Create a table of lower and upper bounds
bounds_table.RdDuring an optimization, it is often necessary to provide lower and upper bounds for the parameters that are being varied. Typically they are specified as numeric vectors, which often leads to confusing code, where the writer and reader must remember which value corresponds to each argument; for example, "the third element of the lower bound vector is for alphaLeaf."
The purpose of bounds_table is to make the process of specifying bounds
simpler and easier to follow. It is expected that this function will be called
after objective_function.
Arguments
- independent_args
The same value that was passed to
objective_function.- bounds_list
A list of named elements, where each element is a numeric vector of length 2. The names should correspond to the independent arguments, and the values should indicate lower and upper bounds for the corresponding parameter (in any order). Any "extra" bounds (that is, bounds that do not correspond to any independent argument) will be ignored.
- initial_ind_arg_values
A numeric vector of initial values for each of the independent arguments, supplied in the same order as in
independent_args.
Details
The main purpose of this function is to create vectors of lower and upper
bounds, which are returned as the columns of a data frame. For each
independent argument in independent_args, the bounds are supplied via
the bounds_list input. The syntax is designed so the code calling this
function is easy for a human to parse. (See example below.)
It is also (optionally) possible to provide an initial guess for each
independent argument via the initial_ind_arg_values argument. When
provided, these will be checked to make sure they do not lie outside the
bounds; an error will be thrown if any do lie outside the bounds. A warning
will also be thrown if any initial guesses lie on the bounds, since this can
be problematic for some optimizers, such as nmkb.
Some optimizers, such as DEoptim, do not require an
initial guess; in this case, there is no strong need to pass an initial guess
to bounds_table.
Value
A data frame with three or four columns: arg_name, lower,
upper, and (optionally) initial_value.
The lower and upper columns are the lower and upper bounds,
determined from bounds_list. The arg_name column is the argument
name, and the rows of the table are ordered as in independent_args.
The initial_value column contains initial values, if they were
provided via the initial_ind_arg_values argument.
Examples
# Make a list of independent arguments; the values are not used for anything
independent_args <- list(
alphaLeaf = 0,
alphaRoot = 0,
alphaStem = 0,
betaLeaf = 0,
betaRoot = 0,
betaStem = 0
)
# Specify bounds and initial guess for each. Note that:
#
# - The bounds will be reordered to follow the same order as the
# `independent_args`, but the initial guess is assumed to already follow the
# same order as the `independent_args`.
#
# - The bounds for the two extra parameters are ignored when forming the table.
#
# - The lower and upper bounds can be supplied as (upper, lower)
# or (lower, upper) pairs.
#
b_ll <- -50 # Lower limit for beta parameters
a_ul <- 50 # Upper limit for alpha parameters
bounds <- bounds_table(
independent_args,
list(
betaStem = c(0, b_ll),
betaRoot = c(0, b_ll),
betaLeaf = c(0, b_ll),
alphaStem = c(0, a_ul),
alphaRoot = c(0, a_ul),
alphaLeaf = c(0, a_ul),
extraPar1 = c(0, 5),
extraPar2 = c(0, 6)
),
c(1, 1, 1, -1, -1, -1)
)
print(bounds)
#> arg_name lower upper initial_value
#> 1 alphaLeaf 0 50 1
#> 2 alphaRoot 0 50 1
#> 3 alphaStem 0 50 1
#> 4 betaLeaf -50 0 -1
#> 5 betaRoot -50 0 -1
#> 6 betaStem -50 0 -1
# Now the properly-ordered lower and upper limits can be accessed as follows:
bounds$lower
#> [1] 0 0 0 -50 -50 -50
bounds$lower
#> [1] 0 0 0 -50 -50 -50