How to shrink Matrix eg. 10830:21600 -> 361:576

Hello Matlab Community, today I'm asking you for support in one specific problem I have here. I did not find any solution yet on this topic

I have elevation data (Etopo1 Global, cell registered) with 21600x10800 data points. resolution: 1arc minute

I also have a grid (Merra2, Nasa) of 576x361 data points. [-180,179 3/8][-90,90]degrees, resolution: 0.625°×0.5°.

Now I want to get an average elevation of each gridelement of Merra2.

This means, that I need to get an average of a matrix 40x37.5.

I have absolutely no idea to get this out of matlab. Ideally I could find a solution that is more flexible and could deal with completely flexible output-raster.

It is acceptable to have not 100% correct values at the south pole and at one lon-line. Is there anybody out there who can help me? Since these calculcations don't have to be performed on a regular basis, it is okay to run it within a for-loop :)

Any help is welcome. Thank you very much.

Kind regards

[Stephen23]

Use one of the interpolation tools:

https://www.mathworks.com/help/matlab/interpolation-1.html

Or subsample using indexing. Or perhaps an image processing tool that applies functions on blocks of data. It all depends on what you want to achieve.

[Beder]

Hi Stephen, thank you very much for your reply.

I tried your approach and did the following:

[testx,testy]=meshgrid(0:2/3:360-2/3,0:0.5:180);
[x,y]=meshgrid(0:1/60:360-1/60,0:1/60:180-1/60);
test=interp2(x,y,data,testx,testy);

Unfortunately this does not give me the same results than the code:

   for o=1:size(data_reduced,1)
       for oo=1:size(data_reduced,2)
           test=data((o-1)*pointspermerra_y+1:pointspermerra_y*o,(oo-1)*pointspermerra_x+1:pointspermerra_x*oo);
           data_reduced(o,oo,1)=sum(sum(test))/(pointspermerra_x*pointspermerra_y);
       end
   end

with pointspermerra_x and _y being size(data,1)/size(merragrid,1) and 2.

Do you have any clue, where I do have my mistake? :) Thank you very much

[Stephen23]

@Peter Albrecht: they give different results because they calculate different things.

You might like to have a look at blockproc, which would let you calculate an average for all blocks of the size that you specify.

[Beder]

Hi Stephen, unfortunately this does not solve my issue. blockproc also only takes integers as inputs

But thank you for your answer and help. I really appreciate it.

[Walter Roberson]

blockproc is not restricted to integers.

aaa = rand(20,30);
blockproc(aaa,[5 5], @(block) std(block.data))

[Beder]

Hi guys, thank you again for investing time in helping me.

I've made some progress so far. I use the lower code to generate my output. Everything works as long as I am using

data=rand(10830,21600)
pointspermerra_x=40
pointspermerra_y=30

but as soon as I am using pointspermerra_x=37.5 it changes the output to a matrix of 361x584 instead of the desired (expected) output of 361x576. Do you have any idea how to deal with this issue now? I don't understand, why it is 8 columns bigger.

myfun = @(block_struct)   (mean2(block_struct.data)* ones(size(block_struct.data,1)/pointspermerra_y,size(block_struct.data,2)/pointspermerra_x));
datatest=blockproc(data,[pointspermerra_y pointspermerra_x],myfun);

[Walter Roberson]

The block size, second argument to blockproc, is intended to be integers.

Warning: BLOCKPROC did not expect a fractional 'BlockSize' parameter.  It will be truncated before use.

[Beder]

Hi Walter, thank you very much. So we missunderstood each other.

I want to have a block size that is not integer. Of couse blockbroc can deal with double as values, but I need a blocksize different from pure integer values!

Kind regards Peter

[Walter Roberson]

Use a 1 pixel horizontal border (that is, an overlap). Your code that calculates mean could give the left and right borders a different weight if you want. Be sure to consider the setting about trimming the border on output.

[Stephen23]

Can you tell us what a non-integer block size means at the edges? If this is our data:

 [1,2,3,5,6,7,9,9,9]

and we want a block size of 3.5, what output would you expect for the mean of the first and second blocks?

[Beder]

hi Stephen, unfortunately I did not see your response until now. the first blocks mean would be (1+2+3+5/2)/3.5 and the second block (5/2+6+7+9)/3.5

[Walter Roberson]

How about if the block size was (say) 3 1/3, then how would that go?

[Beder]

(1+2+3+5/(1/3))/(3 1/3)

(5 2/3 + 6+7+ 9 2/3)/(3 1/3)

Answer 1

[Stephen23]

If you want to interpolate (i.e. estimate values based on a fitted curve) then use one of the interpolation tools:

https://www.mathworks.com/help/matlab/interpolation-1.html

If you want to apply a function to blocks of data (e.g. the mean of each block) then use blockproc:

https://www.mathworks.com/help/images/ref/blockproc.html

You could try using this FEX submssion (by the way, Matt J writes very good code):

https://www.mathworks.com/matlabcentral/fileexchange/48089-separable-block-wise-operations