[Date Index]
[Thread Index]
[Author Index]
"stepwise" integrating a 2D array
*To*: mathgroup at smc.vnet.net
*Subject*: [mg91158] "stepwise" integrating a 2D array
*From*: Claus <clausenator at gmail.com>
*Date*: Fri, 8 Aug 2008 07:12:16 -0400 (EDT)
*Organization*: Comp.Center (RUS), U of Stuttgart, FRG
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
http://www.verbeia.com/mathematica/tips/HTMLLinks/Tricks_A-K_3.html
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}}}
Prev by Date:
**Re: Mathematica and Mathieu DEQ Results?**
Next by Date:
**Re: Derivative of Dot[]**
Previous by thread:
**Re: Purchasing Mathematica**
Next by thread:
**Re: "stepwise" integrating a 2D array**
| |