camodel_mat: Definition of a stochastic cellular automaton based on...
In alexgenin/chouca: A Stochastic Cellular Automaton Engine
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camodel_mat R Documentation
Definition of a stochastic cellular automaton based on numerical arrays
Description
Definition of a stochastic cellular automaton using arrays and matrices
of numbers instead of symbolic expressions (as in camodel)
Usage
camodel_mat(
beta_0 = NULL,
beta_p = NULL,
beta_q = NULL,
all_states,
neighbors,
wrap,
fixed_neighborhood = FALSE,
epsilon = sqrt(.Machine[["double.eps"]]),
build_transitions = TRUE
)
Arguments
beta_0
the constant term of the probabilities of transition (see Details
section), given as a square matrix of real numbers
beta_p
the coefficient for p[i] for i between 1 and the number of states
(see Details section), as a cubic array of numbers
beta_q
the coefficient for q[i] for i between 1 and the number of states
(see Details section), as a cubic array of numbers
all_states
The complete set of states of the model (a character vector). If
unspecified, it will be guessed from the transition rules, but it is a good idea
to pass it here to make sure the model definition is correct.
neighbors
The number of neighbors to use in the cellular automaton (4 for 4-way
or von-Neumann neigborhood, or 8 for an 8-way or Moore neighborhood)
wrap
If TRUE, then the 2D grid on which the model is run wraps around
at the edges (the top/leftmost cells will be considered neighbors of the
bottom/rightmost cells)
fixed_neighborhood
When not using wrapping around the edges
(wrap = FALSE), the number of neighbors per cell is variable, which can
slow down the simulation. Set this option to TRUE to consider that the number
of neighbors is always four or eight, regardless of the position of the cell in the
landscape, at the cost of approximate dynamics at the edges of the landscape.
epsilon
A small value under which the internal model coefficients values are
considered to be equal to zero. The default value should work well here, except
if you run models that have extremely small transition probabilities (<1e-8).
build_transitions
Transition definitions
(as if produced by transition) will be included in the resulting
object if TRUE. Set to FALSE to disable this, which may improve
speed at the cost of loss of some of the package functionality
Details
camodel will perform badly when defining models with a large number of
transitions or states. This function provides a much faster alternative, but it
assumes that all transitions from state i to state j follow the
following form:
P(i \rightarrow j) = \beta^0_{i, j} +
\beta^p_{i, j, 1} p_1 + \beta^p_{i, j, 2} p_2 + ... + \beta^p_{i, j, K} p_K +
\beta^q_{i, j, 1} q_1 + \beta^p_{i, j, 2} q_2 + ... + \beta^p_{i, j, K} q_K
where \beta_0, \beta^p and \beta_q are constant model paramaters,
and p, q are the proportion of cells in the landscape and neighborhood
in each state, respectively. K is the number of states in the model.
\beta^0 is a K x K square matrix, and \beta^p and
\beta^q are a K x K x K cubic arrays (with again, K the number of states).
The function will check that this is valid and throw an error if this is not true.
Make sure the values in those arrays are in the right order (it is
array[from, to, coef_for_state_k]). To make sure the model definition is
correct, you can print the model on the R command line to see if transition
definitions were correctly specified.
The resulting object will be similar to what would be produced by
camodel, but model-building will be much quicker for complicated models
(lots of states and transitions). You can further improve
performance by setting build_transitions to FALSE. In this case, the
generation of symbolic model transitions will be skipped entirely. They are not needed
to run the model, but can be handy to make sure you specified your model correctly.
Disable the generation of symbolic model transitions only when you are sure your model
is correctly-defined.
The diagonal entries in the matrix beta_0 are zero by definition, and the
function will warn if that is not the case. Note that this function will not check
whether the model can yield probabilities below zero or above one.
References
Durrett, Richard, and Simon A. Levin. 1994. “Stochastic Spatial Models: A User’s
Guide to Ecological Applications.” Philosophical Transactions of the Royal Society
of London. Series B: Biological Sciences 343 (1305): 329–50.
https://doi.org/10.1098/rstb.1994.0028.
See Also
camodel
Examples
mod_classic <- camodel(
transition(from = "TREE",
to = "EMPTY",
prob = ~ 0.125 + 0.05 * q["EMPTY"] ),
transition(from = "EMPTY",
to = "TREE",
prob = ~ 0.2 * p["TREE"]),
neighbors = 4,
wrap = TRUE,
all_states = c("EMPTY", "TREE"),
check_model = "quick"
)
states <- c("EMPTY", "TREE")
beta_0_mat <- diag(2) * 0
colnames(beta_0_mat) <- rownames(beta_0_mat) <- states
beta_0_mat["TREE", "EMPTY"] <- 0.125
beta_p_array <- array(0, dim = rep(2, 3),
dimnames = list(states, states, states))
beta_p_array["EMPTY", "TREE", "TREE"] <- 0.2
beta_q_array <- array(0, dim = rep(2, 3),
dimnames = list(states, states, states))
beta_q_array["TREE", "EMPTY", "EMPTY"] <- 0.05
mod_mat <- camodel_mat(beta_0 = beta_0_mat,
beta_p = beta_p_array,
beta_q = beta_q_array,
all_states = states,
neighbors = 4,
wrap = TRUE)
# Voter model (defined as in Durrett & Levin, 1994, p342). See also ?ca_library
gamma <- 0.1
kappa <- 30
coefs <- array(0, dim = rep(kappa, 3))
for ( state in seq.int(kappa) ) {
coefs[ , state, state] <- gamma
coefs[state, state, ] <- 0
}
mod <- camodel_mat(
beta_q = coefs,
wrap = TRUE,
all_states = as.character(seq.int(kappa)),
neighbors = 8,
build_transitions = TRUE
)
# This model takes a long time to run for high values of kappa
nrows <- ncols <- 256
initmm <- generate_initmat(mod, rep(1/kappa, kappa),
nrow = nrows, ncol = ncols)
iters <- seq(0, 128)
run_camodel(mod, initmm, iters, control = list(engine = "compiled"))
alexgenin/chouca documentation built on Aug. 28, 2024, 5:22 a.m.
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View source: R/parsing-advanced.R
| camodel_mat | R Documentation |
Definition of a stochastic cellular automaton based on numerical arrays
Description
Definition of a stochastic cellular automaton using arrays and matrices
of numbers instead of symbolic expressions (as in camodel)
Usage
camodel_mat(
beta_0 = NULL,
beta_p = NULL,
beta_q = NULL,
all_states,
neighbors,
wrap,
fixed_neighborhood = FALSE,
epsilon = sqrt(.Machine[["double.eps"]]),
build_transitions = TRUE
)
Arguments
beta_0 |
the constant term of the probabilities of transition (see Details section), given as a square matrix of real numbers |
beta_p |
the coefficient for p[i] for i between 1 and the number of states (see Details section), as a cubic array of numbers |
beta_q |
the coefficient for q[i] for i between 1 and the number of states (see Details section), as a cubic array of numbers |
all_states |
The complete set of states of the model (a character vector). If unspecified, it will be guessed from the transition rules, but it is a good idea to pass it here to make sure the model definition is correct. |
neighbors |
The number of neighbors to use in the cellular automaton (4 for 4-way or von-Neumann neigborhood, or 8 for an 8-way or Moore neighborhood) |
wrap |
If |
fixed_neighborhood |
When not using wrapping around the edges
( |
epsilon |
A small value under which the internal model coefficients values are considered to be equal to zero. The default value should work well here, except if you run models that have extremely small transition probabilities (<1e-8). |
build_transitions |
Transition definitions
(as if produced by |
Details
camodel will perform badly when defining models with a large number of
transitions or states. This function provides a much faster alternative, but it
assumes that all transitions from state i to state j follow the
following form:
P(i \rightarrow j) = \beta^0_{i, j} +
\beta^p_{i, j, 1} p_1 + \beta^p_{i, j, 2} p_2 + ... + \beta^p_{i, j, K} p_K +
\beta^q_{i, j, 1} q_1 + \beta^p_{i, j, 2} q_2 + ... + \beta^p_{i, j, K} q_K
where \beta_0, \beta^p and \beta_q are constant model paramaters,
and p, q are the proportion of cells in the landscape and neighborhood
in each state, respectively. K is the number of states in the model.
\beta^0 is a K x K square matrix, and \beta^p and
\beta^q are a K x K x K cubic arrays (with again, K the number of states).
The function will check that this is valid and throw an error if this is not true.
Make sure the values in those arrays are in the right order (it is
array[from, to, coef_for_state_k]). To make sure the model definition is
correct, you can print the model on the R command line to see if transition
definitions were correctly specified.
The resulting object will be similar to what would be produced by
camodel, but model-building will be much quicker for complicated models
(lots of states and transitions). You can further improve
performance by setting build_transitions to FALSE. In this case, the
generation of symbolic model transitions will be skipped entirely. They are not needed
to run the model, but can be handy to make sure you specified your model correctly.
Disable the generation of symbolic model transitions only when you are sure your model
is correctly-defined.
The diagonal entries in the matrix beta_0 are zero by definition, and the
function will warn if that is not the case. Note that this function will not check
whether the model can yield probabilities below zero or above one.
References
Durrett, Richard, and Simon A. Levin. 1994. “Stochastic Spatial Models: A User’s Guide to Ecological Applications.” Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 343 (1305): 329–50. https://doi.org/10.1098/rstb.1994.0028.
See Also
camodel
Examples
mod_classic <- camodel(
transition(from = "TREE",
to = "EMPTY",
prob = ~ 0.125 + 0.05 * q["EMPTY"] ),
transition(from = "EMPTY",
to = "TREE",
prob = ~ 0.2 * p["TREE"]),
neighbors = 4,
wrap = TRUE,
all_states = c("EMPTY", "TREE"),
check_model = "quick"
)
states <- c("EMPTY", "TREE")
beta_0_mat <- diag(2) * 0
colnames(beta_0_mat) <- rownames(beta_0_mat) <- states
beta_0_mat["TREE", "EMPTY"] <- 0.125
beta_p_array <- array(0, dim = rep(2, 3),
dimnames = list(states, states, states))
beta_p_array["EMPTY", "TREE", "TREE"] <- 0.2
beta_q_array <- array(0, dim = rep(2, 3),
dimnames = list(states, states, states))
beta_q_array["TREE", "EMPTY", "EMPTY"] <- 0.05
mod_mat <- camodel_mat(beta_0 = beta_0_mat,
beta_p = beta_p_array,
beta_q = beta_q_array,
all_states = states,
neighbors = 4,
wrap = TRUE)
# Voter model (defined as in Durrett & Levin, 1994, p342). See also ?ca_library
gamma <- 0.1
kappa <- 30
coefs <- array(0, dim = rep(kappa, 3))
for ( state in seq.int(kappa) ) {
coefs[ , state, state] <- gamma
coefs[state, state, ] <- 0
}
mod <- camodel_mat(
beta_q = coefs,
wrap = TRUE,
all_states = as.character(seq.int(kappa)),
neighbors = 8,
build_transitions = TRUE
)
# This model takes a long time to run for high values of kappa
nrows <- ncols <- 256
initmm <- generate_initmat(mod, rep(1/kappa, kappa),
nrow = nrows, ncol = ncols)
iters <- seq(0, 128)
run_camodel(mod, initmm, iters, control = list(engine = "compiled"))
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