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f/ on Sparse Arguments Improved

initial writing: 2001-07-29 last updated: 2004-10-26

The monads f/ on sparse arguments have been made more efficient in time and space. The following table compares the time and space required for +/s and +/"1 s for sparse s of various shapes.

   s=: 1 $. shape
   r=: ?. 1e5   $ 1e6
   i=: ?. (1e5,#$s) $ $s
   s=: r (<"1 i)}s

   ts=: 6!:2 , 7!:2@]   NB. time and space
   ts '+/   s'
   ts '+/"1 s'

Shape	Expression	J 5.01				J 4.06				Ratio
10 10 10 10 1e6	+/   s	0.237968		3802752		0.328043		12846848		1.38		3.38
	+/"1 s	0.025751		526144		0.191156		3229632		7.42		6.14
1e6 10 10 10 10	+/   s	0.346326		1050432		0.445293		9520896		1.29		9.06
	+/"1 s	0.051208		3278656		0.206031		6555584		4.02		2.00
2 10 10 10 10 1e6	+/   s	0.225852		3802752		0.430299		21171776		1.91		5.57
	+/"1 s	0.037085		919360		0.221206		3704768		5.96		4.03
1e6 10 10 10 10 2	+/   s	0.362589		1443648		0.475774		14190336		1.31		9.83
	+/"1 s	0.056411		3278656		0.421492		21172160		7.47		6.46
4$1e6	+/   s	0.299557		3802752		0.381521		12846848		1.27		3.38
	+/"1 s	0.044956		3278656		0.180579		6555584		4.02		2.00
8$1e3	+/   s	0.338152		5900096		0.551470		21235712		1.63		3.60
	+/"1 s	0.078596		5376000		0.464777		10750080		5.91		2.00

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