Given a resistance matrix, return the resistance between two specified nodes.
resistance(A, earth.node, input.node, current.input.vector=NULL, give.pots = FALSE)
Resistance matrix
Number of node that is earthed
Number of node at which current is put in: a nominal 1 Amp
Vector of
currents that are fed into each node. If supplied, overrides the
value of input.node
, and effectively sets give.pots
to TRUE
because if various currents are fed into the network
at various points, the concept of “resistance” becomes
meaningless.
Setting this argument to c(0,...,0,1,0,..0)
(where the
“1” is element jj
) is equivalent to not setting
current.input.vector
and setting input.node
to
jj
.
Boolean, with TRUE
meaning to return the
potential of each node (out.node
being at zero potential);
and default FALSE
meaning to return just the resistance between
in.node
and out.node
.
The function's connection to resistor physics is quite opaque. It is effectively a matrix version of Kirchoff's law, that the (algebraic) sum of currents into a node is zero.
B. Bollob\'as, 1998. Modern Graph Theory. Springer.
F. Y. Wu, 2004. “Theory of resistor networks: the two point resistance”, Journal of Physics A, volume 37, pp6653-6673
G. Venezian 1994. “On the resistance between two points on a grid”, American Journal of Physics, volume 62, number 11, pp1000-1004.
J. Cserti 2000. “Application of the lattice Green's function for calculating the resistance of an infinte network of resistors”, American Journal of Physics, volume 68, number 10, p896-906
D. Atkinson and F. J. van Steenwijk 1999. “Infinite resistive lattices”, American Journal of Physics, volume 67, number 6, pp486-492
# NOT RUN {
resistance(cube(),earth.node=1, input.node=7) #known to be 5/6 ohm
resistance(cube(),1,7, give=TRUE)
# }
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