linear algebra - Strange performance of Outer

The following takes 0.07 seconds on my laptop.

list1 = RandomReal[1.,1000000];
(Outer[Times, list1, RandomReal[1., 2]];) // AbsoluteTiming

But this takes 1.2 seconds:

list1 = RandomReal[1.,1000000];
(Outer[Times, list1, {1.,2.}];) // AbsoluteTiming

What is wrong here?

Both version 10.3 and 7 have this timing result.

Answer

It seems like RandomReal[1., 2] is automatically a packed array, whereas {1., 2.} is not. Notice;

(Outer[Times, list1, Developer`ToPackedArray@{1., 2.}];) // AbsoluteTiming // First
(* 0.032425 *)

whereas

(Outer[Times, list1, {1., 2.}];) // AbsoluteTiming // First
(* 0.542086 *)

Also:

list1 = Developer`FromPackedArray@RandomReal[1., 1000000];
(Outer[Times, list1, RandomReal[1., 2]];) // AbsoluteTiming
(* 0.473775 *)

Packed arrays are good for both memory usage and for built-in Mathematica operations that are optimized for packed arrays (for instance). See What is a packed array?.

Comments

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