uncert(obj, ...)
## S3 method for class 'default':
uncert(obj, c, method = c("GUM", "MC"), cor,
cov, distrib=NULL, distrib.pars=NULL, B=200, x=NULL,
keep.x = TRUE, u=obj, ...)
## S3 method for class 'expression':
uncert(obj, x, u, method=c("GUM", "NUM", "kragten", "k2", "MC"),
cor, cov, distrib=NULL, distrib.pars=NULL,
B=200, delta=0.01, keep.x = TRUE, ...)
## S3 method for class 'function':
uncert(obj, x, u, method=c("NUM", "kragten", "k2", "MC"),
cor, cov, distrib=NULL, distrib.pars=NULL,
B=200, delta=0.01, keep.x = TRUE, ...)
## S3 method for class 'formula':
uncert(obj, x, u, method=c("GUM", "NUM", "kragten", "k2", "MC"),
cor, cov, distrib=NULL, distrib.pars=NULL,
B=200, delta=0.01, keep.x = TRUE, ...)u is set to the value of obj, alloweval. For the function method, a list of
parameters supplied to FUN via do.call.cor is set to the identity matrix.method="MC", a character vector of length
length(x) or a named list of names of distribution functions associated
with u. See Details for defaults. The list format may include
user-specified functimethod="MC", a list of
lists of parameters describing the distributions associated with u
to be passed to the relevant distribution function. If distrib is present
but distrib.pars is nomethod="MC", if keepx=TRUE, the simulated replicates of
x are included in the return object.method="MC" of class uncert-class and uncertMC-class for details.(t(c) %*% cov) %*% c; standard uncertainties are first combined with
the correlation matrix provided to form the covariance matrix. Since the correlation
matrix defaults to the identity matrix, the default is combination without
correlation.
The default method takes obj as a vector of uncertainty contributions unless u
is specified, in which case u is used. It is not necessary to specify both.
The expression method requires obj to be a differentiable R expression which can
be evaluated in the environment x to provide a numeric value.
For the function method, obj must be an R function which takes parameters from x and
returns a numeric value.
For the formula method, obj must be a formula with no left-hand side (e.g. ~a*x+b*x^2)
which can be evaluated in the environment x to provide a numeric value.
The formula and expression methods first calculate derivatives for the expression or formula,
evaluate them using the supplied values of x and then pass the resulting sensitivity
coefficients, with supplied u, cor or cov to uncert.default.
The derivatives for the deriv
applied to expr and formula.
Numerical derivatives are computed in different ways depending on the method specified:
- For method="NUM", the derivatives are calculated as
$(f(x+delta*u)-f(x-delta*u))/(2*delta*u)$.
- For method="kragten", derivatives are calculated as
$(f(x+u*sign(delta))-f(x))/u$.
- For method="k2", derivatives are calculated as
$(f(x+u)-f(x-u))/(2*u)$.
"NUM" is likely to give a close approximation to analytical differentiation provided that
delta is appreciably less than 1 but not so small as to give step sizes near machine
precision. "k2" is equivalent to "NUM" with delta=1.0. Both will give zero coefficients
at stationary points (e.g minima), leading to under-estimation of uncertainty if
the curvature is large. "kragten" uses a deliberately one-sided (and large) step to
avoid this problem; as a result, "kragten" is a poorer (sometimes much poorer) estimate of
the analytical differential but likely a better approximation to the truth.
Since these methods rely on u, if u is unspecified and cov is
provided, u is extracted from cov (using sqrt(diag(cov))). It is
assumed that the row and column order in cov is identical to the order of named
parameters in x.
Derivatives (and uncertainty contributions) are computed for all parameters in
x. Additional parameters used in FUN, expr or formula
may be included in ...; these will be treated as constants in the
uncertainty calculation.
If distrib is missing, or if it is a list with some members missing, the distribution
is assumed Normal and distrib$name is set to "norm". Similarly, if distrib.pars
or a member of it is missing, the default parameters for x$name are
list(mean=x$name, sd=u$name). If the list is not named, names(x) are used
(so the list must be in order of names(x)).
If method="MC", uncert calls uncertMC. Distributions and
distribution parameters are required and B must be present and >1. See uncertMC
for details of distribution specification.
For other evaluation methods, the distributions are silently ignored.uncert-class, deriv
For method="MC" see uncertMC and uncertMC-class.expr <- expression(a+b*2+c*3+d/2)
x <- list(a=1, b=3, c=2, d=11)
u <- lapply(x, function(x) x/10)
u.expr<-uncert(expr, x, u, method="NUM")
u.expr
#Compare with default:
uncert(u=c(0.1, 0.3, 0.2, 1.1), c=c(1.0, 2.0, 3.0, 0.5))
#... or with function method
f <- function(a,b,c,d) a+b*2+c*3+d/2
u.fun<-uncert(f, x, u, method="NUM")
u.fun
#.. or with the formula method
u.form<-uncert(~a+b*2+c*3+d/2, x, u, method="NUM")
u.form
#An example with correlation
u.cor<-diag(1,4)
u.cor[3,4]<-u.cor[4,3]<-0.5
u.formc<-uncert(~a+b*2+c*3+d/2, x, u, method="NUM", cor=u.cor)
u.formc
#A Monte Carlo example
#See uncertMC for a less linear example
u.formc.MC<-uncert(~a+b*2+c*3+d/2, x, u, method="MC", cor=u.cor, B=200)
u.formc.MCRun the code above in your browser using DataLab