.32696512496847, -1.35832084118318e-06,
1.48523202547124, -2.18384459466602e-06, 1.86769120771211), .Dim = c(7L,
7L)), structure(c(364.715151404168, 0.000153673123723023, 68.1155623594796,
6.42545242390361e-05, 30.4083183469599, 9.08550242207575e-06,
17.7649215869971, 0.000108489210505120, 0.000153673123723023,
21.6451868798598, 2.8779475315759e-05, 8.72699297597999, 1.26145290270224e-05,
5.09954042113057, 9.00406362783467e-06, 3.44286431441111, 68.1155623594796,
2.8779475315759e-05, 13.7564931448027, 1.20334086366145e-05,
5.69478531926101, 1.70150762055735e-06, 3.32696512504015, 2.03175577140692e-05,
6.42545242390361e-05, 8.72699297597999, 1.20334086366145e-05,
4.68901511262663, 5.2733754020427e-06, 2.15564304139812, 3.77169573807455e-06,
1.45534418573975, 30.4083183469599, 1.26145290270224e-05, 5.69478531926101,
5.2733754020427e-06, 3.54228019129879, 7.01970118490705e-07,
1.48523202550310, 9.0313126358506e-06, 9.08550242207575e-06,
5.09954042113057, 1.70150762055735e-06, 2.15564304139812, 7.01970118490705e-07,
2.25963076324395, 8.13834786857419e-07, 0.850417379985028, 17.7649215869971,
9.00406362783467e-06, 3.32696512504015, 3.77169573807455e-06,
1.48523202550310, 8.13834786857419e-07, 1.86769120773168, 5.54878084401015e-06,
0.000108489210505120, 3.44286431441111, 2.03175577140692e-05,
1.45534418573975, 9.0313126358506e-06, 0.850417379985028, 5.54878084401015e-06,
1.57414421854416), .Dim = c(8L, 8L)), structure(c(594.280145860191,
0.00332096015316808, 111.107856287996, 0.00140266349755414, 49.6010448687294,
0.00077320915692121, 28.9775535325382, 0.000688977032408123,
19.3509389865028, 0.00332096015316808, 21.6451869235586, 0.0006219401845456,
8.72699299444589, 0.000277414804505137, 5.09954043167311, 0.000163703711155572,
3.44286432242005, 0.000266983118243996, 111.107856287996, 0.0006219401845456,
21.8079704251945, 0.000262686920134203, 9.28914578292315, 0.000144804461229855,
5.42683566260733, 0.000129029703136393, 3.62399005419742, 0.00140266349755414,
8.72699299444589, 0.000262686920134203, 4.68901512042982, 0.000117170737889685,
2.15564304585311, 6.9143540630858e-05, 1.45534418912411, 0.000112819772208653,
49.6010448687294, 0.000277414804505137, 9.28914578292315, 0.000117170737889685,
5.14688350728912, 6.45863457149036e-05, 2.42266144077597, 5.75628583159839e-05,
1.61783063130970, 0.00077320915692121, 5.09954043167311, 0.000144804461229855,
2.15564304585311, 6.45863457149036e-05, 2.25963076578739, 3.81358895673912e-05,
0.850417381917223, 6.44109972053659e-05, 28.9775535325382, 0.000163703711155572,
5.42683566260733, 6.9143540630858e-05, 2.42266144077597, 3.81358895673912e-05,
2.41534924873259, 3.39015195152107e-05, 0.945156979052586, 0.000688977032408123,
3.44286432242005, 0.000129029703136393, 1.45534418912411, 5.75628583159839e-05,
0.850417381917223, 3.39015195152107e-05, 1.57414422001201, 4.89316084565545e-05,
19.3509389865028, 0.000266983118243996, 3.62399005419742, 0.000112819772208653,
1.61783063130970, 6.44109972053659e-05, 0.945156979052586, 4.89316084565545e-05,
1.63116698408955), .Dim = c(9L, 9L)), structure(c(594.281908667211,
0.130779031350136, 111.108186421594, 0.0552808724220031, 49.601192246349,
0.0322564593189654, 28.977639642486, 0.0219443357631424, 19.3509974632924,
0.0504946081258542, 0.130779031350136, 30.8609206348895, 0.0244919334012417,
12.6226052662169, 0.0109334122679083, 7.37590666831766, 0.0063898009143201,
4.97971266918774, 0.00449509132352050, 3.65096425809516, 111.108186421594,
0.0244919334012417, 21.8080322516969, 0.0103528480960937, 9.28917338339402,
0.00604090002230419, 5.42685178903895, 0.00410967419238971, 3.62400100556801,
0.00945648982543631, 0.0552808724220031, 12.6226052662169, 0.0103528480960937,
6.33574184315555, 0.00462160150669055, 3.11789309824064, 0.00270099700228912,
2.10499026908388, 0.00190009691440726, 1.54331077840778, 49.601192246349,
0.0109334122679083, 9.28917338339402, 0.00462160150669055, 5.1468958286394,
0.00269671023332643, 2.42266863990723, 0.00183459468212579, 1.61783552019996,
0.00422154839667336, 0.0322564593189654, 7.37590666831766, 0.00604090002230419,
3.11789309824064, 0.00269671023332643, 2.82191298938985, 0.00157603595301269,
1.23003226631038, 0.00110879043186041, 0.901819869003527, 28.977639642486,
0.00638980091432011, 5.42685178903895, 0.00270099700228912, 2.42266863990723,
0.00157603595301269, 2.41535345504844, 0.00107218750880477, 0.945159835538435,
0.00246657065711778, 0.0219443357631424, 4.97971266918774, 0.00410967419238971,
2.10499026908388, 0.00183459468212579, 1.23003226631038, 0.00107218750880477,
1.83043448565397, 0.000754025886218155, 0.608847711958374, 19.3509974632924,
0.00449509132352050, 3.62400100556801, 0.00190009691440726, 1.61783552019996,
0.00110879043186041, 0.945159835538435, 0.000754025886218155,
1.6311689239133, 0.00167503450298739, 0.0504946081258542, 3.65096425809516,
0.00945648982543631, 1.54331077840778, 0.00422154839667336, 0.901819869003527,
0.00246657065711777, 0.608847711958374, 0.00167503450298739,
1.44638944997938), .Dim = c(10L, 10L)), structure(c(875.35991599822,
0.234753309658509, 163.747694185620, 0.0992316272241327, 73.1006519026939,
0.0579166958257177, 42.7063191971557, 0.0393474894274913, 28.5188819360194,
0.0795543625397017, 20.3529811872338, 0.234753309658509, 30.8609590962783,
0.0439639471750806, 12.6226215241520, 0.0196261569675241, 7.37591616036079,
0.0114682115746842, 4.97971910683243, 0.00788640671214772, 3.65097500766259,
0.00752882287184567, 163.747694185620, 0.0439639471750806, 31.6662129181615,
0.0185838232641971, 13.6900868549836, 0.0108464777750782, 7.99792072776532,
0.00736888842665815, 5.34093692120329, 0.0148987198405616, 3.8116497316874,
0.0992316272241327, 12.6226215241520, 0.0185838232641971, 6.3357487155141,
0.00829609386255197, 3.11789711060281, 0.00484768159918726, 2.10499299032752,
0.00333363291511101, 1.54331532233547, 0.00318249333751333, 73.1006519026939,
0.0196261569675241, 13.6900868549836, 0.00829609386255197, 7.11156253943566,
0.00484202817651426, 3.570451614439, 0.00328958118680428, 2.38431431143163,
0.006651082222375, 1.70160613004667, 0.0579166958257177, 7.37591616036079,
0.0108464777750781, 3.11789711060281, 0.00484202817651426, 2.82191533196991,
0.00282935764702690, 1.23003385508298, 0.00194574699801294, 0.901822521933145,
0.00185806892485493, 42.7063191971557, 0.0114682115746842, 7.99792072776532,
0.00484768159918726, 3.570451614439, 0.00282935764702690, 3.0859026883538,
0.00192220890381615, 1.39294637463994, 0.00388593484029732, 0.9940996784309,
0.0393474894274913, 4.97971910683243, 0.00736888842665815, 2.10499299032752,
0.00328958118680428, 1.23003385508298, 0.00192220890381615, 1.83043556318316,
0.00132166226506858, 0.608849511214659, 0.00126016995243566,
28.5188819360194, 0.00788640671214772, 5.34093692120329, 0.00333363291511102,
2.38431431143163, 0.00194574699801294, 1.39294637463994, 0.00132166226506858,
1.93019660844604, 0.00262287269851804, 0.66385051599005, 0.0795543625397017,
3.65097500766259, 0.0148987198405616, 1.54331532233547, 0.006651082222375,
0.901822521933145, 0.00388593484029732, 0.608849511214659, 0.00262287269851804,
1.44639245437426, 0.00210422950022608, 20.3529811872338, 0.00752882287184567,
3.8116497316874, 0.00318249333751333, 1.70160613004667, 0.00185806892485493,
0.9940996784309, 0.00126016995243566, 0.66385051599005, 0.00210422950022608,
1.47376825081888), .Dim = c(11L, 11L)), structure(c(877.834413401248,
5.45319119108603, 164.211111179698, 2.30513418953969, 73.3075316079886,
1.3469159677134, 42.8271813330919, 0.909593193760506, 28.5996323910902,
0.717732540808027, 20.4109422071954, 1.84207308924979, 5.45319119108603,
41.8660601276342, 1.02125848538486, 17.2746229688772, 0.455912285086717,
10.0942712579571, 0.266352919809908, 6.81496983049696, 0.178180072475712,
4.99682131022092, 0.129762122386862, 3.88472583461895, 164.211111179698,
1.02125848538486, 31.7530003644273, 0.431699122316912, 13.7288307110272,
0.252246677757455, 8.02055545256433, 0.170346084489884, 5.35605964192773,
0.134414954813103, 3.82250451036343, 0.344978326850289, 2.30513418953968,
17.2746229688772, 0.431699122316912, 8.30221112054473, 0.192719998063092,
4.26698168558885, 0.112590811586839, 2.88077769176687, 0.0753190128677788,
2.11222231610507, 0.0548521222048209, 1.64212487859206, 73.3075316079886,
0.455912285086717, 13.7288307110272, 0.192719998063092, 7.12885866284659,
0.112608473664316, 3.58055626156175, 0.0760462446716918, 2.39106543201354,
0.0600058011580506, 1.70645194589338, 0.154006036688034, 1.3469159677134,
10.0942712579571, 0.252246677757455, 4.26698168558885, 0.112608473664316,
3.49337254218303, 0.0657880841463511, 1.68335665019649, 0.0440097546884277,
1.2342581939653, 0.0320507506536225, 0.959560865930497, 42.8271813330919,
0.266352919809908, 8.02055545256433, 0.112590811586839, 3.58055626156175,
0.0657880841463511, 3.09180597032337, 0.0444277110256887, 1.39689047757807,
0.0350565384703461, 0.99693067460209, 0.0899725689123183, 0.909593193760506,
6.81496983049696, 0.170346084489884, 2.88077769176687, 0.0760462446716918,
1.68335665019649, 0.0444277110256887, 2.13648865702706, 0.0297204541014723,
0.833287741602, 0.0216442400987866, 0.647831026622058, 28.5996323910902,
0.178180072475712, 5.35605964192773, 0.0753190128677788, 2.39106543201354,
0.0440097546884277, 1.39689047757807, 0.0297204541014723, 1.93283174396332,
0.023448587952198, 0.665741962201525, 0.0601125060986542, 0.717732540808027,
4.99682131022092, 0.134414954813103, 2.11222231610507, 0.0600058011580506,
1.2342581939653, 0.0350565384703461, 0.833287741602, 0.023448587952198,
1.61097997292126, 0.0170525006458588, 0.475074593688724, 20.4109422071954,
0.129762122386862, 3.82250451036343, 0.0548521222048209, 1.70645194589338,
0.0320507506536225, 0.99693067460209, 0.0216442400987866, 0.665741962201525,
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-6.58522125718264e-11, 6.3584693066332e-11, -2.85382384390687e-10,
6.02142335992539e-10, -1.14118847704958e-09, 7.03948899172246e-09,
0.014051283323416), .Dim = c(20L, 20L)))
`MMnorm12` <-
list(structure(c(0.977205023723124, 0), .Dim = c(2L, 1L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427), .Dim = c(2L, 2L)),
structure(c(0.977205023723124, 0, 2.23606816251288e-10, 1.23280888807427,
0.183008240031890, -3.30454577584812e-15), .Dim = 2:3), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013
), .Dim = c(2L, 4L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08), .Dim = c(2L, 5L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136), .Dim = c(2L, 6L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08), .Dim = c(2L,
7L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692), .Dim = c(2L, 8L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06), .Dim = c(2L, 9L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819
), .Dim = c(2L, 10L)), structure(c(0.977205023723124, 0,
2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05), .Dim = c(2L, 11L
)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043
), .Dim = c(2L, 12L)), structure(c(0.977205023723124, 0,
2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05, 0.00147644047823897,
0.11694220725043, 0.0137470668940847, -0.00303574979864906
), .Dim = c(2L, 13L)), structure(c(0.977205023723124, 0,
2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05, 0.00147644047823897,
0.11694220725043, 0.0137470668940847, -0.00303574979864906,
-0.00928615179284165, 0.103085593678959), .Dim = c(2L, 14L
)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412), .Dim = c(2L,
15L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412,
-1.98978137872651, -0.806390449226108), .Dim = c(2L, 16L)),
structure(c(0.977205023723124, 0, 2.23606816251288e-10, 1.23280888807427,
0.183008240031890, -3.30454577584812e-15, -1.79998266292003e-09,
0.521124588000013, 0.081698992568508, -1.3929854269323e-08,
-7.7519022437197e-08, 0.3045144998136, 0.0477295778133786,
8.9464549897464e-08, 2.22665619947903e-07, 0.205587566336692,
0.0318733652194164, 9.47446740454069e-06, 5.68335880297501e-05,
0.150729840706819, 0.0227469480714439, 8.52261690623742e-05,
0.00147644047823897, 0.11694220725043, 0.0137470668940847,
-0.00303574979864906, -0.00928615179284165, 0.103085593678959,
0.234330805463596, 0.0465189445727412, -1.98978137872651,
-0.806390449226108, 14.0490612099788, 7.9137204989213), .Dim = c(2L,
17L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412,
-1.98978137872651, -0.806390449226108, 14.0490612099788,
7.9137204989213, -87.5203589925242, -54.7276872419126), .Dim = c(2L,
18L)), structure(c(0.977205023723124, 0, 2.23606816251288e-10,
1.23280888807427, 0.183008240031890, -3.30454577584812e-15,
-1.79998266292003e-09, 0.521124588000013, 0.081698992568508,
-1.3929854269323e-08, -7.7519022437197e-08, 0.3045144998136,
0.0477295778133786, 8.9464549897464e-08, 2.22665619947903e-07,
0.205587566336692, 0.0318733652194164, 9.47446740454069e-06,
5.68335880297501e-05, 0.150729840706819, 0.0227469480714439,
8.52261690623742e-05, 0.00147644047823897, 0.11694220725043,
0.0137470668940847, -0.00303574979864906, -0.00928615179284165,
0.103085593678959, 0.234330805463596, 0.0465189445727412,
-1.98978137872651, -0.806390449226108, 14.0490612099788,
7.9137204989213, -87.5203589925242, -54.7276872419126, 503.59029517106,
320.39056589639), .Dim = c(2L, 19L)), structure(c(0.977205023723124,
0, 2.23606816251288e-10, 1.23280888807427, 0.183008240031890,
-3.30454577584812e-15, -1.79998266292003e-09, 0.521124588000013,
0.081698992568508, -1.3929854269323e-08, -7.7519022437197e-08,
0.3045144998136, 0.0477295778133786, 8.9464549897464e-08,
2.22665619947903e-07, 0.205587566336692, 0.0318733652194164,
9.47446740454069e-06, 5.68335880297501e-05, 0.150729840706819,
0.0227469480714439, 8.52261690623742e-05, 0.00147644047823897,
0.11694220725043, 0.0137470668940847, -0.00303574979864906,
-0.00928615179284165, 0.103085593678959, 0.234330805463596,
0.0465189445727412, -1.98978137872651, -0.806390449226108,
14.0490612099788, 7.9137204989213, -87.5203589925242, -54.7276872419126,
503.59029517106, 320.39056589639, 4131932941.74848, 4305467590.14660
), .Dim = c(2L, 20L)))
`ddst.polynomial.fun` <-
list(function (x)
{
w <- 0
w <- 1 + x * w
w
}, function (x)
{
w <- 0
w <- 3.46410161513775 + x * w
w <- -1.73205080756888 + x * w
w
}, function (x)
{
w <- 0
w <- 13.4164078649987 + x * w
w <- -13.4164078649987 + x * w
w <- 2.23606797749979 + x * w
w
}, function (x)
{
w <- 0
w <- 52.9150262212918 + x * w
w <- -79.3725393319377 + x * w
w <- 31.7490157327751 + x * w
w <- -2.64575131106459 + x * w
w
}, function (x)
{
w <- 0
w <- 210 + x * w
w <- -420 + x * w
w <- 270 + x * w
w <- -60 + x * w
w <- 3 + x * w
w
}, function (x)
{
w <- 0
w <- 835.78944716956 + x * w
w <- -2089.4736179239 + x * w
w <- 1857.30988259902 + x * w
w <- -696.491205974634 + x * w
w <- 99.498743710662 + x * w
w <- -3.3166247903554 + x * w
w
}, function (x)
{
w <- 0
w <- 3331.52937852873 + x * w
w <- -9994.58813558618 + x * w
w <- 11357.4865177116 + x * w
w <- -6057.3261427795 + x * w
w <- 1514.33153569488 + x * w
w <- -151.433153569488 + x * w
w <- 3.60555127546399 + x * w
w
}, function (x)
{
w <- 0
w <- 13292.0788441839 + x * w
w <- -46522.2759546435 + x * w
w <- 64415.4590141218 + x * w
w <- -44732.9576486957 + x * w
w <- 16266.5300540712 + x * w
w <- -2927.97540973281 + x * w
w <- 216.887067387615 + x * w
w <- -3.87298334620742 + x * w
w
}, function (x)
{
w <- 0
w <- 53064.3694016993 + x * w
w <- -212257.477606797 + x * w
w <- 346687.213424435 + x * w
w <- -297160.468649516 + x * w
w <- 142865.609927652 + x * w
w <- -38097.4959807072 + x * w
w <- 5195.11308827826 + x * w
w <- -296.863605044472 + x * w
w <- 4.12310562561767 + x * w
w
}, function (x)
{
w <- 0
w <- 211929.666634948 + x * w
w <- -953683.499857264 + x * w
w <- 1795168.94090779 + x * w
w <- -1832568.29384337 + x * w
w <- 1099540.97630602 + x * w
w <- -392693.205823580 + x * w
w <- 80552.4524766317 + x * w
w <- -8630.61990821054 + x * w
w <- 392.300904918661 + x * w
w <- -4.35889894354068 + x * w
w
}, function (x)
{
w <- 0
w <- 846658.355097261 + x * w
w <- -4233291.77548631 + x * w
w <- 9023595.6266945 + x * w
w <- -10694631.8538601 + x * w
w <- 7706425.89469334 + x * w
w <- -3467891.652612 + x * w
w <- 963303.236836668 + x * w
w <- -157273.997850885 + x * w
w <- 13610.2498140189 + x * w
w <- -504.083326445142 + x * w
w <- 4.58257569495585 + x * w
w
}, function (x)
{
w <- 0
w <- 3383133.02315354 + x * w
w <- -18607231.6273445 + x * w
w <- 44302932.4460583 + x * w
w <- -59808958.8021787 + x * w
w <- 50365438.9913083 + x * w
w <- -27421183.4508234 + x * w
w <- 9678064.74734945 + x * w
w <- -2160282.30967622 + x * w
w <- 288037.641290162 + x * w
w <- -20574.1172350116 + x * w
w <- 633.049761077279 + x * w
w <- -4.79583152331273 + x * w
w
}, function (x)
{
w <- 0
w <- 13520780 + x * w
w <- -81124680 + x * w
w <- 213393180 + x * w
w <- -323323000 + x * w
w <- 311775750 + x * w
w <- -199536480 + x * w
w <- 85765680 + x * w
w <- -24504480 + x * w
w <- 4504500 + x * w
w <- -500500 + x * w
w <- 30030.0000000000 + x * w
w <- -780 + x * w
w <- 5.00000000000002 + x * w
w
}, function (x)
{
w <- 0
w <- 54043102.8876026 + x * w
w <- -351280168.769417 + x * w
w <- 1011686886.05592 + x * w
w <- -1700196016.84398 + x * w
w <- 1848039148.74345 + x * w
w <- -1360828827.71109 + x * w
w <- 691214642.646902 + x * w
w <- -241925124.926416 + x * w
w <- 57298055.9036248 + x * w
w <- -8842292.57771988 + x * w
w <- 832215.772020695 + x * w
w <- -42556.4883419674 + x * w
w <- 945.699740932607 + x * w
w <- -5.19615242270665 + x * w
w
}, function (x)
{
w <- 0
w <- 216034502.501892 + x * w
w <- -1512241517.51324 + x * w
w <- 4732755860.36552 + x * w
w <- -8737395434.52097 + x * w
w <- 10572248475.7704 + x * w
w <- -8810207063.14198 + x * w
w <- 5171208493.58333 + x * w
w <- -2149073659.67100 + x * w
w <- 626813150.737374 + x * w
w <- -125362630.147475 + x * w
w <- 16495082.9141414 + x * w
w <- -1332935.99306193 + x * w
w <- 58805.9996939088 + x * w
w <- -1130.88460949825 + x * w
w <- 5.38516480713452 + x * w
w
}, function (x)
{
w <- 0
w <- 863657799.906573 + x * w
w <- -6477433499.2993 + x * w
w <- 21889258032.1149 + x * w
w <- -44039102469.374 + x * w
w <- 58718803292.4986 + x * w
w <- -54653655372.2487 + x * w
w <- 36435770248.1658 + x * w
w <- -17567246369.6514 + x * w
w <- 6110346563.357 + x * w
w <- -1512156472.74997 + x * w
w <- 259226823.899994 + x * w
w <- -29457593.6249993 + x * w
w <- 2067199.55263153 + x * w
w <- -79507.6751012128 + x * w
w <- 1336.26344707920 + x * w
w <- -5.56776436283004 + x * w
w
}, function (x)
{
w <- 0
w <- 3452943955.96051 + x * w
w <- -27623551647.6841 + x * w
w <- 100246760011.757 + x * w
w <- -218315166247.826 + x * w
w <- 318062612895.539 + x * w
w <- -327150116121.126 + x * w
w <- 244352864510.224 + x * w
w <- -134259815664.958 + x * w
w <- 54375225344.3081 + x * w
w <- -16111177879.795 + x * w
w <- 3432381374.39111 + x * w
w <- -510602187.92595 + x * w
w <- 50654978.9609077 + x * w
w <- -3117229.4745174 + x * w
w <- 105470.170190438 + x * w
w <- -1562.52103985834 + x * w
w <- 5.74456264653804 + x * w
w
}, function (x)
{
w <- 0
w <- 13805800579.8575 + x * w
w <- -117349304928.789 + x * w
w <- 455173061541.969 + x * w
w <- -1066811862988.99 + x * w
w <- 1686251009240.66 + x * w
w <- -1899842803744.48 + x * w
w <- 1572283699650.60 + x * w
w <- -970644528865.934 + x * w
w <- 449372467067.562 + x * w
w <- -155552007831.079 + x * w
w <- 39821314004.7563 + x * w
w <- -7391077220.57976 + x * w
w <- 964053550.510404 + x * w
w <- -84270415.2544059 + x * w
w <- 4586145.04785882 + x * w
w <- -137584.351435765 + x * w
w <- 1810.32041362848 + x * w
w <- -5.91607978309963 + x * w
w
}, function (x)
{
w <- 0
w <- 55201892960.2267 + x * w
w <- -496817036642.04 + x * w
w <- 2051144622707.85 + x * w
w <- -5147970817776.57 + x * w
w <- 8774950257573.7 + x * w
w <- -10749314065527.8 + x * w
w <- 9766849876742.99 + x * w
w <- -6697268486909.48 + x * w
w <- 3492971926362.27 + x * w
w <- -1386099970778.68 + x * w
w <- 415829991233.604 + x * w
w <- -93052865171.156 + x * w
w <- 15198634644.6222 + x * w
w <- -1753688612.84102 + x * w
w <- 136155948.201942 + x * w
w <- -6601500.51888205 + x * w
w <- 176825.906755769 + x * w
w <- -2080.30478536199 + x * w
w <- 6.08276253029823 + x * w
w
}, function (x)
{
w <- 0
w <- 220731101683.863 + x * w
w <- -2096945465996.7 + x * w
w <- 9181220688958.53 + x * w
w <- -24568266473231.6 + x * w
w <- 44924830122480.7 + x * w
w <- -59459333985636.2 + x * w
w <- 58858734652448 + x * w
w <- -44406813197605.9 + x * w
w <- 25784601211513.1 + x * w
w <- -11555321283678.1 + x * w
w <- 3984593546095.89 + x * w
w <- -1047896354655.09 + x * w
w <- 206991872524.462 + x * w
w <- -30007697496.1498 + x * w
w <- 3086506028.17541 + x * w
w <- -214340696.40107 + x * w
w <- 9319160.71309 + x * w
w <- -224257.878122487 + x * w
w <- 2373.09923939139 + x * w
w <- -6.24499799839841 + x * w
w
}, function (x)
{
w <- 0
w <- 882648449733.328 + x * w
w <- -8826484497333.28 + x * w
w <- 40850780814580.9 + x * w
w <- -116102219157230 + x * w
w <- 226713117138105 + x * w
w <- -322436433263082 + x * w
w <- 345467607067588 + x * w
w <- -284502735232131 + x * w
w <- 182124857023599 + x * w
w <- -91062428511799.6 + x * w
w <- 35543722096541.1 + x * w
w <- -10770824877739.7 + x * w
w <- 2507002342232.53 + x * w
w <- -440791620612.312 + x * w
w <- 57139654523.8183 + x * w
w <- -5274429648.35246 + x * w
w <- 329651853.022028 + x * w
w <- -12927523.6479227 + x * w
w <- 281033.122780928 + x * w
w <- -2689.31217972179 + x * w
w <- 6.40312423743286 + x * w
w
})
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