Looking for an elegant way to construct this tensor-product-ish list

I would like to make the following matrix:

{
  {{1, 13}, {1, 14}, {1, 15}, {1, 16}, {2, 13}, {2, 14}, {2, 15},{2, 16}, ..., 
   {32, 13}, {32, 14}, {32, 15}, {32, 16}},
  {{1, 9}, {1, 10}, {1, 11}, {1, 12}, {2, 9}, {2, 10}, {2, 11}, {2, 12}, ..., 
   {32, 9}, {32, 10}, {32, 11}, {32, 12}},
   ...
  {{1, 1}, {1, 2}, {1, 3}, {1, 4}, {2, 1}, {2, 2}, {2, 3},{2, 4}, ..., 
   {32, 1}, {32, 2}, {32, 3}, {32, 4}}
}

I'd like to make this out of these two things:

A = {Range[13, 16], Range[9, 12], Range[5, 8], Range[4]}

and

B = Range[32]

In other words, I'd like to glue copies of A all in a row with each entry indexed by B.

Is there a good way to do this?

Answer

You could do this:

Outer[List, B, #] & /@ A

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[ ...

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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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