Create an samc object that contains the absorbing Markov chain data

```
samc(data, absorption, fidelity, model)
# S4 method for SpatRaster,SpatRaster,SpatRaster,list
samc(data, absorption, fidelity, model)
# S4 method for RasterLayer,RasterLayer,RasterLayer,list
samc(data, absorption, fidelity, model)
# S4 method for SpatRaster,SpatRaster,missing,list
samc(data, absorption, model)
# S4 method for RasterLayer,RasterLayer,missing,list
samc(data, absorption, model)
# S4 method for matrix,matrix,matrix,list
samc(data, absorption, fidelity, model)
# S4 method for matrix,matrix,missing,list
samc(data, absorption, model)
# S4 method for dgCMatrix,missing,missing,missing
samc(data)
# S4 method for matrix,missing,missing,missing
samc(data)
```

- data
A

`SpatRaster-class`

or`RasterLayer-class`

or`matrix`

or Matrix package dgCMatrix sparse matrix.- absorption
A

`SpatRaster-class`

or`RasterLayer-class`

or`matrix`

- fidelity
A

`SpatRaster-class`

or`RasterLayer-class`

or`matrix`

- model
A list with args for constructing a transition matrix.

A `samc-class`

object

This function is used to create a `samc-class`

object. There are
multiple options for creating this object.

**Option 1: Raster or Matrix Maps**

`samc(data = matrix, absorption = matrix, fidelity = matrix, model = list())`

`samc(data = SpatRaster, absorption = SpatRaster, fidelity = SpatRaster, model = list())`

`samc(data = RasterLayer, absorption = RasterLayer, fidelity = RasterLayer, model = list())`

The `samc-class`

object can be created from a combination of
resistance (or conductance), absorption, and fidelity data. These different landscape data
inputs must be the same type (a matrix, SpatRaster, or RasterLayer), and have identical
properties, including dimensions, location of NA cells, and CRS (if using
raster inputs).

The `data`

and `absorption`

inputs are always mandatory for this approach. The
`fidelity`

input is optional. If the `fidelity`

input is not provided, then it
is assumed that there is no site fidelity (i.e., individuals will always move
to an adjacent cell each time step).

The `model`

parameter is mandatory. It is used when calculating the values for
the transition matrix. `model`

must be constructed as a list with a
transition function, the number of directions (4 or 8), and if the transition
function is symmetric (TRUE or FALSE; currently not used). Here is the template:
`list(fun = `function`, dir = `numeric`, sym = `logical`)`

When using raster inputs, SpatRaster objects (from the terra package) are recommended over RasterLayer objects (from the raster package). Internally, samc is using SpatRaster objects, which means RasterLayer objects are being converted to SpatRaster objects, which is a source of memory inefficiency.

**Option 2: P Matrix**

`samc(data = matrix)`

`samc(data = dgCMatrix)`

The `data`

parameter can be used alone to create a `samc-class`

object
directly from a preconstructed P matrix. This matrix must be either a base R
matrix, or a sparse matrix (dgCMatrix format) from the Matrix package. It
must meet the following requirements:

The number of rows must equal the number of columns (a square matrix)

Total absorption must be a single column on the right-hand side of the matrix

At the bottom of the matrix, there must be a row filled with 0's except for the last element (bottom-right of the matrix diagonal), which must be set to 1

Every disconnected region of the matrix must have at least one non-zero absorbing value

Each row must sum to 1

All values must be in the range of 0-1

Additionally, the columns and rows of the P matrix may be named (e.g., using
dimnames(), rowname(), colnames(), etc). When specifying `origin`

or `dest`

inputs
to metrics, these names may be used instead of cell numbers. This has the
advantage of making the code for an analysis easier to read and interpret,
which may also help to eliminate unintentional mistakes. There are two
requirements for naming the rows/cols of a P matrix. First, since the P matrix
represents a pairwise matrix, the row and column names must be the same. Second,
there must be no duplicate names. The exception to these rules is the very last
column and the very last row of the P matrix. Since these are not part of the
pairwise transition matrix, they may have whatever names the user prefers.

**Additional Information**

Depending on the data used to construct the samc-class object, some metrics
may cause crashes. This is a result of the underlying P matrix having specific
properties that make some equations unsolvable. One known case is a P matrix
that represents a disconnected graph, which can lead to the `cond_passage()`

function crashing. In terms of raster/matrix inputs, a disconnected graph
occurs when one or more pixels/cells are unreachable from other pixels/cells
due to the presence of a full barrier made up of NA values. In a raster, these
may be obvious as islands but can be as inconspicuous as a rogue isolated
pixel. There may be other currently unknown situations that lead to unsolvable
metrics.

Future work is planned towards identifying these issues during the creation of the samc-class object and handling them appropriately to prevent inadvertent crashes.

**Version 3 Changes**

Support for creating samc-class objects from TransitionLayer objects was removed so that the package is not dependent on gdistance.

**Version 2 Changes**

Version 1.5.0 officially removed support for the deprecated `resistance`

, `tr_fun`

,
`directions`

, `p_mat`

, `latlon`

, and `override`

arguments. Old
code will have to be updated to the new samc() function structure in order to work.

```
# "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)
```