Resistor mesh: Difference between revisions

</pre>

 

{{works with|Mathematica|8.0}}

Use <b>KirchhoffMatrix</b>, <b>PseudoInverse</b>, and <b>GridGraph</b> to compute the resistance between <em>any</em> two nodes in an <em>m</em> by <em>n</em> grid to the desired precision.

<lang mathematica>resistanceGraph[g_, prec_:$MachinePrecision]:=

With[{M = PseudoInverse[N[ KirchhoffMatrix[g], prec]]},

Outer[Plus, Diagonal[M], Diagonal[M]] - M - Transpose[M]

]

r = resistanceGraph[GridGraph[{10, 10}], 40];

r[[12, 68]]</lang>

{{Out}}

<pre>1.608991241730729655954495520510088761201</pre>

{{trans|Maxima}}

<lang mathematica>gridresistor[p_, q_, ai_, aj_, bi_, bj_] :=

{{Out}}

<pre>1.608991241730729655954495520510088761201</pre>

{{works with|Mathematica|9.0}}

Alternative implementation using <b>GridGraph</b>.

<lang mathematica>graphresistor[g_, a_, b_] :=

LinearSolve[