list manipulation - Part extraction vs functions like First, Last?

There are many ways to extract different parts of lists in Mathematica. For example, the first part of a list v can be accessed either as v[[1]] or First[v] or Take[v,1]. Likewise the last element can be accessed as v[[-1]], Last[v] or Take[v,-1]. Similarly v[[2;;]] is equivalent to Rest[v] and to Drop[v,1], and v[[;;-2]] is equivalent to Most[v] and Drop[v,-1].

The more specialized functions First, Last, Rest and Most are marginally more efficient. On the other hand, it makes sense to use the more general Part ([[ ]]) or Take/Drop if it is part of a calculation that also requires parts to be accessed that do not have a specialist function.

Beyond these considerations, are there any reasons to prefer Part over Take/Drop or the more specialized functions, other than personal preferences over coding style?

Comments

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

functions - What best practices or performance considerations are there for choosing between Cases, Position, Pick and Select?

Cases , Select , Pick and Position each have different syntaxes and purposes, but there are times when you can express the same calculation equivalently using either of them. So with this input: test = RandomInteger[{-25, 25}, {20, 2}] {{-15, 13}, {-8, 16}, {-8, -19}, {7, 6}, {-21, 9}, {-3, -25}, {21, -18}, {4, 4}, {2, -2}, {-24, 8}, {-17, -8}, {4, -18}, {22, -24}, {-4, -3}, {21, 0}, {19, 18}, {-23, -8}, {23, -25}, {14, -2}, {-1, -13}} You can get the following equivalent results: Cases[test, {_, _?Positive}] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} Select[test, #[[2]] > 0 &] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} Pick[test, Sign[test[[All, 2]] ], 1] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} test[[Flatten@Position[test[[All, 2]], _?Positive] ]] {{-15, 13}, {-8, 16}, {7, 6}, {-21, 9}, {4, 4}, {-24, 8}, {19, 18}} Are there performance or other considerations that should guide which you shou...

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