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Re: why cell arrays are used in 'interp2'
From: |
Ben Abbott |
Subject: |
Re: why cell arrays are used in 'interp2' |
Date: |
Tue, 25 Dec 2012 12:59:13 -0500 |
On Dec 25, 2012, at 10:52 AM, Sergei Steshenko wrote:
> ----- Original Message -----
>> From: Ben Abbott <address@hidden>
>> To: Sergei Steshenko <address@hidden>
>> Cc: Octave users list <address@hidden>
>> Sent: Tuesday, December 25, 2012 5:27 PM
>> Subject: Re: why cell arrays are used in 'interp2'
>>
>> On Dec 24, 2012, at 10:25 PM, Sergei Steshenko wrote:
>>
>>> Hello,
>>>
>>> looking into 'octave-3.6.2/share/octave/3.6.2/m/general/interp2.m'
>> file I see:
>>>
>>> "
>>> 265 ## construct the cubic hermite base functions in x, y
>>> 266
>>> 267 ## formulas:
>>> 268 ## b{1,1} = ( 2*t.^3 - 3*t.^2 + 1);
>>> 269 ## b{2,1} = h.*( t.^3 - 2*t.^2 + t );
>>> 270 ## b{1,2} = (-2*t.^3 + 3*t.^2 );
>>> 271 ## b{2,2} = h.*( t.^3 - t.^2 );
>>> 272
>>> 273 ## optimized equivalents of the above:
>>> 274 t1 = tx.^2;
>>> 275 t2 = tx.*t1 - t1;
>>> 276 xb{2,2} = hx.*t2;
>>> 277 t1 = t2 - t1;
>>> 278 xb{2,1} = hx.*(t1 + tx);
>>> 279 t2 += t1;
>>> 280 xb{1,2} = -t2;
>>> 281 xb{1,1} = t2 + 1;
>>> 282
>>> 283 t1 = ty.^2;
>>> 284 t2 = ty.*t1 - t1;
>>> 285 yb{2,2} = hy.*t2;
>>> 286 t1 = t2 - t1;
>>> 287 yb{2,1} = hy.*(t1 + ty);
>>> 288 t2 += t1;
>>> 289 yb{1,2} = -t2;
>>> 290 yb{1,1} = t2 + 1;
>>> 291
>>> 292 ZI = zeros (size (XI));
>>> 293 for i = 1:2
>>> 294 for j = 1:2
>>> 295 zidx = sub2ind (size (Z), yidx+(j-1), xidx+(i-1));
>>> 296 ZI += xb{1,i} .* yb{1,j} .* Z(zidx);
>>> 297 ZI += xb{2,i} .* yb{1,j} .* DX(zidx);
>>> 298 ZI += xb{1,i} .* yb{2,j} .* DY(zidx);
>>> 299 ZI += xb{2,i} .* yb{2,j} .* DXY(zidx);
>>> 300 endfor
>>> 301 endfor
>>>
>>> ".
>>>
>>> It looks to me only numeric data is used as array elements, so why cell
>> arrays and not regular 2d matrices ?
>>>
>>> Speed ? Space ? Something else I couldn't think of ?
>>>
>>>
>>> Thanks,
>>> Sergei.
>>
>> The cell-arrays contian 2D matrices whose sizes are [numel(yi), numel(xi)].
>>
>> Ben
>
> 4d matirces are also supported by Octave directly through m(t, u, v, x)
> notation, so are cell arrays to improve memory utilization ? Or speed ?
>
> Thanks,
> Sergei.
I don't know if there is speed advantage, but if the 4D array needs to be
"squeezed" before the element-wise multiplication (.*), then the cell approach
may be faster.
If you (someone else?) would like to check, the xb and yb arrays can be changed
to 4D arrays whose size is [numel(yi), numel(xi), 2, 2].
Then the cell array indices "{m,n}" would be replaced by "(:,:,,m,n)". This
will eliminate the need of the user to squeeze() the data before multiplying,
but I don't know what is actually done in the c++ code.
If you do ckeck and find it is faster, I'd be happy to push a changeset for you.
Ben
- why cell arrays are used in 'interp2', Sergei Steshenko, 2012/12/24
- Re: why cell arrays are used in 'interp2', Ben Abbott, 2012/12/25
- Re: why cell arrays are used in 'interp2', Sergei Steshenko, 2012/12/25
- Re: why cell arrays are used in 'interp2',
Ben Abbott <=
- Re: why cell arrays are used in 'interp2', Sergei Steshenko, 2012/12/25
- Re: why cell arrays are used in 'interp2', Michael Goffioul, 2012/12/25
- Message not available
- Re: why cell arrays are used in 'interp2', Michael Goffioul, 2012/12/25
- Message not available
- Re: why cell arrays are used in 'interp2', Michael Goffioul, 2012/12/25
- Re: why cell arrays are used in 'interp2', c., 2012/12/25