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Bisaloo avatar Bisaloo commented on June 12, 2024 1

Using the reprex from #62 (comment), with 500 iterations:

pak::pak("bahadzie/epidemics@benchmarks")
#> ℹ Loading metadata database
#> ✔ Loading metadata database ... done
#> 
#> 
#> ℹ No downloads are needed
#> ✔ 1 pkg + 10 deps: kept 10 [3.5s]

library(epidemics)

# Create stratified populations based on supplied age limits
pop <- function(age_limits = c(0, 20, 40)) {
  # load contact and population data from socialmixr::polymod
  polymod <- socialmixr::polymod
  contact_data <- socialmixr::contact_matrix(
    polymod,
    countries = "United Kingdom",
    age.limits = age_limits,
    symmetric = TRUE
  )
  
  # prepare contact matrix
  contact_matrix <- t(contact_data$matrix)
  contact_matrix
  
  # prepare the demography vector
  demography_vector <- contact_data$demography$population
  names(demography_vector) <- rownames(contact_matrix)
  
  # initial conditions: one in every 1 million is infected
  initial_i <- 1e-6
  initial_condition <- c(
    S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
  )
  ncol <- length(initial_condition)
  nrow <- length(rownames(contact_matrix))
  initial_conditions <- matrix(rep(initial_condition, nrow), ncol = ncol)
  colnames(initial_conditions) <- names(initial_condition)
  rownames(initial_conditions) <- rownames(contact_matrix)
  
  population(
    name = "UK",
    contact_matrix = contact_matrix,
    demography_vector = demography_vector,
    initial_conditions = initial_conditions
  )
}

uk_pop <- pop(c(0, 20, 65)) # ages beyond 80?
#> Using POLYMOD social contact data. To cite this in a publication, use the 'cite' function
#> Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option

# simulate a pandemic, with an R0,
# an infectious period, and an pre-infectious period
pandemic_influenza <- infection(
  r0 = 1.5,
  preinfectious_period = 3,
  infectious_period = 7
)

# an intervention to close schools
close_schools <- intervention(
  time_begin = 200,
  time_end = 260,
  contact_reduction = round(runif(length(uk_pop$demography_vector)), 2)
)

# a vaccination to close schools
vax <- vaccination(
  time_begin = 100,
  time_end = 400,
  nu = runif(length(uk_pop$demography_vector)) * 1e-4
)

# benchmarking using {bench}
bnch <- bench::mark(
  min_iterations = 500,
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  check = FALSE # setting false for now
)
summary(bnch)
#> # A tibble: 2 × 6
#>   expression        min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>   <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 epidemic_cpp   4.21ms   5.25ms     182.     1.56MB    10.8 
#> 2 epidemic_r     22.1ms  25.34ms      39.0    2.71MB     8.68

# benchmarking using {microbenchmark}
mbench <- microbenchmark::microbenchmark(
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  times = 500
)

summary(mbench)
#>           expr       min        lq      mean    median        uq      max neval
#> 1 epidemic_cpp  4.254519  4.873327  5.502002  5.227099  5.762491  16.5548   500
#> 2   epidemic_r 21.874709 24.381577 27.292796 25.971410 28.353433 173.4696   500

Created on 2023-06-05 with reprex v2.0.2

Session info 
sessioninfo::platform_info()
#>  setting  value
#>  version  R version 4.3.0 (2023-04-21)
#>  os       Ubuntu 22.04.2 LTS
#>  system   x86_64, linux-gnu
#>  ui       X11
#>  language en_US
#>  collate  en_GB.UTF-8
#>  ctype    en_GB.UTF-8
#>  tz       Europe/Paris
#>  date     2023-06-05
#>  pandoc   2.19.2 @ /usr/lib/rstudio/resources/app/bin/quarto/bin/tools/ (via rmarkdown)

Created on 2023-06-05 with reprex v2.0.2

from epidemics.

pratikunterwegs avatar pratikunterwegs commented on June 12, 2024

Posting an initial benchmarking of the deafult model in {epidemics} started by @bahadzie in https://github.com/bahadzie/epidemics/blob/benchmarks/vignettes/COMPARE.Rmd.

  1. I’ve added a vaccination regime to benchmark the full functionality,
  2. The epidemic_r() function is limited to three age groups at the moment - it would be better to benchmark both for a larger number of age groups. An older version of {epidemics} had this implemented in R using matrix operations so should be possible to copy.

Using both the {bench} and {microbenchmark} packages the Cpp version is quicker, with the difference larger when using {bench} (not sure why this is).

This benchmarking is on a Mac with an M2 chip.

 r
pak::pak("bahadzie/epidemics@benchmarks")
#> ℹ Loading metadata database
#> ℹ Loading metadata database
#> ✔ Loading metadata database ... done
#> ✔ Loading metadata database ... done
#> 
#>  
#> 
#> ℹ No downloads are needed
#> ℹ No downloads are needed
#> ✔ 1 pkg + 10 deps: kept 8 [5s]
#> ✔ 1 pkg + 10 deps: kept 8 [5s]
library(epidemics)

# Create stratified populations based on supplied age limits
pop <- function(age_limits = c(0, 20, 40)) {
  # load contact and population data from socialmixr::polymod
  polymod <- socialmixr::polymod
  contact_data <- socialmixr::contact_matrix(
    polymod,
    countries = "United Kingdom",
    age.limits = age_limits,
    symmetric = TRUE
  )

  # prepare contact matrix
  contact_matrix <- t(contact_data$matrix)
  contact_matrix

  # prepare the demography vector
  demography_vector <- contact_data$demography$population
  names(demography_vector) <- rownames(contact_matrix)

  # initial conditions: one in every 1 million is infected
  initial_i <- 1e-6
  initial_condition <- c(
    S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
  )
  ncol <- length(initial_condition)
  nrow <- length(rownames(contact_matrix))
  initial_conditions <- matrix(rep(initial_condition, nrow), ncol = ncol)
  colnames(initial_conditions) <- names(initial_condition)
  rownames(initial_conditions) <- rownames(contact_matrix)

  population(
    name = "UK",
    contact_matrix = contact_matrix,
    demography_vector = demography_vector,
    initial_conditions = initial_conditions
  )
}

uk_pop <- pop(c(0, 20, 65)) # ages beyond 80?
#> Using POLYMOD social contact data. To cite this in a publication, use the 'cite' function
#> Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option

# simulate a pandemic, with an R0,
# an infectious period, and an pre-infectious period
pandemic_influenza <- infection(
  r0 = 1.5,
  preinfectious_period = 3,
  infectious_period = 7
)

# an intervention to close schools
close_schools <- intervention(
  time_begin = 200,
  time_end = 260,
  contact_reduction = round(runif(length(uk_pop$demography_vector)), 2)
)

# a vaccination to close schools
vax <- vaccination(
  time_begin = 100,
  time_end = 400,
  nu = runif(length(uk_pop$demography_vector)) * 1e-4
)

# benchmarking using {bench}
bnch <- bench::mark(
  min_iterations = 100, max_iterations = 100,
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  check = FALSE # setting false for now
)
summary(bnch)
#> # A tibble: 2 × 6
#>   expression        min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>   <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 epidemic_cpp   6.73ms   7.33ms      89.0    1.56MB     2.75
#> 2 epidemic_r    26.64ms  28.86ms      34.4    2.69MB     6.07

# benchmarking using {microbenchmark}
mbench <- microbenchmark::microbenchmark(
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  times = 100
)
#> Warning in microbenchmark::microbenchmark(epidemic_cpp = epidemic(model =
#> "default", : less accurate nanosecond times to avoid potential integer overflows
summary(mbench)
#>           expr      min       lq     mean   median       uq       max neval
#> 1 epidemic_cpp 14.78911 18.92238 19.52856 19.78615 20.32046  24.46855   100
#> 2   epidemic_r 24.46983 28.73629 31.10285 30.25005 31.57761 122.99360   100

Created on 2023-06-05 by the reprex package (v2.0.1)

from epidemics.

pratikunterwegs avatar pratikunterwegs commented on June 12, 2024

Benchmarking the default model with 1000 iterations on an M2 chip; the Rcpp implementation is roughly 1.5x faster.

pak::pak("bahadzie/epidemics@benchmarks")
#> ℹ Loading metadata database
#> ℹ Loading metadata database
#> ✔ Loading metadata database ... done
#> ✔ Loading metadata database ... done
#> 
#>  
#> 
#> ℹ No downloads are needed
#> ℹ No downloads are needed
#> ✔ 1 pkg + 10 deps: kept 8 [5.6s]
#> ✔ 1 pkg + 10 deps: kept 8 [5.6s]
library(epidemics)

# Create stratified populations based on supplied age limits
pop <- function(age_limits = c(0, 20, 40)) {
  # load contact and population data from socialmixr::polymod
  polymod <- socialmixr::polymod
  contact_data <- socialmixr::contact_matrix(
    polymod,
    countries = "United Kingdom",
    age.limits = age_limits,
    symmetric = TRUE
  )

  # prepare contact matrix
  contact_matrix <- t(contact_data$matrix)
  contact_matrix

  # prepare the demography vector
  demography_vector <- contact_data$demography$population
  names(demography_vector) <- rownames(contact_matrix)

  # initial conditions: one in every 1 million is infected
  initial_i <- 1e-6
  initial_condition <- c(
    S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
  )
  ncol <- length(initial_condition)
  nrow <- length(rownames(contact_matrix))
  initial_conditions <- matrix(rep(initial_condition, nrow), ncol = ncol)
  colnames(initial_conditions) <- names(initial_condition)
  rownames(initial_conditions) <- rownames(contact_matrix)

  population(
    name = "UK",
    contact_matrix = contact_matrix,
    demography_vector = demography_vector,
    initial_conditions = initial_conditions
  )
}

uk_pop <- pop(c(0, 20, 65)) # ages beyond 80?
#> Using POLYMOD social contact data. To cite this in a publication, use the 'cite' function
#> Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option

# simulate a pandemic, with an R0,
# an infectious period, and an pre-infectious period
pandemic_influenza <- infection(
  r0 = 1.5,
  preinfectious_period = 3,
  infectious_period = 7
)

# an intervention to close schools
close_schools <- intervention(
  time_begin = 200,
  time_end = 260,
  contact_reduction = round(runif(length(uk_pop$demography_vector)), 2)
)

# a vaccination to close schools
vax <- vaccination(
  time_begin = 100,
  time_end = 400,
  nu = runif(length(uk_pop$demography_vector)) * 1e-4
)

# benchmarking using {bench}
bnch <- bench::mark(
  min_iterations = 1000, max_iterations = 1000,
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  check = FALSE # setting false for now
)
summary(bnch)
#> # A tibble: 2 × 6
#>   expression        min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>   <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 epidemic_cpp    6.6ms   22.5ms      47.0    1.56MB     1.35
#> 2 epidemic_r     15.8ms   28.5ms      35.8    2.69MB     6.02

# benchmarking using {microbenchmark}
mbench <- microbenchmark::microbenchmark(
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  times = 1000
)
#> Warning in microbenchmark::microbenchmark(epidemic_cpp = epidemic(model =
#> "default", : less accurate nanosecond times to avoid potential integer overflows
summary(mbench)
#>           expr      min       lq     mean   median       uq       max neval
#> 1 epidemic_cpp  7.24142 18.40187 19.33215 19.78393 20.29320 116.95586  1000
#> 2   epidemic_r 19.26077 28.41257 29.92554 29.64601 31.18464  57.17938  1000

Created on 2023-06-05 by the reprex package (v2.0.1)

from epidemics.

pratikunterwegs avatar pratikunterwegs commented on June 12, 2024

Checking with options(matprod = "internal") in case %*% on MacOS is the issue - does not seem to be, as the results are fairly similar to earlier runs on MacOS.

pak::pak("bahadzie/epidemics@benchmarks")
#> 
#> ✔ Updated metadata database: 4.86 MB in 4 files.
#> ✔ Updated metadata database: 4.86 MB in 4 files.
#> 
#> ℹ Updating metadata database
#> ℹ Updating metadata database
#> ✔ Updating metadata database ... done
#> ✔ Updating metadata database ... done
#> 
#>  
#> 
#> → Will update 1 package.
#> → Will update 1 package.
#> → Will download 1 package with unknown size.
#> → Will download 1 package with unknown size.
#> + epidemics 0.0.0.9000 → 0.0.0.9000 👷🏿‍♂️🔧 ⬇ (GitHub: 0df5c96)
#> + epidemics 0.0.0.9000 → 0.0.0.9000 👷🏿‍♂️🔧 ⬇ (GitHub: 0df5c96)
#> ℹ Getting 1 pkg with unknown size
#> ℹ Getting 1 pkg with unknown size
#> ✔ Cached copy of epidemics 0.0.0.9000 (source) is the latest build
#> ✔ Cached copy of epidemics 0.0.0.9000 (source) is the latest build
#> ℹ Packaging epidemics 0.0.0.9000
#> ℹ Packaging epidemics 0.0.0.9000
#> ✔ Packaged epidemics 0.0.0.9000 (1.8s)
#> ✔ Packaged epidemics 0.0.0.9000 (1.8s)
#> ℹ Building epidemics 0.0.0.9000
#> ℹ Building epidemics 0.0.0.9000
#> ✔ Built epidemics 0.0.0.9000 (10s)
#> ✔ Built epidemics 0.0.0.9000 (10s)
#> ✔ Installed epidemics 0.0.0.9000 (github::bahadzie/epidemics@0df5c96) (61ms)
#> ✔ Installed epidemics 0.0.0.9000 (github::bahadzie/epidemics@0df5c96) (61ms)
#> ✔ 1 pkg + 11 deps: kept 7, upd 1 [27.1s]
#> ✔ 1 pkg + 11 deps: kept 7, upd 1 [27.1s]
library(epidemics)
options(matprod = "internal")

# Create stratified populations based on supplied age limits
pop <- function(age_limits = c(0, 20, 40)) {
  # load contact and population data from socialmixr::polymod
  polymod <- socialmixr::polymod
  contact_data <- socialmixr::contact_matrix(
    polymod,
    countries = "United Kingdom",
    age.limits = age_limits,
    symmetric = TRUE
  )

  # prepare contact matrix
  contact_matrix <- t(contact_data$matrix)
  contact_matrix

  # prepare the demography vector
  demography_vector <- contact_data$demography$population
  names(demography_vector) <- rownames(contact_matrix)

  # initial conditions: one in every 1 million is infected
  initial_i <- 1e-6
  initial_condition <- c(
    S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
  )
  ncol <- length(initial_condition)
  nrow <- length(rownames(contact_matrix))
  initial_conditions <- matrix(rep(initial_condition, nrow), ncol = ncol)
  colnames(initial_conditions) <- names(initial_condition)
  rownames(initial_conditions) <- rownames(contact_matrix)

  population(
    name = "UK",
    contact_matrix = contact_matrix,
    demography_vector = demography_vector,
    initial_conditions = initial_conditions
  )
}

uk_pop <- pop(c(0, 20, 65)) # ages beyond 80?
#> Using POLYMOD social contact data. To cite this in a publication, use the 'cite' function
#> Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option

# simulate a pandemic, with an R0,
# an infectious period, and an pre-infectious period
pandemic_influenza <- infection(
  r0 = 1.5,
  preinfectious_period = 3,
  infectious_period = 7
)

# an intervention to close schools
close_schools <- intervention(
  time_begin = 200,
  time_end = 260,
  contact_reduction = round(runif(length(uk_pop$demography_vector)), 2)
)

# a vaccination to close schools
vax <- vaccination(
  time_begin = 100,
  time_end = 400,
  nu = runif(length(uk_pop$demography_vector)) * 1e-4
)

# benchmarking using {bench}
bnch <- bench::mark(
  min_iterations = 1000, max_iterations = 1000,
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  check = FALSE # setting false for now
)
summary(bnch)
#> # A tibble: 2 × 6
#>   expression        min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>   <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 epidemic_cpp   6.69ms   23.6ms      44.7    1.56MB     1.33
#> 2 epidemic_r    18.93ms   30.4ms      33.6    2.69MB     5.66

# benchmarking using {microbenchmark}
mbench <- microbenchmark::microbenchmark(
  "epidemic_cpp" = epidemic(
    model = "default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  "epidemic_r" = r_epidemic(
    model = "r_default",
    population = uk_pop,
    infection = pandemic_influenza,
    intervention = close_schools,
    vaccination = vax,
    time_end = 600, increment = 1.0
  ),
  times = 1000
)
#> Warning in microbenchmark::microbenchmark(epidemic_cpp = epidemic(model =
#> "default", : less accurate nanosecond times to avoid potential integer overflows
summary(mbench)
#>           expr      min       lq     mean   median       uq       max neval
#> 1 epidemic_cpp 10.76369 19.99843 20.58345 20.82152 21.21734 118.59910  1000
#> 2   epidemic_r 20.97130 31.24284 32.58153 32.33664 33.76649  50.74873  1000

Created on 2023-06-12 by the reprex package (v2.0.1)

from epidemics.

pratikunterwegs avatar pratikunterwegs commented on June 12, 2024

Posting a benchmark of the Vacamole model after some speed-ups implemented in #86. Now achieving an approx 2x speedup on an M2 Mac. Similar speed-up expected for the default model which has received the same edits.

library(epidemics)

polymod <- socialmixr::polymod
contact_data <- socialmixr::contact_matrix(
  polymod,
  countries = "United Kingdom",
  age.limits = c(0, 60),
  symmetric = TRUE
)
#> Using POLYMOD social contact data. To cite this in a publication, use the 'cite' function
#> Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option
contact_matrix <- t(contact_data$matrix)
demography_vector <- contact_data$demography$population

# // 0| 1| 2|3| 4|5| 6|7| 8|9|10
# // S|V1|V2|E|EV|I|IV|H|HV|D|R

# make initial conditions - order is important
initial_conditions <- c(
  S = 1 - 1e-6,
  V1 = 0, V2 = 0,
  E = 0, EV = 0,
  I = 1e-6, IV = 0,
  H = 0, HV = 0, D = 0, R = 0
)
initial_conditions <- rbind(
  initial_conditions,
  initial_conditions
)

# create a population
uk_population <- population(
  name = "UK population",
  contact_matrix = matrix(1, 2, 2),
  demography_vector = 67e6 * c(0.4, 0.6),
  initial_conditions = initial_conditions
)

# prepare a two dose vaccination regime for three age groups
double_vaccination <- vaccination(
  name = "double_vaccination",
  nu = matrix(
    1e-3,
    nrow = 2, ncol = 2
  ),
  time_begin = matrix(
    00,
    nrow = 2, ncol = 2
  ),
  time_end = matrix(
    200,
    nrow = 2, ncol = 2
  )
)

# make infection class for Vacamole model
# note extra arguments passed as ...
infect <- infection(
  name = "covid", r0 = 5, infectious_period = 10,
  preinfectious_period = 5,
  eta = 1 / 1000, omega = 1 / 1000,
  susc_reduction_vax = 0.5,
  hosp_reduction_vax = 0.7,
  mort_reduction_vax = 0.9
)

microbenchmark::microbenchmark(
  "vacamole_new_cpp" = epidemic_vacamole_cpp(
      population = uk_population,
      infection = infect,
      vaccination = double_vaccination,
      time_end = 500, increment = 1
    )
)
#> Warning in microbenchmark::microbenchmark(vacamole_new_cpp =
#> epidemic_vacamole_cpp(population = uk_population, : less accurate nanosecond
#> times to avoid potential integer overflows
#> Unit: milliseconds
#>              expr      min       lq     mean   median       uq      max neval
#>  vacamole_new_cpp 7.920052 8.636712 8.831481 8.753028 8.850362 13.34374   100

bench::mark(
  "vacamole_new_cpp" = epidemic_vacamole_cpp(
      population = uk_population,
      infection = infect,
      vaccination = double_vaccination,
      time_end = 500, increment = 1
    )
)
#> # A tibble: 1 × 6
#>   expression            min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>       <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 vacamole_new_cpp   4.67ms   8.04ms      142.     894KB     4.12

Created on 2023-08-09 by the reprex package (v2.0.1)

from epidemics.

pratikunterwegs avatar pratikunterwegs commented on June 12, 2024

Closing in favour of moving this to a dedicated Discussion item in the repo.

from epidemics.

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