Raul, What happens to M when you involve }
I don't understand how and what definition of } is used.
u=:2 3 0
v=:i.3 3
GG=: 13 :'x`({.x)`y'
]M=: u GG v
2 3 0 2
0 1 2 0
3 4 5 0
6 7 8 0
HH=: [`([:{.[)`]}
u HH v
0 1 2
3 4 5
2 3 0
5!:4 <'GG'
-- 4
-- : -+- ,:'x`({.x)`y'
5!:4 <'HH'
-- [
│ -- [:
-- } ---+---+- {.
│ L- [
L- ]
5!:4 <'FF'
-- [
│ -- {.
-- } ---+- @ -+- [
L- ]
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Raul Miller
Sent: Monday, January 13, 2014 12:53 AM
To: Programming forum
Subject: Re: [Jprogramming] Tacit?
FF=: [`({.@[)`]}
Or something using multiple and add with some bit valued intermediate
results.
Thanks,
--
Raul
On Mon, Jan 13, 2014 at 12:39 AM, km <[email protected]> wrote:
> Here is a simpler question. Is there a tacit version of ff below?
>
> u =: 2 3 0
> v =: i. 3 3
> ff =: 4 : 'x ({. x)} y'
> u ff v
> 0 1 2
> 3 4 5
> 2 3 0
>
> --Kip Murray
>
> Sent from my iPad
>
>> On Jan 12, 2014, at 10:41 PM, Raul Miller <[email protected]> wrote:
>>
>> Sometimes it helps to inspect intermediate results. With recursion,
>> though, it can be a bit tricky for a casual observer to see the
>> intermediate results. With that in mind, here's what I am seeing for
>> your example:
>>
>> a1=: (calcU calcL) saveAA
>> a2=: (calcU calcL) a1
>> a3=: (calcU calcL) a2
>>
>> A4=: ((({.@[ ,: ]) ,&.:(|."1) a3"_) calcL) a2
>> A5=: ((({.@[ ,: ]) ,&.:(|."1) A4"_) calcL) a1
>> A6=: ((({.@[ ,: ]) ,&.:(|."1) A5"_) calcL) saveAA
>>
>> a1, a2 and a3 are progressively smaller square matrices (2x2, 1x1,
>> 0x0)
>>
>> A4, A5 and A6 are progressively larger matrices which are twice as
>> tall as wide. If you could compute them in reverse order it might
>> have made sense to make it twice as wide as tall (with intermediate
>> lu side by side instead of interleave stacked)?
>>
>> A6 is the same as lumain saveAA
>>
>> I should go back and re-read km's implementation. But I will note
>> that you can cut code size slightly using some cross hooks:
>>
>> lumain =: (((,:~ {.)~ ,&.:(|."1) $:@calcU) calcL)^:(*@#)
>> lu =: [: (,:~ |:)/ 1 0 2 |: _2 ]\ lumain
>>
>> Anyways, I think your O(n^3) space is largely because all
>> intermediate values from what I have characterized as a (calcU calcL)
>> hook are "pre"-computed and placed on the stack before proceeding
>> with further computations.
>>
>> Thanks,
>>
>> --
>> Raul
>>
>>> On Sun, Jan 12, 2014 at 10:10 PM, Henry Rich <[email protected]>
wrote:
>>> calcL =: (% {.)@:({."1)
>>> calcU =: (}.@[ - {.@[ *"1 0 ])&:(}."1)
>>> lumain =: ((({.@[ ,: ]) ,&.:(|."1) $:@calcU) calcL)^:(*@#)
>>> lu =: [: (|:@] ,: [)/ 1 0 2 |: _2 ]\ lumain NB. Half this code
>>> is handling joining ragged lists.
>>> NB. Is there a better way?
>>>
>>> saveAA =: 3 3 $ 2 1 4 _4 _1 _11 2 4 _2
>>> lu saveAA
>>>
>>> 1 0 0
>>> _2 1 0
>>> 1 3 1
>>>
>>> 2 1 4
>>> 0 1 _3
>>> 0 0 3
>>>
>>> I suspect that a vectorized explicit version is a better way to go.
>>> This version has memory requirements of O(n^3).
>>>
>>> Henry Rich
>>>
>>>
>>>> On 1/12/2014 9:00 PM, km wrote:
>>>>
>>>> Verb LU below produces the matrices L and U of the LU decomposition
>>>> of a square matrix A. L is lower triangular, U is upper
>>>> triangular, and A is L
>>>> +/ . * U .
>>>>
>>>> Should one attempt a tacit version?
>>>>
>>>> eye =: =@i.@] NB. eye 3 is a 3 by 3 identity matrix
>>>>
>>>> rop =: 3 : 0 NB. row op: subtract c times row i0 from row i1
>>>> :
>>>> 'i1 c i0' =. x
>>>> ( (i1 { y) - c * i0 { y ) i1 } y
>>>> )
>>>>
>>>> LU =: 3 : 0 NB. square matrices L and U for y -: L +/ . * U
>>>> m =. # y
>>>> L =. eye(m)
>>>> U =. y
>>>> for_j. i. <: m do.
>>>> p =. (< j , j) { U
>>>> for_i. j + >: i. <: m - j do.
>>>> c =. p %~ (< i , j) { U
>>>> L =. c (< i , j) } L
>>>> U =. (i, c, j) rop U
>>>> end.
>>>> end.
>>>> L ,: U
>>>> )
>>>>
>>>> saveAA
>>>> 2 1 4
>>>> _4 _1 _11
>>>> 2 4 _2
>>>>
>>>> LU saveAA
>>>> 1 0 0
>>>> _2 1 0
>>>> 1 3 1
>>>>
>>>> 2 1 4
>>>> 0 1 _3
>>>> 0 0 3
>>>>
>>>> saveAA -: +/ . */ LU saveAA
>>>> 1
>>>>
>>>> --Kip Murray
>>>>
>>>> Sent from my iPad
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