I don't think I agree with your timings; what happens at rank 0 seems
unimportant.
However, timings at full rank give the same conclusions:
l =. 1e6 3 ?...@$ 0
r =. 1e6 1 ?...@$ 0
r %. l
0.300885
0.300854
0.298569
ts 'r %. l'
0.617212 1.25832e8
mp =: +/ . *
ts '(t mp r) %. (t =. |:l) mp l'
0.127838 3.356e7
(t mp r) %. (t =. |:l) mp l
0.300885
0.300854
0.298569
So Roger: if you're not premultiplying by the transpose, why not? (This
is not my area of expertise so I won't be surprised if there is a good
reason)
Henry Rich
On 10/9/2010 9:02 PM, Marshall Lochbaum wrote:
> Bit of a problem with the matrix division thing...
>
> l=.10*<:+:1e6 ?...@$ 0
> r=.10*<:+:1e6 ?...@$ 0
> 6!:2 'l %."0 r'
> 3.09424
> 6!:2 'l (+/ .*~ %.)"0 r'
> 0.481168
> 6!:2 'l %"0 r'
> 0.1251
>
> It appears that multiplying by the inverse is much faster than doing matrix
> division, which certainly shouldn't be true.
> It probably also explains the speed disparity between %. and +/@:* -...@% ]
> +/@:* ] because the latter uses % in place of %. .
>
> Marshall
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of Henry Rich
> Sent: Saturday, October 09, 2010 5:22 PM
> To: Programming forum
> Subject: Re: [Jprogramming] Puzzle: line-circle/sphere intersection
>
> It seems odd to me that
>
> +/@:* -...@% ] +/@:* ]
>
> would be faster than
>
> %.
>
> for lists. I thought the first step of %. for non-square arrays would
> be multiplying by the transpose of y (just as in the longer version),
> followed by taking the inverse (now of a 1x1 matrix, which should be quick).
>
> Henry Rich
>
> On 10/9/2010 12:40 PM, R.E. Boss wrote:
>> Nice solution.
>> I had forgotten the projecting properties of %.
>>
>> Performance improvement is possible by substituting %. by +/@:* -...@% ]
>> +/@:* ]
>>
>> 'C S E'=:10000 ,@#"(0 1) 0 0 0, 1 2 3 ,: _2 8 1
>> R=:10000
>>
>> rank'C (R>:+/&.:*:)@:([- ]* 0>.1<.%.)&(-&S) E';'C
>> (R>:+/&.:*:)@:([- ]*
>> 0>.1<.(+/@:* -...@% ] +/@:* ]))&(-&S) E'
>> +----+-----+----+----+
>> |rank|tm*sz|time|size|
>> +----+-----+----+----+
>> | 1 |2.63 |1.18|2.23|
>> +----+-----+----+----+
>> | 0 |1.00 |1.00|1.00|
>> +----+-----+----+----+
>>
>> -:/".&>'C (R>:+/&.:*:)@:([- ]* 0>.1<.%.)&(-&S) E';'C
>> (R>:+/&.:*:)@:([- ]*
>> 0>.1<.(+/@:* -...@% ] +/@:* ]))&(-&S) E'
>> 1
>>
>>
>> R.E. Boss
>>
>>
>>> -----Oorspronkelijk bericht-----
>>> Van: [email protected] [mailto:programming-
>>> [email protected]] Namens Marshall Lochbaum
>>> Verzonden: donderdag 7 oktober 2010 22:44
>>> Aan: 'Programming forum'
>>> Onderwerp: Re: [Jprogramming] Puzzle: line-circle/sphere intersection
>>>
>>> Alright. Take the projection of the center onto the line segment
>>> using %. .
>>> This is not allowed to be more than 0 or less than 1, so use
>>> (0>.1<.]) to take the endpoints if it is. Then find this point on the
>>> line again and see if it is inside the circle.
>>> C (R>:+/&.:*:)@:([- ]* 0>.1<.%.)&(-&S) E
>>>
>>> Not tested yet, but I will update on that...
>>> Marshall
>>>
>>> -----Original Message-----
>>> From: [email protected]
>>> [mailto:[email protected]] On Behalf Of Henry Rich
>>> Sent: Thursday, October 07, 2010 7:58 AM
>>> To: Programming forum
>>> Subject: Re: [Jprogramming] Puzzle: line-circle/sphere intersection
>>>
>>> I intend that a segment wholly inside the circle/sphere to be counted
>>> as intersecting. In other words, the circle/sphere is solid and we
>>> want to know if the segment touches any of it.
>>>
>>> Henry Rich
>>>
>>> On 10/7/2010 7:52 AM, R.E. Boss wrote:
>>>> That was bad reading from my side.
>>>> The formulas should be:
>>>>
>>>> ((S-C)<R)*.((E-C)<R) -...@+. ((S-C)>R)*.((E-C)>R)
>>>>
>>>> D=: +&.*:/"1 (S,:E)-"1 C
>>>>
>>>> (D<R) -...@+.&(*./) D>R
>>>>
>>>> Apart from that, the mathematics is not correct either. I will give
>>> it
>>>> another thought.
>>>>
>>>>
>>>> R.E. Boss
>>>>
>>>>
>>>>> -----Oorspronkelijk bericht-----
>>>>> Van: [email protected] [mailto:programming-
>>>>> [email protected]] Namens Bo Jacoby
>>>>> Verzonden: donderdag 7 oktober 2010 13:02
>>>>> Aan: Programming forum
>>>>> Onderwerp: Re: [Jprogramming] Puzzle: line-circle/sphere
>>> intersection
>>>>>
>>>>> Hello Boss.
>>>>>
>>>>> I do not understand your notation. Henry wrote "startpoint S and
>>>>> endpoint E". You wrote "endpoints A and B", but you use E in your
>>> pseudo
>>> code.
>>>>> Please explain.
>>>>>
>>>>> It seems to me that you must compute the distances (s) from C to S,
>>>>> (e) from C to E and (p) from C to the closest point P, (the
>>>>> perihelion), and you must determine (b) if P is between S and E.
>>>>> Intersection occurs if (s<R and e>R) or (s>R and e<R) or (b and p<R
>>> and
>>> (s>R or e>R)).
>>>>>
>>>>> --- Den tors 7/10/10 skrev R.E. Boss<[email protected]>:
>>>>>
>>>>> Fra: R.E. Boss<[email protected]>
>>>>> Emne: Re: [Jprogramming] Puzzle: line-circle/sphere intersection
>>>>> Til: "'Programming forum'"<[email protected]>
>>>>> Dato: torsdag 7. oktober 2010 09.49
>>>>>
>>>>> Since the word 'intersect' is used, I assume you mean the boundary
>>> of
>>>>> the circle/sphere (and not the area), so that a line segment which
>>> is
>>>>> completely inside is not intersecting. One point at the boundary
>>>>> means intersecting, I assume.
>>>>> So the segment is not intersecting if and only if it is completely
>>>>> inside or completely outside the circle/sphere.
>>>>>
>>>>>
>>>>> If the line segment is given by the endpoints A and B, the pseudo
>>>>> code is rather straightforward:
>>>>>
>>>>> ((A-E)<R)*.((B-E)<R) -...@+. ((A-E)>R)*.((B-E)>R)
>>>>>
>>>>> so ones gets
>>>>>
>>>>> D=: +&.*:/"1 (A,:B)-"1 E
>>>>>
>>>>> (D<R) -...@+.&(*./) D>R
>>>>>
>>>>> (untested)
>>>>>
>>>>>
>>>>> R.E. Boss
>>>>>
>>>>>
>>>>>> -----Oorspronkelijk bericht-----
>>>>>> Van: [email protected] [mailto:programming-
>>>>>> [email protected]] Namens Henry Rich
>>>>>> Verzonden: woensdag 6 oktober 2010 22:54
>>>>>> Aan: Programming forum
>>>>>> Onderwerp: [Jprogramming] Puzzle: line-circle/sphere intersection
>>>>>>
>>>>>> Given circle/sphere with center C and radius R, and a line-segment
>>>>>> with startpoint S and endpoint E, write the J code to tell whether
>>>>>> the line-segment intersects the circle/sphere.
>>>>>>
>>>>>> R is an atom, the rest are lists with 2 or 3 atoms.
>>>>>>
>>>>>> This problem arises in collision detection for games and
>>> simulators,
>>>>>> or if you are trying to see whether a path intersects a round
>>> obstacle.
>>>>>>
>>>>>> I found a solution whose brevity surprised me.
>>>>>>
>>>>>> Henry Rich
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