QMath: Transformation of coordinate systems
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value Note See Also Examples

The functions provide mathematical c functions as RMmodels

RFcalc(model, params, ...)
R.minus(x, y, factor)
R.plus(x, y, factor)
R.div(x, y, factor)
R.mult(x, y, factor)
R.const(x)
R.c(a, b, c, d, e, f, g, h, i, j, l, m, n, o, p, q, ncol, factor)
R.p(proj, new, factor)
R.is(x, is, y)
R.lon()
R.lat()

R.gamma(x)
R.acos(x)
R.asin(x)
R.atan(x)
R.atan2(y, x)
R.cos(x)
R.sin(x)
R.tan(x)
R.acosh(x)
R.asinh(x)
R.atanh(x)
R.cosh(x)
R.sinh(x)
R.tanh(x)
R.exp(x)
R.log(x)
R.expm1(x)
R.log1p(x)
R.exp2(x)
R.log2(x)
R.pow(x, y)
R.sqrt(x)
R.hypot(x, y)
R.cbrt(x)
R.ceil(x)
R.fabs(x)
R.floor(x)
R.fmod(x, y)
R.round(x)
R.trunc(x)
R.erf(x)
R.erfc(x)
R.lgamma(x)
R.remainder(x, y)
R.fdim(x, y)
R.fmax(x, y)
R.fmin(x, y)

## S4 method for signature 'ANY,RMmodel'
e1 %% e2
## S4 method for signature 'RMmodel,ANY'
e1 %% e2
## S4 method for signature 'RMmodel,character'
e1 * e2
## S4 method for signature 'character,RMmodel'
e1 * e2
## S4 method for signature 'RMmodel,character'
e1 + e2
## S4 method for signature 'RMmodel,factor'
e1 + e2
## S4 method for signature 'RMmodel,list'
e1 + e2
## S4 method for signature 'character,RMmodel'
e1 + e2
## S4 method for signature 'data.frame,RMmodel'
e1 + e2
## S4 method for signature 'factor,RMmodel'
e1 + e2
## S4 method for signature 'RMmodel,character'
e1 - e2
## S4 method for signature 'character,RMmodel'
e1 - e2
## S4 method for signature 'RMmodel,character'
e1 / e2
## S4 method for signature 'character,RMmodel'
e1 / e2
## S4 method for signature 'ANY,RMmodel'
e1 ^ e2
## S4 method for signature 'RMmodel,ANY'
e1 ^ e2
## S4 method for signature 'RMmodel,character'
e1 ^ e2
## S4 method for signature 'character,RMmodel'
e1 ^ e2
## S4 method for signature 'RMmodel'
abs(x)
## S4 method for signature 'RMmodel'
acosh(x)
## S4 method for signature 'RMmodel'
asin(x)
## S4 method for signature 'RMmodel'
asinh(x)
## S4 method for signature 'ANY,RMmodel'
atan2(y,x)
## S4 method for signature 'RMmodel,ANY'
atan2(y,x)
## S4 method for signature 'RMmodel'
atan(x)
## S4 method for signature 'RMmodel'
atanh(x)
## S4 method for signature 'RMmodel'
ceiling(x)
## S4 method for signature 'RMmodel'
cos(x)
## S4 method for signature 'RMmodel'
cosh(x)
## S4 method for signature 'RMmodel'
exp(x)
## S4 method for signature 'RMmodel'
expm1(x)
## S4 method for signature 'RMmodel'
floor(x)
## S4 method for signature 'RMmodel'
lgamma(x)
## S4 method for signature 'RMmodel'
log1p(x)
## S4 method for signature 'RMmodel'
log2(x)
## S4 method for signature 'RMmodel'
log(x)
## S4 method for signature 'RMmodel,missing'
round(x,digits)
## S4 method for signature 'RMmodel'
sin(x)
## S4 method for signature 'RMmodel'
sinh(x)
## S4 method for signature 'RMmodel'
sqrt(x)
## S4 method for signature 'RMmodel'
tan(x)
## S4 method for signature 'RMmodel'
tanh(x)
## S4 method for signature 'RMmodel'
trunc(x)

`model,params`	\argModel `model` is usually a `R.model` given here.
`e1,e2,x,y,a, b, c, d, e, f, g, h, i, j, l, m, n, o, p, q`	constant or object of class `RMmodel`, in particular `R.model`
`ncol`	in contrast to c, `R.c` also allows for defining matrices; `ncol` gives the number of columns
`factor`	constant factor multiplied with the function. This is useful when linear models are built
`is`	one of `"=="`, `"!="`, `"<="`, `"<"`, `">="`, `">"`
`proj`	selection of a component of the vector giving the location. Default value is 1.
`new`	coordinate system or other `kind of isotropy` which is supposed to be present at this model. It shold always be given if the coordinates are not cartesian.
`digits`	number of digits. Does not work with a RMmodel
`...`	\argDots

R.plus: adds two values
R.minus: substracts two values
R.mult: multiplies two values
R.div: devides two values
R.const: defines a constant
R.c: builds a vector
R.is: evaluates equalities and inequalities; note that TRUE is returned if the equality or inequality holds up to a tolerance given by RFoptions()$nugget$tol
R.p: takes a component out of the vector giving the location
R.lon, R.lat: longitudinal and latitudinal coordinate, given in the spherical system, i.e. in radians. (earth system is in degrees).
R.round: Note that R.round rounds away from zero.

For the remaining models see the corresponding C functions for their return value. (For any ‘R.model’ type ‘man model’ under Linux.)

Formally, the functions return an object of class RMmodel, except for RFcalc that returns a scalar. Neither vectors nor parentheses are allowed.

Instead of R.model the standard function can be used in case there is no ambiguity, i.e., c(...),asin(x), atan(x), atan2(y, x), cos(x), sin(x), tan(x), acosh(x), asinh(x), atanh(x), cosh(x), sinh(x), tanh(x), exp(x), log(x), expm1(x), log2(x), log1p(x), exp2(x), ^, sqrt(x), hypot(a,b), cbrt(x), ceiling(x), abs(x), floor(x), round(x), trunc(x), erf(x), erfc(x), lgamma(x). See the examples below.

The function RFcalc is intended for simple calculations only and it is not excessively tested. Especially, binary operators should be used with caution.

Note that all the functions here are NOT recognized as being positive definite (or negative definite), e.g. cos in R^1:

please use the functions given in RMmodels for definite functions (for cos see RMbessel)
Using uncapsulated substraction to build up a covariance function is ambiguous, see the example in RMtrend

RMmodel, RFfctn, RMtrend

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again


## simple calculation
RFcalc(3 + R.sin(pi/4))

## calculation performed on a field
RFfctn(R.p(1) + R.p(2), 1:3, 1:3) 
RFfctn(10 + R.p(2), 1:3, 1:3) 

## calculate the distances between two vectors
print(RFfctn(R.p(new="iso"), 1:10, 1:10))

## simulation of a non-stationary field where
## anisotropy by a transform the coordinates (x_1^2, x_2^1.5)
x <- seq(0.1, 6, 0.12)
Aniso <- R.c(R.p(1)^2, R.p(2)^1.5)
z <- RFsimulate(RMexp(Aniso=Aniso), x, x)


## calculating norms can be abbreviated:
x <- seq(-5, 5, 5) #0.1)
z2 <- RFsimulate(RMexp() + -40 + exp(0.5 * R.p(new="isotropic")), x, x)
z1 <- RFsimulate(RMexp() + -40 + exp(0.5 * sqrt(R.p(1)^2 + R.p(2)^2)), x, x)
stopifnot(all.equal(z1, z2))
plot(z1)