Re: "stepwise" integrating a 2D array

• To: mathgroup at smc.vnet.net
• Subject: [mg91262] Re: "stepwise" integrating a 2D array
• From: Claus <claus.haslauer at web.de>
• Date: Tue, 12 Aug 2008 04:46:36 -0400 (EDT)
• References: <g7h9mc\$b73\$1@smc.vnet.net> <g7k0am\$i86\$1@smc.vnet.net>

```Jens-Peer,
beautiful!
Thanks Jens-Peer!

> Hi,
>
> try
>
> hvAccumulate[m_] :=
>   Reverse[Rest[FoldList[#1 + #2 & , 0, #]] & /@
>     Transpose[
>      Rest[FoldList[#1 + #2 & , 0, #]] & /@ Transpose[Reverse[m]]]]
>
> and
>
> hvAccumulate[{{a1, a2}, {b1, b2}}]
>
> gives
>
> {{a1 + b1, a1 + a2 + b1 + b2},
>   {b1, b1 + b2}}
>
> Regards
>    Jens
>
> Claus wrote:
>> Hi,
>> I have an array, consisting of n tuples (x,y,z).
>> The first entry is the point at the bottom left (thinking in a
>> coordinate system, smallest (x,y) pair).
>> Now I want to do something like an "stepwise"/empirical integral over (x,y).
>>
>> Schematically, if I had a 2x2 array (only the z-values),like
>>
>> a1  a2
>> b1  b2
>>
>> I would want an array like this:
>>
>> a1+b1    b1+b2+a1+a2
>> b1       b1+b2
>>
>> In the code below, "xyzVals" is the array that I want to integrate,
>> containing the (x,y,z) tuples.
>>
>> I could do a bunch of for loops, but I am trying to not use do loops in
>> mathematica whenever possible.
>> Is it possible to do it without?
>> I tried some of the examples from
>> and I also thought about an array with sub-arrays,
>> but couldn't get it for me to work.
>>
>> Thanks for any pointers!
>> Claus
>>
>>
>> In[13]:= X = RandomReal[{0, 1}, 500];
>> Y = RandomReal[{0, 1}, 500];
>> BinWidth = 0.2;
>> DensVals =
>>   Flatten[BinCounts[
>>     Transpose[{X, Y}], {0, 1, BinWidth}, {0, 1, BinWidth}]]
>>
>> Out[16]= {16, 16, 17, 26, 23, 23, 16, 18, 25, 17, 13, 26, 26, 21, 19, \
>> 15, 32, 20, 21, 15, 11, 26, 16, 19, 23}
>>
>> In[17]:= xyzVals = Table[{i/(1/BinWidth) + (BinWidth/2),
>>     j/(1/BinWidth) + (BinWidth/2),
>>     DensVals[[(1/BinWidth) i + j + 1]]}
>>    , {i, 0, (1/BinWidth) - 1}
>>    , {j, 0, (1/BinWidth) - 1}]
>>
>> Out[17]= {{{0.1, 0.1, 16}, {0.1, 0.3, 16}, {0.1, 0.5, 17}, {0.1, 0.7,
>>     26}, {0.1, 0.9, 23}}, {{0.3, 0.1, 23}, {0.3, 0.3, 16}, {0.3, 0.5,
>>     18}, {0.3, 0.7, 25}, {0.3, 0.9, 17}}, {{0.5, 0.1, 13}, {0.5, 0.3,
>>     26}, {0.5, 0.5, 26}, {0.5, 0.7, 21}, {0.5, 0.9, 19}}, {{0.7, 0.1,
>>     15}, {0.7, 0.3, 32}, {0.7, 0.5, 20}, {0.7, 0.7, 21}, {0.7, 0.9,
>>     15}}, {{0.9, 0.1, 11}, {0.9, 0.3, 26}, {0.9, 0.5, 16}, {0.9, 0.7,
>>     19}, {0.9, 0.9, 23}}}
>>
>

```

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