Conditional Mean First Passage Time — cond

Calculate the mean number of steps to first passage

Usage

cond_passage(samc, init, origin, dest)

# S4 method for class 'samc,missing,missing,location'
cond_passage(samc, dest)

# S4 method for class 'samc,missing,location,location'
cond_passage(samc, origin, dest)

# S4 method for class 'samc,ANY,missing,location'
cond_passage(samc, init, dest)

Arguments

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.

Value

See Details

Details

\(\tilde{t}=\tilde{B}_j^{-1}\tilde{F}\tilde{B}_j{\cdot}1\)

cond_passage(samc, dest)

The result is a vector where each element corresponds to a cell in the landscape, and can be mapped back to the landscape using the map function. Element i is the mean number of steps before absorption starting from location i conditional on absorption into j

Note that mathematically, the formula actually does not return a value for when i is equal to j. This leads to a situation where the resultant vector is actually one element short and the index for some of the elements may be shifted. The cond_passage() function fills inserts a 0 value for vector indices corresponding to i == j. This corrects the final result so that vector indices work as expected, and allows the vector to be properly used in the map function.
cond_passage(samc, origin, dest)

The result is a numeric value representing the mean number of steps before absorption starting from a given origin conditional on absorption into j.

As described above, mathematically the formula does not return a result for when the origin and dest inputs are equal, so the function simply returns a 0 in this case.

WARNING: This function is not compatible when used with data where there are states with total absorption present. When present, states representing total absorption leads to unsolvable linear equations. The only exception to this is when there is a single total absorption state that corresponds to input to the dest parameter. In this case, the total absorption is effectively ignored when the linear equations are solved.

WARNING: This function will crash when used with data representing a disconnected graph. This includes, for example, isolated pixels or islands in raster data. This is a result of the transition matrix for disconnected graphs leading to some equations being unsolvable. Different options are being explored for how to best identify these situations in data and handle them accordingly.

Performance

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

Examples

# "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: 50%  (~9s remaining)       
Computing: 98%  (~0s remaining)       
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)