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####Time Series Assignment #####
rm(list = ls())
mydata = read.csv(file.choose(), header = T)
attach(mydata)
library(tseries)## Warning: package 'tseries' was built under R version 3.4.3library(TSA)## Warning: package 'TSA' was built under R version 3.4.3## Loading required package: leaps## Loading required package: locfit## Warning: package 'locfit' was built under R version 3.4.3## locfit 1.5-9.1 2013-03-22## Loading required package: mgcv## Loading required package: nlme## Warning: package 'nlme' was built under R version 3.4.3## This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(forecast)## Warning: package 'forecast' was built under R version 3.4.3##
## Attaching package: 'forecast'## The following object is masked from 'package:nlme':
##
## getResponselibrary(fpp) ## Warning: package 'fpp' was built under R version 3.4.3## Loading required package: fma## Warning: package 'fma' was built under R version 3.4.3## Loading required package: expsmooth## Warning: package 'expsmooth' was built under R version 3.4.3## Loading required package: lmtest## Warning: package 'lmtest' was built under R version 3.4.3## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(astsa)## Warning: package 'astsa' was built under R version 3.4.3##
## Attaching package: 'astsa'## The following object is masked from 'package:fpp':
##
## oil## The following objects are masked from 'package:fma':
##
## chicken, sales## The following object is masked from 'package:forecast':
##
## gaslibrary(DT)## Warning: package 'DT' was built under R version 3.4.3names(mydata)## [1] "OzBeer"#Plotting a time series for quarterly data. Frequency given in question is give as 4
beer.ts = ts(OzBeer, frequency = 4)
plot(beer.ts, col= "blue", main= "quarterly Beer Sales Data", xlab = "Years", ylab= "ML")
#Just looking how the seasons are distributed
seasonplot(beer.ts, year.labels = F, year.labels.left = F, col=1:40, pch=16,
main= "Quarterly Beer Sales ",
xlab = "quarters")
#There is some seasonality involved
#Visual representation via box plot
boxplot(beer.ts~cycle(beer.ts), col="blue", main="Quarterly Beer Sales")
#Splitting the screen into 2*2 matrix
par(mfrow = c(2,2))
#Using Moving averages doing EDA
plot(beer.ts, col="gray", main = "1 Year Moving Average Smoothing")
lines(ma(beer.ts, order = 3), col = "red", lwd=3)
plot(beer.ts, col="gray", main = "3 Year Moving Average Smoothing")
lines(ma(beer.ts, order = 12), col = "blue", lwd=3)
plot(beer.ts, col="gray", main = "5 Year Moving Average Smoothing")
lines(ma(beer.ts, order = 36), col = "green", lwd=3)
plot(beer.ts, col="gray", main = "6 Year Moving Average Smoothing")
####Holt Winters Method####
#Doing a as seasonal variation is varying with time
fit = hw(beer.ts, seasonal = "multiplicative")
lines(fitted(fit),col="red")
fitted(fit)## Qtr1 Qtr2 Qtr3 Qtr4
## 1 262.8866 226.7882 238.4577 301.2943
## 2 263.5998 225.2712 237.7963 301.5312
## 3 265.1197 227.8819 241.6990 307.3475
## 4 269.9930 231.1087 243.9793 311.0253
## 5 272.8780 235.3873 248.6318 318.2765
## 6 279.0451 241.2209 255.2671 325.9709
## 7 287.6819 247.1007 262.5403 336.2945
## 8 296.9251 255.8731 271.9620 348.5675
## 9 308.5445 267.0340 285.3296 368.1862
## 10 326.1079 283.0524 303.1741 390.5147
## 11 345.6767 298.7547 317.8096 406.3450
## 12 358.0190 308.4920 328.9435 420.7172
## 13 369.3112 320.2329 340.8569 434.7004
## 14 383.3970 330.5917 351.6527 451.1784
## 15 397.3572 341.8388 364.9801 468.5601
## 16 413.3036 356.6229 381.1280 488.4571
## 17 431.0477 371.3347 395.7600 506.5171
## 18 446.5091 386.3690 411.6686 529.5638#plotting the model
forecast(fit,8)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 19 Q1 467.4689 449.6426 485.2953 440.2059 494.7320
## 19 Q2 404.1306 388.6368 419.6244 380.4349 427.8264
## 19 Q3 430.8064 414.1248 447.4881 405.2941 456.3188
## 19 Q4 552.4171 530.6915 574.1427 519.1906 585.6435
## 20 Q1 487.6920 468.0895 507.2945 457.7126 517.6715
## 20 Q2 421.4266 404.0029 438.8502 394.7794 448.0738
## 20 Q3 449.0489 429.8322 468.2656 419.6595 478.4384
## 20 Q4 575.5641 549.9233 601.2049 536.3498 614.7783plot(fit)
fit$model## Holt-Winters' multiplicative method
##
## Call:
## hw(y = beer.ts, seasonal = "multiplicative")
##
## Smoothing parameters:
## alpha = 0.0643
## beta = 0.0406
## gamma = 1e-04
##
## Initial states:
## l = 256.4184
## b = 0.022
## s=1.1734 0.9247 0.8768 1.0251
##
## sigma: 0.0298
##
## AIC AICc BIC
## 650.6460 653.5492 671.1360attributes(fit)## $names
## [1] "model" "mean" "level" "x" "upper"
## [6] "lower" "fitted" "method" "series" "residuals"
##
## $class
## [1] "forecast"#AIc - 650.64
#Resetting to a 1*1 matrix
par(mfrow=c(1,1))
#######################
###ARIMA###
#Visual representation of log plot to see how correlation is there in dataset
lag.plot(beer.ts, lags = 16,do.lines = T)
#We can see the correlation is declining from lag 1 to lag 16
#which makes sense since the correlation normally diminished by time.
#Seasonal effect is also visible in the plots
#Differencing is done to make the dataset linear
d_beer = diff(log(beer.ts))
#Plotting the differenced dataset
plot(d_beer, main="Differentiated quarterly Sales of Beer")
#Lets do the ACF & PACF plot to identify the "P" & "Q" values
acf2(d_beer)
## ACF PACF
## [1,] -0.09 -0.09
## [2,] -0.79 -0.81
## [3,] -0.04 -0.73
## [4,] 0.88 0.24
## [5,] -0.06 0.08
## [6,] -0.76 0.05
## [7,] -0.03 -0.08
## [8,] 0.81 0.04
## [9,] -0.04 0.03
## [10,] -0.73 -0.02
## [11,] -0.01 0.02
## [12,] 0.76 0.10
## [13,] -0.04 -0.01
## [14,] -0.67 0.12
## [15,] -0.03 -0.09
## [16,] 0.73 0.08
## [17,] -0.06 -0.09
## [18,] -0.61 0.09
## [19,] -0.04 -0.04d.acf = acf(diff(log(beer.ts)))
#Looking at the ACF & PACF Plots, P can be 2 & Q can be 4
#For using in ARIMA, we can use only P or Q
#Lets do some iteration
#par(mfrow = c(2,2))
#fitting an arima model
fit = arima(log(beer.ts), c(0, 1, 2),seasonal = list(order = c(0, 1, 2), period = 4))
acf(residuals(fit))
pacf(residuals(fit))
fit##
## Call:
## arima(x = log(beer.ts), order = c(0, 1, 2), seasonal = list(order = c(0, 1,
## 2), period = 4))
##
## Coefficients:
## ma1 ma2 sma1 sma2
## -1.0651 0.3171 -0.7356 0.0226
## s.e. 0.1189 0.1220 0.1768 0.1590
##
## sigma^2 estimated as 0.0009847: log likelihood = 134.73, aic = -261.46#AIC = (261.46)
#Iterate arima using q = 0 and p=4
fit1 = arima(log(beer.ts), c(4, 1, 0),seasonal = list(order = c(4, 1, 0), period = 4))
acf(residuals(fit1))
pacf(residuals(fit1))
fit1##
## Call:
## arima(x = log(beer.ts), order = c(4, 1, 0), seasonal = list(order = c(4, 1,
## 0), period = 4))
##
## Coefficients:
## ar1 ar2 ar3 ar4 sar1 sar2 sar3
## -1.0046 -0.8018 -0.5040 -0.0881 -0.9254 -0.7732 -0.5791
## s.e. 0.1467 0.1861 0.2052 0.1357 0.1770 0.2196 0.2048
## sar4
## -0.3439
## s.e. 0.1620
##
## sigma^2 estimated as 0.0009167: log likelihood = 136.56, aic = -257.12#AIC = (257.12)
fit2 = arima(log(beer.ts), c(3, 1, 0),seasonal = list(order = c(3, 1, 0), period = 4))
acf(residuals(fit2))
pacf(residuals(fit2))
fit2##
## Call:
## arima(x = log(beer.ts), order = c(3, 1, 0), seasonal = list(order = c(3, 1,
## 0), period = 4))
##
## Coefficients:
## ar1 ar2 ar3 sar1 sar2 sar3
## -1.0607 -0.7264 -0.2884 -0.7469 -0.4792 -0.2845
## s.e. 0.1334 0.1777 0.1748 0.1727 0.1598 0.1394
##
## sigma^2 estimated as 0.001014: log likelihood = 133.96, aic = -255.92#AIC = (255.92)
#Seeing the AIC chart, the bars are crossing the blue lines
fit3 = arima(log(beer.ts), c(0, 1, 3),seasonal = list(order = c(0, 1, 3), period = 4))
acf(residuals(fit3))
pacf(residuals(fit3))
fit3##
## Call:
## arima(x = log(beer.ts), order = c(0, 1, 3), seasonal = list(order = c(0, 1,
## 3), period = 4))
##
## Coefficients:
## ma1 ma2 ma3 sma1 sma2 sma3
## -1.0923 0.3936 -0.0639 -0.7069 -0.0260 0.0729
## s.e. 0.1465 0.2427 0.1689 0.1887 0.1711 0.1598
##
## sigma^2 estimated as 0.000979: log likelihood = 134.97, aic = -257.94#AIC - (257.94)
fit4 = arima(log(beer.ts), c(0, 1, 4),seasonal = list(order = c(0, 1, 4), period = 4))
acf(residuals(fit4))
pacf(residuals(fit4))
fit4##
## Call:
## arima(x = log(beer.ts), order = c(0, 1, 4), seasonal = list(order = c(0, 1,
## 4), period = 4))
##
## Coefficients:
## ma1 ma2 ma3 ma4 sma1 sma2 sma3 sma4
## -1.0589 0.3444 0.0623 -0.1118 -0.7020 -0.0005 -0.0627 0.1292
## s.e. 0.1442 0.2148 0.2224 0.1486 0.1775 0.1658 0.2159 0.1729
##
## sigma^2 estimated as 0.0009623: log likelihood = 135.43, aic = -254.85#AIC - (254.85)
fit5 = arima(log(beer.ts), c(0, 1, 6),seasonal = list(order = c(0, 1, 6), period = 4))
acf(residuals(fit5))
pacf(residuals(fit5))
fit5##
## Call:
## arima(x = log(beer.ts), order = c(0, 1, 6), seasonal = list(order = c(0, 1,
## 6), period = 4))
##
## Coefficients:
## ma1 ma2 ma3 ma4 ma5 ma6 sma1 sma2
## -0.9026 -0.0630 0.3021 -0.8436 0.6866 -0.0064 0.0723 -0.3117
## s.e. 0.1580 0.2522 0.2549 0.2019 0.2154 0.1486 0.2914 0.2589
## sma3 sma4 sma5 sma6
## -0.0199 0.0533 0.2503 -0.2498
## s.e. 0.2351 0.2455 0.2015 0.2180
##
## sigma^2 estimated as 0.0007778: log likelihood = 139.07, aic = -254.15#AIC - (254.15)
fit6 = arima(log(beer.ts), c(0, 1, 8),seasonal = list(order = c(0, 1, 8), period = 4))
acf(residuals(fit6))
pacf(residuals(fit6))
fit6##
## Call:
## arima(x = log(beer.ts), order = c(0, 1, 8), seasonal = list(order = c(0, 1,
## 8), period = 4))
##
## Coefficients:
## ma1 ma2 ma3 ma4 ma5 ma6 ma7 ma8
## -0.9106 0.0194 0.2975 -0.7179 0.5508 -0.2024 0.1976 0.0380
## s.e. 0.1576 0.2424 0.2306 0.2604 0.2491 0.1992 0.1991 0.1497
## sma1 sma2 sma3 sma4 sma5 sma6 sma7 sma8
## -0.1977 -0.3265 0.0302 0.3101 0.3478 -0.3200 0.0746 -0.4070
## s.e. 0.6946 0.2299 0.7372 0.7649 0.3393 0.3506 0.3343 0.4204
##
## sigma^2 estimated as 0.0005879: log likelihood = 141.94, aic = -251.88fit6$sigma2## [1] 0.0005879408fit6$model## $phi
## numeric(0)
##
## $theta
## [1] -9.105817e-01 1.944100e-02 2.974953e-01 -9.156061e-01 7.308196e-01
## [6] -2.062638e-01 1.388146e-01 -1.465235e-01 1.883839e-01 3.367020e-02
## [11] -1.361915e-01 2.570482e-01 -2.073088e-01 6.667030e-02 -5.553735e-02
## [16] 2.760579e-01 -2.657814e-01 -8.147977e-05 9.823212e-02 1.262984e-01
## [21] -1.458781e-01 -5.601745e-02 1.647632e-01 -5.579007e-01 4.829560e-01
## [26] -7.662412e-02 -2.646147e-02 3.175366e-01 -2.441708e-01 6.622383e-02
## [31] -4.105146e-02 -4.727167e-01 4.116940e-01 -2.301006e-02 -1.063425e-01
## [36] 2.950308e-01 -2.241809e-01 8.238641e-02 -8.043554e-02 -1.547283e-02
##
## $Delta
## [1] 1 0 0 1 -1
##
## $Z
## [1] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [24] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 -1
##
## $a
## [1] -4.658523e-02 -2.211980e-02 5.260989e-02 -8.311632e-03 -1.676740e-02
## [6] 5.690665e-03 -3.473773e-03 -1.715149e-02 4.817311e-02 -4.972965e-02
## [11] 2.128552e-02 1.284688e-02 -1.479461e-02 1.966647e-02 -5.993046e-03
## [16] -1.014284e-02 -1.467175e-03 2.738582e-02 -3.092381e-02 7.509032e-03
## [21] 2.048743e-03 -1.098107e-02 2.408062e-03 -1.873338e-03 1.473109e-03
## [26] 1.709514e-02 -1.349808e-03 -4.700287e-03 -3.167952e-03 -1.161314e-02
## [31] 6.498399e-05 -6.696227e-03 1.540149e-02 -3.199758e-03 3.224356e-03
## [36] 1.577349e-03 -5.325637e-03 6.645872e-04 -2.283198e-03 2.933515e-05
## [41] 6.512056e-05 6.056550e+00 5.959458e+00 6.127742e+00 6.226734e+00
## [46] 5.973301e+00
##
## $P
## [,1] [,2] [,3] [,4]
## [1,] 0.000000e+00 -2.220446e-16 4.857226e-17 -5.551115e-17
## [2,] -2.220446e-16 1.660062e-01 -1.689239e-01 4.146492e-02
## [3,] 4.857226e-17 -1.689239e-01 3.362621e-01 -2.076723e-01
## [4,] -5.551115e-17 4.146492e-02 -2.076723e-01 3.384983e-01
## [5,] -2.220446e-16 9.870048e-03 2.779446e-02 -1.974090e-01
## [6,] 2.220446e-16 -8.845086e-02 1.058085e-01 -5.940826e-03
## [7,] -5.551115e-17 7.746709e-02 -1.713988e-01 1.329701e-01
## [8,] 1.110223e-16 -3.122082e-02 1.094037e-01 -1.807766e-01
## [9,] 0.000000e+00 3.197798e-02 -6.288106e-02 1.161618e-01
## [10,] 5.551115e-17 1.299601e-02 2.214598e-02 -6.729358e-02
## [11,] 1.387779e-17 -3.147849e-03 1.311994e-02 2.886696e-02
## [12,] -2.775558e-17 -8.218412e-03 3.920948e-03 1.355335e-02
## [13,] 0.000000e+00 9.607801e-03 -1.509475e-02 -5.424114e-04
## [14,] 4.163336e-17 -1.115107e-01 1.093054e-01 -9.140676e-03
## [15,] 0.000000e+00 9.987868e-02 -2.012572e-01 1.038366e-01
## [16,] 0.000000e+00 -6.982418e-03 1.053970e-01 -1.988149e-01
## [17,] 5.551115e-17 -2.658429e-02 1.849113e-02 1.023249e-01
## [18,] -5.551115e-17 7.104985e-02 -9.681611e-02 2.904335e-02
## [19,] 1.734723e-17 -6.009431e-02 1.310093e-01 -1.062183e-01
## [20,] -4.163336e-17 2.932599e-02 -8.721204e-02 1.328195e-01
## [21,] -1.387779e-17 -2.817125e-02 5.386165e-02 -8.590271e-02
## [22,] -5.551115e-17 -2.130515e-02 -1.020906e-02 5.833254e-02
## [23,] 3.469447e-17 1.391061e-02 -3.215918e-02 -1.603040e-02
## [24,] -5.551115e-17 1.081289e-02 4.786559e-03 -3.313334e-02
## [25,] 0.000000e+00 -1.807099e-02 2.504446e-02 9.344033e-03
## [26,] 1.110223e-16 3.938253e-02 -4.619206e-02 7.389619e-03
## [27,] -2.775558e-17 -2.634152e-02 5.659200e-02 -3.013219e-02
## [28,] -4.510281e-17 -3.257901e-03 -2.216880e-02 5.381348e-02
## [29,] 0.000000e+00 9.532312e-03 -1.167091e-02 -2.245774e-02
## [30,] -8.326673e-17 -9.238680e-03 1.324256e-02 -1.794418e-03
## [31,] 1.387779e-17 1.844840e-03 -7.223751e-03 5.362789e-03
## [32,] -2.775558e-17 -1.937540e-03 2.611609e-03 -5.316260e-03
## [33,] -5.551115e-17 4.545696e-03 -5.509537e-03 1.602324e-03
## [34,] 5.551115e-17 -1.270573e-02 2.349435e-02 -2.181225e-02
## [35,] -2.775558e-17 1.824095e-02 -3.583940e-02 3.817458e-02
## [36,] 4.163336e-17 -1.514021e-02 3.259827e-02 -3.747604e-02
## [37,] 0.000000e+00 1.318051e-02 -2.571338e-02 2.988542e-02
## [38,] -2.775558e-17 -5.572652e-03 1.384231e-02 -1.635847e-02
## [39,] 0.000000e+00 2.514819e-03 -4.484453e-03 6.635656e-03
## [40,] -1.387779e-17 -9.354880e-04 2.127085e-03 -1.821199e-03
## [41,] -3.469447e-18 -2.356528e-04 5.077950e-04 -5.243695e-04
## [42,] -4.638030e-21 1.222003e-16 -6.423811e-18 4.334205e-17
## [43,] 4.930381e-32 4.812500e-17 9.593604e-17 1.088724e-16
## [44,] -6.162976e-33 6.348504e-18 5.282570e-17 3.849570e-17
## [45,] 1.337831e-21 9.948454e-17 1.672611e-17 6.627141e-17
## [46,] -2.598756e-20 5.822664e-17 5.062425e-17 -8.824360e-18
## [,5] [,6] [,7] [,8]
## [1,] -2.220446e-16 2.220446e-16 -5.551115e-17 1.110223e-16
## [2,] 9.870048e-03 -8.845086e-02 7.746709e-02 -3.122082e-02
## [3,] 2.779446e-02 1.058085e-01 -1.713988e-01 1.094037e-01
## [4,] -1.974090e-01 -5.940826e-03 1.329701e-01 -1.807766e-01
## [5,] 3.310178e-01 -1.896820e-01 -1.029991e-02 1.317162e-01
## [6,] -1.896820e-01 3.558214e-01 -2.151942e-01 6.922026e-03
## [7,] -1.029991e-02 -2.151942e-01 3.807592e-01 -2.305538e-01
## [8,] 1.317162e-01 6.922026e-03 -2.305538e-01 3.848808e-01
## [9,] -1.770437e-01 1.108849e-01 2.467215e-02 -2.357794e-01
## [10,] 1.245492e-01 -1.957601e-01 1.249749e-01 2.114954e-02
## [11,] -7.449749e-02 1.363900e-01 -2.039656e-01 1.273301e-01
## [12,] 2.555596e-02 -6.519775e-02 1.290642e-01 -2.026229e-01
## [13,] 2.069434e-02 1.066185e-02 -5.416411e-02 1.258899e-01
## [14,] -3.860019e-02 1.253465e-01 -7.128056e-02 -2.498312e-02
## [15,] 2.415740e-02 -1.296607e-01 1.965471e-01 -9.889631e-02
## [16,] 9.974551e-02 3.280664e-02 -1.360772e-01 1.992174e-01
## [17,] -2.039385e-01 1.193894e-01 1.667371e-02 -1.305677e-01
## [18,] 1.116665e-01 -2.465227e-01 1.549403e-01 -9.150344e-04
## [19,] 2.224496e-02 1.449901e-01 -2.745043e-01 1.707415e-01
## [20,] -9.848100e-02 -3.463628e-03 1.657439e-01 -2.799906e-01
## [21,] 1.220579e-01 -6.816147e-02 -2.734774e-02 1.709727e-01
## [22,] -9.577828e-02 1.449710e-01 -8.551685e-02 -2.018272e-02
## [23,] 6.691778e-02 -1.128736e-01 1.574535e-01 -9.178464e-02
## [24,] -1.127732e-02 5.407516e-02 -1.028240e-01 1.556226e-01
## [25,] -4.347936e-02 1.310533e-02 3.549880e-02 -9.854646e-02
## [26,] 3.861230e-02 -1.055218e-01 5.926311e-02 2.357830e-02
## [27,] -1.589846e-02 8.504907e-02 -1.395484e-01 6.864795e-02
## [28,] -2.839558e-02 -1.711547e-02 8.552911e-02 -1.392489e-01
## [29,] 5.722420e-02 -3.817600e-02 -9.390946e-03 8.365930e-02
## [30,] -3.565522e-02 8.257184e-02 -5.660409e-02 -6.780531e-03
## [31,] 6.967303e-03 -5.060071e-02 9.308066e-02 -5.755838e-02
## [32,] 2.605358e-03 1.250666e-02 -5.467912e-02 9.336434e-02
## [33,] -2.725317e-03 -3.706020e-03 1.735102e-02 -5.553889e-02
## [34,] 1.427144e-02 -1.732667e-02 5.059656e-03 1.847711e-02
## [35,] -3.095291e-02 2.063695e-02 -1.982588e-02 2.803260e-03
## [36,] 3.496203e-02 -1.902305e-02 1.087015e-02 -1.695989e-02
## [37,] -3.039640e-02 1.767853e-02 -5.757570e-03 8.059245e-03
## [38,] 1.841741e-02 -9.472238e-03 2.675673e-03 -3.908858e-03
## [39,] -8.097853e-03 4.012403e-03 7.230412e-04 1.606504e-03
## [40,] 3.597127e-03 -2.819023e-03 2.809166e-04 1.144942e-03
## [41,] 8.426265e-04 -5.813562e-04 4.074492e-05 1.181890e-04
## [42,] 9.091130e-17 -7.376952e-17 2.447284e-17 6.651254e-19
## [43,] 6.433358e-18 -6.980719e-17 3.765944e-17 -4.054499e-17
## [44,] -4.338385e-17 1.374261e-17 7.337633e-18 2.965487e-18
## [45,] -5.894369e-17 3.652599e-17 -1.391555e-17 -4.032236e-17
## [46,] 6.610137e-17 -5.844193e-17 -1.405561e-17 5.208942e-18
## [,9] [,10] [,11] [,12]
## [1,] 0.000000e+00 5.551115e-17 1.387779e-17 -2.775558e-17
## [2,] 3.197798e-02 1.299601e-02 -3.147849e-03 -8.218412e-03
## [3,] -6.288106e-02 2.214598e-02 1.311994e-02 3.920948e-03
## [4,] 1.161618e-01 -6.729358e-02 2.886696e-02 1.355335e-02
## [5,] -1.770437e-01 1.245492e-01 -7.449749e-02 2.555596e-02
## [6,] 1.108849e-01 -1.957601e-01 1.363900e-01 -6.519775e-02
## [7,] 2.467215e-02 1.249749e-01 -2.039656e-01 1.290642e-01
## [8,] -2.357794e-01 2.114954e-02 1.273301e-01 -2.026229e-01
## [9,] 3.901228e-01 -2.347281e-01 2.146377e-02 1.266123e-01
## [10,] -2.347281e-01 3.838003e-01 -2.279809e-01 2.336069e-02
## [11,] 2.146377e-02 -2.279809e-01 3.768563e-01 -2.299792e-01
## [12,] 1.266123e-01 2.336069e-02 -2.299792e-01 3.761754e-01
## [13,] -2.017880e-01 1.209011e-01 2.952996e-02 -2.283692e-01
## [14,] 1.083636e-01 -1.791001e-01 9.141963e-02 2.547779e-02
## [15,] -8.271308e-03 8.832811e-02 -1.522633e-01 9.439971e-02
## [16,] -9.999419e-02 -5.024522e-03 8.447647e-02 -1.529410e-01
## [17,] 1.947677e-01 -9.865782e-02 -7.780261e-03 8.461253e-02
## [18,] -1.159571e-01 1.943503e-01 -9.276028e-02 -1.044017e-02
## [19,] -1.406956e-02 -1.163438e-01 1.895895e-01 -8.988043e-02
## [20,] 1.747711e-01 -1.728864e-02 -1.120331e-01 1.903502e-01
## [21,] -2.829484e-01 1.809189e-01 -2.411425e-02 -1.139989e-01
## [22,] 1.674583e-01 -2.757383e-01 1.720070e-01 -2.546104e-02
## [23,] -1.759734e-02 1.603057e-01 -2.670213e-01 1.732871e-01
## [24,] -9.091140e-02 -2.047807e-02 1.633053e-01 -2.659950e-01
## [25,] 1.541453e-01 -8.351888e-02 -2.833527e-02 1.610015e-01
## [26,] -9.571522e-02 1.310638e-01 -5.902608e-02 -2.147194e-02
## [27,] 2.191163e-02 -7.643427e-02 1.106287e-01 -6.463996e-02
## [28,] 6.767388e-02 1.978400e-02 -7.457065e-02 1.114243e-01
## [29,] -1.381317e-01 6.577617e-02 2.197854e-02 -7.401477e-02
## [30,] 8.479008e-02 -1.269378e-01 5.500224e-02 1.799356e-02
## [31,] -8.410504e-03 7.677946e-02 -1.194756e-01 5.794723e-02
## [32,] -5.718087e-02 -6.151321e-03 7.472009e-02 -1.203715e-01
## [33,] 9.362170e-02 -5.896511e-02 -4.341458e-03 7.534781e-02
## [34,] -6.089263e-02 7.987757e-02 -4.685806e-02 9.208249e-04
## [35,] 2.408955e-02 -4.969030e-02 7.033957e-02 -5.123877e-02
## [36,] 4.953952e-04 2.504084e-02 -5.130246e-02 7.024274e-02
## [37,] -1.592527e-02 -4.374224e-03 3.016666e-02 -4.971882e-02
## [38,] 9.531005e-03 -5.858899e-03 -1.393253e-02 2.653885e-02
## [39,] -5.271082e-03 2.074670e-03 1.141404e-03 -1.121706e-02
## [40,] 2.090929e-03 -2.521814e-03 -5.189440e-04 1.497760e-04
## [41,] 4.954260e-04 -4.572410e-04 -1.830659e-04 4.278484e-04
## [42,] -4.982619e-18 -2.515054e-17 -5.983865e-18 1.929559e-17
## [43,] -1.116098e-17 9.838787e-18 1.947424e-18 4.395934e-18
## [44,] -3.892819e-18 1.573758e-17 -8.147601e-18 -6.013910e-18
## [45,] -1.856117e-17 -8.265565e-18 2.983312e-18 -1.311616e-18
## [46,] -1.257390e-17 7.237987e-19 4.698387e-18 3.202895e-18
## [,13] [,14] [,15] [,16]
## [1,] 0.000000e+00 4.163336e-17 0.000000e+00 0.000000e+00
## [2,] 9.607801e-03 -1.115107e-01 9.987868e-02 -6.982418e-03
## [3,] -1.509475e-02 1.093054e-01 -2.012572e-01 1.053970e-01
## [4,] -5.424114e-04 -9.140676e-03 1.038366e-01 -1.988149e-01
## [5,] 2.069434e-02 -3.860019e-02 2.415740e-02 9.974551e-02
## [6,] 1.066185e-02 1.253465e-01 -1.296607e-01 3.280664e-02
## [7,] -5.416411e-02 -7.128056e-02 1.965471e-01 -1.360772e-01
## [8,] 1.258899e-01 -2.498312e-02 -9.889631e-02 1.992174e-01
## [9,] -2.017880e-01 1.083636e-01 -8.271308e-03 -9.999419e-02
## [10,] 1.209011e-01 -1.791001e-01 8.832811e-02 -5.024522e-03
## [11,] 2.952996e-02 9.141963e-02 -1.522633e-01 8.447647e-02
## [12,] -2.283692e-01 2.547779e-02 9.439971e-02 -1.529410e-01
## [13,] 3.709304e-01 -2.062146e-01 5.486732e-03 9.754583e-02
## [14,] -2.062146e-01 3.032452e-01 -1.433798e-01 -7.865454e-03
## [15,] 5.486732e-03 -1.433798e-01 2.435213e-01 -1.308040e-01
## [16,] 9.754583e-02 -7.865454e-03 -1.308040e-01 2.414527e-01
## [17,] -1.514682e-01 1.007576e-01 -1.086796e-02 -1.314559e-01
## [18,] 8.258057e-02 -1.660418e-01 1.108451e-01 -9.083983e-03
## [19,] -9.101815e-03 9.574102e-02 -1.743049e-01 1.091994e-01
## [20,] -9.281915e-02 -7.089916e-03 9.495562e-02 -1.731099e-01
## [21,] 1.957351e-01 -1.067233e-01 3.799908e-03 9.247492e-02
## [22,] -1.069277e-01 1.678605e-01 -8.033088e-02 -8.236621e-04
## [23,] -3.255378e-02 -7.548507e-02 1.376866e-01 -7.543029e-02
## [24,] 1.708277e-01 -2.555684e-02 -8.089024e-02 1.387811e-01
## [25,] -2.593944e-01 1.462053e-01 -4.242296e-03 -8.447335e-02
## [26,] 1.400653e-01 -1.723434e-01 6.861355e-02 7.959963e-03
## [27,] -3.862497e-03 6.348006e-02 -1.033405e-01 5.804038e-02
## [28,] -6.648745e-02 6.427232e-03 5.430017e-02 -1.022166e-01
## [29,] 1.097295e-01 -6.227644e-02 3.055913e-03 5.510922e-02
## [30,] -6.428596e-02 6.690764e-02 -2.522425e-02 -2.273360e-03
## [31,] 1.107429e-02 -3.195246e-02 3.882888e-02 -2.138403e-02
## [32,] 5.984390e-02 3.038236e-03 -2.526405e-02 3.788292e-02
## [33,] -1.219117e-01 6.525202e-02 -1.426664e-03 -2.450474e-02
## [34,] 6.354566e-02 -6.018117e-02 1.103960e-02 5.390550e-03
## [35,] 1.051479e-02 1.004643e-02 -1.289329e-02 5.352416e-03
## [36,] -5.031114e-02 1.220633e-02 8.165996e-03 -1.321230e-02
## [37,] 6.594931e-02 -3.511222e-02 -6.662468e-04 1.039278e-02
## [38,] -4.098786e-02 2.641359e-02 -8.187447e-04 -5.486781e-03
## [39,] 2.008383e-02 -1.111112e-02 4.559816e-04 2.765392e-03
## [40,] -8.830061e-03 9.011796e-03 -1.465124e-03 -8.786152e-04
## [41,] -2.048259e-03 1.784698e-03 -2.399444e-04 -2.305225e-04
## [42,] -9.276009e-18 1.012406e-17 -8.697075e-18 9.585747e-18
## [43,] -1.497516e-17 1.384114e-17 1.393244e-17 -3.172640e-17
## [44,] 1.172931e-18 4.200698e-17 -8.709256e-19 -4.104662e-18
## [45,] 1.341169e-17 -5.104016e-17 6.032250e-18 -1.580266e-17
## [46,] -3.821286e-17 1.073645e-17 -7.727746e-18 1.189776e-17
## [,17] [,18] [,19] [,20]
## [1,] 5.551115e-17 -5.551115e-17 1.734723e-17 -4.163336e-17
## [2,] -2.658429e-02 7.104985e-02 -6.009431e-02 2.932599e-02
## [3,] 1.849113e-02 -9.681611e-02 1.310093e-01 -8.721204e-02
## [4,] 1.023249e-01 2.904335e-02 -1.062183e-01 1.328195e-01
## [5,] -2.039385e-01 1.116665e-01 2.224496e-02 -9.848100e-02
## [6,] 1.193894e-01 -2.465227e-01 1.449901e-01 -3.463628e-03
## [7,] 1.667371e-02 1.549403e-01 -2.745043e-01 1.657439e-01
## [8,] -1.305677e-01 -9.150344e-04 1.707415e-01 -2.799906e-01
## [9,] 1.947677e-01 -1.159571e-01 -1.406956e-02 1.747711e-01
## [10,] -9.865782e-02 1.943503e-01 -1.163438e-01 -1.728864e-02
## [11,] -7.780261e-03 -9.276028e-02 1.895895e-01 -1.120331e-01
## [12,] 8.461253e-02 -1.044017e-02 -8.988043e-02 1.903502e-01
## [13,] -1.514682e-01 8.258057e-02 -9.101815e-03 -9.281915e-02
## [14,] 1.007576e-01 -1.660418e-01 9.574102e-02 -7.089916e-03
## [15,] -1.086796e-02 1.108451e-01 -1.743049e-01 9.495562e-02
## [16,] -1.314559e-01 -9.083983e-03 1.091994e-01 -1.731099e-01
## [17,] 2.441186e-01 -1.400337e-01 -1.489370e-03 1.070669e-01
## [18,] -1.400337e-01 2.626144e-01 -1.541069e-01 8.334758e-03
## [19,] -1.489370e-03 -1.541069e-01 2.724439e-01 -1.635170e-01
## [20,] 1.070669e-01 8.334758e-03 -1.635170e-01 2.730382e-01
## [21,] -1.724817e-01 9.908748e-02 1.676748e-02 -1.615335e-01
## [22,] 9.174417e-02 -1.704684e-01 9.707609e-02 1.869672e-02
## [23,] 7.977408e-04 8.584993e-02 -1.647293e-01 9.462829e-02
## [24,] -7.543002e-02 3.967229e-03 8.230646e-02 -1.660153e-01
## [25,] 1.375763e-01 -7.686244e-02 6.335918e-03 8.595040e-02
## [26,] -7.859437e-02 1.317081e-01 -7.410159e-02 -6.012764e-03
## [27,] 2.234510e-03 -6.975718e-02 1.255441e-01 -6.340156e-02
## [28,] 5.943417e-02 -7.655085e-04 -6.738375e-02 1.235817e-01
## [29,] -1.025135e-01 6.201501e-02 -3.417026e-03 -6.785060e-02
## [30,] 5.104413e-02 -9.860598e-02 6.048115e-02 4.368051e-03
## [31,] 1.225461e-03 4.643288e-02 -9.591127e-02 5.436808e-02
## [32,] -2.219419e-02 1.445429e-03 4.677216e-02 -9.421275e-02
## [33,] 3.814995e-02 -2.134096e-02 3.070836e-04 4.580392e-02
## [34,] -1.653668e-02 2.360796e-02 -1.072213e-02 -1.183843e-02
## [35,] -2.080336e-03 -1.317770e-03 1.189092e-02 -1.761240e-05
## [36,] 6.783580e-03 -7.440911e-03 3.623304e-03 1.097740e-02
## [37,] -1.257780e-02 8.742443e-03 -1.003987e-02 1.235428e-03
## [38,] 6.398597e-03 -7.968403e-03 6.384330e-03 -2.741516e-03
## [39,] -2.328613e-03 2.351239e-03 -5.659422e-03 7.996938e-04
## [40,] 1.601819e-03 -7.845189e-04 1.439256e-03 -3.614982e-03
## [41,] 3.362009e-04 -2.136228e-04 3.891430e-04 -5.899267e-04
## [42,] -3.516188e-17 3.575476e-17 -1.293161e-17 -2.643259e-17
## [43,] 5.076746e-19 9.751919e-18 -2.459680e-17 -1.592478e-17
## [44,] 9.892972e-18 -3.714472e-18 -2.056860e-17 1.556862e-18
## [45,] 2.904667e-17 1.385309e-18 -6.204626e-18 1.490295e-17
## [46,] -3.624565e-17 1.836760e-17 -1.043068e-17 -6.763283e-17
## [,21] [,22] [,23] [,24]
## [1,] -1.387779e-17 -5.551115e-17 3.469447e-17 -5.551115e-17
## [2,] -2.817125e-02 -2.130515e-02 1.391061e-02 1.081289e-02
## [3,] 5.386165e-02 -1.020906e-02 -3.215918e-02 4.786559e-03
## [4,] -8.590271e-02 5.833254e-02 -1.603040e-02 -3.313334e-02
## [5,] 1.220579e-01 -9.577828e-02 6.691778e-02 -1.127732e-02
## [6,] -6.816147e-02 1.449710e-01 -1.128736e-01 5.407516e-02
## [7,] -2.734774e-02 -8.551685e-02 1.574535e-01 -1.028240e-01
## [8,] 1.709727e-01 -2.018272e-02 -9.178464e-02 1.556226e-01
## [9,] -2.829484e-01 1.674583e-01 -1.759734e-02 -9.091140e-02
## [10,] 1.809189e-01 -2.757383e-01 1.603057e-01 -2.047807e-02
## [11,] -2.411425e-02 1.720070e-01 -2.670213e-01 1.633053e-01
## [12,] -1.139989e-01 -2.546104e-02 1.732871e-01 -2.659950e-01
## [13,] 1.957351e-01 -1.069277e-01 -3.255378e-02 1.708277e-01
## [14,] -1.067233e-01 1.678605e-01 -7.548507e-02 -2.555684e-02
## [15,] 3.799908e-03 -8.033088e-02 1.376866e-01 -8.089024e-02
## [16,] 9.247492e-02 -8.236621e-04 -7.543029e-02 1.387811e-01
## [17,] -1.724817e-01 9.174417e-02 7.977408e-04 -7.543002e-02
## [18,] 9.908748e-02 -1.704684e-01 8.584993e-02 3.967229e-03
## [19,] 1.676748e-02 9.707609e-02 -1.647293e-01 8.230646e-02
## [20,] -1.615335e-01 1.869672e-02 9.462829e-02 -1.660153e-01
## [21,] 2.672562e-01 -1.665114e-01 2.372703e-02 9.764632e-02
## [22,] -1.665114e-01 2.570931e-01 -1.554855e-01 2.597377e-02
## [23,] 2.372703e-02 -1.554855e-01 2.452620e-01 -1.576140e-01
## [24,] 9.764632e-02 2.597377e-02 -1.576140e-01 2.437199e-01
## [25,] -1.733099e-01 8.979622e-02 3.371211e-02 -1.541231e-01
## [26,] 1.084983e-01 -1.459371e-01 6.269095e-02 2.330648e-02
## [27,] -2.477721e-02 8.455526e-02 -1.221938e-01 7.120289e-02
## [28,] -6.074864e-02 -2.204975e-02 8.212124e-02 -1.233390e-01
## [29,] 1.252267e-01 -5.913670e-02 -2.374221e-02 8.125273e-02
## [30,] -8.056047e-02 1.130207e-01 -4.787623e-02 -1.787849e-02
## [31,] 1.381719e-02 -7.162148e-02 1.049245e-01 -5.217574e-02
## [32,] 5.159887e-02 1.165635e-02 -6.974377e-02 1.062275e-01
## [33,] -9.229639e-02 5.324348e-02 1.010899e-02 -7.068037e-02
## [34,] 6.296634e-02 -7.595485e-02 3.879823e-02 2.519763e-03
## [35,] -2.627096e-02 4.910788e-02 -6.385299e-02 4.507325e-02
## [36,] -1.204420e-04 -2.656816e-02 4.978531e-02 -6.361499e-02
## [37,] 1.589272e-02 4.702936e-03 -3.126964e-02 4.739484e-02
## [38,] -1.037627e-02 4.769204e-03 1.489023e-02 -2.594937e-02
## [39,] 5.971808e-03 -2.057348e-03 -2.803344e-03 1.091870e-02
## [40,] -2.391169e-03 2.874442e-03 7.747324e-04 -1.351463e-03
## [41,] -5.619173e-04 5.071426e-04 2.666847e-04 -6.028231e-04
## [42,] -1.396175e-17 2.170380e-17 -3.855328e-17 8.318204e-17
## [43,] 7.715562e-18 1.647651e-18 -4.723502e-17 -3.080034e-17
## [44,] -4.052084e-18 2.218603e-17 7.716462e-18 1.466846e-18
## [45,] 4.692941e-17 2.671290e-17 4.146911e-18 1.402337e-17
## [46,] -1.168183e-17 6.301799e-18 1.350745e-17 1.447432e-17
## [,25] [,26] [,27] [,28]
## [1,] 0.000000e+00 1.110223e-16 -2.775558e-17 -4.510281e-17
## [2,] -1.807099e-02 3.938253e-02 -2.634152e-02 -3.257901e-03
## [3,] 2.504446e-02 -4.619206e-02 5.659200e-02 -2.216880e-02
## [4,] 9.344033e-03 7.389619e-03 -3.013219e-02 5.381348e-02
## [5,] -4.347936e-02 3.861230e-02 -1.589846e-02 -2.839558e-02
## [6,] 1.310533e-02 -1.055218e-01 8.504907e-02 -1.711547e-02
## [7,] 3.549880e-02 5.926311e-02 -1.395484e-01 8.552911e-02
## [8,] -9.854646e-02 2.357830e-02 6.864795e-02 -1.392489e-01
## [9,] 1.541453e-01 -9.571522e-02 2.191163e-02 6.767388e-02
## [10,] -8.351888e-02 1.310638e-01 -7.643427e-02 1.978400e-02
## [11,] -2.833527e-02 -5.902608e-02 1.106287e-01 -7.457065e-02
## [12,] 1.610015e-01 -2.147194e-02 -6.463996e-02 1.114243e-01
## [13,] -2.593944e-01 1.400653e-01 -3.862497e-03 -6.648745e-02
## [14,] 1.462053e-01 -1.723434e-01 6.348006e-02 6.427232e-03
## [15,] -4.242296e-03 6.861355e-02 -1.033405e-01 5.430017e-02
## [16,] -8.447335e-02 7.959963e-03 5.804038e-02 -1.022166e-01
## [17,] 1.375763e-01 -7.859437e-02 2.234510e-03 5.943417e-02
## [18,] -7.686244e-02 1.317081e-01 -6.975718e-02 -7.655085e-04
## [19,] 6.335918e-03 -7.410159e-02 1.255441e-01 -6.738375e-02
## [20,] 8.595040e-02 -6.012764e-03 -6.340156e-02 1.235817e-01
## [21,] -1.733099e-01 1.084983e-01 -2.477721e-02 -6.074864e-02
## [22,] 8.979622e-02 -1.459371e-01 8.455526e-02 -2.204975e-02
## [23,] 3.371211e-02 6.269095e-02 -1.221938e-01 8.212124e-02
## [24,] -1.541231e-01 2.330648e-02 7.120289e-02 -1.233390e-01
## [25,] 2.350110e-01 -1.271897e-01 9.018770e-04 7.379452e-02
## [26,] -1.271897e-01 1.508038e-01 -5.681256e-02 -6.562198e-03
## [27,] 9.018770e-04 -5.681256e-02 9.186834e-02 -5.081950e-02
## [28,] 7.379452e-02 -6.562198e-03 -5.081950e-02 9.145362e-02
## [29,] -1.211229e-01 6.676204e-02 -6.399874e-04 -5.167365e-02
## [30,] 6.772991e-02 -8.120295e-02 3.428945e-02 2.560650e-03
## [31,] -8.139915e-03 3.934591e-02 -5.826305e-02 3.218685e-02
## [32,] -5.497107e-02 -1.885350e-04 3.299685e-02 -5.762036e-02
## [33,] 1.083814e-01 -6.139128e-02 5.061341e-03 3.236906e-02
## [34,] -5.384007e-02 6.017582e-02 -2.279825e-02 2.072617e-03
## [35,] -1.126248e-02 -1.478048e-02 2.907262e-02 -2.066885e-02
## [36,] 4.408067e-02 -7.362331e-03 -1.835050e-02 2.990777e-02
## [37,] -5.782902e-02 2.639571e-02 7.271291e-03 -2.010197e-02
## [38,] 3.520564e-02 -2.202475e-02 -2.655676e-03 1.004234e-02
## [39,] -1.690221e-02 8.743143e-03 -5.994756e-04 -4.644893e-03
## [40,] 7.589786e-03 -7.133776e-03 8.215538e-04 1.349291e-04
## [41,] 1.752559e-03 -1.414534e-03 1.256273e-04 1.847301e-04
## [42,] -5.141149e-17 -4.276170e-17 1.083387e-17 -2.614917e-17
## [43,] 3.674636e-18 -2.563881e-17 -1.056541e-17 -1.635577e-17
## [44,] -1.437459e-17 3.693303e-17 -1.956310e-17 -6.499682e-18
## [45,] -3.062043e-17 -9.655856e-18 -4.754281e-19 -1.505614e-17
## [46,] -6.653826e-18 -3.225214e-17 -7.032966e-18 -8.187032e-17
## [,29] [,30] [,31] [,32]
## [1,] 0.000000e+00 -8.326673e-17 1.387779e-17 -2.775558e-17
## [2,] 9.532312e-03 -9.238680e-03 1.844840e-03 -1.937540e-03
## [3,] -1.167091e-02 1.324256e-02 -7.223751e-03 2.611609e-03
## [4,] -2.245774e-02 -1.794418e-03 5.362789e-03 -5.316260e-03
## [5,] 5.722420e-02 -3.565522e-02 6.967303e-03 2.605358e-03
## [6,] -3.817600e-02 8.257184e-02 -5.060071e-02 1.250666e-02
## [7,] -9.390946e-03 -5.660409e-02 9.308066e-02 -5.467912e-02
## [8,] 8.365930e-02 -6.780531e-03 -5.755838e-02 9.336434e-02
## [9,] -1.381317e-01 8.479008e-02 -8.410504e-03 -5.718087e-02
## [10,] 6.577617e-02 -1.269378e-01 7.677946e-02 -6.151321e-03
## [11,] 2.197854e-02 5.500224e-02 -1.194756e-01 7.472009e-02
## [12,] -7.401477e-02 1.799356e-02 5.794723e-02 -1.203715e-01
## [13,] 1.097295e-01 -6.428596e-02 1.107429e-02 5.984390e-02
## [14,] -6.227644e-02 6.690764e-02 -3.195246e-02 3.038236e-03
## [15,] 3.055913e-03 -2.522425e-02 3.882888e-02 -2.526405e-02
## [16,] 5.510922e-02 -2.273360e-03 -2.138403e-02 3.788292e-02
## [17,] -1.025135e-01 5.104413e-02 1.225461e-03 -2.219419e-02
## [18,] 6.201501e-02 -9.860598e-02 4.643288e-02 1.445429e-03
## [19,] -3.417026e-03 6.048115e-02 -9.591127e-02 4.677216e-02
## [20,] -6.785060e-02 4.368051e-03 5.436808e-02 -9.421275e-02
## [21,] 1.252267e-01 -8.056047e-02 1.381719e-02 5.159887e-02
## [22,] -5.913670e-02 1.130207e-01 -7.162148e-02 1.165635e-02
## [23,] -2.374221e-02 -4.787623e-02 1.049245e-01 -6.974377e-02
## [24,] 8.125273e-02 -1.787849e-02 -5.217574e-02 1.062275e-01
## [25,] -1.211229e-01 6.772991e-02 -8.139915e-03 -5.497107e-02
## [26,] 6.676204e-02 -8.120295e-02 3.934591e-02 -1.885350e-04
## [27,] -6.399874e-04 3.428945e-02 -5.826305e-02 3.299685e-02
## [28,] -5.167365e-02 2.560650e-03 3.218685e-02 -5.762036e-02
## [29,] 9.098766e-02 -4.773960e-02 -3.865952e-04 3.302912e-02
## [30,] -4.773960e-02 7.166853e-02 -3.427567e-02 -4.433020e-03
## [31,] -3.865952e-04 -3.427567e-02 6.240898e-02 -3.145714e-02
## [32,] 3.302912e-02 -4.433020e-03 -3.145714e-02 6.152088e-02
## [33,] -5.819082e-02 3.642164e-02 -6.875212e-03 -3.072266e-02
## [34,] 2.692763e-02 -3.644716e-02 2.188876e-02 -2.372617e-03
## [35,] 6.692144e-03 9.898288e-03 -2.528743e-02 1.839382e-02
## [36,] -2.071082e-02 3.902853e-03 1.221351e-02 -2.589320e-02
## [37,] 2.843413e-02 -1.156748e-02 -2.706151e-03 1.414428e-02
## [38,] -1.649348e-02 1.128246e-02 3.152118e-04 -6.293685e-03
## [39,] 7.326588e-03 -3.916164e-03 2.611173e-03 2.943982e-03
## [40,] -3.648886e-03 2.702910e-03 -7.279651e-04 1.648904e-03
## [41,] -8.220590e-04 5.623417e-04 -1.714845e-04 1.506856e-04
## [42,] -4.555869e-18 3.508412e-17 -5.450825e-19 2.930269e-17
## [43,] 8.975952e-19 1.644310e-17 4.459051e-17 -3.217814e-17
## [44,] 1.156535e-17 6.094194e-18 -3.249285e-17 -7.411059e-18
## [45,] 2.575384e-17 2.605561e-17 3.650346e-18 -4.199460e-18
## [46,] -2.979725e-17 1.902944e-17 1.321742e-17 3.905060e-18
## [,33] [,34] [,35] [,36]
## [1,] -5.551115e-17 5.551115e-17 -2.775558e-17 4.163336e-17
## [2,] 4.545696e-03 -1.270573e-02 1.824095e-02 -1.514021e-02
## [3,] -5.509537e-03 2.349435e-02 -3.583940e-02 3.259827e-02
## [4,] 1.602324e-03 -2.181225e-02 3.817458e-02 -3.747604e-02
## [5,] -2.725317e-03 1.427144e-02 -3.095291e-02 3.496203e-02
## [6,] -3.706020e-03 -1.732667e-02 2.063695e-02 -1.902305e-02
## [7,] 1.735102e-02 5.059656e-03 -1.982588e-02 1.087015e-02
## [8,] -5.553889e-02 1.847711e-02 2.803260e-03 -1.695989e-02
## [9,] 9.362170e-02 -6.089263e-02 2.408955e-02 4.953952e-04
## [10,] -5.896511e-02 7.987757e-02 -4.969030e-02 2.504084e-02
## [11,] -4.341458e-03 -4.685806e-02 7.033957e-02 -5.130246e-02
## [12,] 7.534781e-02 9.208249e-04 -5.123877e-02 7.024274e-02
## [13,] -1.219117e-01 6.354566e-02 1.051479e-02 -5.031114e-02
## [14,] 6.525202e-02 -6.018117e-02 1.004643e-02 1.220633e-02
## [15,] -1.426664e-03 1.103960e-02 -1.289329e-02 8.165996e-03
## [16,] -2.450474e-02 5.390550e-03 5.352416e-03 -1.321230e-02
## [17,] 3.814995e-02 -1.653668e-02 -2.080336e-03 6.783580e-03
## [18,] -2.134096e-02 2.360796e-02 -1.317770e-03 -7.440911e-03
## [19,] 3.070836e-04 -1.072213e-02 1.189092e-02 3.623304e-03
## [20,] 4.580392e-02 -1.183843e-02 -1.761240e-05 1.097740e-02
## [21,] -9.229639e-02 6.296634e-02 -2.627096e-02 -1.204420e-04
## [22,] 5.324348e-02 -7.595485e-02 4.910788e-02 -2.656816e-02
## [23,] 1.010899e-02 3.879823e-02 -6.385299e-02 4.978531e-02
## [24,] -7.068037e-02 2.519763e-03 4.507325e-02 -6.361499e-02
## [25,] 1.083814e-01 -5.384007e-02 -1.126248e-02 4.408067e-02
## [26,] -6.139128e-02 6.017582e-02 -1.478048e-02 -7.362331e-03
## [27,] 5.061341e-03 -2.279825e-02 2.907262e-02 -1.835050e-02
## [28,] 3.236906e-02 2.072617e-03 -2.066885e-02 2.990777e-02
## [29,] -5.819082e-02 2.692763e-02 6.692144e-03 -2.071082e-02
## [30,] 3.642164e-02 -3.644716e-02 9.898288e-03 3.902853e-03
## [31,] -6.875212e-03 2.188876e-02 -2.528743e-02 1.221351e-02
## [32,] -3.072266e-02 -2.372617e-03 1.839382e-02 -2.589320e-02
## [33,] 6.096113e-02 -3.490656e-02 1.027729e-03 1.865965e-02
## [34,] -3.490656e-02 3.955421e-02 -1.922435e-02 6.010884e-03
## [35,] 1.027729e-03 -1.922435e-02 2.849934e-02 -2.378176e-02
## [36,] 1.865965e-02 6.010884e-03 -2.378176e-02 2.920343e-02
## [37,] -2.735705e-02 7.195000e-03 1.540600e-02 -2.316673e-02
## [38,] 1.719837e-02 -8.403020e-03 -7.525491e-03 1.271928e-02
## [39,] -8.559033e-03 3.509881e-03 2.151751e-03 -5.429068e-03
## [40,] 3.774150e-03 -3.520099e-03 -3.793067e-04 1.384162e-03
## [41,] 8.728323e-04 -6.650148e-04 -1.501591e-04 4.091072e-04
## [42,] -6.196931e-18 -4.665943e-17 8.262765e-18 -2.498065e-17
## [43,] -4.960563e-18 -2.151329e-17 -1.570309e-17 2.387614e-17
## [44,] -8.840552e-18 6.212372e-18 -8.980858e-18 6.316743e-18
## [45,] -9.996315e-18 -1.396102e-17 -2.902841e-18 -9.381912e-18
## [46,] 2.090679e-18 -3.027247e-17 -9.192568e-18 1.974121e-18
## [,37] [,38] [,39] [,40]
## [1,] 0.000000e+00 -2.775558e-17 0.000000e+00 -1.387779e-17
## [2,] 1.318051e-02 -5.572652e-03 2.514819e-03 -9.354880e-04
## [3,] -2.571338e-02 1.384231e-02 -4.484453e-03 2.127085e-03
## [4,] 2.988542e-02 -1.635847e-02 6.635656e-03 -1.821199e-03
## [5,] -3.039640e-02 1.841741e-02 -8.097853e-03 3.597127e-03
## [6,] 1.767853e-02 -9.472238e-03 4.012403e-03 -2.819023e-03
## [7,] -5.757570e-03 2.675673e-03 7.230412e-04 2.809166e-04
## [8,] 8.059245e-03 -3.908858e-03 1.606504e-03 1.144942e-03
## [9,] -1.592527e-02 9.531005e-03 -5.271082e-03 2.090929e-03
## [10,] -4.374224e-03 -5.858899e-03 2.074670e-03 -2.521814e-03
## [11,] 3.016666e-02 -1.393253e-02 1.141404e-03 -5.189440e-04
## [12,] -4.971882e-02 2.653885e-02 -1.121706e-02 1.497760e-04
## [13,] 6.594931e-02 -4.098786e-02 2.008383e-02 -8.830061e-03
## [14,] -3.511222e-02 2.641359e-02 -1.111112e-02 9.011796e-03
## [15,] -6.662468e-04 -8.187447e-04 4.559816e-04 -1.465124e-03
## [16,] 1.039278e-02 -5.486781e-03 2.765392e-03 -8.786152e-04
## [17,] -1.257780e-02 6.398597e-03 -2.328613e-03 1.601819e-03
## [18,] 8.742443e-03 -7.968403e-03 2.351239e-03 -7.845189e-04
## [19,] -1.003987e-02 6.384330e-03 -5.659422e-03 1.439256e-03
## [20,] 1.235428e-03 -2.741516e-03 7.996938e-04 -3.614982e-03
## [21,] 1.589272e-02 -1.037627e-02 5.971808e-03 -2.391169e-03
## [22,] 4.702936e-03 4.769204e-03 -2.057348e-03 2.874442e-03
## [23,] -3.126964e-02 1.489023e-02 -2.803344e-03 7.747324e-04
## [24,] 4.739484e-02 -2.594937e-02 1.091870e-02 -1.351463e-03
## [25,] -5.782902e-02 3.520564e-02 -1.690221e-02 7.589786e-03
## [26,] 2.639571e-02 -2.202475e-02 8.743143e-03 -7.133776e-03
## [27,] 7.271291e-03 -2.655676e-03 -5.994756e-04 8.215538e-04
## [28,] -2.010197e-02 1.004234e-02 -4.644893e-03 1.349291e-04
## [29,] 2.843413e-02 -1.649348e-02 7.326588e-03 -3.648886e-03
## [30,] -1.156748e-02 1.128246e-02 -3.916164e-03 2.702910e-03
## [31,] -2.706151e-03 3.152118e-04 2.611173e-03 -7.279651e-04
## [32,] 1.414428e-02 -6.293685e-03 2.943982e-03 1.648904e-03
## [33,] -2.735705e-02 1.719837e-02 -8.559033e-03 3.774150e-03
## [34,] 7.195000e-03 -8.403020e-03 3.509881e-03 -3.520099e-03
## [35,] 1.540600e-02 -7.525491e-03 2.151751e-03 -3.793067e-04
## [36,] -2.316673e-02 1.271928e-02 -5.429068e-03 1.384162e-03
## [37,] 2.532515e-02 -1.491523e-02 6.588008e-03 -3.177260e-03
## [38,] -1.491523e-02 1.013775e-02 -3.802309e-03 2.502001e-03
## [39,] 6.588008e-03 -3.802309e-03 2.020642e-03 -8.175003e-04
## [40,] -3.177260e-03 2.502001e-03 -8.175003e-04 9.226554e-04
## [41,] -7.238499e-04 5.272084e-04 -1.939093e-04 1.740646e-04
## [42,] 2.714757e-18 2.415881e-17 1.887907e-18 1.115127e-17
## [43,] -1.645744e-18 1.351742e-17 3.301198e-18 7.378695e-18
## [44,] 1.067992e-17 -6.120129e-18 2.860080e-18 -2.458172e-18
## [45,] 1.701711e-17 -2.031198e-18 6.882970e-18 3.470194e-19
## [46,] -1.454505e-17 1.739532e-17 -1.883472e-18 7.060762e-18
## [,41] [,42] [,43] [,44]
## [1,] -3.469447e-18 -4.638030e-21 4.930381e-32 -6.162976e-33
## [2,] -2.356528e-04 1.222003e-16 4.812500e-17 6.348504e-18
## [3,] 5.077950e-04 -6.423811e-18 9.593604e-17 5.282570e-17
## [4,] -5.243695e-04 4.334205e-17 1.088724e-16 3.849570e-17
## [5,] 8.426265e-04 9.091130e-17 6.433358e-18 -4.338385e-17
## [6,] -5.813562e-04 -7.376952e-17 -6.980719e-17 1.374261e-17
## [7,] 4.074492e-05 2.447284e-17 3.765944e-17 7.337633e-18
## [8,] 1.181890e-04 6.651254e-19 -4.054499e-17 2.965487e-18
## [9,] 4.954260e-04 -4.982619e-18 -1.116098e-17 -3.892819e-18
## [10,] -4.572410e-04 -2.515054e-17 9.838787e-18 1.573758e-17
## [11,] -1.830659e-04 -5.983865e-18 1.947424e-18 -8.147601e-18
## [12,] 4.278484e-04 1.929559e-17 4.395934e-18 -6.013910e-18
## [13,] -2.048259e-03 -9.276009e-18 -1.497516e-17 1.172931e-18
## [14,] 1.784698e-03 1.012406e-17 1.384114e-17 4.200698e-17
## [15,] -2.399444e-04 -8.697075e-18 1.393244e-17 -8.709256e-19
## [16,] -2.305225e-04 9.585747e-18 -3.172640e-17 -4.104662e-18
## [17,] 3.362009e-04 -3.516188e-17 5.076746e-19 9.892972e-18
## [18,] -2.136228e-04 3.575476e-17 9.751919e-18 -3.714472e-18
## [19,] 3.891430e-04 -1.293161e-17 -2.459680e-17 -2.056860e-17
## [20,] -5.899267e-04 -2.643259e-17 -1.592478e-17 1.556862e-18
## [21,] -5.619173e-04 -1.396175e-17 7.715562e-18 -4.052084e-18
## [22,] 5.071426e-04 2.170380e-17 1.647651e-18 2.218603e-17
## [23,] 2.666847e-04 -3.855328e-17 -4.723502e-17 7.716462e-18
## [24,] -6.028231e-04 8.318204e-17 -3.080034e-17 1.466846e-18
## [25,] 1.752559e-03 -5.141149e-17 3.674636e-18 -1.437459e-17
## [26,] -1.414534e-03 -4.276170e-17 -2.563881e-17 3.693303e-17
## [27,] 1.256273e-04 1.083387e-17 -1.056541e-17 -1.956310e-17
## [28,] 1.847301e-04 -2.614917e-17 -1.635577e-17 -6.499682e-18
## [29,] -8.220590e-04 -4.555869e-18 8.975952e-19 1.156535e-17
## [30,] 5.623417e-04 3.508412e-17 1.644310e-17 6.094194e-18
## [31,] -1.714845e-04 -5.450825e-19 4.459051e-17 -3.249285e-17
## [32,] 1.506856e-04 2.930269e-17 -3.217814e-17 -7.411059e-18
## [33,] 8.728323e-04 -6.196931e-18 -4.960563e-18 -8.840552e-18
## [34,] -6.650148e-04 -4.665943e-17 -2.151329e-17 6.212372e-18
## [35,] -1.501591e-04 8.262765e-18 -1.570309e-17 -8.980858e-18
## [36,] 4.091072e-04 -2.498065e-17 2.387614e-17 6.316743e-18
## [37,] -7.238499e-04 2.714757e-18 -1.645744e-18 1.067992e-17
## [38,] 5.272084e-04 2.415881e-17 1.351742e-17 -6.120129e-18
## [39,] -1.939093e-04 1.887907e-18 3.301198e-18 2.860080e-18
## [40,] 1.740646e-04 1.115127e-17 7.378695e-18 -2.458172e-18
## [41,] 3.408523e-05 1.809891e-18 1.136302e-18 -4.786807e-19
## [42,] 1.809891e-18 4.638030e-21 -3.425031e-32 3.940827e-33
## [43,] 1.136302e-18 -3.425031e-32 1.732570e-20 1.005744e-35
## [44,] -4.786807e-19 3.940827e-33 1.005744e-35 -1.550502e-23
## [45,] -1.303205e-19 -8.863926e-33 -1.314176e-32 -2.612318e-33
## [46,] 1.214007e-18 -1.451476e-32 -9.282341e-33 2.218711e-33
## [,45] [,46]
## [1,] 1.337831e-21 -2.598756e-20
## [2,] 9.948454e-17 5.822664e-17
## [3,] 1.672611e-17 5.062425e-17
## [4,] 6.627141e-17 -8.824360e-18
## [5,] -5.894369e-17 6.610137e-17
## [6,] 3.652599e-17 -5.844193e-17
## [7,] -1.391555e-17 -1.405561e-17
## [8,] -4.032236e-17 5.208942e-18
## [9,] -1.856117e-17 -1.257390e-17
## [10,] -8.265565e-18 7.237987e-19
## [11,] 2.983312e-18 4.698387e-18
## [12,] -1.311616e-18 3.202895e-18
## [13,] 1.341169e-17 -3.821286e-17
## [14,] -5.104016e-17 1.073645e-17
## [15,] 6.032250e-18 -7.727746e-18
## [16,] -1.580266e-17 1.189776e-17
## [17,] 2.904667e-17 -3.624565e-17
## [18,] 1.385309e-18 1.836760e-17
## [19,] -6.204626e-18 -1.043068e-17
## [20,] 1.490295e-17 -6.763283e-17
## [21,] 4.692941e-17 -1.168183e-17
## [22,] 2.671290e-17 6.301799e-18
## [23,] 4.146911e-18 1.350745e-17
## [24,] 1.402337e-17 1.447432e-17
## [25,] -3.062043e-17 -6.653826e-18
## [26,] -9.655856e-18 -3.225214e-17
## [27,] -4.754281e-19 -7.032966e-18
## [28,] -1.505614e-17 -8.187032e-17
## [29,] 2.575384e-17 -2.979725e-17
## [30,] 2.605561e-17 1.902944e-17
## [31,] 3.650346e-18 1.321742e-17
## [32,] -4.199460e-18 3.905060e-18
## [33,] -9.996315e-18 2.090679e-18
## [34,] -1.396102e-17 -3.027247e-17
## [35,] -2.902841e-18 -9.192568e-18
## [36,] -9.381912e-18 1.974121e-18
## [37,] 1.701711e-17 -1.454505e-17
## [38,] -2.031198e-18 1.739532e-17
## [39,] 6.882970e-18 -1.883472e-18
## [40,] 3.470194e-19 7.060762e-18
## [41,] -1.303205e-19 1.214007e-18
## [42,] -8.863926e-33 -1.451476e-32
## [43,] -1.314176e-32 -9.282341e-33
## [44,] -2.612318e-33 2.218711e-33
## [45,] -1.337831e-21 -5.081620e-33
## [46,] -5.081620e-33 -2.598756e-20
##
## $T
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 1 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 1 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 1 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 1 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 1 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 1 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 1 0 0
## [11,] 0 0 0 0 0 0 0 0 0 0 0 1 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0 0 1
## [13,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [14,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [23,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [24,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [25,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [26,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [27,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [28,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [29,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [30,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [31,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [32,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [33,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [34,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [35,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [36,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [37,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [38,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [39,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [40,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [41,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [42,] 1 0 0 0 0 0 0 0 0 0 0 0 0
## [43,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [44,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [45,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [46,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0
## [13,] 1 0 0 0 0 0 0 0 0 0 0
## [14,] 0 1 0 0 0 0 0 0 0 0 0
## [15,] 0 0 1 0 0 0 0 0 0 0 0
## [16,] 0 0 0 1 0 0 0 0 0 0 0
## [17,] 0 0 0 0 1 0 0 0 0 0 0
## [18,] 0 0 0 0 0 1 0 0 0 0 0
## [19,] 0 0 0 0 0 0 1 0 0 0 0
## [20,] 0 0 0 0 0 0 0 1 0 0 0
## [21,] 0 0 0 0 0 0 0 0 1 0 0
## [22,] 0 0 0 0 0 0 0 0 0 1 0
## [23,] 0 0 0 0 0 0 0 0 0 0 1
## [24,] 0 0 0 0 0 0 0 0 0 0 0
## [25,] 0 0 0 0 0 0 0 0 0 0 0
## [26,] 0 0 0 0 0 0 0 0 0 0 0
## [27,] 0 0 0 0 0 0 0 0 0 0 0
## [28,] 0 0 0 0 0 0 0 0 0 0 0
## [29,] 0 0 0 0 0 0 0 0 0 0 0
## [30,] 0 0 0 0 0 0 0 0 0 0 0
## [31,] 0 0 0 0 0 0 0 0 0 0 0
## [32,] 0 0 0 0 0 0 0 0 0 0 0
## [33,] 0 0 0 0 0 0 0 0 0 0 0
## [34,] 0 0 0 0 0 0 0 0 0 0 0
## [35,] 0 0 0 0 0 0 0 0 0 0 0
## [36,] 0 0 0 0 0 0 0 0 0 0 0
## [37,] 0 0 0 0 0 0 0 0 0 0 0
## [38,] 0 0 0 0 0 0 0 0 0 0 0
## [39,] 0 0 0 0 0 0 0 0 0 0 0
## [40,] 0 0 0 0 0 0 0 0 0 0 0
## [41,] 0 0 0 0 0 0 0 0 0 0 0
## [42,] 0 0 0 0 0 0 0 0 0 0 0
## [43,] 0 0 0 0 0 0 0 0 0 0 0
## [44,] 0 0 0 0 0 0 0 0 0 0 0
## [45,] 0 0 0 0 0 0 0 0 0 0 0
## [46,] 0 0 0 0 0 0 0 0 0 0 0
## [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35]
## [1,] 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0
## [13,] 0 0 0 0 0 0 0 0 0 0 0
## [14,] 0 0 0 0 0 0 0 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0
## [21,] 0 0 0 0 0 0 0 0 0 0 0
## [22,] 0 0 0 0 0 0 0 0 0 0 0
## [23,] 0 0 0 0 0 0 0 0 0 0 0
## [24,] 1 0 0 0 0 0 0 0 0 0 0
## [25,] 0 1 0 0 0 0 0 0 0 0 0
## [26,] 0 0 1 0 0 0 0 0 0 0 0
## [27,] 0 0 0 1 0 0 0 0 0 0 0
## [28,] 0 0 0 0 1 0 0 0 0 0 0
## [29,] 0 0 0 0 0 1 0 0 0 0 0
## [30,] 0 0 0 0 0 0 1 0 0 0 0
## [31,] 0 0 0 0 0 0 0 1 0 0 0
## [32,] 0 0 0 0 0 0 0 0 1 0 0
## [33,] 0 0 0 0 0 0 0 0 0 1 0
## [34,] 0 0 0 0 0 0 0 0 0 0 1
## [35,] 0 0 0 0 0 0 0 0 0 0 0
## [36,] 0 0 0 0 0 0 0 0 0 0 0
## [37,] 0 0 0 0 0 0 0 0 0 0 0
## [38,] 0 0 0 0 0 0 0 0 0 0 0
## [39,] 0 0 0 0 0 0 0 0 0 0 0
## [40,] 0 0 0 0 0 0 0 0 0 0 0
## [41,] 0 0 0 0 0 0 0 0 0 0 0
## [42,] 0 0 0 0 0 0 0 0 0 0 0
## [43,] 0 0 0 0 0 0 0 0 0 0 0
## [44,] 0 0 0 0 0 0 0 0 0 0 0
## [45,] 0 0 0 0 0 0 0 0 0 0 0
## [46,] 0 0 0 0 0 0 0 0 0 0 0
## [,36] [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46]
## [1,] 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0
## [7,] 0 0 0 0 0 0 0 0 0 0 0
## [8,] 0 0 0 0 0 0 0 0 0 0 0
## [9,] 0 0 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0
## [13,] 0 0 0 0 0 0 0 0 0 0 0
## [14,] 0 0 0 0 0 0 0 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0
## [21,] 0 0 0 0 0 0 0 0 0 0 0
## [22,] 0 0 0 0 0 0 0 0 0 0 0
## [23,] 0 0 0 0 0 0 0 0 0 0 0
## [24,] 0 0 0 0 0 0 0 0 0 0 0
## [25,] 0 0 0 0 0 0 0 0 0 0 0
## [26,] 0 0 0 0 0 0 0 0 0 0 0
## [27,] 0 0 0 0 0 0 0 0 0 0 0
## [28,] 0 0 0 0 0 0 0 0 0 0 0
## [29,] 0 0 0 0 0 0 0 0 0 0 0
## [30,] 0 0 0 0 0 0 0 0 0 0 0
## [31,] 0 0 0 0 0 0 0 0 0 0 0
## [32,] 0 0 0 0 0 0 0 0 0 0 0
## [33,] 0 0 0 0 0 0 0 0 0 0 0
## [34,] 0 0 0 0 0 0 0 0 0 0 0
## [35,] 1 0 0 0 0 0 0 0 0 0 0
## [36,] 0 1 0 0 0 0 0 0 0 0 0
## [37,] 0 0 1 0 0 0 0 0 0 0 0
## [38,] 0 0 0 1 0 0 0 0 0 0 0
## [39,] 0 0 0 0 1 0 0 0 0 0 0
## [40,] 0 0 0 0 0 1 0 0 0 0 0
## [41,] 0 0 0 0 0 0 0 0 0 0 0
## [42,] 0 0 0 0 0 0 1 0 0 1 -1
## [43,] 0 0 0 0 0 0 1 0 0 0 0
## [44,] 0 0 0 0 0 0 0 1 0 0 0
## [45,] 0 0 0 0 0 0 0 0 1 0 0
## [46,] 0 0 0 0 0 0 0 0 0 1 0
##
## $V
## [,1] [,2] [,3] [,4]
## [1,] 1.000000e+00 -9.105817e-01 1.944100e-02 2.974953e-01
## [2,] -9.105817e-01 8.291590e-01 -1.770262e-02 -2.708937e-01
## [3,] 1.944100e-02 -1.770262e-02 3.779526e-04 5.783606e-03
## [4,] 2.974953e-01 -2.708937e-01 5.783606e-03 8.850343e-02
## [5,] -9.156061e-01 8.337342e-01 -1.780030e-02 -2.723885e-01
## [6,] 7.308196e-01 -6.654709e-01 1.420787e-02 2.174154e-01
## [7,] -2.062638e-01 1.878200e-01 -4.009975e-03 -6.136251e-02
## [8,] 1.388146e-01 -1.264021e-01 2.698696e-03 4.129670e-02
## [9,] -1.465235e-01 1.334217e-01 -2.848565e-03 -4.359006e-02
## [10,] 1.883839e-01 -1.715390e-01 3.662373e-03 5.604333e-02
## [11,] 3.367020e-02 -3.065947e-02 6.545824e-04 1.001672e-02
## [12,] -1.361915e-01 1.240135e-01 -2.647699e-03 -4.051633e-02
## [13,] 2.570482e-01 -2.340634e-01 4.997275e-03 7.647063e-02
## [14,] -2.073088e-01 1.887716e-01 -4.030291e-03 -6.167338e-02
## [15,] 6.667030e-02 -6.070875e-02 1.296137e-03 1.983410e-02
## [16,] -5.553735e-02 5.057129e-02 -1.079702e-03 -1.652210e-02
## [17,] 2.760579e-01 -2.513733e-01 5.366843e-03 8.212592e-02
## [18,] -2.657814e-01 2.420157e-01 -5.167058e-03 -7.906872e-02
## [19,] -8.147977e-05 7.419399e-05 -1.584048e-06 -2.423985e-05
## [20,] 9.823212e-02 -8.944837e-02 1.909731e-03 2.922359e-02
## [21,] 1.262984e-01 -1.150050e-01 2.455368e-03 3.757318e-02
## [22,] -1.458781e-01 1.328339e-01 -2.836017e-03 -4.339805e-02
## [23,] -5.601745e-02 5.100846e-02 -1.089035e-03 -1.666493e-02
## [24,] 1.647632e-01 -1.500304e-01 3.203163e-03 4.901628e-02
## [25,] -5.579007e-01 5.080142e-01 -1.084615e-02 -1.659728e-01
## [26,] 4.829560e-01 -4.397709e-01 9.389149e-03 1.436771e-01
## [27,] -7.662412e-02 6.977252e-02 -1.489650e-03 -2.279531e-02
## [28,] -2.646147e-02 2.409533e-02 -5.144375e-04 -7.872161e-03
## [29,] 3.175366e-01 -2.891430e-01 6.173231e-03 9.446565e-02
## [30,] -2.441708e-01 2.223375e-01 -4.746925e-03 -7.263966e-02
## [31,] 6.622383e-02 -6.030221e-02 1.287458e-03 1.970128e-02
## [32,] -4.105146e-02 3.738070e-02 -7.980815e-04 -1.221261e-02
## [33,] -4.727167e-01 4.304471e-01 -9.190086e-03 -1.406310e-01
## [34,] 4.116940e-01 -3.748810e-01 8.003745e-03 1.224770e-01
## [35,] -2.301006e-02 2.095254e-02 -4.473386e-04 -6.845384e-03
## [36,] -1.063425e-01 9.683354e-02 -2.067405e-03 -3.163639e-02
## [37,] 2.950308e-01 -2.686496e-01 5.735694e-03 8.777026e-02
## [38,] -2.241809e-01 2.041350e-01 -4.358301e-03 -6.669274e-02
## [39,] 8.238641e-02 -7.501956e-02 1.601674e-03 2.450957e-02
## [40,] -8.043554e-02 7.324313e-02 -1.563748e-03 -2.392919e-02
## [41,] -1.547283e-02 1.408927e-02 -3.008073e-04 -4.603093e-03
## [42,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [43,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [44,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [45,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,5] [,6] [,7] [,8]
## [1,] -9.156061e-01 7.308196e-01 -2.062638e-01 1.388146e-01
## [2,] 8.337342e-01 -6.654709e-01 1.878200e-01 -1.264021e-01
## [3,] -1.780030e-02 1.420787e-02 -4.009975e-03 2.698696e-03
## [4,] -2.723885e-01 2.174154e-01 -6.136251e-02 4.129670e-02
## [5,] 8.383346e-01 -6.691429e-01 1.888564e-01 -1.270995e-01
## [6,] -6.691429e-01 5.340972e-01 -1.507416e-01 1.014485e-01
## [7,] 1.888564e-01 -1.507416e-01 4.254476e-02 -2.863244e-02
## [8,] -1.270995e-01 1.014485e-01 -2.863244e-02 1.926951e-02
## [9,] 1.341579e-01 -1.070823e-01 3.022251e-02 -2.033961e-02
## [10,] -1.724855e-01 1.376747e-01 -3.885679e-02 2.615045e-02
## [11,] -3.082864e-02 2.460684e-02 -6.944943e-03 4.673917e-03
## [12,] 1.246978e-01 -9.953142e-02 2.809138e-02 -1.890538e-02
## [13,] -2.353549e-01 1.878559e-01 -5.301974e-02 3.568206e-02
## [14,] 1.898132e-01 -1.515053e-01 4.276030e-02 -2.877749e-02
## [15,] -6.104373e-02 4.872396e-02 -1.375167e-02 9.254814e-03
## [16,] 5.085034e-02 -4.058778e-02 1.145535e-02 -7.709398e-03
## [17,] -2.527603e-01 2.017485e-01 -5.694076e-02 3.832088e-02
## [18,] 2.433511e-01 -1.942383e-01 5.482109e-02 -3.689436e-02
## [19,] 7.460338e-05 -5.954701e-05 1.680633e-05 -1.131059e-05
## [20,] -8.994193e-02 7.178995e-02 -2.026173e-02 1.363606e-02
## [21,] -1.156396e-01 9.230135e-02 -2.605079e-02 1.753207e-02
## [22,] 1.335669e-01 -1.066106e-01 3.008938e-02 -2.025002e-02
## [23,] 5.128992e-02 -4.093865e-02 1.155437e-02 -7.776043e-03
## [24,] -1.508582e-01 1.204122e-01 -3.398469e-02 2.287155e-02
## [25,] 5.108173e-01 -4.077248e-01 1.150747e-01 -7.744479e-02
## [26,] -4.421975e-01 3.529537e-01 -9.961635e-02 6.704137e-02
## [27,] 7.015752e-02 -5.599841e-02 1.580478e-02 -1.063655e-02
## [28,] 2.422828e-02 -1.933856e-02 5.458043e-03 -3.673239e-03
## [29,] -2.907385e-01 2.320620e-01 -6.549632e-02 4.407874e-02
## [30,] 2.235643e-01 -1.784448e-01 5.036360e-02 -3.389448e-02
## [31,] -6.063495e-02 4.839767e-02 -1.365958e-02 9.192838e-03
## [32,] 3.758697e-02 -3.000121e-02 8.467430e-03 -5.698544e-03
## [33,] 4.328223e-01 -3.454706e-01 9.750434e-02 -6.562000e-02
## [34,] -3.769496e-01 3.008740e-01 -8.491758e-02 5.714916e-02
## [35,] 2.106815e-02 -1.681620e-02 4.746143e-03 -3.194133e-03
## [36,] 9.736785e-02 -7.771719e-02 2.193461e-02 -1.476190e-02
## [37,] -2.701320e-01 2.156143e-01 -6.085417e-02 4.095460e-02
## [38,] 2.052614e-01 -1.638358e-01 4.624040e-02 -3.111959e-02
## [39,] -7.543350e-02 6.020960e-02 -1.699334e-02 1.143644e-02
## [40,] 7.364728e-02 -5.878387e-02 1.659094e-02 -1.116563e-02
## [41,] 1.416702e-02 -1.130785e-02 3.191485e-03 -2.147855e-03
## [42,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [43,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [44,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [45,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,9] [,10] [,11] [,12]
## [1,] -1.465235e-01 1.883839e-01 3.367020e-02 -1.361915e-01
## [2,] 1.334217e-01 -1.715390e-01 -3.065947e-02 1.240135e-01
## [3,] -2.848565e-03 3.662373e-03 6.545824e-04 -2.647699e-03
## [4,] -4.359006e-02 5.604333e-02 1.001672e-02 -4.051633e-02
## [5,] 1.341579e-01 -1.724855e-01 -3.082864e-02 1.246978e-01
## [6,] -1.070823e-01 1.376747e-01 2.460684e-02 -9.953142e-02
## [7,] 3.022251e-02 -3.885679e-02 -6.944943e-03 2.809138e-02
## [8,] -2.033961e-02 2.615045e-02 4.673917e-03 -1.890538e-02
## [9,] 2.146915e-02 -2.760268e-02 -4.933477e-03 1.995526e-02
## [10,] -2.760268e-02 3.548851e-02 6.342925e-03 -2.565629e-02
## [11,] -4.933477e-03 6.342925e-03 1.133682e-03 -4.585595e-03
## [12,] 1.995526e-02 -2.565629e-02 -4.585595e-03 1.854813e-02
## [13,] -3.766362e-02 4.842376e-02 8.654864e-03 -3.500778e-02
## [14,] 3.037562e-02 -3.905365e-02 -6.980128e-03 2.823369e-02
## [15,] -9.768768e-03 1.255961e-02 2.244802e-03 -9.079928e-03
## [16,] 8.137530e-03 -1.046235e-02 -1.869954e-03 7.563715e-03
## [17,] -4.044899e-02 5.200488e-02 9.294925e-03 -3.759674e-02
## [18,] 3.894324e-02 -5.006895e-02 -8.948913e-03 3.619717e-02
## [19,] 1.193871e-05 -1.534948e-05 -2.743440e-06 1.109685e-05
## [20,] -1.439332e-02 1.850535e-02 3.307495e-03 -1.337838e-02
## [21,] -1.850569e-02 2.379259e-02 4.252493e-03 -1.720077e-02
## [22,] 2.137458e-02 -2.748110e-02 -4.911745e-03 1.986736e-02
## [23,] 8.207876e-03 -1.055279e-02 -1.886119e-03 7.629101e-03
## [24,] -2.414169e-02 3.103875e-02 5.547611e-03 -2.243935e-02
## [25,] 8.174560e-02 -1.050995e-01 -1.878463e-02 7.598134e-02
## [26,] -7.076443e-02 9.098116e-02 1.626122e-02 -6.577450e-02
## [27,] 1.122724e-02 -1.443475e-02 -2.579949e-03 1.043555e-02
## [28,] 3.877228e-03 -4.984916e-03 -8.909629e-04 3.603827e-03
## [29,] -4.652660e-02 5.981881e-02 1.069152e-02 -4.324579e-02
## [30,] 3.577677e-02 -4.599786e-02 -8.221279e-03 3.325399e-02
## [31,] -9.703351e-03 1.247551e-02 2.229770e-03 -9.019123e-03
## [32,] 6.015005e-03 -7.733436e-03 -1.382211e-03 5.590860e-03
## [33,] 6.926412e-02 -8.905223e-02 -1.591646e-02 6.437999e-02
## [34,] -6.032287e-02 7.755655e-02 1.386182e-02 -5.606923e-02
## [35,] 3.371516e-03 -4.334726e-03 -7.747533e-04 3.133775e-03
## [36,] 1.558168e-02 -2.003322e-02 -3.580573e-03 1.448295e-02
## [37,] -4.322896e-02 5.557906e-02 9.933745e-03 -4.018069e-02
## [38,] 3.284777e-02 -4.223207e-02 -7.548214e-03 3.053153e-02
## [39,] -1.207155e-02 1.552028e-02 2.773967e-03 -1.122033e-02
## [40,] 1.178570e-02 -1.515277e-02 -2.708281e-03 1.095464e-02
## [41,] 2.267134e-03 -2.914833e-03 -5.209732e-04 2.107268e-03
## [42,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [43,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [44,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [45,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,13] [,14] [,15] [,16]
## [1,] 2.570482e-01 -2.073088e-01 6.667030e-02 -5.553735e-02
## [2,] -2.340634e-01 1.887716e-01 -6.070875e-02 5.057129e-02
## [3,] 4.997275e-03 -4.030291e-03 1.296137e-03 -1.079702e-03
## [4,] 7.647063e-02 -6.167338e-02 1.983410e-02 -1.652210e-02
## [5,] -2.353549e-01 1.898132e-01 -6.104373e-02 5.085034e-02
## [6,] 1.878559e-01 -1.515053e-01 4.872396e-02 -4.058778e-02
## [7,] -5.301974e-02 4.276030e-02 -1.375167e-02 1.145535e-02
## [8,] 3.568206e-02 -2.877749e-02 9.254814e-03 -7.709398e-03
## [9,] -3.766362e-02 3.037562e-02 -9.768768e-03 8.137530e-03
## [10,] 4.842376e-02 -3.905365e-02 1.255961e-02 -1.046235e-02
## [11,] 8.654864e-03 -6.980128e-03 2.244802e-03 -1.869954e-03
## [12,] -3.500778e-02 2.823369e-02 -9.079928e-03 7.563715e-03
## [13,] 6.607378e-02 -5.328835e-02 1.713748e-02 -1.427578e-02
## [14,] -5.328835e-02 4.297693e-02 -1.382134e-02 1.151338e-02
## [15,] 1.713748e-02 -1.382134e-02 4.444928e-03 -3.702692e-03
## [16,] -1.427578e-02 1.151338e-02 -3.702692e-03 3.084397e-03
## [17,] 7.096019e-02 -5.722923e-02 1.840486e-02 -1.533153e-02
## [18,] -6.831864e-02 5.509882e-02 -1.771973e-02 1.476080e-02
## [19,] -2.094423e-05 1.689147e-05 -5.432280e-06 4.525171e-06
## [20,] 2.525039e-02 -2.036438e-02 6.549164e-03 -5.455552e-03
## [21,] 3.246478e-02 -2.618277e-02 8.420352e-03 -7.014279e-03
## [22,] -3.749771e-02 3.024181e-02 -9.725737e-03 8.101684e-03
## [23,] -1.439919e-02 1.161291e-02 -3.734700e-03 3.111061e-03
## [24,] 4.235210e-02 -3.415686e-02 1.098481e-02 -9.150514e-03
## [25,] -1.434074e-01 1.156577e-01 -3.719541e-02 3.098433e-02
## [26,] 1.241430e-01 -1.001210e-01 3.219882e-02 -2.682210e-02
## [27,] -1.969609e-02 1.588485e-02 -5.108553e-03 4.255501e-03
## [28,] -6.801873e-03 5.485695e-03 -1.764194e-03 1.469600e-03
## [29,] 8.162223e-02 -6.582813e-02 2.117026e-02 -1.763514e-02
## [30,] -6.276367e-02 5.061875e-02 -1.627894e-02 1.356060e-02
## [31,] 1.702272e-02 -1.372878e-02 4.415162e-03 -3.677896e-03
## [32,] -1.055220e-02 8.510327e-03 -2.736913e-03 2.279889e-03
## [33,] -1.215110e-01 9.799831e-02 -3.151616e-02 2.625343e-02
## [34,] 1.058252e-01 -8.534778e-02 2.744776e-02 -2.286440e-02
## [35,] -5.914695e-03 4.770187e-03 -1.534087e-03 1.277918e-03
## [36,] -2.733515e-02 2.204574e-02 -7.089886e-03 5.905981e-03
## [37,] 7.583714e-02 -6.116247e-02 1.966979e-02 -1.638523e-02
## [38,] -5.762529e-02 4.647466e-02 -1.494620e-02 1.245041e-02
## [39,] 2.117728e-02 -1.707943e-02 5.492727e-03 -4.575523e-03
## [40,] -2.067581e-02 1.667499e-02 -5.362662e-03 4.467177e-03
## [41,] -3.977263e-03 3.207653e-03 -1.031578e-03 8.593199e-04
## [42,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [43,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [44,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [45,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,17] [,18] [,19] [,20]
## [1,] 2.760579e-01 -2.657814e-01 -8.147977e-05 9.823212e-02
## [2,] -2.513733e-01 2.420157e-01 7.419399e-05 -8.944837e-02
## [3,] 5.366843e-03 -5.167058e-03 -1.584048e-06 1.909731e-03
## [4,] 8.212592e-02 -7.906872e-02 -2.423985e-05 2.922359e-02
## [5,] -2.527603e-01 2.433511e-01 7.460338e-05 -8.994193e-02
## [6,] 2.017485e-01 -1.942383e-01 -5.954701e-05 7.178995e-02
## [7,] -5.694076e-02 5.482109e-02 1.680633e-05 -2.026173e-02
## [8,] 3.832088e-02 -3.689436e-02 -1.131059e-05 1.363606e-02
## [9,] -4.044899e-02 3.894324e-02 1.193871e-05 -1.439332e-02
## [10,] 5.200488e-02 -5.006895e-02 -1.534948e-05 1.850535e-02
## [11,] 9.294925e-03 -8.948913e-03 -2.743440e-06 3.307495e-03
## [12,] -3.759674e-02 3.619717e-02 1.109685e-05 -1.337838e-02
## [13,] 7.096019e-02 -6.831864e-02 -2.094423e-05 2.525039e-02
## [14,] -5.722923e-02 5.509882e-02 1.689147e-05 -2.036438e-02
## [15,] 1.840486e-02 -1.771973e-02 -5.432280e-06 6.549164e-03
## [16,] -1.533153e-02 1.476080e-02 4.525171e-06 -5.455552e-03
## [17,] 7.620797e-02 -7.337107e-02 -2.249314e-05 2.711775e-02
## [18,] -7.337107e-02 7.063977e-02 2.165581e-05 -2.610827e-02
## [19,] -2.249314e-05 2.165581e-05 6.638953e-09 -8.003931e-06
## [20,] 2.711775e-02 -2.610827e-02 -8.003931e-06 9.649549e-03
## [21,] 3.486568e-02 -3.356777e-02 -1.029077e-05 1.240656e-02
## [22,] -4.027081e-02 3.877170e-02 1.188612e-05 -1.432992e-02
## [23,] -1.546406e-02 1.488840e-02 4.564289e-06 -5.502713e-03
## [24,] 4.548420e-02 -4.379101e-02 -1.342487e-05 1.618504e-02
## [25,] -1.540129e-01 1.482797e-01 4.545762e-05 -5.480377e-02
## [26,] 1.333238e-01 -1.283607e-01 -3.935114e-05 4.744179e-02
## [27,] -2.115270e-02 2.036527e-02 6.243316e-06 -7.526950e-03
## [28,] -7.304898e-03 7.032967e-03 2.156074e-06 -2.599366e-03
## [29,] 8.765851e-02 -8.439534e-02 -2.587281e-05 3.119230e-02
## [30,] -6.740528e-02 6.489606e-02 1.989498e-05 -2.398541e-02
## [31,] 1.828161e-02 -1.760106e-02 -5.395903e-06 6.505307e-03
## [32,] -1.133258e-02 1.091071e-02 3.344863e-06 -4.032572e-03
## [33,] -1.304972e-01 1.256393e-01 3.851685e-05 -4.643596e-02
## [34,] 1.136514e-01 -1.094206e-01 -3.354473e-05 4.044158e-02
## [35,] -6.352109e-03 6.115646e-03 1.874854e-06 -2.260327e-03
## [36,] -2.935669e-02 2.826386e-02 8.664763e-06 -1.044625e-02
## [37,] 8.144558e-02 -7.841370e-02 -2.403904e-05 2.898150e-02
## [38,] -6.188690e-02 5.958311e-02 1.826620e-05 -2.202176e-02
## [39,] 2.274342e-02 -2.189678e-02 -6.712826e-06 8.092992e-03
## [40,] -2.220487e-02 2.137827e-02 6.553870e-06 -7.901354e-03
## [41,] -4.271397e-03 4.112390e-03 1.260723e-06 -1.519929e-03
## [42,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [43,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [44,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [45,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,21] [,22] [,23] [,24]
## [1,] 1.262984e-01 -1.458781e-01 -5.601745e-02 1.647632e-01
## [2,] -1.150050e-01 1.328339e-01 5.100846e-02 -1.500304e-01
## [3,] 2.455368e-03 -2.836017e-03 -1.089035e-03 3.203163e-03
## [4,] 3.757318e-02 -4.339805e-02 -1.666493e-02 4.901628e-02
## [5,] -1.156396e-01 1.335669e-01 5.128992e-02 -1.508582e-01
## [6,] 9.230135e-02 -1.066106e-01 -4.093865e-02 1.204122e-01
## [7,] -2.605079e-02 3.008938e-02 1.155437e-02 -3.398469e-02
## [8,] 1.753207e-02 -2.025002e-02 -7.776043e-03 2.287155e-02
## [9,] -1.850569e-02 2.137458e-02 8.207876e-03 -2.414169e-02
## [10,] 2.379259e-02 -2.748110e-02 -1.055279e-02 3.103875e-02
## [11,] 4.252493e-03 -4.911745e-03 -1.886119e-03 5.547611e-03
## [12,] -1.720077e-02 1.986736e-02 7.629101e-03 -2.243935e-02
## [13,] 3.246478e-02 -3.749771e-02 -1.439919e-02 4.235210e-02
## [14,] -2.618277e-02 3.024181e-02 1.161291e-02 -3.415686e-02
## [15,] 8.420352e-03 -9.725737e-03 -3.734700e-03 1.098481e-02
## [16,] -7.014279e-03 8.101684e-03 3.111061e-03 -9.150514e-03
## [17,] 3.486568e-02 -4.027081e-02 -1.546406e-02 4.548420e-02
## [18,] -3.356777e-02 3.877170e-02 1.488840e-02 -4.379101e-02
## [19,] -1.029077e-05 1.188612e-05 4.564289e-06 -1.342487e-05
## [20,] 1.240656e-02 -1.432992e-02 -5.502713e-03 1.618504e-02
## [21,] 1.595129e-02 -1.842417e-02 -7.074915e-03 2.080933e-02
## [22,] -1.842417e-02 2.128043e-02 8.171720e-03 -2.403535e-02
## [23,] -7.074915e-03 8.171720e-03 3.137955e-03 -9.229616e-03
## [24,] 2.080933e-02 -2.403535e-02 -9.229616e-03 2.714692e-02
## [25,] -7.046198e-02 8.138551e-02 3.125218e-02 -9.192153e-02
## [26,] 6.099658e-02 -7.045271e-02 -2.705396e-02 7.957339e-02
## [27,] -9.677505e-03 1.117778e-02 4.292288e-03 -1.262484e-02
## [28,] -3.342041e-03 3.860149e-03 1.482304e-03 -4.359877e-03
## [29,] 4.010437e-02 -4.632165e-02 -1.778759e-02 5.231837e-02
## [30,] -3.083838e-02 3.561918e-02 1.367783e-02 -4.023037e-02
## [31,] 8.363965e-03 -9.660608e-03 -3.709690e-03 1.091125e-02
## [32,] -5.184734e-03 5.988509e-03 2.299598e-03 -6.763771e-03
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## [25,] 8.632302e-03 0 0 0 0 0
## [26,] -7.472695e-03 0 0 0 0 0
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## [36,] 1.645419e-03 0 0 0 0 0
## [37,] -4.564961e-03 0 0 0 0 0
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## [40,] 1.244565e-03 0 0 0 0 0
## [41,] 2.394084e-04 0 0 0 0 0
## [42,] 0.000000e+00 0 0 0 0 0
## [43,] 0.000000e+00 0 0 0 0 0
## [44,] 0.000000e+00 0 0 0 0 0
## [45,] 0.000000e+00 0 0 0 0 0
## [46,] 0.000000e+00 0 0 0 0 0
##
## $h
## [1] 0
##
## $Pn
## [,1] [,2] [,3] [,4]
## [1,] 1.166008e+00 -1.079504e+00 6.093498e-02 3.073661e-01
## [2,] -1.079504e+00 1.165423e+00 -2.253382e-01 -2.430982e-01
## [3,] 6.093498e-02 -2.253382e-01 3.394465e-01 -1.916095e-01
## [4,] 3.073661e-01 -2.430982e-01 -1.916095e-01 4.195217e-01
## [5,] -1.004105e+00 9.394821e-01 -2.467955e-02 -4.620966e-01
## [6,] 8.083312e-01 -8.368134e-01 1.480515e-01 2.071398e-01
## [7,] -2.374347e-01 2.972869e-01 -1.838070e-01 7.038101e-02
## [8,] 1.707655e-01 -1.893175e-01 1.183278e-01 -1.357618e-01
## [9,] -1.335131e-01 1.555860e-01 -6.985839e-02 8.096703e-02
## [10,] 1.852002e-01 -1.584645e-01 3.182445e-02 -1.847378e-02
## [11,] 2.546415e-02 -2.672286e-02 1.445068e-02 3.557945e-02
## [12,] -1.265584e-01 1.089508e-01 -2.692929e-03 -1.980814e-02
## [13,] 1.453666e-01 -1.249743e-01 -7.497960e-03 3.777704e-02
## [14,] -1.072316e-01 -1.223437e-02 1.037016e-01 -3.740753e-02
## [15,] 5.965625e-02 4.464823e-02 -1.981396e-01 1.195623e-01
## [16,] -8.212879e-02 6.905338e-02 1.011050e-01 -2.204645e-01
## [17,] 3.472212e-01 -3.480458e-01 3.663674e-02 1.938544e-01
## [18,] -3.260015e-01 3.728658e-01 -1.138528e-01 -5.689245e-02
## [19,] 2.923019e-02 -8.715597e-02 1.325369e-01 -9.851307e-02
## [20,] 7.008347e-02 -3.555811e-02 -8.354951e-02 1.512939e-01
## [21,] 1.049197e-01 -1.253072e-01 5.934470e-02 -5.824528e-02
## [22,] -1.318776e-01 1.007886e-01 -1.710091e-02 2.356888e-02
## [23,] -4.521984e-02 5.577568e-02 -3.452235e-02 -2.795060e-02
## [24,] 1.466874e-01 -1.249920e-01 1.245237e-02 5.534278e-03
## [25,] -5.184465e-01 4.619129e-01 -2.049298e-03 -1.273214e-01
## [26,] 4.565334e-01 -3.832815e-01 -2.233385e-02 1.277344e-01
## [27,] -7.987724e-02 4.760977e-02 5.241766e-02 -5.118828e-02
## [28,] -1.693331e-02 1.241916e-02 -2.305373e-02 4.934977e-02
## [29,] 3.083011e-01 -2.758965e-01 4.440752e-03 5.881216e-02
## [30,] -2.423279e-01 2.151113e-01 5.786259e-04 -6.567339e-02
## [31,] 6.429470e-02 -5.767995e-02 -3.863742e-03 2.231123e-02
## [32,] -3.651089e-02 3.186467e-02 7.035681e-04 -1.494073e-02
## [33,] -4.854160e-01 4.539496e-01 -3.087714e-02 -1.263560e-01
## [34,] 4.299239e-01 -4.107344e-01 4.596197e-02 9.151809e-02
## [35,] -3.814566e-02 5.355665e-02 -3.783287e-02 2.811917e-02
## [36,] -9.316652e-02 7.111445e-02 2.772943e-02 -6.203526e-02
## [37,] 2.894600e-01 -2.548050e-01 -1.058634e-02 1.061887e-01
## [38,] -2.216670e-01 1.996493e-01 2.258106e-03 -7.479113e-02
## [39,] 8.145050e-02 -7.289301e-02 -2.278909e-04 2.810646e-02
## [40,] -8.067123e-02 7.375088e-02 -2.088753e-03 -2.308658e-02
## [41,] -1.547283e-02 1.408927e-02 -3.008073e-04 -4.603093e-03
## [42,] 1.363859e-16 -4.071629e-18 7.038898e-19 7.929535e-17
## [43,] 8.562994e-17 -3.115220e-17 1.004110e-16 1.314449e-16
## [44,] -3.607262e-17 3.974496e-17 5.094056e-17 2.898675e-17
## [45,] -9.819410e-18 1.085767e-16 1.621288e-17 6.368260e-17
## [46,] 9.145965e-17 -2.647183e-17 5.540525e-17 1.529176e-17
## [,5] [,6] [,7] [,8]
## [1,] -1.004105e+00 8.083312e-01 -2.374347e-01 1.707655e-01
## [2,] 9.394821e-01 -8.368134e-01 2.972869e-01 -1.893175e-01
## [3,] -2.467955e-02 1.480515e-01 -1.838070e-01 1.183278e-01
## [4,] -4.620966e-01 2.071398e-01 7.038101e-02 -1.357618e-01
## [5,] 1.195700e+00 -8.857745e-01 1.941664e-01 -1.533805e-02
## [6,] -8.857745e-01 9.161944e-01 -3.797950e-01 1.253047e-01
## [7,] 1.941664e-01 -3.797950e-01 4.291082e-01 -2.653269e-01
## [8,] -1.533805e-02 1.253047e-01 -2.653269e-01 4.098900e-01
## [9,] -6.206924e-02 1.832734e-02 5.185948e-02 -2.553328e-01
## [10,] -3.493551e-02 -6.737066e-02 8.726255e-02 4.827269e-02
## [11,] -9.642589e-02 1.540429e-01 -2.091509e-01 1.310595e-01
## [12,] 1.345414e-01 -1.529339e-01 1.548354e-01 -2.211578e-01
## [13,] -1.044878e-01 1.114368e-01 -8.376519e-02 1.471793e-01
## [14,] 5.374207e-02 5.100853e-02 -4.944493e-02 -4.068753e-02
## [15,] -2.721544e-02 -8.830419e-02 1.843993e-01 -9.015946e-02
## [16,] 1.704705e-01 -2.412888e-02 -1.193533e-01 1.871893e-01
## [17,] -5.029473e-01 3.600994e-01 -5.403112e-02 -7.971611e-02
## [18,] 3.924019e-01 -4.725222e-01 2.213241e-01 -4.865897e-02
## [19,] -2.926552e-03 1.652539e-01 -2.804565e-01 1.750223e-01
## [20,] -1.588332e-01 4.512151e-02 1.514727e-01 -2.697266e-01
## [21,] 3.170654e-02 4.573798e-03 -4.871260e-02 1.863385e-01
## [22,] 1.778776e-02 5.354734e-02 -5.866256e-02 -3.949660e-02
## [23,] 1.058587e-01 -1.442222e-01 1.666617e-01 -9.840723e-02
## [24,] -1.375968e-01 1.557657e-01 -1.326940e-01 1.771054e-01
## [25,] 4.029796e-01 -3.463061e-01 1.410703e-01 -1.744746e-01
## [26,] -3.545304e-01 2.109686e-01 -3.370102e-02 9.043905e-02
## [27,] 5.288764e-02 2.967442e-02 -1.232829e-01 5.694968e-02
## [28,] -1.381350e-02 -2.885443e-02 8.897725e-02 -1.417288e-01
## [29,] -2.082686e-01 1.755528e-01 -7.217046e-02 1.288110e-01
## [30,] 1.730249e-01 -8.542118e-02 -7.258747e-03 -4.227020e-02
## [31,] -4.839993e-02 -6.028613e-03 7.998829e-02 -4.814222e-02
## [32,] 3.404663e-02 -1.280440e-02 -4.724439e-02 8.801721e-02
## [33,] 4.152896e-01 -3.402191e-01 1.161965e-01 -1.266296e-01
## [34,] -3.559566e-01 2.807167e-01 -8.248597e-02 8.144082e-02
## [35,] 1.896138e-03 -5.807407e-03 -1.205827e-02 -2.783291e-03
## [36,] 1.151922e-01 -8.361045e-02 2.984169e-02 -3.060442e-02
## [37,] -2.796642e-01 2.183458e-01 -6.470045e-02 5.045157e-02
## [38,] 2.093054e-01 -1.631422e-01 4.781384e-02 -3.637269e-02
## [39,] -7.823876e-02 6.047770e-02 -1.586276e-02 1.353518e-02
## [40,] 7.306697e-02 -5.874410e-02 1.670804e-02 -1.066961e-02
## [41,] 1.416702e-02 -1.130785e-02 3.191485e-03 -2.147855e-03
## [42,] -2.654108e-17 2.078278e-17 -3.300431e-18 2.063994e-17
## [43,] -6.730666e-17 -1.044450e-17 2.022257e-17 -2.800422e-17
## [44,] -1.232000e-17 -1.126461e-17 1.468312e-17 -2.317460e-18
## [45,] -5.048658e-17 2.971779e-17 -1.191575e-17 -4.176064e-17
## [46,] -1.268127e-17 4.980196e-18 -3.268488e-17 1.860730e-17
## [,9] [,10] [,11] [,12]
## [1,] -1.335131e-01 1.852002e-01 2.546415e-02 -1.265584e-01
## [2,] 1.555860e-01 -1.584645e-01 -2.672286e-02 1.089508e-01
## [3,] -6.985839e-02 3.182445e-02 1.445068e-02 -2.692929e-03
## [4,] 8.096703e-02 -1.847378e-02 3.557945e-02 -1.980814e-02
## [5,] -6.206924e-02 -3.493551e-02 -9.642589e-02 1.345414e-01
## [6,] 1.832734e-02 -6.737066e-02 1.540429e-01 -1.529339e-01
## [7,] 5.185948e-02 8.726255e-02 -2.091509e-01 1.548354e-01
## [8,] -2.553328e-01 4.827269e-02 1.310595e-01 -2.211578e-01
## [9,] 4.054107e-01 -2.559344e-01 1.854801e-02 1.411038e-01
## [10,] -2.559344e-01 4.132162e-01 -2.239364e-01 3.259081e-03
## [11,] 1.854801e-02 -2.239364e-01 3.774124e-01 -2.327431e-01
## [12,] 1.411038e-01 3.259081e-03 -2.327431e-01 3.899120e-01
## [13,] -2.184331e-01 1.439901e-01 3.270459e-02 -2.441472e-01
## [14,] 1.206421e-01 -1.961320e-01 8.907782e-02 3.711670e-02
## [15,] -1.510221e-02 9.780348e-02 -1.509605e-01 8.792463e-02
## [16,] -9.059008e-02 -1.806926e-02 8.268288e-02 -1.440268e-01
## [17,] 1.550094e-01 -4.350773e-02 -1.973831e-04 4.692517e-02
## [18,] -7.862844e-02 1.425706e-01 -9.987975e-02 2.494400e-02
## [19,] -1.741654e-02 -1.117011e-01 1.902279e-01 -9.305307e-02
## [20,] 1.667462e-01 -6.157089e-03 -1.105026e-01 1.827434e-01
## [21,] -2.949622e-01 1.975836e-01 -2.182294e-02 -1.253868e-01
## [22,] 1.825588e-01 -2.966848e-01 1.691269e-01 -1.114707e-02
## [23,] -1.241946e-02 1.531233e-01 -2.680088e-01 1.781952e-01
## [24,] -1.077078e-01 2.820695e-03 1.665087e-01 -2.819164e-01
## [25,] 2.135097e-01 -1.658652e-01 -3.965750e-02 2.172736e-01
## [26,] -1.479903e-01 2.035763e-01 -4.905595e-02 -7.102404e-02
## [27,] 3.105793e-02 -8.912139e-02 1.088842e-01 -5.597009e-02
## [28,] 6.961282e-02 1.709444e-02 -7.494045e-02 1.132622e-01
## [29,] -1.734336e-01 1.147445e-01 2.871145e-02 -1.074777e-01
## [30,] 1.125377e-01 -1.654274e-01 4.971010e-02 4.429581e-02
## [31,] -1.577253e-02 8.699156e-02 -1.180715e-01 5.096869e-02
## [32,] -5.300021e-02 -1.195045e-02 7.392274e-02 -1.164086e-01
## [33,] 1.492040e-01 -1.360651e-01 -1.494234e-02 1.280348e-01
## [34,] -1.101208e-01 1.481636e-01 -3.746906e-02 -4.574308e-02
## [35,] 2.845739e-02 -5.574907e-02 6.950652e-02 -4.709845e-02
## [36,] 1.116338e-02 1.024294e-02 -5.333710e-02 8.035502e-02
## [37,] -4.906973e-02 4.160150e-02 3.648811e-02 -8.113678e-02
## [38,] 3.491287e-02 -4.106688e-02 -1.877346e-02 5.059857e-02
## [39,] -1.459753e-02 1.501168e-02 2.920181e-03 -2.005768e-02
## [40,] 1.132814e-02 -1.533505e-02 -2.280703e-03 8.905824e-03
## [41,] 2.267134e-03 -2.914833e-03 -5.209732e-04 2.107268e-03
## [42,] -2.059994e-17 -3.487266e-18 -3.005266e-18 4.491781e-18
## [43,] -2.096599e-17 2.343962e-17 3.817475e-18 -4.898331e-18
## [44,] 2.376560e-19 1.000807e-17 -8.935382e-18 -2.098592e-18
## [45,] -1.743665e-17 -9.825421e-18 2.768839e-18 -2.456731e-19
## [46,] -2.304941e-17 1.525471e-17 6.696319e-18 -6.726947e-18
## [,13] [,14] [,15] [,16]
## [1,] 1.453666e-01 -1.072316e-01 5.965625e-02 -8.212879e-02
## [2,] -1.249743e-01 -1.223437e-02 4.464823e-02 6.905338e-02
## [3,] -7.497960e-03 1.037016e-01 -1.981396e-01 1.011050e-01
## [4,] 3.777704e-02 -3.740753e-02 1.195623e-01 -2.204645e-01
## [5,] -1.044878e-01 5.374207e-02 -2.721544e-02 1.704705e-01
## [6,] 1.114368e-01 5.100853e-02 -8.830419e-02 -2.412888e-02
## [7,] -8.376519e-02 -4.944493e-02 1.843993e-01 -1.193533e-01
## [8,] 1.471793e-01 -4.068753e-02 -9.015946e-02 1.871893e-01
## [9,] -2.184331e-01 1.206421e-01 -1.510221e-02 -9.059008e-02
## [10,] 1.439901e-01 -1.961320e-01 9.780348e-02 -1.806926e-02
## [11,] 3.270459e-02 8.907782e-02 -1.509605e-01 8.268288e-02
## [12,] -2.441472e-01 3.711670e-02 8.792463e-02 -1.440268e-01
## [13,] 3.890533e-01 -2.195832e-01 1.292410e-02 8.730680e-02
## [14,] -2.195832e-01 3.131067e-01 -1.488660e-01 -3.124992e-04
## [15,] 1.292410e-02 -1.488660e-01 2.465735e-01 -1.350059e-01
## [16,] 8.730680e-02 -3.124992e-04 -1.350059e-01 2.472375e-01
## [17,] -1.081800e-01 6.882550e-02 6.896860e-03 -1.559127e-01
## [18,] 4.193784e-02 -1.360611e-01 9.416595e-02 1.387822e-02
## [19,] -5.457675e-03 9.305287e-02 -1.728094e-01 1.071406e-01
## [20,] -8.408182e-02 -1.353513e-02 9.854129e-02 -1.780463e-01
## [21,] 2.088155e-01 -1.163723e-01 9.167897e-03 8.508481e-02
## [22,] -1.233690e-01 1.799886e-01 -8.707811e-02 8.465250e-03
## [23,] -3.819135e-02 -7.132643e-02 1.353730e-01 -7.224519e-02
## [24,] 1.891152e-01 -3.904691e-02 -7.338530e-02 1.284491e-01
## [25,] -3.240293e-01 1.938841e-01 -3.076748e-02 -4.795611e-02
## [26,] 1.969815e-01 -2.143284e-01 9.197109e-02 -2.419637e-02
## [27,] -1.382082e-02 7.082595e-02 -1.074273e-01 6.366660e-02
## [28,] -6.859853e-02 7.984500e-03 5.343381e-02 -1.010238e-01
## [29,] 1.481655e-01 -9.062928e-02 1.882947e-02 3.339375e-02
## [30,] -9.449706e-02 8.919326e-02 -3.762242e-02 1.479522e-02
## [31,] 1.908993e-02 -3.786530e-02 4.211838e-02 -2.591268e-02
## [32,] 5.529207e-02 6.395951e-03 -2.713205e-02 4.045460e-02
## [33,] -1.824287e-01 1.098932e-01 -2.626192e-02 9.685964e-03
## [34,] 1.171444e-01 -9.971902e-02 3.303572e-02 -2.489152e-02
## [35,] 5.759157e-03 1.355449e-02 -1.484493e-02 8.039239e-03
## [36,] -6.192625e-02 2.077437e-02 3.399334e-03 -6.650038e-03
## [37,] 1.020364e-01 -6.173234e-02 1.414334e-02 -9.995591e-03
## [38,] -6.862317e-02 4.679915e-02 -1.215986e-02 1.012653e-02
## [39,] 3.023829e-02 -1.860170e-02 4.623219e-03 -2.971646e-03
## [40,] -1.888737e-02 1.643071e-02 -5.592492e-03 4.803534e-03
## [41,] -3.977263e-03 3.207653e-03 -1.031578e-03 8.593199e-04
## [42,] 7.727849e-18 -2.419064e-18 -1.718951e-18 -2.104045e-20
## [43,] -4.299639e-18 5.966204e-18 1.831351e-17 -3.775782e-17
## [44,] -3.324256e-18 4.532439e-17 -2.716503e-18 -1.563855e-18
## [45,] 1.218734e-17 -5.013700e-17 5.529793e-18 -1.511093e-17
## [46,] -2.680731e-17 2.322998e-18 -3.047082e-18 5.453884e-18
## [,17] [,18] [,19] [,20]
## [1,] 3.472212e-01 -3.260015e-01 2.923019e-02 7.008347e-02
## [2,] -3.480458e-01 3.728658e-01 -8.715597e-02 -3.555811e-02
## [3,] 3.663674e-02 -1.138528e-01 1.325369e-01 -8.354951e-02
## [4,] 1.938544e-01 -5.689245e-02 -9.851307e-02 1.512939e-01
## [5,] -5.029473e-01 3.924019e-01 -2.926552e-03 -1.588332e-01
## [6,] 3.600994e-01 -4.725222e-01 1.652539e-01 4.512151e-02
## [7,] -5.403112e-02 2.213241e-01 -2.804565e-01 1.514727e-01
## [8,] -7.971611e-02 -4.865897e-02 1.750223e-01 -2.697266e-01
## [9,] 1.550094e-01 -7.862844e-02 -1.741654e-02 1.667462e-01
## [10,] -4.350773e-02 1.425706e-01 -1.117011e-01 -6.157089e-03
## [11,] -1.973831e-04 -9.987975e-02 1.902279e-01 -1.105026e-01
## [12,] 4.692517e-02 2.494400e-02 -9.305307e-02 1.827434e-01
## [13,] -1.081800e-01 4.193784e-02 -5.457675e-03 -8.408182e-02
## [14,] 6.882550e-02 -1.360611e-01 9.305287e-02 -1.353513e-02
## [15,] 6.896860e-03 9.416595e-02 -1.728094e-01 9.854129e-02
## [16,] -1.559127e-01 1.387822e-02 1.071406e-01 -1.780463e-01
## [17,] 3.475164e-01 -2.371125e-01 7.214983e-03 1.279368e-01
## [18,] -2.371125e-01 3.537604e-01 -1.622793e-01 -1.125972e-02
## [19,] 7.214983e-03 -1.622793e-01 2.731767e-01 -1.617601e-01
## [20,] 1.279368e-01 -1.125972e-02 -1.617601e-01 2.772506e-01
## [21,] -1.412380e-01 6.975321e-02 1.939767e-02 -1.552273e-01
## [22,] 5.247283e-02 -1.335971e-01 9.377010e-02 1.077016e-02
## [23,] -1.266811e-02 9.849285e-02 -1.658629e-01 9.191032e-02
## [24,] -3.174850e-02 -3.704477e-02 8.598371e-02 -1.571986e-01
## [25,] -1.681004e-02 6.808885e-02 -6.660814e-03 5.478892e-02
## [26,] 5.735507e-02 4.066947e-03 -6.265693e-02 2.142740e-02
## [27,] -2.155185e-02 -4.742448e-02 1.235417e-01 -6.820262e-02
## [28,] 5.439166e-02 3.968838e-03 -6.780825e-02 1.225639e-01
## [29,] -1.070562e-02 -2.418221e-02 4.311654e-03 -4.932001e-02
## [30,] -2.111780e-02 -3.085408e-02 5.440633e-02 -1.019718e-02
## [31,] 2.037155e-02 2.845687e-02 -9.429949e-02 5.823254e-02
## [32,] -3.306664e-02 1.165343e-02 4.585688e-02 -9.640726e-02
## [33,] -1.064003e-01 1.143754e-01 -1.186162e-02 1.662775e-02
## [34,] 1.114888e-01 -9.659350e-02 5.546760e-05 1.400236e-02
## [35,] -1.343959e-02 9.347289e-03 1.093466e-02 -2.310376e-03
## [36,] -2.096014e-02 1.860730e-02 1.287749e-03 5.377577e-03
## [37,] 7.361944e-02 -7.218702e-02 -2.783510e-03 1.863356e-02
## [38,] -5.961082e-02 5.400698e-02 8.274463e-04 -1.606492e-02
## [39,] 2.192624e-02 -2.042132e-02 -3.617572e-03 5.695316e-03
## [40,] -2.242097e-02 2.177017e-02 -5.830595e-04 -8.463766e-03
## [41,] -4.271397e-03 4.112390e-03 1.260723e-06 -1.519929e-03
## [42,] 5.453356e-18 -2.378355e-18 -9.512485e-18 -1.823477e-17
## [43,] 2.600710e-17 -1.418916e-17 -2.245018e-17 -1.077795e-17
## [44,] -8.489620e-19 6.370990e-18 -2.147289e-17 -6.113001e-19
## [45,] 2.612219e-17 4.131069e-18 -6.450819e-18 1.431267e-17
## [46,] -9.002473e-18 -7.210658e-18 -8.137266e-18 -6.213404e-17
## [,21] [,22] [,23] [,24]
## [1,] 1.049197e-01 -1.318776e-01 -4.521984e-02 1.466874e-01
## [2,] -1.253072e-01 1.007886e-01 5.577568e-02 -1.249920e-01
## [3,] 5.934470e-02 -1.710091e-02 -3.452235e-02 1.245237e-02
## [4,] -5.824528e-02 2.356888e-02 -2.795060e-02 5.534278e-03
## [5,] 3.170654e-02 1.778776e-02 1.058587e-01 -1.375968e-01
## [6,] 4.573798e-03 5.354734e-02 -1.442222e-01 1.557657e-01
## [7,] -4.871260e-02 -5.866256e-02 1.666617e-01 -1.326940e-01
## [8,] 1.863385e-01 -3.949660e-02 -9.840723e-02 1.771054e-01
## [9,] -2.949622e-01 1.825588e-01 -1.241946e-02 -1.077078e-01
## [10,] 1.975836e-01 -2.966848e-01 1.531233e-01 2.820695e-03
## [11,] -2.182294e-02 1.691269e-01 -2.680088e-01 1.665087e-01
## [12,] -1.253868e-01 -1.114707e-02 1.781952e-01 -2.819164e-01
## [13,] 2.088155e-01 -1.233690e-01 -3.819135e-02 1.891152e-01
## [14,] -1.163723e-01 1.799886e-01 -7.132643e-02 -3.904691e-02
## [15,] 9.167897e-03 -8.707811e-02 1.353730e-01 -7.338530e-02
## [16,] 8.508481e-02 8.465250e-03 -7.224519e-02 1.284491e-01
## [17,] -1.412380e-01 5.247283e-02 -1.266811e-02 -3.174850e-02
## [18,] 6.975321e-02 -1.335971e-01 9.849285e-02 -3.704477e-02
## [19,] 1.939767e-02 9.377010e-02 -1.658629e-01 8.598371e-02
## [20,] -1.552273e-01 1.077016e-02 9.191032e-02 -1.571986e-01
## [21,] 2.766970e-01 -1.783780e-01 1.965806e-02 1.108456e-01
## [22,] -1.783780e-01 2.720087e-01 -1.503710e-01 9.383163e-03
## [23,] 1.965806e-02 -1.503710e-01 2.470157e-01 -1.633028e-01
## [24,] 1.108456e-01 9.383163e-03 -1.633028e-01 2.621737e-01
## [25,] -2.199607e-01 1.484334e-01 5.381838e-02 -2.193453e-01
## [26,] 1.495781e-01 -1.975719e-01 4.498578e-02 8.073981e-02
## [27,] -3.196472e-02 9.358952e-02 -1.190960e-01 6.115408e-02
## [28,] -6.227233e-02 -2.013456e-02 8.277794e-02 -1.254692e-01
## [29,] 1.529683e-01 -9.400611e-02 -3.569867e-02 1.200380e-01
## [30,] -1.023656e-01 1.404284e-01 -3.847833e-02 -4.836409e-02
## [31,] 1.960256e-02 -7.889333e-02 1.024310e-01 -4.408727e-02
## [32,] 4.831355e-02 1.578580e-02 -6.832781e-02 1.016344e-01
## [33,] -1.359751e-01 1.081449e-01 2.893428e-02 -1.317472e-01
## [34,] 1.016518e-01 -1.245800e-01 2.212502e-02 5.660554e-02
## [35,] -2.970338e-02 5.342222e-02 -6.237364e-02 4.027441e-02
## [36,] -8.503753e-03 -1.603086e-02 5.339847e-02 -7.533563e-02
## [37,] 4.193891e-02 -2.803551e-02 -4.249541e-02 8.380981e-02
## [38,] -3.032231e-02 2.984014e-02 2.348687e-02 -5.383577e-02
## [39,] 1.330089e-02 -1.126954e-02 -5.962139e-03 2.116543e-02
## [40,] -9.650129e-03 1.199850e-02 3.903305e-03 -1.150016e-02
## [41,] -1.954194e-03 2.257147e-03 8.667484e-04 -2.549353e-03
## [42,] -1.689057e-18 6.277793e-18 -4.384274e-17 1.003404e-16
## [43,] 1.542072e-17 -8.037248e-18 -5.055590e-17 -2.002783e-17
## [44,] -7.297971e-18 2.626591e-17 9.115422e-18 -3.071202e-18
## [45,] 4.604572e-17 2.782364e-17 4.527777e-18 1.278789e-17
## [46,] -3.449770e-18 -4.045389e-18 9.959476e-18 2.598350e-17
## [,25] [,26] [,27] [,28]
## [1,] -5.184465e-01 4.565334e-01 -7.987724e-02 -1.693331e-02
## [2,] 4.619129e-01 -3.832815e-01 4.760977e-02 1.241916e-02
## [3,] -2.049298e-03 -2.233385e-02 5.241766e-02 -2.305373e-02
## [4,] -1.273214e-01 1.277344e-01 -5.118828e-02 4.934977e-02
## [5,] 4.029796e-01 -3.545304e-01 5.288764e-02 -1.381350e-02
## [6,] -3.463061e-01 2.109686e-01 2.967442e-02 -2.885443e-02
## [7,] 1.410703e-01 -3.370102e-02 -1.232829e-01 8.897725e-02
## [8,] -1.744746e-01 9.043905e-02 5.694968e-02 -1.417288e-01
## [9,] 2.135097e-01 -1.479903e-01 3.105793e-02 6.961282e-02
## [10,] -1.658652e-01 2.035763e-01 -8.912139e-02 1.709444e-02
## [11,] -3.965750e-02 -4.905595e-02 1.088842e-01 -7.494045e-02
## [12,] 2.172736e-01 -7.102404e-02 -5.597009e-02 1.132622e-01
## [13,] -3.240293e-01 1.969815e-01 -1.382082e-02 -6.859853e-02
## [14,] 1.938841e-01 -2.143284e-01 7.082595e-02 7.984500e-03
## [15,] -3.076748e-02 9.197109e-02 -1.074273e-01 5.343381e-02
## [16,] -4.795611e-02 -2.419637e-02 6.366660e-02 -1.010238e-01
## [17,] -1.681004e-02 5.735507e-02 -2.155185e-02 5.439166e-02
## [18,] 6.808885e-02 4.066947e-03 -4.742448e-02 3.968838e-03
## [19,] -6.660814e-03 -6.265693e-02 1.235417e-01 -6.780825e-02
## [20,] 5.478892e-02 2.142740e-02 -6.820262e-02 1.225639e-01
## [21,] -2.199607e-01 1.495781e-01 -3.196472e-02 -6.227233e-02
## [22,] 1.484334e-01 -1.975719e-01 9.358952e-02 -2.013456e-02
## [23,] 5.381838e-02 4.498578e-02 -1.190960e-01 8.277794e-02
## [24,] -2.193453e-01 8.073981e-02 6.115408e-02 -1.254692e-01
## [25,] 4.655299e-01 -3.301799e-01 3.641800e-02 8.132365e-02
## [26,] -3.301799e-01 3.295528e-01 -8.808733e-02 -1.319219e-02
## [27,] 3.641800e-02 -8.808733e-02 9.734032e-02 -4.965949e-02
## [28,] 8.132365e-02 -1.319219e-02 -4.965949e-02 9.169954e-02
## [29,] -2.582040e-01 1.874729e-01 -2.176013e-02 -5.615095e-02
## [30,] 1.754771e-01 -1.760829e-01 5.089009e-02 6.079849e-03
## [31,] -3.672752e-02 6.451957e-02 -6.266755e-02 3.125313e-02
## [32,] -3.873709e-02 -1.448385e-02 3.549803e-02 -5.709014e-02
## [33,] 3.242138e-01 -2.514489e-01 3.831472e-02 3.941850e-02
## [34,] -2.449988e-01 2.285063e-01 -5.225015e-02 -4.170940e-03
## [35,] 5.698372e-03 -2.971586e-02 3.168579e-02 -2.011489e-02
## [36,] 8.550566e-02 -4.384033e-02 -1.196814e-02 3.126078e-02
## [37,] -1.865327e-01 1.397296e-01 -1.255814e-02 -2.430564e-02
## [38,] 1.337663e-01 -1.088153e-01 1.252960e-02 1.326150e-02
## [39,] -5.311786e-02 4.063391e-02 -6.179234e-03 -5.827755e-03
## [40,] 4.345895e-02 -3.871943e-02 6.347928e-03 1.306475e-03
## [41,] 8.632302e-03 -7.472695e-03 1.185592e-03 4.094338e-04
## [42,] -1.120553e-16 1.064003e-17 1.490447e-18 -2.812990e-17
## [43,] -3.439933e-17 7.888352e-18 -1.643148e-17 -1.759933e-17
## [44,] 1.664512e-18 2.280932e-17 -1.709195e-17 -5.975818e-18
## [45,] -2.625380e-17 -1.350103e-17 1.973413e-19 -1.491352e-17
## [46,] -4.733144e-17 3.567733e-18 -1.330018e-17 -8.319891e-17
## [,29] [,30] [,31] [,32]
## [1,] 3.083011e-01 -2.423279e-01 6.429470e-02 -3.651089e-02
## [2,] -2.758965e-01 2.151113e-01 -5.767995e-02 3.186467e-02
## [3,] 4.440752e-03 5.786259e-04 -3.863742e-03 7.035681e-04
## [4,] 5.881216e-02 -6.567339e-02 2.231123e-02 -1.494073e-02
## [5,] -2.082686e-01 1.730249e-01 -4.839993e-02 3.404663e-02
## [6,] 1.755528e-01 -8.542118e-02 -6.028613e-03 -1.280440e-02
## [7,] -7.217046e-02 -7.258747e-03 7.998829e-02 -4.724439e-02
## [8,] 1.288110e-01 -4.227020e-02 -4.814222e-02 8.801721e-02
## [9,] -1.734336e-01 1.125377e-01 -1.577253e-02 -5.300021e-02
## [10,] 1.147445e-01 -1.654274e-01 8.699156e-02 -1.195045e-02
## [11,] 2.871145e-02 4.971010e-02 -1.180715e-01 7.392274e-02
## [12,] -1.074777e-01 4.429581e-02 5.096869e-02 -1.164086e-01
## [13,] 1.481655e-01 -9.449706e-02 1.908993e-02 5.529207e-02
## [14,] -9.062928e-02 8.919326e-02 -3.786530e-02 6.395951e-03
## [15,] 1.882947e-02 -3.762242e-02 4.211838e-02 -2.713205e-02
## [16,] 3.339375e-02 1.479522e-02 -2.591268e-02 4.045460e-02
## [17,] -1.070562e-02 -2.111780e-02 2.037155e-02 -3.306664e-02
## [18,] -2.418221e-02 -3.085408e-02 2.845687e-02 1.165343e-02
## [19,] 4.311654e-03 5.440633e-02 -9.429949e-02 4.585688e-02
## [20,] -4.932001e-02 -1.019718e-02 5.823254e-02 -9.640726e-02
## [21,] 1.529683e-01 -1.023656e-01 1.960256e-02 4.831355e-02
## [22,] -9.400611e-02 1.404284e-01 -7.889333e-02 1.578580e-02
## [23,] -3.569867e-02 -3.847833e-02 1.024310e-01 -6.832781e-02
## [24,] 1.200380e-01 -4.836409e-02 -4.408727e-02 1.016344e-01
## [25,] -2.582040e-01 1.754771e-01 -3.672752e-02 -3.873709e-02
## [26,] 1.874729e-01 -1.760829e-01 6.451957e-02 -1.448385e-02
## [27,] -2.176013e-02 5.089009e-02 -6.266755e-02 3.549803e-02
## [28,] -5.615095e-02 6.079849e-03 3.125313e-02 -5.709014e-02
## [29,] 1.725048e-01 -1.118129e-01 1.661340e-02 2.337536e-02
## [30,] -1.118129e-01 1.220308e-01 -4.763784e-02 3.154929e-03
## [31,] 1.661340e-02 -4.763784e-02 6.595425e-02 -3.347038e-02
## [32,] 2.337536e-02 3.154929e-03 -3.347038e-02 6.266413e-02
## [33,] -1.865384e-01 1.373042e-01 -3.364148e-02 -1.552295e-02
## [34,] 1.406027e-01 -1.257970e-01 4.559514e-02 -1.583471e-02
## [35,] -3.393852e-03 1.782598e-02 -2.739081e-02 1.958826e-02
## [36,] -4.534474e-02 2.326537e-02 7.076226e-03 -2.297590e-02
## [37,] 1.049695e-01 -7.172507e-02 1.325493e-02 5.080492e-03
## [38,] -7.510389e-02 5.735085e-02 -1.190770e-02 6.473158e-04
## [39,] 2.886271e-02 -2.084377e-02 7.102426e-03 3.935445e-04
## [40,] -2.497896e-02 1.946857e-02 -5.176248e-03 4.174941e-03
## [41,] -4.913190e-03 3.778013e-03 -1.024670e-03 6.351822e-04
## [42,] 3.150680e-17 6.738490e-18 6.975612e-18 2.503193e-17
## [43,] 2.353879e-17 -1.353112e-18 4.931222e-17 -3.485945e-17
## [44,] 2.027486e-18 1.359106e-17 -3.448193e-17 -6.281526e-18
## [45,] 2.315716e-17 2.809663e-17 3.108822e-18 -3.891945e-18
## [46,] -5.607763e-18 1.625509e-20 1.826202e-17 1.040395e-18
## [,33] [,34] [,35] [,36]
## [1,] -4.854160e-01 4.299239e-01 -3.814566e-02 -9.316652e-02
## [2,] 4.539496e-01 -4.107344e-01 5.355665e-02 7.111445e-02
## [3,] -3.087714e-02 4.596197e-02 -3.783287e-02 2.772943e-02
## [4,] -1.263560e-01 9.151809e-02 2.811917e-02 -6.203526e-02
## [5,] 4.152896e-01 -3.559566e-01 1.896138e-03 1.151922e-01
## [6,] -3.402191e-01 2.807167e-01 -5.807407e-03 -8.361045e-02
## [7,] 1.161965e-01 -8.248597e-02 -1.205827e-02 2.984169e-02
## [8,] -1.266296e-01 8.144082e-02 -2.783291e-03 -3.060442e-02
## [9,] 1.492040e-01 -1.101208e-01 2.845739e-02 1.116338e-02
## [10,] -1.360651e-01 1.481636e-01 -5.574907e-02 1.024294e-02
## [11,] -1.494234e-02 -3.746906e-02 6.950652e-02 -5.333710e-02
## [12,] 1.280348e-01 -4.574308e-02 -4.709845e-02 8.035502e-02
## [13,] -1.824287e-01 1.171444e-01 5.759157e-03 -6.192625e-02
## [14,] 1.098932e-01 -9.971902e-02 1.355449e-02 2.077437e-02
## [15,] -2.626192e-02 3.303572e-02 -1.484493e-02 3.399334e-03
## [16,] 9.685964e-03 -2.489152e-02 8.039239e-03 -6.650038e-03
## [17,] -1.064003e-01 1.114888e-01 -1.343959e-02 -2.096014e-02
## [18,] 1.143754e-01 -9.659350e-02 9.347289e-03 1.860730e-02
## [19,] -1.186162e-02 5.546760e-05 1.093466e-02 1.287749e-03
## [20,] 1.662775e-02 1.400236e-02 -2.310376e-03 5.377577e-03
## [21,] -1.359751e-01 1.016518e-01 -2.970338e-02 -8.503753e-03
## [22,] 1.081449e-01 -1.245800e-01 5.342222e-02 -1.603086e-02
## [23,] 2.893428e-02 2.212502e-02 -6.237364e-02 5.339847e-02
## [24,] -1.317472e-01 5.660554e-02 4.027441e-02 -7.533563e-02
## [25,] 3.242138e-01 -2.449988e-01 5.698372e-03 8.550566e-02
## [26,] -2.514489e-01 2.285063e-01 -2.971586e-02 -4.384033e-02
## [27,] 3.831472e-02 -5.225015e-02 3.168579e-02 -1.196814e-02
## [28,] 3.941850e-02 -4.170940e-03 -2.011489e-02 3.126078e-02
## [29,] -1.865384e-01 1.406027e-01 -3.393852e-03 -4.534474e-02
## [30,] 1.373042e-01 -1.257970e-01 1.782598e-02 2.326537e-02
## [31,] -3.364148e-02 4.559514e-02 -2.739081e-02 7.076226e-03
## [32,] -1.552295e-02 -1.583471e-02 1.958826e-02 -2.297590e-02
## [33,] 2.630427e-01 -2.138865e-01 1.690800e-02 5.744543e-02
## [34,] -2.138865e-01 1.980734e-01 -3.328921e-02 -2.834096e-02
## [35,] 1.690800e-02 -3.328921e-02 2.974726e-02 -2.073384e-02
## [36,] 5.744543e-02 -2.834096e-02 -2.073384e-02 3.664764e-02
## [37,] -1.478610e-01 1.139231e-01 5.936389e-03 -4.629520e-02
## [38,] 1.094797e-01 -9.013486e-02 -2.737089e-04 3.043095e-02
## [39,] -4.246737e-02 3.354186e-02 -5.128821e-04 -1.193714e-02
## [40,] 3.735807e-02 -3.326475e-02 2.259833e-03 7.829966e-03
## [41,] 7.314264e-03 -6.370071e-03 3.560307e-04 1.645419e-03
## [42,] -6.297712e-17 3.629734e-18 3.800782e-18 -3.587855e-17
## [43,] -4.060882e-17 1.005970e-17 -1.850445e-17 1.703412e-17
## [44,] 6.176695e-18 -7.088124e-18 -7.800752e-18 9.199022e-18
## [45,] -5.907878e-18 -1.758207e-17 -2.581558e-18 -8.597213e-18
## [46,] -3.599534e-17 3.459611e-18 -1.218550e-17 -5.335778e-18
## [,37] [,38] [,39] [,40]
## [1,] 2.894600e-01 -2.216670e-01 8.145050e-02 -8.067123e-02
## [2,] -2.548050e-01 1.996493e-01 -7.289301e-02 7.375088e-02
## [3,] -1.058634e-02 2.258106e-03 -2.278909e-04 -2.088753e-03
## [4,] 1.061887e-01 -7.479113e-02 2.810646e-02 -2.308658e-02
## [5,] -2.796642e-01 2.093054e-01 -7.823876e-02 7.306697e-02
## [6,] 2.183458e-01 -1.631422e-01 6.047770e-02 -5.874410e-02
## [7,] -6.470045e-02 4.781384e-02 -1.586276e-02 1.670804e-02
## [8,] 5.045157e-02 -3.637269e-02 1.353518e-02 -1.066961e-02
## [9,] -4.906973e-02 3.491287e-02 -1.459753e-02 1.132814e-02
## [10,] 4.160150e-02 -4.106688e-02 1.501168e-02 -1.533505e-02
## [11,] 3.648811e-02 -1.877346e-02 2.920181e-03 -2.280703e-03
## [12,] -8.113678e-02 5.059857e-02 -2.005768e-02 8.905824e-03
## [13,] 1.020364e-01 -6.862317e-02 3.023829e-02 -1.888737e-02
## [14,] -6.173234e-02 4.679915e-02 -1.860170e-02 1.643071e-02
## [15,] 1.414334e-02 -1.215986e-02 4.623219e-03 -5.592492e-03
## [16,] -9.995591e-03 1.012653e-02 -2.971646e-03 4.803534e-03
## [17,] 7.361944e-02 -5.961082e-02 2.192624e-02 -2.242097e-02
## [18,] -7.218702e-02 5.400698e-02 -2.042132e-02 2.177017e-02
## [19,] -2.783510e-03 8.274463e-04 -3.617572e-03 -5.830595e-04
## [20,] 1.863356e-02 -1.606492e-02 5.695316e-03 -8.463766e-03
## [21,] 4.193891e-02 -3.032231e-02 1.330089e-02 -9.650129e-03
## [22,] -2.803551e-02 2.984014e-02 -1.126954e-02 1.199850e-02
## [23,] -4.249541e-02 2.348687e-02 -5.962139e-03 3.903305e-03
## [24,] 8.380981e-02 -5.383577e-02 2.116543e-02 -1.150016e-02
## [25,] -1.865327e-01 1.337663e-01 -5.311786e-02 4.345895e-02
## [26,] 1.397296e-01 -1.088153e-01 4.063391e-02 -3.871943e-02
## [27,] -1.255814e-02 1.252960e-02 -6.179234e-03 6.347928e-03
## [28,] -2.430564e-02 1.326150e-02 -5.827755e-03 1.306475e-03
## [29,] 1.049695e-01 -7.510389e-02 2.886271e-02 -2.497896e-02
## [30,] -7.172507e-02 5.735085e-02 -2.084377e-02 1.946857e-02
## [31,] 1.325493e-02 -1.190770e-02 7.102426e-03 -5.176248e-03
## [32,] 5.080492e-03 6.473158e-04 3.935445e-04 4.174941e-03
## [33,] -1.478610e-01 1.094797e-01 -4.246737e-02 3.735807e-02
## [34,] 1.139231e-01 -9.013486e-02 3.354186e-02 -3.326475e-02
## [35,] 5.936389e-03 -2.737089e-04 -5.128821e-04 2.259833e-03
## [36,] -4.629520e-02 3.043095e-02 -1.193714e-02 7.829966e-03
## [37,] 9.718324e-02 -6.994379e-02 2.680799e-02 -2.320379e-02
## [38,] -6.994379e-02 5.227835e-02 -1.928667e-02 1.783822e-02
## [39,] 2.680799e-02 -1.928667e-02 7.710299e-03 -6.452722e-03
## [40,] -2.320379e-02 1.783822e-02 -6.452722e-03 6.503963e-03
## [41,] -4.564961e-03 3.468712e-03 -1.274751e-03 1.244565e-03
## [42,] 3.657354e-17 -1.770070e-18 1.141535e-17 1.714977e-18
## [43,] 1.961178e-17 -2.761492e-18 9.282806e-18 1.454315e-18
## [44,] 1.724937e-18 7.375518e-19 3.402577e-19 3.754234e-20
## [45,] 1.457912e-17 -1.641986e-19 6.196950e-18 1.026476e-18
## [46,] 8.166147e-18 3.194710e-21 4.507181e-18 7.312509e-19
## [,41] [,42] [,43] [,44]
## [1,] -1.547283e-02 1.363859e-16 8.562994e-17 -3.607262e-17
## [2,] 1.408927e-02 -4.071629e-18 -3.115220e-17 3.974496e-17
## [3,] -3.008073e-04 7.038898e-19 1.004110e-16 5.094056e-17
## [4,] -4.603093e-03 7.929535e-17 1.314449e-16 2.898675e-17
## [5,] 1.416702e-02 -2.654108e-17 -6.730666e-17 -1.232000e-17
## [6,] -1.130785e-02 2.078278e-17 -1.044450e-17 -1.126461e-17
## [7,] 3.191485e-03 -3.300431e-18 2.022257e-17 1.468312e-17
## [8,] -2.147855e-03 2.063994e-17 -2.800422e-17 -2.317460e-18
## [9,] 2.267134e-03 -2.059994e-17 -2.096599e-17 2.376560e-19
## [10,] -2.914833e-03 -3.487266e-18 2.343962e-17 1.000807e-17
## [11,] -5.209732e-04 -3.005266e-18 3.817475e-18 -8.935382e-18
## [12,] 2.107268e-03 4.491781e-18 -4.898331e-18 -2.098592e-18
## [13,] -3.977263e-03 7.727849e-18 -4.299639e-18 -3.324256e-18
## [14,] 3.207653e-03 -2.419064e-18 5.966204e-18 4.532439e-17
## [15,] -1.031578e-03 -1.718951e-18 1.831351e-17 -2.716503e-18
## [16,] 8.593199e-04 -2.104045e-20 -3.775782e-17 -1.563855e-18
## [17,] -4.271397e-03 5.453356e-18 2.600710e-17 -8.489620e-19
## [18,] 4.112390e-03 -2.378355e-18 -1.418916e-17 6.370990e-18
## [19,] 1.260723e-06 -9.512485e-18 -2.245018e-17 -2.147289e-17
## [20,] -1.519929e-03 -1.823477e-17 -1.077795e-17 -6.113001e-19
## [21,] -1.954194e-03 -1.689057e-18 1.542072e-17 -7.297971e-18
## [22,] 2.257147e-03 6.277793e-18 -8.037248e-18 2.626591e-17
## [23,] 8.667484e-04 -4.384274e-17 -5.055590e-17 9.115422e-18
## [24,] -2.549353e-03 1.003404e-16 -2.002783e-17 -3.071202e-18
## [25,] 8.632302e-03 -1.120553e-16 -3.439933e-17 1.664512e-18
## [26,] -7.472695e-03 1.064003e-17 7.888352e-18 2.280932e-17
## [27,] 1.185592e-03 1.490447e-18 -1.643148e-17 -1.709195e-17
## [28,] 4.094338e-04 -2.812990e-17 -1.759933e-17 -5.975818e-18
## [29,] -4.913190e-03 3.150680e-17 2.353879e-17 2.027486e-18
## [30,] 3.778013e-03 6.738490e-18 -1.353112e-18 1.359106e-17
## [31,] -1.024670e-03 6.975612e-18 4.931222e-17 -3.448193e-17
## [32,] 6.351822e-04 2.503193e-17 -3.485945e-17 -6.281526e-18
## [33,] 7.314264e-03 -6.297712e-17 -4.060882e-17 6.176695e-18
## [34,] -6.370071e-03 3.629734e-18 1.005970e-17 -7.088124e-18
## [35,] 3.560307e-04 3.800782e-18 -1.850445e-17 -7.800752e-18
## [36,] 1.645419e-03 -3.587855e-17 1.703412e-17 9.199022e-18
## [37,] -4.564961e-03 3.657354e-17 1.961178e-17 1.724937e-18
## [38,] 3.468712e-03 -1.770070e-18 -2.761492e-18 7.375518e-19
## [39,] -1.274751e-03 1.141535e-17 9.282806e-18 3.402577e-19
## [40,] 1.244565e-03 1.714977e-18 1.454315e-18 3.754234e-20
## [41,] 2.394084e-04 0.000000e+00 0.000000e+00 0.000000e+00
## [42,] 0.000000e+00 4.638030e-21 -2.423398e-32 -2.786676e-34
## [43,] 0.000000e+00 -2.423398e-32 1.732570e-20 -2.639064e-33
## [44,] 0.000000e+00 -2.786676e-34 -2.639064e-33 -1.550502e-23
## [45,] 0.000000e+00 -1.001268e-32 -1.386298e-32 -2.308495e-33
## [46,] 0.000000e+00 -3.813481e-33 -2.563767e-33 -6.115672e-34
## [,45] [,46]
## [1,] -9.819410e-18 9.145965e-17
## [2,] 1.085767e-16 -2.647183e-17
## [3,] 1.621288e-17 5.540525e-17
## [4,] 6.368260e-17 1.529176e-17
## [5,] -5.048658e-17 -1.268127e-17
## [6,] 2.971779e-17 4.980196e-18
## [7,] -1.191575e-17 -3.268488e-17
## [8,] -4.176064e-17 1.860730e-17
## [9,] -1.743665e-17 -2.304941e-17
## [10,] -9.825421e-18 1.525471e-17
## [11,] 2.768839e-18 6.696319e-18
## [12,] -2.456731e-19 -6.726947e-18
## [13,] 1.218734e-17 -2.680731e-17
## [14,] -5.013700e-17 2.322998e-18
## [15,] 5.529793e-18 -3.047082e-18
## [16,] -1.511093e-17 5.453884e-18
## [17,] 2.612219e-17 -9.002473e-18
## [18,] 4.131069e-18 -7.210658e-18
## [19,] -6.450819e-18 -8.137266e-18
## [20,] 1.431267e-17 -6.213404e-17
## [21,] 4.604572e-17 -3.449770e-18
## [22,] 2.782364e-17 -4.045389e-18
## [23,] 4.527777e-18 9.959476e-18
## [24,] 1.278789e-17 2.598350e-17
## [25,] -2.625380e-17 -4.733144e-17
## [26,] -1.350103e-17 3.567733e-18
## [27,] 1.973413e-19 -1.330018e-17
## [28,] -1.491352e-17 -8.319891e-17
## [29,] 2.315716e-17 -5.607763e-18
## [30,] 2.809663e-17 1.625509e-20
## [31,] 3.108822e-18 1.826202e-17
## [32,] -3.891945e-18 1.040395e-18
## [33,] -5.907878e-18 -3.599534e-17
## [34,] -1.758207e-17 3.459611e-18
## [35,] -2.581558e-18 -1.218550e-17
## [36,] -8.597213e-18 -5.335778e-18
## [37,] 1.457912e-17 8.166147e-18
## [38,] -1.641986e-19 3.194710e-21
## [39,] 6.196950e-18 4.507181e-18
## [40,] 1.026476e-18 7.312509e-19
## [41,] 0.000000e+00 0.000000e+00
## [42,] -1.001268e-32 -3.813481e-33
## [43,] -1.386298e-32 -2.563767e-33
## [44,] -2.308495e-33 -6.115672e-34
## [45,] -1.337831e-21 -5.852162e-33
## [46,] -5.852162e-33 -2.598756e-20fit6$ttable## NULL#AIC - (251.88)
fit7 = arima(log(beer.ts), c(0, 1, 10),seasonal = list(order = c(0, 1, 10), period = 4))
acf(residuals(fit7))
pacf(residuals(fit7))
fit7##
## Call:
## arima(x = log(beer.ts), order = c(0, 1, 10), seasonal = list(order = c(0, 1,
## 10), period = 4))
##
## Coefficients:
## ma1 ma2 ma3 ma4 ma5 ma6 ma7 ma8
## -0.8863 -0.0087 0.2037 -0.8981 0.7446 -0.1410 0.1895 0.556
## s.e. 0.1520 0.1776 0.1958 0.2477 0.2791 0.1905 0.1711 0.266
## ma9 ma10 sma1 sma2 sma3 sma4 sma5 sma6
## -0.4083 -0.1277 0.1040 -0.8410 -0.4568 0.3785 0.8642 -0.2135
## s.e. 0.2718 0.1707 0.4044 0.3085 0.3504 0.3667 0.3304 0.4307
## sma7 sma8 sma9 sma10
## -0.4833 -0.4650 0.2314 0.7828
## s.e. 0.3305 0.3225 0.3295 0.4171
##
## sigma^2 estimated as 0.0004309: log likelihood = 146.27, aic = -252.54#AIC - (252.54)
fit8 = arima(log(beer.ts), c(2, 1, 1),seasonal = list(order = c(0, 1, 1), period = 4))
acf(residuals(fit8))
pacf(residuals(fit8))
fit8##
## Call:
## arima(x = log(beer.ts), order = c(2, 1, 1), seasonal = list(order = c(0, 1,
## 1), period = 4))
##
## Coefficients:
## ar1 ar2 ma1 sma1
## -0.4936 -0.1729 -0.5959 -0.7017
## s.e. 0.2157 0.1992 0.1967 0.1153
##
## sigma^2 estimated as 0.0009788: log likelihood = 134.92, aic = -261.85#AIC - (-261.85)
#Fit 8 p & Q values are taken from below R auto functions
#Conculsion - Fit 6 is the lowest model
############################
#Some other R functions to forecast Time Series
#using sarima function
par(mar=c(1,1,1,1))
beer.sarima= sarima(beer.ts,2,1,1,0,1,1,4)## initial value 2.856030
## iter 2 value 2.395107
## iter 3 value 2.336666
## iter 4 value 2.331009
## iter 5 value 2.285166
## iter 6 value 2.277357
## iter 7 value 2.277215
## iter 8 value 2.277023
## iter 9 value 2.276980
## iter 10 value 2.276953
## iter 11 value 2.276952
## iter 12 value 2.276951
## iter 13 value 2.276950
## iter 14 value 2.276950
## iter 15 value 2.276950
## iter 15 value 2.276950
## iter 15 value 2.276950
## final value 2.276950
## converged
## initial value 2.344512
## iter 2 value 2.343747
## iter 3 value 2.343500
## iter 4 value 2.343452
## iter 5 value 2.343438
## iter 6 value 2.343438
## iter 7 value 2.343437
## iter 7 value 2.343437
## iter 7 value 2.343437
## final value 2.343437
## converged
beer.sarima## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), include.mean = !no.constant, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ar2 ma1 sma1
## -0.5280 -0.2791 -0.5445 -0.6170
## s.e. 0.1922 0.1700 0.1852 0.1044
##
## sigma^2 estimated as 103.1: log likelihood = -252.08, aic = 514.16
##
## $degrees_of_freedom
## [1] 63
##
## $ttable
## Estimate SE t.value p.value
## ar1 -0.5280 0.1922 -2.7464 0.0078
## ar2 -0.2791 0.1700 -1.6421 0.1056
## ma1 -0.5445 0.1852 -2.9405 0.0046
## sma1 -0.6170 0.1044 -5.9075 0.0000
##
## $AIC
## [1] 5.746389
##
## $AICc
## [1] 5.786793
##
## $BIC
## [1] 4.87287beer.sarima$AIC## [1] 5.746389#AIC value is 5.74
#Using Auto Arima
arimaauto = auto.arima(beer.ts)
arimaauto## Series: beer.ts
## ARIMA(2,1,1)(0,1,1)[4]
##
## Coefficients:
## ar1 ar2 ma1 sma1
## -0.5280 -0.2791 -0.5445 -0.6170
## s.e. 0.1922 0.1700 0.1852 0.1044
##
## sigma^2 estimated as 109.6: log likelihood=-252.08
## AIC=514.16 AICc=515.14 BIC=525.18#AIC value is 514.16
#Testing Ljung
Box.test(residuals(fit6), lag = 4, type = "Ljung")##
## Box-Ljung test
##
## data: residuals(fit6)
## X-squared = 0.93987, df = 4, p-value = 0.9188#Since p value is 0.9188 the data is independantly distributed
#Therefore, we failed to reject the Null hypothesis
#Prediction
arima.predict = predict(fit6, n.ahead = 4*4)
ts.plot(beer.ts,2.718^arima.predict$pred, log="y", lty=c(1,3),
col="blue",
main = "Final Plot",
xlab="quarters",
ylab="ML")
?ts.plot## starting httpd help server ...## done###ARIMA Using ETS Function in R###
ets.beer = ets(beer.ts)
plot(forecast(ets.beer), h=8,xlab = "quarters")## Warning in plot.window(xlim, ylim, log, ...): "h" is not a graphical
## parameter## Warning in title(main = main, xlab = xlab, ylab = ylab, ...): "h" is not a
## graphical parameter## Warning in box(...): "h" is not a graphical parameter
summary(ets.beer)## ETS(M,A,M)
##
## Call:
## ets(y = beer.ts)
##
## Smoothing parameters:
## alpha = 0.0423
## beta = 0.042
## gamma = 1e-04
##
## Initial states:
## l = 255.9068
## b = 0.1377
## s=1.1826 0.9234 0.869 1.025
##
## sigma: 0.0299
##
## AIC AICc BIC
## 651.5936 654.4968 672.0836
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 1.388551 9.467959 7.948689 0.4409128 2.473188 0.5870014
## ACF1
## Training set -0.1294156#Neural Network ARIMA
beer.nn = nnetar(beer.ts)
plot(forecast(beer.nn), main="Forecast using Neural Networks",
xlab = "Quarter")
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