Re: why cell arrays are used in 'interp2'

[Sergei Steshenko]

----- 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.

>