Description Usage Arguments Details Value Examples
Arithmetic operations for three-velocities
1 2 3 4 5 6 7 8 9 |
e1,e2,u,v |
Objects of class “ |
r |
Scalar value for circle-dot multiplication |
The function Ops.3vel()
passes unary and binary arithmetic
operators “+
”, “-
” and “*
”
to the appropriate specialist function.
The most interesting operators are “+
” and
“*
”, which are passed to add3()
and dot3()
respectively. These are defined, following Ungar, as:
see PDF
and
see PDF
where u and v are three-vectors
and r a scalar. Function dot3()
has special dispensation
for zero velocity and does not treat NA
entries entirely
consistently.
Arithmetic operations, executed via Ops.4vel()
, are not defined
on four-velocities.
The package is designed so that natural R idiom may be used for three velocity addition, see the examples section.
Returns an object of class 3vel
, except for prod3()
which returns a numeric vector.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | u <- as.3vel(c(-0.7, 0.1,-0.1))
v <- as.3vel(c( 0.1, 0.2, 0.3))
w <- as.3vel(c( 0.5, 0.2,-0.3))
x <- r3vel(10) # random three velocities
y <- r3vel(10) # random three velocities
u+v # add3(u,v)
u-v # add3(u,neg3(v))
-v # neg3(v)
gyr(u,v,w)
## package is vectorized:
u+x
x+y
f <- gyrfun(u,v)
g <- gyrfun(v,u)
f(g(x)) - x # should be zero by eqn10
g(f(x)) - x
(u+v) - f(v+u) # zero by eqn 10
(u+(v+w)) - ((u+v)+f(w)) # zero by eqn 11
((u+v)+w) - (u+(v+g(w))) # zero by eqn 11
## NB, R idiom is unambiguous. But always always ALWAYS use brackets.
## Ice report in lat 42.n to 41.25n Long 49w to long 50.30w saw much
## heavy pack ice and great number large icebergs also field
## ice. Weather good clear
## -u+v == (-u) + v == neg3(u) + v == add3(neg3(u),v)
## u+v+w == (u+v)+w == add3(add3(u,v),w)
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