How to use an array as an indexing table to add search result as a new row to the querying array ?

Hi, :

I thank you at first.

My question is , 'How to use an array as an indexing table to add search result as a new row to the querying array ?'

For example, the Q matrix is 1000 x 1, the Idx matrix is 5 x 3, as below:

Idx =

     1     2    10
     2     3    20
     3     4    30
     4     5    40
     5     6    50

Then use Q( : ) every cell to search Idx by the logical expression, " if Idx(1 , 1 , : ) < Q(:,1) < Idx(1, 2 , :) "

,to search which row will the Q(:) be located, then return the columns 3 of the Idx(,,3) respectively to store every it in Q by added a new column 2.

For example Q(1) = 3.5, then Idx(3, 1) = 3, Idx(3, 2) = 4, so that " Idx(3, 1) < Q(1) < Idx(3, 2)", so the Q(1) should have the returned result from Idx's column3 = 30, then store this '30', to a new column2 to Q(1,2) = '30'

Is it possible to avoid using loop, or any existing similar function to simplify it ?

Thank you very much.

Best regards.

Answer 1

[Andrei Bobrov]

Q_new = [Q,Idx(discretize(Q,[Idx(:,1);Idx(end,2)]),3)];

[Tamura Kentai]

Hi, Andrei:

Thank you for the answer.But I got the following error message:

I don't know why.

Best regards.

Undefined function 'discretize' for input arguments of type 'double'.

[Andrei Bobrov]

Please attach your data as mat-file.

[madhan ravi]

+1 Andrei.

Tamura: "But I got the following error message:

I don't know why."

Because that function was introduced in 2015a ( https://in.mathworks.com/help/matlab/ref/double.discretize.html#bunpi8p_seealso ) and you're using 2013b.

[Andrei Bobrov]

Other variant (for MATLAB >= R2015a):

Inew = [-inf,1,nan;Idx;6,inf,nan];
out = [Q,Inew(discretize(Q,[Inew(:,1);Inew(end,2)]),3)];

[Tamura Kentai]

Hi, Andrei:

I have uploaded the Idx.mat & Q.mat.

It's simplified, the original file size is too large, approx to 38M. It including extra columns & rows, so I think the example as 'Idx.mat & Q.mat' could represent the question.

Thank you very much.

Best regards.

[Tamura Kentai]

Hi, Andrei:

I'm sorry, I tried the following code, it shows same error message:

As Madhan said, discretize() was introduced in 2015.

Though I could 'edit discretize', and see 'doc discretize', there are contents, but I don't know the details. I guess it's not supported before version of 2015. Is it possible to use others except 'discretize()' ?

Thank you very much.

Best regards.

Inew = [-inf,1,nan;Idx;6,inf,nan];
out = [Q,Inew(discretize(Q,[Inew(:,1);Inew(end,2)]),3)];
Undefined function 'discretize' for input arguments of type 'double'.

[Andrei Bobrov]

for old MATLAB (MATLAB < R2015a):

Idx = [(1:5)',(2:6)',10*(1:5)'];

Inew = [-inf,1,nan;Idx;6,inf,nan];
[~,ii] = histc(Q,[Inew(:,1);Inew(end,2)]);
out = [Q,Inew(ii,3)];

[Tamura Kentai]

Hi, Andrei:

Thank you very much.

This is exactly what I want. I appreciate your help.

Best regards.

[Tamura Kentai]

Hi, Andrei:

I beg your pardon.

I discovered it after I tried some successfully.

Is it possible, to get an interpolating value between 2 index ?

For example, if the indexing value of Q(1) is 3.5, which is the middle value of the row4 & row5, then return the value (40 -30) * ( (3.5 -3) / (4-3) ) + 30 = 35 .

Thank you very much.

Best regards.

>> [Inew(:,1) Inew(:,3)]

ans =

  -Inf   NaN
     1    10
     2    20
     3    30
     4    40
     5    50
     6   NaN

Answer 2

[Tamura Kentai]

Hi, Andrei:

I'm sorry, after some hours, I think I have one solution. It's the following:

% index_array_search.m
load('Idx.mat');
load('Q.mat');

Idx = [(1:5)',(2:6)',10*(1:5)'];
Inew = [-inf,1,nan;Idx;6,inf,nan];
[~,ii] = histc(Q,[Inew(:,1);Inew(end,2)]);
out = [Q,Inew(ii,3),Inew(ii+1,3), Inew(ii,1), Inew(ii+1, 1)];
out = [out,( ( out(:,1)-out(:,4) ).*( out(:,3) - out(:,2) ) ./ (out(:,5)-out(:,4)) + out(:,2) )];

I add those necessary for computing into the array.

It looks pretty fine.

Thank you for the ideas.

Best regards.

>> index_array_search
>> out

out =

    1.1000   10.0000   20.0000    1.0000    2.0000   11.0000
    2.2000   20.0000   30.0000    2.0000    3.0000   22.0000
    3.3000   30.0000   40.0000    3.0000    4.0000   33.0000
    4.4000   40.0000   50.0000    4.0000    5.0000   44.0000
    5.5000   50.0000       NaN    5.0000    6.0000       NaN

[Andrei Bobrov]

Hi Tamura!

I suggest using interpolation.

Please read about function from MATLAB: interp1 and griddedInterpolant.

Code:

Q = rand(20,1)*8 - 1;
ii = [(1:6)',10*(1:6)'];

1) interp1:

out = [Q,interp1(ii(:,1),ii(:,2),Q)];

2) griddedInterpolant:

F = griddedInterpolant(ii(:,1),ii(:,2),'linear','none');
out = [Q, F(Q)];

[Tamura Kentai]

Hi, Andrei:

Thank you for the suggestions. These are very helpful.

Best regards.

[Tamura Kentai]

Hi, Andrei:

In fact, I am thinking if there are other options other than 'linear', actually I mean it's 'linear' distribution in log-log plane.

For example, if plot the 'y=-x' using 'loglog(x,y)', the line will be straight, but if add some constant offset, eg: 'y=-x + 500', the plot 'loglog(x,y)', it won't be straight line in log-log plane.

If you think it's interesting. In fact I have tried survey ,but no good result except using manually adjusting such math equations.

Thank you very much.

Best regards.