Filling in Matrix (Interpolation

If I have a (10,3) matrix like so,

      10    20    1
       0     0    0
       0     0    0
      40    80    4
       0     0    0
      60   120    6
       0     0    0
       0     0    0
       0     0    0
      80   200   10

Is there any way I can interpolate the data to get it to turn like so which displays the average values in between the endpoints? Using interp1 was not clear to me and resulted in NaN everywhere.

    10    20    1
    20    40    2
    30    60    3
    40    80    4
    50   100    5
    60   120    6 
    65   140    7
    70   160    8
    75   180    9
    80   200   10

Any and all help/guidance is very much appreciated.

Answer 1

[Stephen23]

Here is one easy way to use interp1, it just takes two lines of code:

>> M = [10,20,1;0,0,0;0,0,0;40,80,4;0,0,0;60,120,6;0,0,0;0,0,0;0,0,0;80,200,10];
>> X = ~all(M==0,2);
>> N = interp1(find(X),M(X,:),1:size(M,1))
N =
    10    20     1
    20    40     2
    30    60     3
    40    80     4
    50   100     5
    60   120     6
    65   140     7
    70   160     8
    75   180     9
    80   200    10

[D. Plotnick]

Very nice, hadn't thought about using the logical indexing. Also, I hadn't realized interp1 could handle multiple rows like that. Has that always been true? And, more importantly, does that work on pages as well? i.e., interp1 will always assume it is working along the first dimension of any N-D array?

Scratch that, I just tried it and it works. Amazing!

Try

 M = repmat(M,1,1,5);
 X = all(~all(M==0,2),3);
 N = interp1(find(X),M(X,:,:),1:size(M,1))

[Stephen23]

It works along columns, exactly as the documentation says: "...you can pass v as an array. Each column of array v contains a different set of 1-D sample values".

Answer 2

[John BG]

Hi Suki

A=[ 10    20    1
         0     0    0
         0     0    0
        40    80    4
         0     0    0
        60   120    6
         0     0    0
         0     0    0
         0     0    0
        80   200   10]  
    B=A;
  [sz1 sz2]=size(B);
  for s=1:1:sz2
     L=B(:,s);
     [nx ny val]=find(L)
     for k=2:1:numel(nx) 
        L([nx(k-1):1:nx(k)])=linspace(val(k-1),val(k),nx(k)-nx(k-1)+1); 
     end
     B(:,s)=L;
  end

    A 

    =
        10    20     1
         0     0     0
         0     0     0
        40    80     4
         0     0     0
        60   120     6
         0     0     0
         0     0     0
         0     0     0
        80   200    10
     B
     =
        10    20     1
        20    40     2
        30    60     3
        40    80     4
        50   100     5
        60   120     6
        65   140     7
        70   160     8
        75   180     9
        80   200    10

Suki

if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?

To any other reader, please if you find this answer of any help solving your question,

please click on the thumbs-up vote link,

thanks in advance

John BG

<mailto:[e-mail] [e-mail]>

Answer 3

[D. Plotnick]

You can either break up the columns, or do it in one go. Example below.

In future, please include how you ran interp1 or any other code, since that will make helping you easier.

 % This returns the right answer
 x = [1,4,6,10]; %indexes of known points
 y1 = [1,4,6,10]; % y values at those points

 Xq = 1:11; % add an extra point so you can see how extrap works.
 Yq = interp1(x,y1,Xq,'linear','extrap');

 % This also returns the right answer

 y2 = [20,80,120,200]; 
 Yq2 = interp1(x,y2,Xq,'linear','extrap');

 % Also the right answer
 y3 = [10 40 60 80];
 Yq3 = interp1(x,y3,Xq,'linear','extrap');

 % In one swell-foop
 % We can do this in one go. The meshgrids are to make sure you have matrices of  % the right size.
 z = 1:3; % Index for columns.
 Y = cat(1,y3,y2,y1); 
 [Xq,Zq] = meshgrid(Xq,z);

 % Extrap does not work with interp2. 
 YqAll = interp2(x,z,Y,Xq,Zq,'linear')'
 % you could also add an extrapval after the 'linear', which sets those
 % NaNs to that number

[Stephen23]

I guess that is one way to avoid the fowl/foul/fell confusion: http://www.quickanddirtytips.com/education/grammar/one-fell-swoop

[D. Plotnick]

Hah, I always assumed it was a Shakespeareanism of some kind but didn't know the specific source. I have to give credit for 'swell-foop' to Piers 'Xanth' Anthony.