Matlab lookup table interpolation

Hello Everyone,

I have a set of tables as shown in the figure. This is the dummy data.

I would like to interpolate these tables at some inbetween value k2 under two circumstances:

• When rows and columns coloured in brown have same steps.
• When rows and columns coloured in brown may have some intermediate values for the table k2.

I was looking at the griddedInterpolant as the potential solution, but I don't know how to make interpolant with two matrices (coloured in green). Any leads would be highly appreciated.

Thanks

[dpb]

You've described interpolating between planes of a 3D array but not given any values for the "k" dimension not the value to which to interpolate. Given the first condition that the X/Y coordinates of the tables are consistent, it's simply linear interpolation across each cell location from 1 to 3 via the fractional value of 2. But, we dunno what those are.

Handling the second case simply means not interpolating a given row/column if the output array contains a value.

You could set up interp3 for this, but since the first two variables aren't being interpolated over, it's overkill; I think I'd just use arrayfun and interp1 as the guts of an anonymous function...or, given you can only use linear, probably just straight-ahead compute and apply the fraction to the entire array with logical addressing to handle the already-present locations. With that reflection, looks like it might be only a one-liner, or maybe two.

Answer 1

[dpb]

OK, the first case with some assumptions...

 commandhistory
M1=repmat([10:10:50].',1,3);
M2=repmat([35:10:75].',1,3);
K=[1:3].';                              % arbitrary values for the interpolating direction
fnk=@(k)(k-K(1))/(K(3)-K(1));           % function compute fraction of input between planes
M=cat(3,M1,zeros(size(M1)),M2);         % build the composite array (not mandatory, just chose to do)
fnI=@(k)M(:,:,1)+k*(M(:,:,3)-M(:,:,1)); % the interpolating function

% example usage
>> I=fnI(fnk(2));                   % get the midpoint for example...
I =
         22.5         22.5         22.5
         32.5         32.5         32.5
         42.5         42.5         42.5
         52.5         52.5         52.5
         62.5         62.5         62.5
>> M(:,:,2)=I;                      % fill in the array or whatever with result

All one would have to do for the second case is build a logical addressing vector for assignment if M(:,:,2) already contains values at some points and only assign where aren't values.

[Umz]

Thanks for you proposed solution and suggestion,thats a good trick.I just forgot that k is simply a vector just as you wrote in your solution.

In my case proposed solution just fell short as I expected all the values in the table to be positive, however I believe this term k*(M(:,:,3)-M(:,:,1) gave few entries a negative sign. Unfortunately, couldn't upload the exact data but still thanks a lot, your suggestion helped me. Finally.I tried with interp3 and it worked as I desired.

[dpb]

Sign wouldn't matter; it would just indicate the second value should be lower than the first...change the second array so third column is negative of original--

M2(:,3)=-M2(:,3);
fnI=@(k)M1+k*(M2-M1);
fnI(fnk(2))
ans =
         22.5         22.5        -12.5
         32.5         32.5        -12.5
         42.5         42.5        -12.5
         52.5         52.5        -12.5
         62.5         62.5        -12.5
M=(cat(3,M1,M2));
mean(M,3)
ans =
         22.5         22.5        -12.5
         32.5         32.5        -12.5
         42.5         42.5        -12.5
         52.5         52.5        -12.5
         62.5         62.5        -12.5

and you notice you still get same result at the middle as the mean as you should -- result will match regardless what value of k is between the two limits.

NB AND WHERE MAY HAVE GONE WRONG...

NB: You MUST redefine the anonymous function fnI after any changes to the values in the M array(s) -- anonymous functions store any variables in their definitions not in the argument list in the function definition itself -- so changing M w/o redefining the interpolating function will continue to return the same result as it did originally; it doesn't know anything about the updated M.

Should have noted this before, probably, a more generic way to write it would be to include the M values in the argument list and pass them to the function.

[Umz]

I guess that what I might have missed, haven't tried this again but will check it. I suppose It should work. Thanks for the help.!