EpiEstim

https://mrc-ide.github.io/EpiEstim/
Admin
EpiEstim is an R package for estimating time-varying instantaneous reproduction numbers during...
Tokens:112,282
Snippets:644
Trust Score:9.7
Update:4 days ago
Show doc for...
Tokens:
Raw
### Example setup for draw_R

Source: https://mrc-ide.github.io/EpiEstim/reference/draw_R.html

Initial setup variables for running draw_R, including defining the number of variants, locations, time steps, and default priors.

```R
n_v <- 2
n_loc <- 3 # 3 locations
T <- 100 # 100 time steps
priors <- default_priors()
```

--------------------------------

### init_mcmc_params example

Source: https://mrc-ide.github.io/EpiEstim/reference/init_mcmc_params.html

Example demonstrating how to use init_mcmc_params to provide a starting point for MCMC estimation using the MockRotavirus dataset.

```R
if (FALSE) { # \dontrun{
## Note the following examples use an MCMC routine
## to estimate the serial interval distribution from data,
## so they may take a few minutes to run

## load data on rotavirus
data("MockRotavirus")

## get clever initial values for shape and scale of a Gamma distribution
## fitted to the the data MockRotavirus$si_data
clever_init_param <- init_mcmc_params(MockRotavirus$si_data, "gamma")

## estimate the serial interval from data using a clever starting point for 
## the MCMC chain
SI_fit_clever <- coarseDataTools::dic.fit.mcmc(dat = MockRotavirus$si_data,
                             dist = "G",
                             init.pars = clever_init_param,
                             burnin = 1000,
                             n.samples = 5000)

## estimate the serial interval from data using a random starting point for 
## the MCMC chain
SI_fit_naive <- coarseDataTools::dic.fit.mcmc(dat = MockRotavirus$si_data,
                             dist = "G",
                             burnin = 1000,
                             n.samples = 5000)


## use check_cdt_samples_convergence to check convergence in both situations
converg_diag_clever <- check_cdt_samples_convergence(SI_fit_clever@samples)
converg_diag_naive <- check_cdt_samples_convergence(SI_fit_naive@samples)
converg_diag_clever
converg_diag_naive
} # }
```

--------------------------------

### Example: Drawing epsilon with multivariant incidence data

Source: https://mrc-ide.github.io/EpiEstim/reference/draw_epsilon.html

Example setup with 4 locations, 3 strains, and 100 time steps. It creates constant incidence, computes lambda with an arbitrary serial interval, sets a constant reproduction number, and calls draw_epsilon with a seed. The output shows two epsilon values.

```R
n_loc <- 4 # 4 locations
n_v <- 3 # 3 strains
T <- 100 # 100 time steps
priors <- default_priors()
# constant incidence 10 per day everywhere
incid <- array(10, dim = c(T, n_loc, n_v))
incid <- process_I_multivariant(incid)
# arbitrary serial interval, same for both variants
w_v <- c(0, 0.2, 0.5, 0.3)
si_distr <- cbind(w_v, w_v, w_v)
lambda <- compute_lambda(incid, si_distr)
# Constant reproduction number of 1
R <- matrix(1, nrow = T, ncol = n_loc)
R[1, ] <- NA # no estimates of R on first time step
draw_epsilon(R, incid$local, lambda, priors, seed = 1)
#> [1] 1.001066 1.032584
```

--------------------------------

### Estimate Rt with three-week sliding windows

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

This example demonstrates how to define custom start and end dates for sliding windows and pass them to the estimate_R function using make_config.

```R
# t_start` is a sequence of start days for the sliding window, starting on day 2
# ending 3 weeks before the last day in the dataset:
t_start <- seq(2, nrow(evd_incid) - 20) 

# `t_end` is a sequence of end dates for the window 3 weeks after each start
# date defined above:
t_end <- t_start + 20

R_window <- estimate_R(incid = evd_incid, 
                             method = "parametric_si",
                             config = make_config(mean_si = 14.2, std_si = 9.6,
                                                  t_start = t_start,
                                                  t_end = t_end))

plot(R_window, legend = FALSE, "R")
```

--------------------------------

### coarse2estim example workflow

Source: https://mrc-ide.github.io/EpiEstim/reference/coarse2estim.html

An example demonstrating the estimation of the serial interval from rotavirus data using dic.fit.mcmc, followed by conversion with coarse2estim and reproduction number estimation using estimate_R.

```R
if (FALSE) { # \dontrun{
## Note the following examples use an MCMC routine
## to estimate the serial interval distribution from data,
## so they may take a few minutes to run

## load data on rotavirus
data("MockRotavirus")

## estimate the serial interval from data
SI.fit <- coarseDataTools::dic.fit.mcmc(
  dat = MockRotavirus$si_data,
  dist = "G",
  init.pars = init_mcmc_params(MockRotavirus$si_data, "G"),
  burnin = 1000,
  n.samples = 5000
)

## use coarse2estim to turn this in the right format for estimate_R
si_sample <- coarse2estim(SI.fit, thin = 10)$si_sample

## use estimate_R to estimate the reproduction number
## based on these estimates of the serial interval
R_si_from_sample <- estimate_R(
  MockRotavirus$incidence,
  method = "si_from_sample",
  si_sample = si_sample,
  config = make_config(list(n2 = 50))
)

plot(R_si_from_sample)
} # }
```

--------------------------------

### Constant aggregation example

Source: https://mrc-ide.github.io/EpiEstim/reference/aggregate_inc.html

Example of aggregating daily incidence data into weekly (7-day) windows.

```R
## Constant aggregation e.g. weekly reporting
data("SARS2003")
incid <- SARS2003$incidence
dt <- 7L
aggregate_inc(incid, dt)
#> Incidence aggregated up to day 105 of 107
#>  [1]   4   7  24 149 158 430 225 180 105  63  47  33  23  11   6
```

--------------------------------

### Configure estimate_R with si_from_data

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

Example of calling estimate_R with the si_from_data method, including configuration for parametric distribution and MCMC control.

```R
estimate_R(incid = incid, 
           method = "si_from_data",
           si_data = data$si_data, # supply dataframe with symptom onset data
           config = make_config(si_parametric_distr = "G", # choose distribution
                                mcmc_control = mcmc_control,
                                seed = overall_seed, # set seed for reproducibility
                                n1 = 500, # number of posterior samples drawn for dist. of the SI
                                n2 = 50)) # number of posterior samples drawn for dist. of Rt for each 
                                          # SI considered
```

--------------------------------

### Example: get_shape_R_flat with constant incidence

Source: https://mrc-ide.github.io/EpiEstim/reference/get_shape_R_flat.html

Example showing how to call get_shape_R_flat with a constant incidence array. Sets n_v=2, n_loc=3, T=100, uses default_priors(), and creates an array of 10s. The output shows the shape values (20.04) repeated for each time step and location.

```R
n_v <- 2
n_loc <- 3 # 3 locations
T <- 100 # 100 time steps
priors <- default_priors()
# constant incidence 10 per day everywhere
incid <- array(10, dim = c(T, n_loc, n_v))
get_shape_R_flat(incid, priors)
```

```R
#>   [1] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [13] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [25] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [37] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [49] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [61] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [73] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [85] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#>  [97] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [109] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [121] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [133] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [145] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [157] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [169] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [181] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [193] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [205] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [217] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [229] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [241] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [253] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [265] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [277] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
#> [289] 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04 20.04
```

--------------------------------

### Configure MCMC control parameters

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

Example of setting up MCMC control parameters including burn-in, thinning, and seed for reproducibility.

```R
mcmc_control <- make_mcmc_control(burnin = burnin, # number of iterations to be discarded as burn-in 
                                  thin = thin, # defining how much the MCMC chains should be thinned
                                  seed = mcmc_seed) # set the seed for reproducibility
```

--------------------------------

### Inspect si_sample matrix

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

Example of inspecting the si_sample matrix used with the si_from_sample method, where each column represents an SI distribution.

```R
head(si_sample[,1:6])
#>               1         11         21         31         41         51
#> [1,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [2,] 0.50864213 0.53282683 0.39873373 0.43800937 0.47079171 0.46166619
#> [3,] 0.23223637 0.27630179 0.27242109 0.25093584 0.23715407 0.23921707
#> [4,] 0.11859018 0.11730828 0.15667303 0.14000878 0.12810521 0.13074405
#> [5,] 0.06311048 0.04613796 0.08431215 0.07734176 0.07102036 0.07289353
#> [6,] 0.03433206 0.01741882 0.04378072 0.04249667 0.03992217 0.04107379
```

--------------------------------

### Example of checking MCMC convergence

Source: https://mrc-ide.github.io/EpiEstim/reference/check_cdt_samples_convergence.html

Demonstrates estimating a serial interval distribution using coarseDataTools and subsequently checking the convergence of the resulting MCMC samples.

```R
if (FALSE) { # \dontrun{
## Note the following examples use an MCMC routine
## to estimate the serial interval distribution from data,
## so they may take a few minutes to run

## load data on rotavirus
data("MockRotavirus")

## estimate the serial interval from data
SI_fit <- coarseDataTools::dic.fit.mcmc(dat = MockRotavirus$si_data,
                     dist = "G",
                     init_pars = init_mcmc_params(MockRotavirus$si_data, "G"),
                     burnin = 1000,
                     n.samples = 5000)

## use check_cdt_samples_convergence to check convergence
converg_diag <- check_cdt_samples_convergence(SI_fit@samples)
converg_diag

} # }
```

--------------------------------

### Estimate R with si_from_sample method

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

Example of calling estimate_R using the si_from_sample method with a matrix of serial interval distributions.

```R
estimate_R(incid = incid,
           method = "si_from_sample",
           si_sample = si_sample, # matrix of SI distributions
           config = make_config(list(n2 = 50)))
```

--------------------------------

### Non-constant aggregation example

Source: https://mrc-ide.github.io/EpiEstim/reference/aggregate_inc.html

Example of aggregating daily incidence data using a repeating pattern of window lengths (2, 2, and 3 days).

```R
## Non-constant aggregation e.g. reporting 3x week
data("SARS2003")
incid <- SARS2003$incidence
dt <- c(2L,2L,3L)
aggregate_inc(incid, dt)
#> Incidence aggregated up to day 107 of 107
#>  [1]   1   1   2   2   3   2   0   5  19  58  38  53  51  54  53  56 199 175  58
#> [20]  80  87  68  56  56  33  30  42  20  12  31  17  16  14  10   9  14   5   8
#> [39]  10   3   1   7   2   2   2   2
```

--------------------------------

### Example usage of compute_lambda

Source: https://mrc-ide.github.io/EpiEstim/reference/compute_lambda.html

Demonstrates how to prepare incidence data and serial interval distributions to compute the overall infectivity.

```R
n_v <- 2
n_loc <- 3 # 3 locations
T <- 100 # 100 time steps
priors <- default_priors()
# constant incidence 10 per day everywhere
incid <- array(10, dim = c(T, n_loc, n_v))
incid <- process_I_multivariant(incid)
# arbitrary serial interval, same for both variants
w_v <- c(0, 0.2, 0.5, 0.3)
si_distr <- cbind(w_v, w_v)
lambda <- compute_lambda(incid, si_distr)
```

--------------------------------

### Example usage of get_shape_epsilon

Source: https://mrc-ide.github.io/EpiEstim/reference/get_shape_epsilon.html

Demonstrates setting up multidimensional incidence and lambda arrays to compute the shape of the posterior distribution for epsilon.

```R
n_loc <- 4 # 4 locations
n_v <- 3 # 3 strains
T <- 100 # 100 time steps
priors <- default_priors()
# constant incidence 10 per day everywhere
incid <- array(10, dim = c(T, n_loc, n_v))
incid <- process_I_multivariant(incid)
# arbitrary serial interval, same for both variants
w_v <- c(0, 0.2, 0.5, 0.3)
si_distr <- cbind(w_v, w_v, w_v)
lambda <- compute_lambda(incid, si_distr)
get_shape_epsilon(incid$local, lambda, priors)
#> [1] 3961 3961
```

--------------------------------

### Format si_data for symptom onset date ranges

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

Example of the si_data structure when data provides a range of potential symptom onset dates.

```text
#>    EL  ER  SL  SR
#> 1  21  25  26  28
#> 2  23  26  26  30
#> 3  34  39  41  43
#> 4  46  52  54  55
#> 5 ... ... ... ...
```

--------------------------------

### Sampling R from the posterior distribution example

Source: https://mrc-ide.github.io/EpiEstim/reference/sample_posterior_R.html

Demonstrates estimating the reproduction number using Flu2009 data and then sampling from the posterior distribution of the first weekly window.

```R
## load data on pandemic flu in a school in 2009
data("Flu2009")

## estimate the reproduction number (method "non_parametric_si")
## when not specifying t_start and t_end in config, they are set to estimate
## the reproduction number on sliding weekly windows                          
res <- estimate_R(incid = Flu2009$incidence, 
                  method = "non_parametric_si",
                  config = make_config(list(si_distr = Flu2009$si_distr)))
#> Default config will estimate R on weekly sliding windows.
#>     To change this change the t_start and t_end arguments. 

## Sample R from the first weekly window
win <- 1L
R_median <- res$R$`Median(R)`[win]
R_CrI <- c(res$R$`Quantile.0.025(R)`[win], res$R$`Quantile.0.975(R)`[win])

set.seed(2019-06-06) # fixing the random seed for reproducibility
R_sample <- sample_posterior_R(res, n = 1000, window = win)
hist(R_sample, col = "grey", main = "R sampled from the first weekly window")
abline(v = R_median, col = "red")       # show the median estimated R
abline(v = R_CrI, col = "red", lty = 2) # show the 95%CrI of R
```

--------------------------------

### Estimate R using a vector of incident cases

Source: https://mrc-ide.github.io/EpiEstim/articles/short_demo.html

Shows how to pass a numeric vector (the `I` column) to `estimate_R`. When using a vector, the x-axis in plots is measured in time steps since the start of the outbreak. Uses the same config as the table example.

```R
res_incid_vector <- estimate_R(Flu2009$incidence$I, 
                               method="parametric_si",
                               config = config)
#> Default config will estimate R on weekly sliding windows.
#>     To change this change the t_start and t_end arguments.
plot(res_incid_vector, "R")
```

--------------------------------

### Install EpiEstim from R-universe

Source: https://mrc-ide.github.io/EpiEstim/index.html

Use this command to install the latest version of the EpiEstim package from the mrc-ide R-universe repository.

```R
install.packages('EpiEstim', repos = c('https://mrc-ide.r-universe.dev', 'https://cloud.r-project.org'))
```

--------------------------------

### Estimate advantage and plot results

Source: https://mrc-ide.github.io/EpiEstim/reference/estimate_advantage.html

Sets up dummy incidence data, serial intervals, and initial MCMC values before running estimate_advantage and plotting the convergence of epsilon and R values.

```R
# constant incidence 10 per day everywhere
incid <- array(10, dim = c(T, n_loc, n_v))
# arbitrary serial interval, same for both variants
w_v <- c(0, 0.2, 0.5, 0.3)
si_distr <- cbind(w_v, w_v)

# Dummy initial values for the MCMC
R_init <- matrix(5, nrow = T, ncol = n_loc)
R_init[1, ] <- NA # no estimates of R on first time step
epsilon_init <- 5
x <- estimate_advantage(incid, si_distr, priors)
# Plotting to check outputs
par(mfrow = c(2, 2))
plot(x$epsilon, type = "l",
     xlab = "Iteration", ylab = "epsilon")
# Compare with what we expect with constant incidence in all locations
abline(h = 1, col = "red")
plot(x$R[10, 1, ], type = "l",
     xlab = "Iteration", ylab = "R time 10 location 1")
abline(h = 1, col = "red")
plot(x$R[20, 2, ], type = "l",
     xlab = "Iteration", ylab = "R time 20 location 2")
abline(h = 1, col = "red")
plot(x$R[30, 3, ], type = "l",
     xlab = "Iteration", ylab = "R time 30 location 3")
```

--------------------------------

### Load Flu2009 dataset

Source: https://mrc-ide.github.io/EpiEstim/articles/full_EpiEstim_vignette.html

Loads the example dataset provided within the EpiEstim package.

```R
data(Flu2009) # example dataset within EpiEstim
```

--------------------------------

### Process multivariant incidence data

Source: https://mrc-ide.github.io/EpiEstim/reference/process_I_multivariant.html

Example of creating a constant incidence array and processing it with process_I_multivariant.

```R
incid <- array(10, dim = c(T, n_loc, n_v))
process_I_multivariant(incid)
#> $local
#> , , 1
#> 
#>        [,1]
#>   [1,]    0
#>   [2,]   10
#>   [3,]   10
#>   [4,]   10
#>   [5,]   10
#>   [6,]   10
#>   [7,]   10
#>   [8,]   10
#>   [9,]   10
#>  [10,]   10
#>  [11,]   10
#>  [12,]   10
#>  [13,]   10
#>  [14,]   10
#>  [15,]   10
#>  [16,]   10
#>  [17,]   10
#>  [18,]   10
#>  [19,]   10
#>  [20,]   10
#>  [21,]   10
#>  [22,]   10
#>  [23,]   10
#>  [24,]   10
#>  [25,]   10
#>  [26,]   10
#>  [27,]   10
#>  [28,]   10
#>  [29,]   10
#>  [30,]   10
#>  [31,]   10
#>  [32,]   10
#>  [33,]   10
#>  [34,]   10
#>  [35,]   10
#>  [36,]   10
#>  [37,]   10
#>  [38,]   10
#>  [39,]   10
#>  [40,]   10
#>  [41,]   10
#>  [42,]   10
#>  [43,]   10
#>  [44,]   10
#>  [45,]   10
#>  [46,]   10
#>  [47,]   10
#>  [48,]   10
#>  [49,]   10
#>  [50,]   10
#>  [51,]   10
#>  [52,]   10
#>  [53,]   10
#>  [54,]   10
#>  [55,]   10
#>  [56,]   10
#>  [57,]   10
#>  [58,]   10
#>  [59,]   10
#>  [60,]   10
#>  [61,]   10
#>  [62,]   10
#>  [63,]   10
#>  [64,]   10
#>  [65,]   10
#>  [66,]   10
#>  [67,]   10
#>  [68,]   10
#>  [69,]   10
#>  [70,]   10
#>  [71,]   10
#>  [72,]   10
#>  [73,]   10
#>  [74,]   10
#>  [75,]   10
#>  [76,]   10
#>  [77,]   10
#>  [78,]   10
#>  [79,]   10
#>  [80,]   10
#>  [81,]   10
#>  [82,]   10
#>  [83,]   10
#>  [84,]   10
#>  [85,]   10
#>  [86,]   10
#>  [87,]   10
#>  [88,]   10
#>  [89,]   10
#>  [90,]   10
#>  [91,]   10
#>  [92,]   10
#>  [93,]   10
#>  [94,]   10
#>  [95,]   10
#>  [96,]   10
#>  [97,]   10
#>  [98,]   10
#>  [99,]   10
#> [100,]   10
#> 
#> , , 2
#> 
#>        [,1]
#>   [1,]    0
#>   [2,]   10
#>   [3,]   10
#>   [4,]   10
#>   [5,]   10
#>   [6,]   10
#>   [7,]   10
#>   [8,]   10
#>   [9,]   10
#>  [10,]   10
#>  [11,]   10
#>  [12,]   10
#>  [13,]   10
#>  [14,]   10
#>  [15,]   10
#>  [16,]   10
#>  [17,]   10
#>  [18,]   10
#>  [19,]   10
#>  [20,]   10
#>  [21,]   10
#>  [22,]   10
#>  [23,]   10
#>  [24,]   10
#>  [25,]   10
#>  [26,]   10
#>  [27,]   10
#>  [28,]   10
#>  [29,]   10
#>  [30,]   10
#>  [31,]   10
#>  [32,]   10
#>  [33,]   10
#>  [34,]   10
#>  [35,]   10
#>  [36,]   10
#>  [37,]   10
#>  [38,]   10
#>  [39,]   10
#>  [40,]   10
#>  [41,]   10
#>  [42,]   10
#>  [43,]   10
#>  [44,]   10
#>  [45,]   10
#>  [46,]   10
#>  [47,]   10
#>  [48,]   10
#>  [49,]   10
#>  [50,]   10
#>  [51,]   10
#>  [52,]   10
#>  [53,]   10
#>  [54,]   10
#>  [55,]   10
#>  [56,]   10
#>  [57,]   10
#>  [58,]   10
#>  [59,]   10
#>  [60,]   10
#>  [61,]   10
#>  [62,]   10
#>  [63,]   10
#>  [64,]   10
#>  [65,]   10
#>  [66,]   10
#>  [67,]   10
#>  [68,]   10
#>  [69,]   10
#>  [70,]   10
#>  [71,]   10
#>  [72,]   10
#>  [73,]   10
#>  [74,]   10
#>  [75,]   10
#>  [76,]   10
#>  [77,]   10
#>  [78,]   10
#>  [79,]   10
#>  [80,]   10
#>  [81,]   10
#>  [82,]   10
#>  [83,]   10
#>  [84,]   10
#>  [85,]   10
#>  [86,]   10
#>  [87,]   10
#>  [88,]   10
#>  [89,]   10
#>  [90,]   10
#>  [91,]   10
#>  [92,]   10
#>  [93,]   10
#>  [94,]   10
#>  [95,]   10
#>  [96,]   10
#>  [97,]   10
#>  [98,]   10
#>  [99,]   10
#> [100,]   10
#> 
#> , , 3
#> 
#>        [,1]
#>   [1,]    0
#>   [2,]   10
#>   [3,]   10
#>   [4,]   10
#>   [5,]   10
#>   [6,]   10
#>   [7,]   10
#>   [8,]   10
#>   [9,]   10
#>  [10,]   10
#>  [11,]   10
#>  [12,]   10
#>  [13,]   10
#>  [14,]   10
#>  [15,]   10
#>  [16,]   10
#>  [17,]   10
#>  [18,]   10
#>  [19,]   10
#>  [20,]   10
#>  [21,]   10
#>  [22,]   10
#>  [23,]   10
#>  [24,]   10
#>  [25,]   10
#>  [26,]   10
#>  [27,]   10
#>  [28,]   10
#>  [29,]   10
#>  [30,]   10
#>  [31,]   10
#>  [32,]   10
#>  [33,]   10
#>  [34,]   10
#>  [35,]   10
#>  [36,]   10
#>  [37,]   10
#>  [38,]   10
#>  [39,]   10
#>  [40,]   10
#>  [41,]   10
#>  [42,]   10
#>  [43,]   10
#>  [44,]   10
#>  [45,]   10
#>  [46,]   10
#>  [47,]   10
#>  [48,]   10
#>  [49,]   10
#>  [50,]   10
#>  [51,]   10
#>  [52,]   10
#>  [53,]   10
#>  [54,]   10
#>  [55,]   10
#>  [56,]   10
#>  [57,]   10
#>  [58,]   10
#>  [59,]   10
#>  [60,]   10
#>  [61,]   10
#>  [62,]   10
#>  [63,]   10
#>  [64,]   10
#>  [65,]   10
#>  [66,]   10
#>  [67,]   10
#>  [68,]   10
#>  [69,]   10
#>  [70,]   10
#>  [71,]   10
#>  [72,]   10
#>  [73,]   10
#>  [74,]   10
#>  [75,]   10
#>  [76,]   10
#>  [77,]   10
#>  [78,]   10
#>  [79,]   10
#>  [80,]   10
#>  [81,]   10
#>  [82,]   10
#>  [83,]   10
#>  [84,]   10
#>  [85,]   10
#>  [86,]   10
#>  [87,]   10
#>  [88,]   10
#>  [89,]   10
#>  [90,]   10
#>  [91,]   10
#>  [92,]   10
#>  [93,]   10
#>  [94,]   10
#>  [95,]   10
#>  [96,]   10
#>  [97,]   10
#>  [98,]   10
#>  [99,]   10
#> [100,]   10
#> 
#> 
#> $imported
#> , , 1
#> 
#>        [,1]
#>   [1,]   10
#>   [2,]    0
#>   [3,]    0
#>   [4,]    0
#>   [5,]    0
#>   [6,]    0
#>   [7,]    0
#>   [8,]    0
#>   [9,]    0
#>  [10,]    0
#>  [11,]    0
#>  [12,]    0
#>  [13,]    0
#>  [14,]    0
#>  [15,]    0
```
Tokens:
Raw