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Integrate, minimise, and evaluate a function

Source: R/smoothing.R
tda_integrate.Rd

These take a function written in TDA's expression language, with x as the formal argument, and evaluate it inside TDA. They are not given an R function, because the expression is evaluated by TDA's interpreter.

Usage

tda_integrate(expr, from, to, options = list(), dir = tempfile("tda"))

tda_range(
  expr,
  start = NULL,
  use_derivatives = FALSE,
  max_boxes = NULL,
  max_iter = NULL,
  tol_width = NULL,
  tol_fd = NULL,
  tol_fe = NULL,
  options = list(),
  dir = tempfile("tda")
)

tda_evalf(expr, options = list(), derivatives = 0, dir = tempfile("tda"))

tda_minimize(expr, options = list(), dir = tempfile("tda"))

tda_gmin(
  expr,
  start = NULL,
  use_derivatives = FALSE,
  max_boxes = NULL,
  max_iter = NULL,
  tol_width = NULL,
  tol_fd = NULL,
  tol_fe = NULL,
  options = list(),
  dir = tempfile("tda")
)

Arguments

expr

a single string, e.g. "x*x" or "exp(-x)*sin(x)".

from, to

the limits of integration.

options

a named list of further TDA options, passed through.

dir

working directory.

start

for tda_range and tda_gmin, a starting value for each parameter, as a list: list(2) for one parameter starting at 2 with TDA's default search box (value-1 to value+1); list(c(2, 0, 10)) for the same starting value with an explicit box, [0, 10]. TDA's xp=. (Beware writing the raw comma syntax by hand: TDA reads each further number as another parameter's starting value, not a box width for the one before it; the list form here avoids that.)

use_derivatives

for tda_range and tda_gmin, use the function's derivatives during the search (ns=1); TDA's default does not.

max_boxes, max_iter, tol_width, tol_fd, tol_fe

for tda_range and tda_gmin, the box search's limits and tolerances (nbox=/mxit=/tolbw=/tolfd=/tolfe=). Not the same search as tda_minimize's tda_control-style minimiser, so tda_control does not apply to either of these.

derivatives

for tda_evalf, 0 for the value alone (evalf), 1 for the gradient as well (evalf1), 2 for the Hessian too (evalf2); TDA computes them analytically.

Value

An object with the numeric result in value (tda_integrate, tda_minimize, tda_gmin), the two bounds in range (tda_range), or nothing structured (tda_evalf, see above); tda_minimize/tda_gmin also carry estimates, the parameter values at the minimum, and the run is always in run.

Details

tda_evalf does not report a value at all: xf is a plotting command, drawing the function over the range options$x names (default 1 to 10) to a file called xplot.ps in the run's directory – read it with tda_read_ps(x$run, which = "xplot.ps"), the same way as any other TDA plot.

See also

Other smoothing: tda_interp(), tda_isotonic(), tda_mat(), tda_sma(), tda_smd(), tda_spl()

Examples

tda_integrate("x*x", 0, 1)$value      # 1/3
#> [1] 0.3333333
tda_range("sin(x)")$range             # [-1, 1] over its default domain
#>      lower      upper 
#> -0.8414545  0.8414545 
tda_minimize("(x - 2)^2", options = list(xp = "0"))$estimates
#>   Idx Parameter Value Error Value_E Signif
#> 1   1         x     2    NA      NA     NA

# gmin: a box-search-based *global* minimum, not tda_minimize's
# local search -- its start=/tolerances, not tda_control(). Its
# interval arithmetic does not accept ^, unlike tda_minimize's
# expression -- (x-2)*(x-2), not (x-2)^2
tda_gmin("(x-2)*(x-2)", start = list(c(2, 0, 4)))$value
#> [1] 0

# evalf: the function value at a point, 1.1342
tda_evalf("sin(x) + x^2", options = list(x = 0.7))$value
#> [1] 1.134218