Apologies & the last word. My original cross product was this:
pm1=: 1&|."1 NB. 1st cyclic permutation
pm2=: 2&|."1 NB. 2nd cyclic permutation
pm12=: 4 : '(pm1 x)*pm2 y'
cross=: pm12 - pm12~ NB. cross products of vectors
(The version I gave before
crossX=: ((1: |.[)*(_1: |. ]))-((_1: |.[)*(1:|.]))
I messed up in making a tacit form.)
With the proper form given above
u=. 1e6 3$rand 3e6
v=. 1e6 3$rand 3e6
ts'z=. u cross v'
0.032281 1.00665e8
The timing on cp=: (1 _1 1 * 1 (-/ . *)\. ])@,.
ts'z=. u cp"(1 1) v'
2.12978 3.3558e7
which is 66 times slower. Both give same results.
Patrick
On Sat, 8 Feb 2020, J. Patrick Harrington wrote:
And a little more noise:
u=. 1e6 3$rand 3e6
v=. 1e6 3$rand 3e6
ts'z1=. u cross"(1 1) v'
0.88737 3.35571e7
ts'z2=. u cp"(1 1) v'
2.12978 3.3558e7
ind=. 3e5+ i. 4
ind{z1
_0.0415101 0.458711 _0.371054
_0.0240905 _0.0474326 0.0622632
0.108878 _0.558303 0.207895
_0.294769 0.605469 _0.617259
ind{z2
_0.0415101 0.458711 _0.371054
_0.0240905 _0.0474326 0.0622632
0.108878 _0.558303 0.207895
_0.294769 0.605469 _0.617259
So u cross"(1 1) v is faster.
But u cross v is broken.
Will look into that :-(
On Sat, 8 Feb 2020, J. Patrick Harrington wrote:
Oh-oh. I've screwed something up.
We can get correct results for arrays thus
u cp"(1 1) v
which agrees with
u cross"(1 1) v
but seems *not* to agree with my
u cross v
I'll need to look into this! And into timings.
Sorry for the noise...
Patrick
On Sat, 8 Feb 2020, J. Patrick Harrington wrote:
The formula referenced there
cp=:(1 _1 1 * 1 (-/ . *)\. ])@,.
compared to mine
cross=: ((1: |.[)*(_1: |. ]))-((_1: |.[)*(1:|.]))
agree for single vectors of course
] u=. rand 3
0.622471 0.324707 0.907825
] v=. rand 3
0.0631566 0.38662 0.338598
u cp v
_0.241038 _0.153432 0.220153
u cross v
_0.241038 _0.153432 0.220153
but for arays of vectors
] u=. 4 3$rand 12
0.095767 0.601479 0.285658
0.926716 0.299674 0.417604
0.687686 0.837773 0.792088
0.465073 0.605581 0.190086
] v=. 4 3$rand 12
0.732158 0.199016 0.654682
0.925557 0.409382 0.619391
0.891663 0.888594 0.716629
0.9962 0.477721 0.946355
u cross v
0.492744 _0.104753 0.277464
0.418103 _0.36774 0.313855
_0.492744 0.104753 _0.277464
_0.418103 0.36774 _0.313855
u cp v
| length error: cp
| u cp v
How do you generalize this for such arrays (or |:u arrays)?
I often take cross products of millions of vectors as part
of Monte Carlo scattering computations, so it must be fast.
Patrick
On Sat, 8 Feb 2020, R.E. Boss wrote:
https://code.jsoftware.com/wiki/Phrases/Matrices#Vector_cross_product
R.E. Boss
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