Calculate the probability of being at a transient state at a specific time.

```
distribution(samc, init, origin, dest, time)
# S4 method for samc,missing,missing,missing,numeric
distribution(samc, time)
# S4 method for samc,missing,location,missing,numeric
distribution(samc, origin, time)
# S4 method for samc,missing,missing,location,numeric
distribution(samc, dest, time)
# S4 method for samc,missing,location,location,numeric
distribution(samc, origin, dest, time)
# S4 method for samc,ANY,missing,missing,numeric
distribution(samc, init, time)
```

- samc
A

`samc-class`

object created using the`samc`

function.- init
Sets the initial state \(\psi\) of the transients states. Input must be able to pass the

`check`

function when compared against the`samc-class`

object. Can only contain positive finite values.- origin
A positive integer or character name representing transient state \(\mathit{i}\). Corresponds to row \(\mathit{i}\) of matrix \(\mathbf{P}\) in the

`samc-class`

object. When paired with the`dest`

parameter, multiple values may be provided as a vector.- dest
A positive integer or character name representing transient state \(\mathit{j}\). Corresponds to column \(\mathit{j}\) of matrix \(\mathbf{P}\) in the

`samc-class`

object. When paired with the`origin`

parameter, multiple values may be provided as a vector.- time
A positive integer or a vector of positive integers representing \(\mathit{t}\) time steps. Vectors must be ordered and contain no duplicates. Vectors may not be used for metrics that return dense matrices. The maximum time step value is capped at 10,000 due to numerical precision issues.

See Details

\(Q^t\)

**distribution(samc, time)**The result is a matrix \(M\) where \(M_{i,j}\) is the probability of being at transient state \(\mathit{j}\) after \(\mathit{t}\) time steps if starting at transient state \(\mathit{i}\).

The returned matrix will always be dense and cannot be optimized. Must enable override to use (see

`samc-class`

).**distribution(samc, origin, time)**The result is a vector \(\mathbf{v}\) where \(\mathbf{v}_j\) is the probability of being at transient state \(\mathit{j}\) after \(\mathit{t}\) time steps if starting at transient state \(\mathit{i}\).

If multiple time steps were provided as a vector, then the result will be an ordered named list containing a vector for each time step.

If the samc-class object was created using matrix or RasterLayer maps, then vector \(\mathbf{v}\) can be mapped to a RasterLayer using the

`map`

function.**distribution(samc, dest, time)**The result is a vector \(\mathbf{v}\) where \(\mathbf{v}_i\) is the probability of being at transient state \(\mathit{j}\) after \(\mathit{t}\) time steps if starting at transient state \(\mathit{i}\).

If multiple time steps were provided as a vector, then the result will be an ordered named list containing a vector for each time step.

If the samc-class object was created using matrix or RasterLayer maps, then vector \(\mathbf{v}\) can be mapped to a RasterLayer using the

`map`

function.**distribution(samc, origin, dest, time)**The result is a numeric value that is the probability of being at a transient state \(\mathit{j}\) after \(\mathit{t}\) time steps if starting at transient state \(\mathit{i}\).

If multiple time steps were provided as a vector, then the result will be an ordered named list containing a vector for each time step.

\(\psi^TQ^t\)

**distribution(samc, init, time)**The result is a vector \(\mathbf{v}\) where \(\mathbf{v}_j\) is the probability of being at transient state \(\mathit{i}\) after \(\mathit{t}\) time steps given an initial state \(\psi\).

If the samc-class object was created using matrix or RasterLayer maps, then vector \(\mathbf{v}\) can be mapped to a RasterLayer using the

`map`

function.

Any relevant performance information about this function can be found in the
performance vignette: `vignette("performance", package = "samc")`

```
# "Load" the data. In this case we are using data built into the package.
# In practice, users will likely load raster data using the raster() function
# from the raster package.
res_data <- samc::example_split_corridor$res
abs_data <- samc::example_split_corridor$abs
init_data <- samc::example_split_corridor$init
# Make sure our data meets the basic input requirements of the package using
# the check() function.
check(res_data, abs_data)
#> [1] TRUE
check(res_data, init_data)
#> [1] TRUE
# Setup the details for a random-walk model
rw_model <- list(fun = function(x) 1/mean(x), # Function for calculating transition probabilities
dir = 8, # Directions of the transitions. Either 4 or 8.
sym = TRUE) # Is the function symmetric?
# Create a `samc-class` object with the resistance and absorption data using
# the samc() function. We use the recipricol of the arithmetic mean for
# calculating the transition matrix. Note, the input data here are matrices,
# not RasterLayers.
samc_obj <- samc(res_data, abs_data, model = rw_model)
# Convert the initial state data to probabilities
init_prob_data <- init_data / sum(init_data, na.rm = TRUE)
# Calculate short- and long-term metrics using the analytical functions
short_mort <- mortality(samc_obj, init_prob_data, time = 50)
short_dist <- distribution(samc_obj, origin = 3, time = 50)
long_disp <- dispersal(samc_obj, init_prob_data)
#>
#> Cached diagonal not found.
#> Performing setup. This can take several minutes... Complete.
#> Calculating matrix inverse diagonal...
#>
Computing: 100% (done)
#>
Complete
#> Diagonal has been cached. Continuing with metric calculation...
visit <- visitation(samc_obj, dest = 4)
surv <- survival(samc_obj)
# Use the map() function to turn vector results into RasterLayer objects.
short_mort_map <- map(samc_obj, short_mort)
short_dist_map <- map(samc_obj, short_dist)
long_disp_map <- map(samc_obj, long_disp)
visit_map <- map(samc_obj, visit)
surv_map <- map(samc_obj, surv)
```