I have a particle which is hopping between positions in 3D space
hops = {{1, 1, 1}, {2, 2, 2}, {1, 1, 1}, {2, 2, 2}} I wish to calculate the the total distance hopped.
Is there a good way to do this?
At the moment I have a for loop storing the total, which adds the differences like this
total = 0; For[i = 1, i <= 3, i++ , temp = EuclideanDistance[hops[[i]], hops[[i + 1]]]; total = total + temp ; ]; But, I wonder if I could do this better.
Total[Sqrt[Total[Differences[N@hops]^2, {2}]]] If performance matter then
Total[Sqrt[Dot[Differences[N@hops]^2,ConstantArray[1., Dimensions[hops][[2]]]]]] is even a bit faster.
Generally, try to avoid For (Do is a bit better than For) for it is rather a top level construct in Mathematica.
An alternate approach using RegionMeasure
hops = {{1, 1, 1}, {2, 2, 2}, {1, 1, 1}, {2, 2, 2}}; Total[RegionMeasure /@ Line /@ Partition[hops, 2, 1]] // RepeatedTiming {0.00052, 3 Sqrt[3]} The timing is much slower than the solution provided by Henrik Schumacher
Total[Sqrt[Total[Differences[N@hops]^2, {2}]]] // RepeatedTiming (* {0.000016, 5.19615} *) EDIT: Another variation
Total[EuclideanDistance @@@ Partition[N@hops, 2, 1]] // RepeatedTiming (* {0.000013, 5.19615} *) Using BlockMap and EuclideanDistance
Total@BlockMap[EuclideanDistance @@ # &, N@hops, 2, 1] // RepeatedTiming {0.000061, 5.19615}
A bit slower than Henrik's solution
Total[Sqrt[Total[Differences[N@hops]^2, {2}]]] // RepeatedTiming {0.0000121, 5.19615}
Using ArcLength:
hops = {{1, 1, 1}, {2, 2, 2}, {1, 1, 1}, {2, 2, 2}}; ArcLength@Line@hops 3 Sqrt[3]
