This function allows the construction of convolution matrices which can be be combined with a vector of primary events to produce a vector of secondary events for example in the form of a renewal equation or to simulate reporting delays. Time-varying delays are supported as well as distribution padding (to allow for use in renewal equation like approaches).
Arguments
- dist
A vector of list of vectors describing the distribution to be convolved as a probability mass function.
- t
Integer value indicating the number of time steps to convolve over.
- include_partial
Logical, defaults to FALSE. If TRUE, the convolution include partially complete secondary events.
Value
A matrix with each column indicating a primary event and each row indicating a secondary event.
See also
Helper functions for model modules
add_max_observed_delay(),
add_pmfs(),
enw_reference_by_report(),
enw_reps_with_complete_refs(),
extract_obs_metadata(),
extract_sparse_matrix(),
latest_obs_as_matrix(),
simulate_double_censored_pmf()
Examples
# Simple convolution matrix with a static distribution
convolution_matrix(c(1, 2, 3), 10)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,] 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0
#> [3,] 3 2 1 0 0 0 0 0 0 0
#> [4,] 0 3 2 1 0 0 0 0 0 0
#> [5,] 0 0 3 2 1 0 0 0 0 0
#> [6,] 0 0 0 3 2 1 0 0 0 0
#> [7,] 0 0 0 0 3 2 1 0 0 0
#> [8,] 0 0 0 0 0 3 2 1 0 0
#> [9,] 0 0 0 0 0 0 3 2 1 0
#> [10,] 0 0 0 0 0 0 0 3 2 1
# Include partially reported convolutions
convolution_matrix(c(1, 2, 3), 10, include_partial = TRUE)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,] 1 0 0 0 0 0 0 0 0 0
#> [2,] 2 1 0 0 0 0 0 0 0 0
#> [3,] 3 2 1 0 0 0 0 0 0 0
#> [4,] 0 3 2 1 0 0 0 0 0 0
#> [5,] 0 0 3 2 1 0 0 0 0 0
#> [6,] 0 0 0 3 2 1 0 0 0 0
#> [7,] 0 0 0 0 3 2 1 0 0 0
#> [8,] 0 0 0 0 0 3 2 1 0 0
#> [9,] 0 0 0 0 0 0 3 2 1 0
#> [10,] 0 0 0 0 0 0 0 3 2 1
# Use a list of distributions
convolution_matrix(rep(list(c(1, 2, 3)), 10), 10)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,] 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0
#> [3,] 3 2 1 0 0 0 0 0 0 0
#> [4,] 0 3 2 1 0 0 0 0 0 0
#> [5,] 0 0 3 2 1 0 0 0 0 0
#> [6,] 0 0 0 3 2 1 0 0 0 0
#> [7,] 0 0 0 0 3 2 1 0 0 0
#> [8,] 0 0 0 0 0 3 2 1 0 0
#> [9,] 0 0 0 0 0 0 3 2 1 0
#> [10,] 0 0 0 0 0 0 0 3 2 1
# Use a time-varying list of distributions
convolution_matrix(c(rep(list(c(1, 2, 3)), 10), list(c(4, 5, 6))), 11)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
#> [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,] 3 2 1 0 0 0 0 0 0 0 0
#> [4,] 0 3 2 1 0 0 0 0 0 0 0
#> [5,] 0 0 3 2 1 0 0 0 0 0 0
#> [6,] 0 0 0 3 2 1 0 0 0 0 0
#> [7,] 0 0 0 0 3 2 1 0 0 0 0
#> [8,] 0 0 0 0 0 3 2 1 0 0 0
#> [9,] 0 0 0 0 0 0 3 2 1 0 0
#> [10,] 0 0 0 0 0 0 0 3 2 1 0
#> [11,] 0 0 0 0 0 0 0 0 3 2 4